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Dr. Charlie Mayne`s NMR Lab Manual

1. If the sign of the exponential is changed in the convolution function to give f t exp t T 42 then by the same arguments given above the line width will be decreased However just as the signal to noise ratio was increased before it will now be decreased Problem 23 Show that resolution enhancement is an example of deconvolution as defined above Hint What is the reciprocal of an exponen tial EXPONENTIAL WEIGHTING CT 4 800 __ 1 TC e TC 0 8 Figure 20 2 13 01 40 Part I Lecture Notes 10 7 Lorentzian to Gaussian Transformation Consider a convolution function of the form f t exp ie IT 43 This corresponds to simultaneous convolution with a Gaussian and deconvolution with a Lorentzian In an ideal situation this will convert a Lorentzian line into a Gaussian line This is a technique commonly used in 2D NMR 2 13 01 11 Decoupling and the Nuclear Overhauser Effect 41 11 Decoupling and the Nuclear Overhauser Effect Thus far our discussion has centered mainly on the properties of a single spin 1 2 but spins are not in general isolated They interact with each other in various ways among which are scalar coupling and nuclear dipole dipole interactions Decoupling consists of ir radiating a system of interacting spins continuously and observing the effect on the spec trum Decoupling is termed heteronuclear if the observed and irradiated nuclei are different nucl
2. The fwhm point is found as follows F 0 AT B F a a SR ea B 1 1 2 1 47 v v T vv 471 v v l 277 ne aT To find the 1 point one simply replaces 2 by 100 in the above equation to give F 0 ATB AT B 1 AT B 4 on 100 2 1 47 v Vo 1 1 1 100 1 47 v v T 99 v Vi ART ee se 278 DAL 2 13 01 Appendix 3 Solutions to Problems 151 So the 1 point is about five line widths off resonance Similarly for the dispersion mode F 0 AT B AT B 2a v v T AT I o 100 2 1 47 v v Ty 1 1 2a v v T 100 1 47 v v T Assume that one is negligible compared to the off resonance term to give 1 2a v v Z 1 100 4mr v v T 2a v v T V Vi sf nT This says that the 1 point is ten times further off resonance for the dispersion mode than for the absorption mode T2 0 2 sec Dispersion Absorption 2 13 01 152 Part III Appendices T2 0 4 sec Dispersion Absorption 0 2 SI M 0 2 gro CICCIO INCA Ra Casata ci 10 Br GMM Mihet 2 0 2 4 6 8 10 FeO 1 0 2 Problem 15 on page 24 From Equation 21 the equation for the complex FID is M Me sin o M Me cos o t If the sign of is changed the sign of M will change This indicates that the magnetization is precessing in the opposite sense in the rotating frame Problem 16 on page 27
3. B as its axis Problem 9 If B ef differs appreciably from B it is not possible to produce an accurate 180 degree pulse Explain why and calculate the magnitude of the error for the best approximation to a 180 degree pulse Problem 10 If will the time necessary to produce as nearly as possible a 180 degree pulse be longer or shorter than when Equilibrium 90 x Pulse y y X X z 180 x Pulse 90 y Pulse M y x Bi x M Figure 6 2 13 01 14 Part I Lecture Notes Figure 7 O f Why Will the phase of the magnetization for a 90 degree pulse be the same as for an on resonance pulse In terms of these concepts explain why carbon 13 isn t perturbed by a pulse applied to protons 2 13 01 6 Relaxation Bloch s Equation 15 6 Relaxation Bloch s Equation Thus far our equations provide no means for the magnetization once perturbed to return to thermal equilibrium Since experimentally the magnetization is observed to re turn to thermal equilibrium one must introduce dissipative terms which will allow this to happen Addition of these terms to the previous equation of motion yields the equation of motion referred to as Bloch s equation dM M y MxB dt r T dM M y MxB 15 a MB T 15 dM M Mo y MxB _ dt T In the absence of all external fields but B and with each component of M decays independently an
4. M M o sin o i M 0 cos 0 M 7B sin t i M yB cos a t j M BM B j Mm Bi Li mM B j The last step uses the fact that B B 2 13 01 144 Part III Appendices Problem 5 on page 10 First one must invert the transformation Equation 10 to find l x cos t sin r 0x y sin f cos t Oly z 0 0 1 z Applying this transformation to M one obtains M cos r sin r 0 M M sin t cos t 0 M M 0 0 1 M N M cos t sin t 0 M d d M sin t ot 0 M ne sin t cos t ul 0 0 1 M Z sin t cos t 0 M Xx cos t sin t 0 M y 0 0 OIL M Now writing the differential Equation 7 in matrix form yields M 0 B B M a 7 B 0 B M M B B 0 M and substituting the transformed magnetization gives cos r sin t 0 M sin t cos r 0 M sin t cos t 0 M cos t sin r 0 M 0 0 1 M 0 0 0 M x 0 B B cos sin ar M 0 y B 0 B sin cos at 0 1 x B B 0 0 0 y SN N 2 13 01 Appendix 3 Solutions to Problems 145 which multiplying from the left by the inverse transformation matrix simplifies to M cos t sin t 0 sin r cos or 0 M M sin t cos t 0 cos t sin r 0 M 7 M 0 o 1 o 0 olw cos r sin t O O0 B B cos at sin t 0 M y sin t cos ar 0 B 0 B sin t cos t 0 M 0 o al
5. 2D J Spectrum Preparation I Evolution Decouple 90 x 180 x Figure 41 2 13 01 Detection Decouple 69 70 Part I Lecture Notes Homonuclear 2D J Spectrum Preparation volution Detection 90 x 180 x Figure 42 and 135 degrees the data will appear nearly as for the heteronuclear case A projection on F will then produce effectively a broadband decoupled proton spectrum 2 13 01 17 A Basic Pulsed Fourier Transform Spectrometer 71 17 A Basic Pulsed Fourier Transform Spectrometer A pulse and Fourier transform spectrometer must include hardware and software components to implement all of the parameters and concepts which we have so far dis cussed in a fairly theoretical framework Of course the physical reality never perfectly matches the theoretical model so it is important to understand where the spectrometer falls short of our theoretical models and what effect this has on our data In this section the var ious parts of the spectrometer will be discussed with the intent of showing how the exper iments that have been discussed are actually carried out 2 13 01 72 17 1 17 1 1 17 1 2 17 2 17 2 1 17 2 2 17 2 3 17 2 4 17 2 5 17 2 6 17 3 17 3 1 17 3 2 17 3 3 17 4 17 5 17 6 17 7 17 8 Part I Lecture Notes Generating Bo The Magnet Types of Magnets 17 1 1 1 Iron Core Electromagnets 17 1 1 2 Permanent Magnets 17 1 1 3 Supe
6. 54 Part I Lecture Notes Amplitude Figure 30 The function f is called hypercomplex because it is complex in both the f and t dimen sions The imaginary numbers i and j are defined such that i 1 and j 1 but ij 1 Thus Equation 52 involves four types of terms those involving neither i nor j those involving i those involving j and those involving the product ij These terms are of ten referred to as real real imaginary real real imaginary and imaginary imaginary re spectively Figure 30 shows the real real part of f This will be discussed further in Section 14 3 14 2 The Two Dimensional Fourier Transform The FID must now be subjected to a 2D Fourier transform First each of the FID s is transformed with respect to t applying any convolution functions desired This produces a matrix which is a function of f and v as shown in Figure 31 The time functions in the f domain have the appearance of FID s but in the literature they are often called interferograms Each interferogram is now transformed with respect to t after 2 13 01 14 Fundamental Concepts of Two Dimensional NMR 55 Amplitude Figure 31 applying any convolution functions The result is then a two dimensional Lorentzian line a function of vj and v modified by any convolutions as shown in Figure 32 14 3 Phase Sensitive 2D NMR Figure 32 shows a pure absorption line shape in both dimensions however many 2D experiments do
7. In this session you will learn how to switch from observing protons to observing carbon 13 determine a signal to noise ratio do a 90 and 180 degree pulse width calibration and determine a C T relaxation time 2 1 New Commands and Parameters In addition to the ones you learned in the first laboratory exercise the following commands and parameters should be studied for this laboratory class tn pw p1 array da dssh dssn ds n sw at np fn lb movetof movesw d1 d2 ernst Il dll dot1 t1 n expl dps 2 2 Observation of an X Nucleus The design and construction of probes is an exercise in compromise No one probe can be constructed that is optimal for all experiments that one might wish to perform Thus one must consider whether a given experiment is optimal or even possible with a certain probe In NMR terminology an X nucleus includes all NMR active nuclei other than pro tons and usually F Most broadband probes will observe nuclei with gyromagnetic ra tios in the range from SN to 3p Tuning the probe to the desired frequency is accomplished by changing the capacitance or inductance of resonant circuits Coarse tun ing is normally done by inserting an appropriate range stick which is a fixed capacitor or inductor attached to a plastic rod into the probe Fine tuning is then done by adjusting vari able capacitors attached to adjusting rods protruding from the bottom of the probe Various probes have sli
8. The upfield region of a proton spectrum often very crowded but the corresponding region of a carbon 13 spectrum is usually well resolved In this experiment the one bond scalar interaction is used to set up the chemical shift correlations however by appropriate adjustment of the mixing delays long range interac tions can be emphasized This can be useful in the assignment of quaternary carbons In ad dition to the HETCOR sequence several modifications exist that are used less routinely than the basic HETCOR sequence Two examples that are well suited to investigate long range chemical shift correlations via long range scalar couplings include XCORFE COLOC and the so called relayed coherence transfer experiments 8 0 1 PROCEDURE a For this laboratory we suggest that you use three experiments one for your reference proton spectrum one for the reference carbon spectrum and a third for the 2D data Collect the carbon spectrum with full proton decoupling and for both carbon and proton use the smallest sw that is practical without peaks aliasing from outside the spectral window or if peaks must be aliased e g solvent peaks adjust sw and tof so that the aliased peaks will appear in a region free of signals of interest You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the concentrated sample for this experi ment 2 13 01 120 Part II L
9. del exp rt rts nl dres res delta dsn aph svf lockgain lockpower lockphase go ga au file solvent load copy tn dg dg1 dgs explib ft wt wft wti text su ds dscale jexp sa ra pap ppa pl pscale page In most cases there are menu buttons to access the same functions as these commands You may use them if you prefer A mix of both meth ods will be used in the following procedure 1 3 Setting Up Shimming the Line Shape Test In this exercise you will preform all of the operations that were demonstrated above These operations are basic to all NMR experiments Here you will create an experiment set up the required parameters by loading a predetermined set Determining reasonable pa rameters for data acquisition will be the topic of future sessions optimize magnet homo geneity obtain an FID process it and store the results The line shape test is the most important test in setting up the spectrometer to observe protons If good results are obtained for the chloroform line shape other samples usually present few problems 2 13 01 Laboratory 1 Proton Line shape Proton Resolution 1 3 1 PROCEDURE Log in on the paper log book and on the spectrometer workstation Complete the on screen checklist Insert the proton lineshape sample Open the acqi window by typing the command or by clicking the acqi button in the menu bar Click the eject button to raise the sam ple Be sure to handle th
10. i 1p The coordinates of a peak in the spectrum would be 6 3 e on p and existence of a peak at particular coordinates indicates scalar coupling between the relevant carbon proton pair The pulse sequence and vector diagrams of Figure 40 illustrate how the experiment is accomplished Since polarization transfer from IH to 5C is involved the carbon magne tization is enhanced as was described for the INEPT and DEPT experiments Adjustment of the mixing delay sets the scalar coupling which will produce the maximum polarization transfer hence the maximum enhancement Phase cycling of the last proton pulse through all four quadrature phases will pro duce quadrature detection in F and suppress signals not arising from polarization transfer from the protons 2 13 01 15 Chemical Shift Correlation Experiments 67 reparation Evolution Detection 90 x 90 y ecouple Figure 40 2 13 01 68 Part I Lecture Notes 16 Homonuclear and Heteronuclear J Spectra Much of the complexity of a spectrum often arises from scalar coupling interactions between the nuclei involved Overlapping multiplets can render interpretation difficult and yet the information contained in the scalar couplings is needed for a full structure determi nation J spectra permit one to separate chemical shift and scalar coupling information while retaining the full information content of both types Furthermore overlap between individual multip
11. ure 2 13 01 158 Part III Appendices Coupled Decoupled Pira Problem 26 on page 43 In this case the gyromagnetic ratios cancel from the equation and one is left with an NOE of 1 5 Problem 27 on page 45 Consider the projection of the magnetization on the xZ plane Beginning at thermal equilibrium at point a an off resonance 90 x pulse will take the magnetization to point b The 180 y pulse will then take the magnetization approximately to point c The final 90 x pulse then takes the magnetization to point d which is a far more accurate 180 x pulse than would otherwise have resulted 2 13 01 Appendix 3 Solutions to Problems 159 Problem 28 on page 47 The magnetization will refocus alternately along the positive and negative y axis so the lines in the transformed spectrum will be alternately positive and negative in ampli tude However minor errors in the 180 degree pulse will leave the magnetization much fur ther from the y axis where it ideally ought to be than would be the case with the phase shifted pulse sequence Problem 29 on page 68 The following figure shows the modified pulse sequence During the first half of t4 both chemical shift and scalar coupling evolve The simultaneous 180 degree puls es rotate the magnetization about the x axis as shown but the two vectors are in terchanged as we have seen before so that the chemical shift is refocussed along the negative y axis while the scala
12. 0 5 1 0 1 0 1 5 d1 2 Enter the value x determined in the previous step for the 90 degree proton pulse and collect a data set with the above multiplier array k Save the data for later analysis 1 In addition to the information you found in the on line manuals you can look at the source code for the pulse sequence you are using The source may be found in vnmr psglib and may be viewed with your favorite editor Even if you don t understand the actual code to gen erate the pulse sequence the programmer often puts useful com ments in the code In the future as you start using more complicated pulse sequences the answers to your questions as to how the se quence works what the parameters mean what type of phase cy cling is being used etc can be found in this source code Problem 46 From the source code listing for DEPT what is the meaning of the parameter mult Are your results consistent with the expect ed dependency of intensity as a function of the degree of protonation and the proton pulse width Explain m Ata workstation learn to use the DEPT analysis macros and work up your data for your report Also try experimenting with the interac tive add subtract buffer to see if you can obtain similar results See the add command in the on line manuals for a starting point Problem 47 If you only have enough spectrometer time to take one DEPT spectrum what value of mult would you use Why 2 13 01 Laboratory 6 Hom
13. 21 For convenience the matrix form of Equation 18 will be used yAB 0 M T M 0 M 7YAB YB M 0 dt gt T M 5 i alii ye T T The steady state solution is formed by setting the derivatives to zero and solving the result ing coupled linear equations discarding all terms higher than first order in B4 T M 0 yAB YB M 0 afm M 0 D F T gt yAB 0 2 1 1 AB 1 0 0 7 CAB 5 MS ge na 2 2 iD T TT 1 0 yB Bo 7 2 13 01 Appendix 3 Solutions to Problems 149 Substituting the right hand side into the determinant for the numerator in the usual way gives 0 0 0 0 M rs 0 yB 14 T T _Mo 7B pl T T gt MT ca yB 1 0 0 T 0 T X 0 7 Xo o 14 T 1 E 0 0 2 2 M KE JAB 0 CB 1 T o Mo I T T T M 7B M 1 ALe B 1 D E A 1 OI B Xoo 1 0 Ty 1 ae a o 0 T TT 1 M 0 0 14 T l 2 T M yB 0 7B T cn NT fm I o o T T T 2 13 01 150 Part III Appendices Problem 14 on page 22 First Equation 20 will be recast in terms of Hertz 27 v v T F v AT 2 1 47 v v T 1 F v AT B WW 1 47 v v T i 1 The graphs below show the curves for two different values of 75 Since the equa tions are strictly linear in B it will only scale the curves vertically
14. Thus the decay rate associated with the convolved FID is the sum of the two individual decay rates We know that the full width at half maximum of a Lorentzian is 1T If T is replaced by T 1 Tig the desired result follows immediately 2 13 01 Appendix 3 Solutions to Problems 157 Problem 23 on page 39 Taking the reciprocal of the exponential yields f ef 4 ala Trp Thus multiplying by the positive exponential is the same as dividing by the negative expo nential which corresponds to a deconvolution with a Lorentzian resulting in a narrowing of the lines in the spectrum Problem 24 on page 43 We write the equation for the carbon magnetization from Equation 44 then im pose steady state and saturation of the protons d Ml dt PcME peM ce OME ce 0 pc ME t ME e o M t M 0 0 o ME ME 0 M ce Pc ME ee o tue Pc Yc MC cfi tue YcPc 14 Ncgm M Problem 25 on page 43 The coupled spectrum is a triplet with 1 2 1 intensity ratios due to the coupling to the amide protons The ratio of the y s is about 10 at constant field the ratio of the Ys is the same as the ratio of the Larmor frequencies Thus the value of 77 is 5 and the value of the NOE is 4 So the intensity of the decoupled spectrum is four times greater than the sum of the intensities of the triplet lines and will be negative as shown in the following fig
15. a particular experiment it is best determined on the sample to be analyzed or on a similar sample and not on a standard sample 2 3 1 PROCEDURE a The doped carbon 13 sensitivity sample will be used for this calibra tion It is exactly like the regular carbon 13 sensitivity sample ex cept that it has been doped with a paramagnetic relaxation agent to shorten the relaxation time It is easily recognized by the purple tint imparted by the relaxation reagent b Duplicate the parameter set you used for the S N experiment into some other experiment using the mp command Join the experiment where you just put the parameters using the jexp command d Turn on the decoupler and set the decoupling parameters as you did for the lineshape test above e Set the text to something appropriate f ga This will collect an initial test FID Transform this FID and then use the movetof command to set the transmitter frequency within about 200 Hz of the dioxane peak Take another spectrum to see that you have succeeded The dioxane peak should be near the center of the spectrum The purpose of this step is to ensure that off resonance ef fects will not cause problems with the 180 degree pulse calibration See Figure 7 and the accompanying discussion g Use absolute intensity ai so that peak heights from spectrum to spectrum can be compared with accurate relative intensity relation ships The usual display mode is normalized nm whic
16. about two hours f go g wft2da While the acquisition is in progress you may transform the partially completed 2D FID and observe how the resolution in the vj dimen sion increases as more increments are collected Use a gaussian con volution function of appropriate width to alleviate truncation wiggles in both dimensions Use wti to determine the correct weighting function Use wftida prior to wti to set the convolution function in the vj dimension h foldt This command folds the transformed spectrum about the diagonal and has the effect of helping to eliminate t4 noise and spurious peaks in the spectrum that don t possess symmetry about the diagonal The foldt command requires that sw sw1 i dconi 2 13 01 Laboratory 7 Double Quantum Filtered Homonuclear Correlation Spectroscopy DQCOSY 117 Learn how to use this program to display vertical and horizontal traces and projections and make expansions j Save both the 1D and 2D data sets k Arrange for a session on the workstation Learn to map out the scalar coupling networks and get some additional practice with the fea tures of the wti and dconi programs Make a contour plot with the 1D reference spectrum plotted on the top and side with proper chem ical shift scales Be sure the chemical shifts in the 1D spectra align properly with those of the 2D spectrum You may want to look up the plcosy macro Discuss in your report how the information from the con
17. accommodating only N complex data points then the product of S and A cannot exceed this value Problem 18 Find out what the value of M is for the spectrometer you are using and compute the best resolution you can obtain using a spec tral width sufficient to cover the nominal maximum chemical shift range for IH Do the same for 5C If you have shimmed the magnet to 0 2 Hz line width what is the maximum spectral width you can use while retaining your hard won resolution Resonances which occur outside the spectral width defined by the sampling rate are aliased to a point within the spectral width as shown in Figure 16 This phenomenon is of ten incorrectly referred to as foldover rather than aliasing If only the real or only the imaginary part of the FID is acquired the ability to dis criminate between signals above and below the transmitter in frequency is lost and each line will appear on both sides of the carrier and equidistant from it One will be a phantom image and the other the real line One cannot distinguish between the two without addition al information This phenomenon is correctly termed foldover because it is as though the spectrum were folded about the transmitter frequency and the two halves superimposed Problem 19 If the transmitter is moved a small amount or the spec tral width is changed by a small amount how will images real lines and aliased lines respond How can this information be used to
18. any other notes you want to include about the spectrum In this case for example you probably want to note that the spectrum was taken before any shimming The backslash character starts a new line when the text is printed Type text with no arguments when you want to see how the label will look when printed This text will be saved with the data and will be printed with the parameter listings when you execute pap 2 13 01 83 84 Part II Laboratory Experiments It is also possible and probably more convenient to use any stan dard Unix text editor to create this text file If time permits ask your instructor to show you how Save your spectra in your archive directory Your instructor will show you how Now you are ready to practice shimming Enter the interactive ac quisition window just as you did when locking the spectrometer Shim the magnet as well as you can Adjust only the Z1 Z2 Z3 and ZA shims You will not be required to adjust the other shims at this time Accidentally misadjusting them can cause increased spinning sidebands or worse Alternately shim the magnet and monitor the spectrum by typing ga until you get a satisfactory line shape Your instructor will judge whether your spectrum is good enough to con tinue Monitor the line shape as you did with the unshimmed spec trum above If the standard shims you loaded are recent enough it may be quite easy to meet specifications Even if this is the case yo
19. as ADC OVERFLOW or RECEIVER OVERFLOW occur This procedure will prevent similar problems from disrupting the 2D data acquisition c Join the second experiment and move the parameter set from your setup spectrum to this file with the mp command d cosy This macro makes all the changes to the parameter set necessary to run the COSY experiment but all the values may not be appropriate for your experiment Note the new parameters in both dg and dgl Critically examine the parameters and make any alterations you think are appropriate Each increment must complete the full phase cycle as required by the pulse sequence to obtain satisfactory results Find out what the minimum phase cycle is from the on line manuals or the pulse sequence source code Note that the pulse sequence name is not cosy Enter 90 degree pulse widths for PW and PI as sume a T of one second make sure d2 is zero and set sw1 equal to sw as determined in the set up proton spectrum Set fn in both di mensions to 1 K and use 128 for the number of increments ni The delay d2 is the 1 delay It is incremented by the program and the increment is calculated from sw1 This is not an ordinary array such as you used when you measured 7 s and cannot be displayed it is referred to as an implicit array e pseudo This macro enters pseudo echo convolution functions in both dimen sions based on the acquisition times in f and t The values deter mined should be roug
20. detect the false lines 9 4 Time Averaging Suppose one acquires N identical FID s Each sample of each FID contains a signal component S and a noise component which will be supposed to be random Gaussian dis tributed with standard deviation o Then if one adds the FID s the signal components will add coherently to give a total signal according to S NS 27 2 13 01 30 Part I Lecture Notes 0 0 0 1 0 2 0 3 04 05 0 6 0 7 08 0 9 1 0 Time ms Real Line Aliased Line SW 2 SW 2 r 10 5 0 5 10 Frequency KHz Figure 16 2 13 01 9 The Anatomy of a Free Induction Decay 31 But it can be shown that the standard deviation of the noise in the time averaged FID is given by 0 Nos 28 Hence taking the ratio of the signal to the noise in the summed FID S NS JN S 4N 29 O Nos Os s LAI Thus the signal to noise ratio S of a time averaged FID increases as the square root of the number of FID s averaged Problem 20 After running a sample all day say 12 hours you are beginning to see what you think are signals signal to noise ratio about 2 How much longer will it take to get a publishable spectrum signal to noise ratio about 10 The fact that one is time averaging digitized FID s also has some consequences of which one needs to take account when planning experiments Time averaging cannot pro duce a FID with signal to noise ratio greater than the dynamic
21. interest Non homogeneous or viscous samples can seriously degrade resolution High quality sample tubes such as Wilmad 528 PP or equivalent tubes are of ac ceptable quality Wilmad 535 PP or 545 PP tubes may be used for the best proton work Sample tubes should never be cleaned with cleaning solutions such as potassium dichro mate because the glass will be impregnated with paramagnetic chromium Also do not dry your tubes in a hot drying oven because the thin walls of an NMR tube can warp Some cheaper sample tubes often have enough camber to be beyond the close tolerances allowed between the sample tube and the receiver coil in the probe This will result in difficulty in spinning will score the tube and may damage the probe Take care not to scratch your tubes while cleaning them A scratched tube is likely to break in the probe Test your tubes by dropping them from a height of about 10 cm bottom first on a solid countertop a sound tube will not break If a sample does not spin properly once inserted in the probe eject the sample clean the spinner turbine and sample tube then try again Never touch the lower section of the turbine which is in contact with the air bearings of the spinner housing Handle only the upper larger diameter part of the turbine or better yet handle it with a kimwipe Oils from your fingers accumulate on the bearing surfaces inside the probe eventually causing the samples not to spin With these precautions if t
22. more concentrated sample This spectrum could be acquired using the dilute sample but it would probably take overnight Be aware that there may be a small concentration dependent change in chemical shifts when spec tra taken at different concentrations are used Join the third experiment and move the proton acquisition parame ters to it hmqc This setup macro for the HMQC pulse sequence loads the new ac quisition parameters as well as the proper pulse sequence By default the macro will set up for carbon as the X nucleus For other X nuclei you can supply an argument to the macro Set sw1 and dof to the val ues of sw and tof respectively from your carbon reference spec trum For this experiment we will not use RE decoupling so set dm to n and dmm to c Use nt 8 and the values for pwx and pwxlvl that you just determined Set pw and tpwr for a 90 degree proton pulse If you don t have a reliable calibration check it on the sample provided for this experiment Assume a proton T of two to three seconds unless you know a better value from previous work on this sample an average one bond coupling j of 140 Hz and set the long range coupling parameter jnxh 0 we want one bond correlations for this spectrum Use no presaturation pulses Set np in the F pro ton dimension to 4096 and use 512 increments for ni Set fn 4096 and fn1 2048 Adjust dl to an appropriate value for the relaxation time of the protons in your s
23. not yield this result but rather what is called a phase twist line shape as shown in Figure 33 This line shape has strong tails and a much wider appearance due to the dispersion contribution Figure 31 shows pure amplitude modulation of the v spectra as a function of t4 This phase twist line shape results from phase modulation as a function of t4 as shown in Figure 34 Generally the pulse sequences that produce a phase twist line shape are those that are designed to achieve quadrature detection in the dimension Spec tra with this phase twist line shape are normally displayed as the absolute value of the hy 2 13 01 56 Part I Lecture Notes Amplitude Figure 32 percomplex quantities An alternative method first published by States Haberkorn and Ruben makes use of two data sets to produce a spectrum that can be displayed as a two dimensional pure absorption mode spectrum with lines as in Figure 32 In the time domain one data set is amplitude modulated like that shown in Figure 30 while the second is sim ilar but the amplitude modulation with respect to t4 is 90 degrees out of phase as shown in Figure 35 One then has four data sets or quadrants as mentioned in Section 14 1 which can be transformed to yield the corresponding hypercomplex spectrum Phasing of such a spec trum is somewhat more complex than for a one dimensional spectrum since linear combi nations of all four quadrants of the hypercomplex data are required
24. or More Lines The FID of two or more lines is obtained by summing the FID s corresponding to the individual lines As shown in Figure 13 a two lines give a fairly simple FID In this case the two lines have frequencies of 20 and 25 Hz The frequency associated with the in terference beats gives the separation of the two lines 5 Hz in this case However as one adds more lines to the FID it quickly becomes too complicated to analyze visually 2 13 01 26 Part I Lecture Notes 2 1 Vv TD 0 1 2 0 0 2 0 4 0 6 0 8 1 Time sec 4 2 TD 0 2 4 0 0 2 0 4 0 6 0 8 1 Time sec Figure 13 b shows a FID with four lines Lines at 7 and 63 Hz have been added to the FID of a 9 3 Digitization of Free Induction Decays 9 3 1 Digitization in Amplitude The FID is sampled by the sample and hold unit S H converted to digital form by the analog to digital converter ADC and stored in the computer memory The dynamic range of the digitized FID and consequently of the spectrum depends on the number of bits in the ADC Noise can be introduced due to truncation errors 2 13 01 9 The Anatomy of a Free Induction Decay 27 See Figure 14 for an illustration of this process Problem 16 What is the minimum number of ADC bits required to digitize the LH FID from tert butyl alcohol Assume there is no scalar cou pling How many bits would be required to digitize the IH FID from a 5 mM solutio
25. power to avoid perturbing the other cou plings but it should be obvious immediately which carbon is bonded to the quartet protons e Add text and archive the data as usual Problem 42 How might this experiment be useful in solving re search problems Give hypothetical examples for your own research if you can 3 4 Gated Decoupling and the NOE The phenomenology behind the NOE is discussed in the lecture notes Section 11 on page 41 and will not be repeated in detail here Suffice it to say that a c H NOE 2 13 01 98 Part II Laboratory Experiments depends on the number of protons and their distances from a given carbon atom and on the nature of the relaxation mechanisms involved The value can range from one no enhance ment to about three This is the principal reason why carbon spectra run with broadband decoupling as is normally done should not be integrated with the intention of counting car bon atoms the way one normally counts protons Off resonance effects and relaxation ef fects can also influence the intensities Integration of a 13C spectrum may be preformed on data that was acquired with the decoupler off but overlapping multiplets usually make this a rather unsatisfactory alternative However by running the decoupler gated in such a way as to produce a decoupled spectrum with no NOE referred to as a suppressed NOE ex periment one can circumvent this difficulty Other methods such as the addition of
26. range of the computer mem ory cell into which it is being time averaged When the largest value in a time averaged FID overflows the computer memory cell being used to store it the data must be scaled in order to continue time averaging but for each factor of two by which the data is scaled one bit of the ADC becomes useless decreasing the effective dynamic range of the ADC by a factor of two When this process reaches a point where the least significant effective bit of the ADC represents a value larger than the noise level no amount of additional time averaging can bring additional small signals out of the noise In Section 6 we learned about T relaxation Let us examine what effect longitudi nal relaxation has on time averaging of FID s Suppose we apply a degree pulse to a spin system every f seconds collect a FID after each pulse and time average N such FID s in a total time of T Nt Starting from thermal equilibrium the amplitude of the first FID will be proportional to M sin but if t is short enough so that the magnetization does not fully relax the magnetization available to generate the second FID will be smaller and for the 2 13 01 32 Part I Lecture Notes third FID still smaller and so on A steady state will be reached after a few pulses charac terized by Equation 30 M M cos M M M M e SH where M the z axis magnetization just after the pulse M the z axis magnetization just
27. several weeks ga dres Collect a spectrum showing the line shape prior to any shimming and display it on the screen Place a cursor on the line and use nl to put it precisely on the line Note that nl gives the height of the line in millimeters dres then displays the width of the peak at half height The width of the peak at any other height may be measured using two cursors and the threshold Display the line at two vertical 2 13 01 Laboratory 1 Proton Line shape Proton Resolution scales one to have the entire peak observable on the screen vs 100 wp 25 Hz the best vs value may vary depending on the plotter you are using and another with vs increased by a factor of one hundred with wp 250 Use normalized mode nm Learn how to increase and decrease the vertical scale using the mouse and how to save and recall views of the spectrum using the sn and rn commands The main chloroform resonance will be far off scale under the hundred fold expansion Phase the spectrum using aph Also click the phase button in the menu bar and learn to manually phase the spectrum The line width at 0 55 of full intensity is measured as follows Dis play the hundredfold expanded spectrum with an appropriate hori zontal expansion and set the horizontal threshold bar click the th button in the menu bar at 0 55 of the full height of the line Re member you get the line height using nl Using the left mouse but ton to control the position of th
28. source of the plot 1 e the trace number the carbon shift it represents etc g proj trace ds etc Experiment with projections and traces Include some of them in your report 2 13 01 Laboratory 11 13C Two Dimensional INADEQUATE Direct Detection of Carbon Carbon Bonds 129 Laboratory 11 13C Two Dimensional INADEQUATE Di rect Detection of Carbon Carbon Bonds In this experiment you will obtain a 2D INADEQUATE spectrum of the molecule you have been studying The experiment is discussed in detail in the lecture notes section 15 2 on page 63 This experiment will employ the hypercomplex or States Haberkorn and Ruben method for producing phase sensitive 2D data that does not have the phase twist line shape problem You may also want to review section 14 3 on page 55 of the lecture notes The data from this experiment will allow you to assemble the complete carbon skeleton of the molecule You will need more than the usual amount of time to acquire the data for this experiment Consult your instructor before making your instrument reservation 11 0 1 PROCEDURE a Set up the spectrometer in the way that you should know well by now and obtain a decoupled HE spectrum You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the concen trated sample for this experiment Limit the spectral width to con tain only the lines of interest and
29. the acquisition As the acquisition proceeds monitor the acqui sition with dssh Also experiment with a stacked presentation using the dss command and appropriate values of ho and vo to produce a satisfactory display m ds n Display the last spectrum in the array Do a da if you have forgotten how many values were used for d2 Phase the spectrum Set the threshold th so it is just below the top of the smallest peak in your spectrum The threshold menu button is probably most conve nient for this Note the changed assignments of the mouse buttons when you press this menu button n dil This will display a line listing of your spectrum The list will give for each peak that is above the threshold limit you set a reference number an intensity a frequency and a chemical shift In this ses sion T s for all the lines will be calculated but in some cases only a few may be of interest When this is the case the line numbers as signed to the peaks of interest are used in the t1 n calculation in the next step Problem 38 Learn how to reference the spectrum to TMS using the center peak of the chloroform triplet as a secondary reference Check the rl command in the manual 0 fp tl The fp command examines every spectrum in the array to determine the peak intensities for each peak picked in the previous step t1 cal culates the 7 s for all the lines in the line list When only a few of the lines in a spectrum are of interest
30. the nuclei This interaction can be exploited to measure distances between nuclei 6 2 2 Chemical Shift Anisotropy We measure chemical shifts as the position of lines in a spectrum relative to some standard like TMS Actually the chemical shift depends on the orientation of a molecule with respect to the external field In liquids the molecules tumble rapidly with no preferred orientation so that the chemical shift we measure is an average of that for all possible ori entations of the molecule However modulation of the chemical shift as the molecule tum bles produces relaxation The strength of this interaction is proportional to the square of the external field For a 300 MHz or lower spectrometer this effect is usually negligible but at 500 MHz and above it can be significant 6 2 3 Paramagnetic Interactions Since the electron has a spin and its magnetic moment is about 2000 times greater than that of nuclei dipole dipole interactions of nuclei with electrons can be a dominant relaxation mechanism Fortunately most electrons come in pairs of opposite spin and can cel each other out Molecules or ions with unpaired electrons are called paramagnetic Free radicals and metal ions of iron or chromium are examples If such species are present in a NMR sample even in very low concentration T relaxation may be so rapid that nuclear spin signals are very broad and cannot be resolved from each other Molecular oxygen is mildly parama
31. the t1 command can be given an argument containing a list of the line numbers of interest obtained from a line list as above Details of the fitting process and the result ing 7 values are displayed in the text window If full detail is not needed the tls command gives only a brief summary of the calcu lated values 2 13 01 Laboratory 2 Observation of Carbon 13 Anything sent to the vnmr text window can alternatively be sent to the printer by issuing the printon command When it is desired to resume sending text to the text window on the screen issue the print off command Text is only queued for printing until the printoff command is completed then all the accumulated text is sent to the printer p expl This will display the best fit exponential curves calculated by the program as well as your data points on the screen This can be used to spot bad data points The command pexpl will send the display to the plotter instead This is a very versatile command check the man ual for details Problem 39 Make a log plot of the 7 data for any two lines in the spectrum and determine the value of T Make a table comparing your result with the 7 values calculated from measuring the linewidths by estimating the zero crossing and with the value calculated by the t1 command q Archive your data as before Be sure to use all the data analysis techniques you have learned in preparing your laboratory report Problem 40 Suppose yo
32. what the minimum phase cycle is from the on line manuals or the pulse se 2 13 01 Laboratory 12 Through Space Correlations NOESY e quence source code Be sure pw is set to the correct 90 degree pulse width Use a d1 substantially longer than the mix time Three or more T s is desirable if time permits Make sure d2 is zero and set swl equal to sw as determined in the set up proton spectrum Set np to 2048 and ni to 256 This will give adequate resolution except for the most demanding cases Set fn in both dimensions to 2 K The de lay d2 is the fr delay It is incremented by the program and the in crement is calculated from sw1 This is not an ordinary array such as you used when you measured 7 s and cannot be displayed it is re ferred to as an implicit array time The program will calculate and display the approximate total exper iment time Make sure the experiment will complete in the time you have been allowed If not you may have to reduce ni or d2 go wft2da While the acquisition is in progress you may transform the partially completed 2D FID and observe how the resolution in the vj dimen sion increases as more increments are collected Use a gaussian con volution function of appropriate width to alleviate truncation wiggles in both dimensions Use wti to determine the correct weighting function Use wftlda prior to wti to set the convolution function in the v dimension dconi Learn how to u
33. with only one 13C This is done by phase cycling as shown in Table II The last 90 degree pulse the read pulse is cycled through all four quadrature phases Since the single quantum and double quantum coherences respond differently the receiver can be made to follow the double quantum coherences so that they add construc tively while the single quantum coherences add destructively or cancel out This experi ment is normally performed using the phase sensitive hypercomplex method This is 2 13 01 64 Part I Lecture Notes z Z b d f z y y y x x PA Zu n y y y x X X INADEQUATE 90 x 180 x 90 x 90 x Figure 38 Table II Basic Phase Cycle for 2D INADEQUATE Read Pulse anole Double Receiver Quantum Quantum x x x x y y ay DI X x X X y KY kY Y accomplished by acquiring two data sets identical except that one has the preparation puls es shifted in phase by 45 degrees Special hardware to accomplish less than 90 degree phase shifts is required Shifting the phase of the double quantum preparation by 45 degrees re sults in a phase shift of the modulation observed in the FID by 90 degrees as required by the hypercomplex method 2 13 01 15 Chemical Shift Correlation Experiments 65 N gt CH_ CH CH Figure 39 Then what does one see in the resulting 2D spectrum Consider a three carbon frag ment as shown in Figure 39 From a proton decoupled on
34. you can verify that the spectrometer is correctly adjusted and working well before starting any long experi ment Each time you log in on the spectrometer workstation a checklist will pop up on the screen Verify that each item is satisfied before attempting to run the spectrometer These instruments are used heavily by the department research groups and because of the large number of users strict protocols will be required of you During this and subsequent ses sions spectrometer time magnet hours will of necessity be limited Whenever possible practice and data analysis should be done on workstations other than those attached to the spectrometers Spectrometer hours should be used mainly for data acquisition Consult your instructor for the locations of these workstations Only standard Varian commands and macros are used in this exercise You should become familiar with these and not rely on the convenience features defined by the Depart ment NMR staff until you are comfortable with the standard commands The reason for this is to familiarize you with the system as supplied by Varian Any Varian instrument running vnmr that you may encounter will have this same set of commands and parameters 1 1 Demonstration The following items will be discussed and demonstrated by the instructor System protocols scheduling accounting logs good citizenship b Safety procedures spectrometer components and host workstation operation Saf
35. 2 13 01 14 Fundamental Concepts of Two Dimensional NMR 57 Amplitude Figure 33 14 4 Phase Cycling Phase cycling is used in both one and two dimensional spectroscopy to cancel artifacts and unwanted signals while retaining the information which the experi menter wants The basic idea is to create a series of FID s such that the unwanted coherences alternate in phase while those to be kept have always the same phase Thus when the FID s are added together the unwanted parts interfere destructively but the desired parts interfere constructively Simultaneously of course the signal to noise improves as we have discussed previously However whether or not the signal to noise im provement is needed some minimum number of FID S must be acquired to permit the phase cycle to complete This number may be as small as two or as large as 1024 or more 2 13 01 58 Part I Lecture Notes Amplitude Figure 34 The signals to be cancelled out may be thousands of times larger than the desired signals or they may be much smaller 14 4 1 Elimination of Detector Asymmetry One of the oldest applications of phase cycling eliminates the effects of unequal gain in the two quadrature channels of the spectrometer The gains of the two channels in a spectrometer nearly always differ sufficiently to produce an observable image without phase cycling The image appears as a result of foldover of the part of the signal in the high er ga
36. 3 01 9 The Anatomy of a Free Induction Decay 25 9 The Anatomy of a Free Induction Decay Intelligent operation of an NMR spectrometer requires a clear understanding of the FID and its relationships to the transformed spectrum Since all processing of the FID is done using a digital computer it is also important to understand the consequences of con verting the FID to digital form 9 1 FID of a Single Resonance Figure 12 shows the complex FID of a single resonance such as might be obtained from a sample of chloroform and Figure 11 shows the Lorentzian line which would be ob tained from Fourier transforming this FID They have the following properties a The initial amplitude of the FID is proportional to the height or the integrated intensity of the line b The time constant 7 of the exponential decay of the FID is related to the full width at half maximum L of the absorption mode signal by 25 Thus FID s with short time constants give wide lines and FID s with long time constants give narrow lines The frequency of the oscillation is A the frequency difference be tween the transmitter and the line d The phase of M indicates the sign of the frequency If counter clockwise rotation as viewed from the positive Z axis is taken to be positive then the FID as shown represents a negative frequency If the phase of M is shifted by 180 degrees then the frequency would be positive 92 FID of Two
37. As a rule it is better to use lower lock power and higher lock gain to achieve an adequate lock signal than the reverse If too much lock gain is used however the signal becomes noisy and the lock unstable The values used will depend upon the concentration and T of the deuterium in the sample After a little experience with your samples you will know the minimum lock solvent concentration necessary to produce an adequate lock For shimming it is best to have very little saturation of the lock for acquisition some saturation can be tolerated as long as the lock is stable Lock saturation can be checked by noting the lock level then de creasing the lockpower by six units With no saturation the lock level should decrease to half its former value If it is greater than half by more than about three units of lock level increase the lock gain a few units and repeat the process by decreasing the lockpower by six more units If the shims are far from optimum you may need to accept less than opti mum power and gain settings until after you have shimmed the magnet a little better If you cannot achieve a stable unsaturated lock after shimming then you may want to increase the deuterium content of your sample If this is impossible you may want to just proceed any way with the best compromise you can achieve But be aware that you are operating under nonoptimal lock conditions and you may encounter difficulty shimming with consequent decrease in the q
38. B B ol o0 0 1M M 0 1 ofw 0 B B m i M 1 0 OF M y B5 0 BM M 0 0 O M B B 0 M 0 B B M M wl y L 2 0 Bim dt Y r M M B B 0 If is taken to be intrinsically negative this is the desired result This is reasonable since our original equation says that the magnetization precesses in a negative sense when Yy is positive See Figure 2 Problem 6 on page 12 Equation 13 represents a field rotating in a positive sense If one adds this to a sim ilar equation with replaced by the result is Bj B B cos O oa Opt ji 8 cos 0 i sin 1 j B cos 11 i sin st i 8 cos O st sin 0 1 j 2B cos co 1 i Thus there remains only the oscillatory x component of the field 2 13 01 146 Part III Appendices Problem 7 on page 12 It has been shown previously that ignoring Bj the above conditions lead to Bef 0 Hence one can transform B into the rotating frame to obtain sui cos ar cos 0 51 15A IBN _ Di Di sin t cos ar sin t cos ar cos t sin t sin 0 1 B sin t cos 0 t cos ar sin o t cos o e 1 sin o f yl and if O then y Equilibrium 0 x Pulse 0 y Pulse x 2 13 01 Appendix 3 Solutions to Problems 147 Problem 9 on page 13 As shown in Figure 7 the magnetization rotates about B eff not B Suppose the an gle between B and B is 0 tan B Jy i B th
39. Figure 19 The sin x x function is the Fourier transform of the rectangular function Equation 38 10 4 Apodization The effects of this undesirable convolution can be alleviated by a technique called apodization This consists of smoothing the tail of the FID so as to eliminate the sharp edge produced by the rectangle function Almost any smooth function will produce desirable ef fects one method is shown in Figure 19 10 5 Sensitivity Enhancement An FID can be written in the form f t exp ior 1 T 39 2 13 01 38 Part I Lecture Notes Recall that the width of the line when one Fourier transforms this function is given by Equation 25 Suppose the above function is multiplied by one of the form f t exp t T 40 Problem 22 Show that the complex exponential form of the FID Equation 39 is just another way of writing Equation 22 Show that mul tiplying Equation 39 by Equation 40 gives in the spectrum a Lorentzian line with frequency and width 1 1 pan nT nT 41 corresponding to the convolution of the two Lorentzians APODIZATION iii ye cose 1 8 0 7 Figure 19 2 13 01 10 Digital Filters and Convolution 39 The line width is increased by 1 77 8 which decreases the resolution but as shown in Figure 20 the noise in the spectrum is substantially decreased thus improving the signal to noise ratio of the spectrum 10 6 Resolution Enhancement
40. Fundamentals of High Resolution Pulse and Fourier Transform NMR Spectroscopy 10 11 12 ili Table of Contents Part I Lecture Notes The Nuclear Zeeman Eff Ct suole rana 3 1 1 A magnetic field breaks the degeneracy of nuclear spin states 3 1 2 The differences in level populations are very small 3 Net Magnetization and Nuclear Precession 5 2 1 Classical Equation of Motion of a Magnetic Dipole 5 2 2 Magnetization of an Ensemble of Spins eee eeeeeeeseecseeeseeeeeeeenees 5 23 Nuclear Precession irreali a aiar 6 Detection of Precessing Magnetization eeeeeeeceeseecnseceseeeseeesseecsaeeneensees 8 The aR GLAS rane tarare 10 The Effects of Radio Frequency Fields Pulses 12 5 1 On Resonance Pulses vcs or ined eigen itunes 12 3 2 Off Resonance PUlsess dipl lane Deliri liti 13 Relaxation Bloch s Equations iaia elia asi 15 6 1 Correlation Functions and Spectral Densities 16 62 Relaxation Mechanisms se de RS e ee Tac 18 The CW NMR Experiment ariana ilaria 21 The FT NMR Experiment pirla earn 23 The Anatomy of a Free Induction Decay i 25 9 1 FID ofa Single Resonance isso ranieri lira ni loi 25 92 FID of Two or More Lines ir 25 9 3 Digitization of Free Induction DecayS 26 OA Time Ayera fih etant a tr bdo
41. Observation of a Less Common X Nucleus 103 From Table II choose one nucleus you wish to attempt to observe in this session Note that the entry for protons is given only for reference and is not to be chosen You may choose a nucleus that is relevant to your research or have your instructor help you choose an interesting one Use the Handbook of High Resolution Multinuclear NMR to find the basic information about your chosen nucleus Pay particular attention to natural abundance chemical shift range chemical referencing methods and relaxation times Ask your in structor where to find the handbook With your instructor choose one or two compounds containing the nucleus of in terest and make up appropriate samples One sample should contain a strong easily ob served signal if possible of known chemical shift so that you can reference your spectra Table II Natural Abundance and Larmor frequency of some selected isotopes Nucleus Spin na Coal MHz IH 1 2 99 98 100 0 ILi 3 2 92 6 38 864 lp 3 2 80 4 32 084 DN 1 2 0 37 10 133 170 5 2 0 037 13 557 LE 1 2 100 94 007 23Na 3 2 100 26 451 277A 5 2 100 26 057 si 1 2 4 7 19 865 55Mn 5 2 100 24 664 Se 1 2 7 58 19 067 MBr 3 2 50 54 25 053 med 1 2 12 75 21 205 Sn 1 2 7 61 35 625 19Spt 1 2 33 8 21 499 2 13 01 104 Part II Laboratory Experiments If your first sample contains only a single resonance you may want
42. The methyl protons of tert butyl alcohol are all equivalent so the ratio of the methyl to the hydroxyl protons would be nine to one The largest number expressible in three bits is eight and in four bits sixteen so four bits would be enough for the magnitude of the num ber but one more bit is needed to store the sign so a total of five bits would be needed However if a tert butyl group is used as a bulky substituent in a molecule other single pro ton resonances might be split into multiplets reducing the size of each resonance so that more bits would be needed Pure water is 55 M so it would be 110 M in protons but 10 of the hydrogen is deuterium so the solution is about 100 M in protons The ratio of the two resonances would 2 13 01 Appendix 3 Solutions to Problems 153 then be about 20 000 1 Using a 15 bit ADC the size used on the VXR 500 would permit storage of 214 16 384 this is not enough one would need 16 bits This illustrates why it is necessary to use solvent suppression techniques for obtaining spectra of dilute biolog ical samples in water solution Note also that a 12 bit ADC such as used on the XL 300 would be completely inadequate for this kind of work Problem 17 on page 28 The data points representing the two lines would have to be separated by at least one data point of lower intensity than either of them so the two lines would have to be at least 2 A apart The only values that could be found for
43. a coupling constant would be 2 A 3 A 4 A hence a reasonable error limit would be 1 2A Interpolation schemes can do somewhat better than this if the signal to noise is good Problem 18 on page 29 Suppose your spectrometer has 128 K bytes available for storing the FID then if two bytes 16 bits are used to store a real number four bytes are needed for each complex sample of the FID to give a value of 32 K or 32 768 for Nmax On a 400 MHz machine the nominal spectral widths would be 10 ppm x 400 Hz ppm 4000 Hz for protons and 200 ppm x 100 Hz ppm 20 000 Hz for carbon Using these spectral widths gives 0 12 Hz for protons and 0 61 Hz for carbon One could use a spectral width of 32 768 x 0 2 6554 Hz for any experiment while maintaining 0 2 Hz resolution Note that if double precision is used 8 bytes per complex point all of these values must be reduced by a factor of two Problem 19 on page 29 Changing the frequency of the transmitter or the spectral width does not change the Larmor frequency of a resonance hence if a line moves in the spectrum in a way that is inconsistent with this fact it must not be a real line Consider the following examples 2 13 01 154 Part III Appendices Single Sideband Detection Real Line Aliased Line SW 2 SW 2 10 5 0 5 10 Frequency KHz Transmitter Frequency Decreased by 1 KHz Real Line liased Line I SW 2 10 5 10 Frequency KHz The line should have
44. aboratory Experiments b Acquire the 1D carbon spectrum You should be able to use shims from one of your previous experiments However you can shim on the dioxane sample if necessary c Join a second experiment and retrieve the 1D proton spectrum that you acquired in Laboratory 6 or 7 If you don t have this you will need to acquire a reference proton spectrum d Join the third experiment and move the carbon acquisition parame ters to it e hetcor The setup macro for the HETCOR pulse sequence loads the new ac quisition parameters as well as the proper pulse sequence The mac ro will query you for the location of the proton reference spectrum or you can supply it as an argument to the macro Use nt 8 and ap propriate values for pp and pplvl from Laboratory 5 Set pw and tpwr for a 90 degree carbon pulse If you don t have a reliable cali bration check it on the sample provided for this experiment As sume a proton T of two seconds an average one bond coupling jlxh of 140 Hz and set the long range coupling parameter jnxh 0 you will do only one bond correlations in this exercise Collect the data with decoupled H H multiplets by setting hmult appropriately and use no presaturation pulses Set np in the F carbon dimension to 4096 and use 128 increments for ni Set fn to 8192 and fn1 to 512 f go You can experiment with weighting and transforming the data as the acquisition continues g Be sure to save all th
45. ach of these carefully as they will be very valuable in subsequent sessions and in your later NMR work 5 0 1 PROCEDURE a Join or create an experiment Insert the He sensitivity sample set up for 3C observe and check the lineshape Shim as necessary b Insert the sample provided by your instructor and obtain a carbon spectrum with broadband proton decoupling Use a 90 degree ob serve pulse width nt 1 and 32 K data points set the decoupler off set to zero making sure the value of solvent is correct This will place the center of the broadband proton decoupling near 5 ppm If your proton chemical shifts are known to be localized in some nar row region of proton chemical shifts the decoupler offset can be modified appropriately Remember that the frequency axis increases from right to left not left to right as usual Thus if you wanted to set the decoupler offset to 3 ppm on a 500 MHz spectrometer for exam ple you would set dof to 1000 Hz Narrow the sweep width so as to include only the region of interest and the solvent signal Check the standards book or the stdtests directory for pulse widths and power levels if you do not have them for the instrument and probe you are using Save this spectrum for future reference c You may want to try this step on a workstation prior to your spec trometer session A set of manuals identical to the paper manuals ex ists on line Learn how to use them by looking up the DEPT experimen
46. ample Check that the total acquisition time is reasonable for the time you have available The value of null may be optimized for slightly better suppression of the signals from carbon 12 molecules by moving these parame ters to some other experiment setting nt 1 ni 1 phase 1 and making an array of null over 0 1 to several seconds the spectra ob tained will be dominated by the proton signals from the carbon 12 molecules Choose the value of null that gives minimum average amplitude of the spectrum Return to the HMQC experiment and set the best value of null go You can experiment with weighting and transforming the data as the acquisition continues but go on immediately to the next step Do not wait for the HMQC experiment to complete Join another experiment and move the parameters from the HMQC experiment to the new one Make the following changes to the parameters mbond y 2 13 01 125 126 Part II Laboratory Experiments null 0 taumb 0 055 Be sure that the total acquisition time is reasonable for the time you have available n go Since the HMQC experiment has probably not yet completed this HMBC experiment will be queued and will start acquisition as soon as the experiment in progress complete acquisition o Be sure to save all four FID s At this point you can continue on a workstation if necessary p Use the appropriate commands to weight transform and plot your data These data ar
47. ample This oscillatory behavior occurs only when M has x or y components Recall that this is not the case at ther sample rf coil Figure 4 2 13 01 3 Detection of Precessing Magnetization 9 mal equilibrium This voltage is generally of the order of microvolts but can be amplified and recorded This is the NMR signal 2 13 01 10 Part I Lecture Notes 4 The Rotating Frame Consider a coordinate system rotating about the Z axis of a laboratory fixed frame at an angular frequency The rotating primed coordinate system is then related to the laboratory fixed system by the transformation x xcos t ysin t y xsin rt ycos ar 10 LT Problem 5 Show that under this transformation the equation of mo tion for the bulk magnetization becomes dM f where Bay 2 2 c 12 Thus in the rotating frame the equation has the same form as in the laboratory frame except that the z component of the external field is reduced by a factor y This factor is often called the fictitious field This means that the solutions will have the same form as in the laboratory frame except that the precession frequency will be the difference between the Larmor frequency and the rotating frame frequency In what follows the primes will not be carried but it should be assumed that all equations are in a rotating frame The rotating frame used should be evident from the context Figure 5 illustrates t
48. ance of H is about 99 98 the remainder being 2H For carbon on the other hand the natural abundance of the isotope that is NMR active BC is only 1 1 while the rest is essentially all 12C which is NMR inactive The element iridium has two natural isotopes 191r and 3Ir the former has an abundance of 37 3 while the later is 62 7 Each has a spin of 3 2 both are NMR active but each isotope has a different gyromagnetic ratio y and hence resonates at a different frequency Even many low abundance quadrupolar nuclei such as 2H can be observed fair ly easily with modern spectrometers Relative receptivity or sensitivity gives you an idea of how strong a signal you might expect to get from a particular nucleus The values are generally given relative to ei ther protons or carbon 13 For nuclei of natural abundances N for the reference nucleus and N for the nucleus of interest the relative receptivity D is defined as SL Le 1 IAG r N 57 where x refers to the nucleus of interest and r refers to the reference nucleus The absolute value is used so that D will always be positive in spite of the negative yof some nuclei Relative sensitivities for some of the common nuclei with respect to protons are given in Table I 2 13 01 102 Part II Laboratory Experiments Although many nuclei have low natural abundance and low sensitivities time aver aging allows collection of many of these on a routine bas
49. annel Pulse Widths The extent to which the magnetization is perturbed from thermal equilibrium is de termined by the transmitter power and length of time the transmitter is left on See the lec ture notes Section 5 on page 12 for more detail Our objective is to determine the length of the pulse necessary to produce a 90 or a 180 degree pulse at a given transmitter power This is done by observing the amplitude of a strong signal near the carrier as a function of 2 13 01 Laboratory 2 Observation of Carbon 13 87 pw the amplitude will trace out one full cycle of a sine function between zero and 360 de grees The pulse widths corresponding to the positive maximum and the first zero crossing will be the 90 and 180 degree points respectively Due to a small off resonance effect and to B inhomogeneity the 180 degree zero crossing will not be a perfect null but will appear as a dispersion mode signal with much reduced amplitude compared to the 90 degree point Calibration of the 90 and 180 degree pulses is required for 2D NMR pulse sequences T and T determinations and determining optimal values for pw when rapid pulsing is re quired The pulse width calibration for a particular nucleus will vary depending upon the type of sample and will be different from one nucleus to another even using the same probe Samples that are highly ionic are likely to cause longer than normal 90 degree puls es If the pulse width calibration is critical for
50. ansfer DEPT 107 Laboratory 5 Distortionless Enhancement by Polarization Transfer DEPT The observation of many nuclei is hindered by both low natural abundance and low gyromagnetic ratio leading to poor sensitivity and consequently to severe limitations on the problems to which NMR spectroscopy of these nuclei can be applied When such an insensitive nucleus is coupled to a nucleus with a higher gyromagnetic ratio e g H bya dipole dipole interaction enhancement of the insensitive nucleus can be achieved by taking advantage of the NOE as has been shown in a previous laboratory exercise A different method which relies on the scalar coupling between the sensitive and insensitive nuclei can be used to transfer the high degree of polarization of the sensitive nucleus to the insensitive nucleus The DEPT experiment is one of a large family of one and two dimensional exper iments that make use of this polarization transfer technique The DEPT and the closely related INEPT experiments result in signal enhance ments on the order of the ratio of the y of the sensitive nucleus to that of the less sensitive nucleus The latter method however results not only in polarization transfer via scalar cou pling hence a signal enhancement but also produces multiplet intensity ratios which do not conform to those characteristic of thermal equilibrium In fact the sum of the intensities of all the lines of a multiplet will be zero whereas the DEPT se
51. appeared at 1 KHz instead it appeared at 3 KHz 2 13 01 Appendix 3 Solutions to Problems 155 Quadrature Detection Real Line Aliased Line SW 2 SW 2 10 5 0 5 10 Frequency KHz Spectral Width Increased by 2 KHz eal Line Aliased Line SW 2 SW 2 Frequency KHz The position of the line should not have changed instead it moved from 2 KHz to 4 KHz Many other examples can be analyzed Problem 20 on page 31 In order to improve the signal to noise by a factor of 5 one must take 25 times as many transients Since 12 hr have already been invested it would take 25 x 12 300hr 12 5 days to complete the job Problem 21 on page 35 The ratio of the time required using the direct calculation to that using the FFT would be N Nlog N 2 13 01 156 Part III Appendices Substituting 1024 2 yields 102 4 or it would take more than 100 times longer to do the calculation directly For 32 K the result is 2184 5 or more than 2000 times longer Thus if it were necessary to do line broadening by the direct computation of the convolution some thing that takes 10 sec would take over 6 hr Problem 22 on page 38 Equation 21 gives the form we have used previously M M e sin 0t M M e cos art Using the familiar identity e cos x isin x yields M iM M e cos t isin t M e Be M se oO oO Multiplying Equation 39 and Equation 40 together gives FOLO ME at o
52. art III Appendices Appendix 1 Locking and Shimming the Spectrometer 137 Las Obtaining Lock scarola loan 137 122 Shimmins th Magneti pavo palio enii 139 Appendix 2 Sample Preparation ssh sentent 141 Appendix 3 Solutions to Problems usino ir 143 1 8 01 vi 1 8 01 Part Lecture Notes by Charles L Mayne 1 The Nuclear Zeeman Effect l 1 1 the z component of angular momentum is lifted For a nucleus of angular momentum The Nuclear Zeeman Effect A magnetic field breaks the degeneracy of nuclear spin states When a nuclear spin is placed in a magnetic field the degeneracy associated with I 1 2 two energy levels result as shown in Figure 1 the nuclear spin Each type of nucleus has a characteristic gyromagnetic factor y which together with the strength of the external magnetic field By determines the Larmor fre quency If By 7 05 Tesla for example then for protons Vo 9 27 300 MHz and for C Vo 75 MHz Of course these are nominal values which are affected by chemical shifts etc Also y can be negative as in SN for example causing the spins to precess in The angular frequency is referred to as the resonance or Larmor frequency of the opposite sense 1 2 The differences in level populations are very small Problem 1 A certain sample has 1 million chloroform molecules At 300 K using Boltzmann statistics how many fewer protons w
53. atei 29 Digital Filters and Convolution rara 35 10 1 The Convolution Th orie din eines titine 35 102 D convoluti n 5258 liti ee 37 10 3 Truncation GE the ID esta an lin 37 TO Apodizaloni soleil nee 37 10 5 Sensitivity Enhancement ies sheer lee a heehee Ae 37 10 6 Resolution Enhancement entente 39 10 7 Lorentzian to Gaussian Transformation 40 Decoupling and the Nuclear Overhauser Effect i 41 11 1 Equation of Motion for a Two Spin System 41 t12 Homon cl ar Decoupling rale ns A en ee ds 43 11 3 Broadband Decoupling issues Rimini 44 Multiple Pulse Experiments Spin Echoes Measurement of 7 and 7 45 12 1 Measurement of 7 by Inversion Recovery 45 12 2 Hahn Spin Echoes siii calli rl a ec 46 1 8 01 12 3 Measurement of T by the Carr Purcell Meiboom Gill Method 46 13 Polarization Transfer INEPT and DEPT iii 48 lode INFPR Earle 48 13 2 DEPT eda 48 14 Fundamental Concepts of Two Dimensional NMR 53 14 1 The Generic 2D Pulse Segudeice sushi en 53 14 2 The Two Dimensional Fourier Transform iii 54 14 3 Phase Sensitive 2D NMR Lino ari aroietni postata 55 144 Phase Cycling nenien n na aiar 57 14 5 Pulse Field Gradients ESS ne Re pese ole e 61 15 Chemical Shift Correlation Experiments 62 15 1 Homonuclear Shift Correlation COSY i 62 15 2 Carbon Carbon Homo
54. ation of Observe Channel Pulse Widths eee eeeeeteeeeeetees 86 2 4 Determination of a Carbon Tasmanie 88 1 8 01 Laboratory 3 Decoupling and the NOE 95 3 1 New Commands and Parameters urea 95 3 2 Homonuclear Single Frequency Decoupling 95 3 3 Heteronuclear Single Frequency Decoupling 96 3 4 Gated Decoupling and the NOEs 2a aelulas 97 Laboratory 4 Observation of a Less Common X Nucleus i 101 41 New Commands and Parameters durano ia 102 4 2 Outside preparation rire AZ Te 102 43 1 General Considerations ossee eeri nr i ave ee lende 104 4A PROCEDURES eeoa cpio a e A E ila ates ata 104 Laboratory 5 Distortionless Enhancement by Polarization Transfer DEPT 107 Laboratory 6 Homonuclear Correlation Spectroscopy COSY i 111 Laboratory 7 Double Quantum Filtered Homonuclear Correlation Spectroscopy DQCOSY rullante ao 115 Laboratory 8 Heteronuclear Chemical Shift Correlation Spectroscopy HEITCOR creenin EA E E E EA 119 Laboratory 9 Indirect Detection of Heteronuclear Chemical Shift Correlation HMQC HMBC iii 123 Laboratory 10 Heteronuclear Two Dimensional J Spectroscopy 127 Laboratory 11 13C Two Dimensional INADEQUATE Direct Detection of Carbon Carbon Bonds ses hein lega io 129 Laboratory 12 Through Space Correlations NOESY ii 131 P
55. ation of motion becomes X M _ Xi dt ay dM M T YM AB Ph 18 2 aM _ gg MM di T where AB y Problem 13 If B is small show that the steady state solution of these equations is TEPE T E LE x Xo o 14 Ty 1 1 19 M X 0T B y Xo 1 0 T 1 M M where _M Ko B o Suppose one keeps B and B constant and changes slowly Then the NMR signal has the form 20 2 13 01 22 Part I Lecture Notes Absorption Dispersion 0 Frequency Figure 11 where A represents various constants including the efficiency with which one can detect and amplify the voltage induced in the receiver coil This equation represents the basic con tinuous wave cw NMR experiment Figure 11 shows the form of these two signals F represents what is termed the dispersion mode signal while F is the absorption mode The latter is the signal usually displayed when one records a cw spectrum Problem 14 Make a scaled plot similar to Figure 11 What is the effect on the curves of changing B or T gt What is the full width at half max imum fwhm of the absorption curve How many fwhm units does it take for the absorption mode to fall to one percent of its maximum value How many for the dispersion signal 2 13 01 8 The FT NMR Experiment 23 8 The FT NMR Experiment If one applies a 90 degree pulse along the x axis the magnetizat
56. atory 3 on page 95 This second experiment is for demonstration purposes only to com pare the results of the 1D and 2D methods b Move the carbon observe parameters to the experiment where you want to do the 2D then use the het2dj setup macro Review the doc umentation for hints on how to set the experiment up Set up the ac quisition with the following considerations run the gated decoupler mode swl 500 Hz use WALTZ decoupling and nt a multiple of 4 Be sure the number of transients used is sufficient to give reason able signal to noise in a 1D spectrum Repetition rates are governed by the carbon T s that you determined in Laboratory 2 on page 85 Set the number of increments ni so as to have a total run time of about one hour The pulse sequence library psglib and the on line manuals as you found in the past contains many of the answers to your questions concerning new parameters for the pulse sequences 2 13 01 128 Part II Laboratory Experiments you are using get used to using it c go Remember to save your data d wti wft2d etc Interactively weight and transform your data This is not hypercom plex data e foldj The FOLDJ command will make the data symmetric by folding about the center of the Fl axis of your data f plhet2dj Plot the 2D data with the 1D carbon spectrum along the F axis Ob tain traces of any two multiplets found along F and plot separately Clearly label the spectrum as to the
57. before the pulse M the thermal equilibrium magnetization Substituting the first line of Equation 30 into the second and solving for M gives Equation 31 s e 1 M M 31 e cos The xy magnetization following the pulse is M sin and the amplitude of the FID is pro portional to this quantity Hence the signal amplitude for each FID can be rewritten for this case as Equation 32 r S 0 r KM sin KM sino 1 32 e cos Then we know from Equation 29 that the signal to noise after N FID s is proportional to VN Hence we can write Equation 33 VN KM VN o e 1 S 0 r S 0 r in 0 33 Os Os e cos 2 13 01 9 The Anatomy of a Free Induction Decay 33 However the interesting question is What values of and r will give maximum signal to noise per unit time To answer this we write Equation 34 70 1 S 8 r _ KM NN ee 1 1 T OsT e cos KM e 1 2__sin 34 Os NL TL re cos i e 1 K sin re cos The explicit dependence on N has been eliminated by using the fact that pei t Tr and all of the constants have been absorbed into a new constant by defining 3 KM Os y T T Equation 34 tells us how signal to noise per unit time depends on the values of and r Figure 17 shows a contour plot of this equation Note that 90 degree pulses never give max imum signal to noise per unit time regardless
58. ck and shim as you did in Laboratory 1 f Check the carbon 13 lineshape at 50 0 55 and 0 11 of full height as you learned to do for proton lineshape in Laboratory 1 Shim the magnet as needed to achieve performance similar to that in the file you retrieved from stdtests Add appropriate text and save the FID in the archive for use in preparing your report g You have been using decoupled dioxane dm y to check the line shape Now let s see what happens when the decoupler is turned off by setting dm n and acquiring another spectrum Remember that the decoupler doesn t actually turn off until after the su command is executed The dioxane peak should be a 1 2 1 triplet Be sure to wait at least one minute between successive acquisitions to allow for full relax ation You can increase d1 if you want to ensure this but usually the time to process the data will be sufficient Note the fine structure in each of the dioxane triplet resonances This is due to long range cou pling to the six protons not directly bonded to the carbon 13 Save this FID for your report also Note the difference in S N between the coupled and decoupled spectra h Retrieve the latest signal to noise test for this probe Transform this data and measure the S N using the dsn command Now acquire a spectrum and check that the S N is close to that of the standard data set Your results should be within 5 of the standard 2 3 Calibration of Observe Ch
59. ctroscopy 2nd Ed Elsevier Science Publishers New York 1984 Intermediate g C Brevard P Granger Handbook of High Resolution Multinuclear NMR John Wiley and Sons New York 1981 h A Bax Two Dimensional Nuclear Magnetic Resonance in Liquids D Reidel Pub Co Boston 1982 i E Fukushima S B W Roeder Experimental Pulse NMR A Nuts and Bolts Approach Addison Wesley Pub Co Reading Mass 1981 j Reinhard Benn and Harald G nther Angew Chem Int Ed Engl 22 350 1983 k Horst Kessler Mathias Gehrke and Christian Griesinger Angew Chem Int Ed Engl 27 490 1988 Advanced L C P Slichter Principles of Magnetic Resonance 2nd Ed Springer Verlag New York 1980 m A Abragam The Principles of Nuclear Magnetism Oxford Univer sity Press London 1961 latest printing 1973 n R R Ernst G Bodenhausen and A Wokaum Principles of Nucle ar Magnetic Resonance in One and Two Dimensions Oxford Uni versity Press New York 1987 2 13 01 74 2 13 01 Part I Lecture Notes Part Il Laboratory Experiments Introduction 77 Introduction This section contains a series of laboratory exercises designed to introduce you to various aspects of high resolution pulse and Fourier transform NMR The experiments are designed to illustrate the principles presented in the accompanying lecture series They are designed around a Varian Inova 500 NMR spectrometer although any spectromete
60. curve occurs when 57o 1 This means that when the field strength of a spectrometer is increased the correlation time 2 13 01 18 Part I Lecture Notes 1x10 1x10 1x102 1x10 1x104 1x10 1x10 1x107 1x10 1x109 1x10719 1x101 1x102 1x103 1x1 0 4 Motional 1x10 NAIL 7 1imit mio 1x10718 R1 1 11 R2 1 T2 1 sec 6 1x10718 1x10 17 1x10716 1x10715 1x10714 1x10 13 O 1x10 1x10 4 1x10710 1x109 1x108 1x107 4x10 1x10 1x104 1x108 1x102 1x10 1x10 corresponding to the maximum will decrease but the motional narrowing limit will remain the same 6 2 Relaxation Mechanisms Any process that causes the magnetic field seen by the nucleus to fluctuate random ly can cause relaxation The following are the most important relaxation mechanisms for high resolution NMR of liquids They are arranged roughly in order of decreasing importance for organic molecules 6 2 1 Dipole Dipole Interactions Every other magnetic nucleus in a sample will create a magnetic field at a nucleus of interest The nuclei can be in the same or different molecules The strength of the inter action is inversely proportional to the sixth power of the distance between the nuclei thus 2 13 01 6 Relaxation Bloch s Equation 19 the nuclei must be very near each other within a few Angstroms for a significant interac tion to occur The modulation is caused by rotation and translation of
61. d justed for a short period of time usually a few milliseconds During this time Spins at the center of the sample would not be affected and would precess at their usual Larmor fre quency But as one moves higher in the sample the spins would precess a little faster than at the center and as one moves lower they would precess a little more slowly Thus the Larmor frequency would be a linear function of the z coordinate of the particular spin If one applies a ninety degree pulse followed immediately by a PFG the transverse magneti zation would seem to quickly disappear because the spins would dephase in the rotating frame due to their different Larmor frequencies The magnetization as a function of z would look like a helix or cork screw Now suppose we apply a PFG of opposite sign 1 e the cur rent flows in the opposite direction in the coil for the same period of time Now the spins above center in the sample would precess more slowly while those below center would precess more rapidly At the end of the second PFG the magnetization would have pre cessed back to its original phase and an echo would form This is called a gradient recalled echo Now imagine we have a dilute solution of protein in water We apply a ninety de gree pulse followed by a PFG All the magnetization dephases Now we wait for a short period of time then apply the opposite PFG to recall the echo The proton signals from the protein form the echo as expected bu
62. d exponentially to thermal equilibrium This process is called relaxation Problem 11 Show that under the above stated restrictions each of the above equations has a solution of the form M A C 16 What are A C and amp in each case The decay of M and M is called transverse or spin spin or 7 relaxation and that of M is called longitudinal spin lattice or T relaxation Problem 12 If one now assumes that what is the form of Bloch s equation This is the equation of motion for a Free Induction Decay FID Recall that Equation 8 deals with this case in the absence of relax ation 2 13 01 16 Part I Lecture Notes 0 9 0 8 0 7 gt 0 6 0 5 0 4 0 3 0 2 0 1 0 0x10 1x107122x107123x107124x107125x107126x10712 tau To Memo 6 1 Correlation Functions and Spectral Densities The rotational correlation time is a measure of how fast a molecule is tumbling in a liquid The spin lattice and spin spin relaxation times are related to the rotational correla tion time by 1 2 2 To y p p2 _0__ T FRE 1 T i i 17 2 p2 2 2 To y Br 8 B ph Ty F Sal where B q x y z is the average of the square of the strength of a random field acting on a nucleus is the Larmor frequency and T is the correlation time of the molecular tumbling This correlation time gives a measure of the time required for the molecule to lose its memory of rotational pos
63. done far faster than computing the convolution directly The former takes only 2Nlog N operations whereas the latter requires N operations This increase in computa tional efficiency is the power of the convolution theorem Problem 21 Compute the increased computational efficiency of the FFT method over direct computation for convolution of two 1K 1024 point data tables and for two 32K 32 768 point data tables 2 13 01 36 Part I Lecture Notes Convolution x x O x O so O e oF le x x x Figure 18 2 13 01 10 Digital Filters and Convolution 37 10 2 Deconvolution If a spectrum has been convolved with some particular function perhaps due to an artifact of the instrumentation such as magnet inhomogeneity it is possible to conceive of undoing the process by writing a t a 37 This is indeed possible however certain limitations apply since one must avoid dividing x by zero and of course it is impossible to recover data lost because the original c t was zero over some particular interval 10 3 Truncation of the FID If one stops taking data before the FID has completely died away into the noise this can be viewed as convolution The FID has been multiplied by a function of the form 0 1 lt 0 f t 41 O lt t lt A 38 0 t gt A where A is the spectrometer acquisition time This corresponds to convolving the spectrum with a sin x x function See
64. e cursor pair and the right mouse button to control the spacing between the cursors place a cursor on each side of the peak where it intersects the threshold bar The value of delta displayed at the bottom of the screen gives the width of the line If delta is in ppm it may be changed to hertz by setting ax is h The value of delta in hertz may also be obtained by typing delta on the command line Note that the current value of any pa rameter may be obtained this way Make another measurement with the threshold set at 0 11 of the line height Once the magnet is properly shimmed the three values obtained should closely match those of the spectrum from which you took the starting shims and the line shape should be symmetrical devoid of chairs resulting from incorrect even order Z gradients If you spend the time to get proper line shape on the chloroform sample it is usually easy to get adequate resolution on all other samples If you cannot get good chloroform line shape you should not expect to get good results on other samples pl pscale pap page You can do this step and all the subsequent plotting for this experi ment later on one of the data processing workstations if you wish Make a hardcopy for the 50 0 55 and 0 11 measurements Use the text command to label the spectra appropriately Be sure to include in the text the line widths measured at various heights your name the name of the spectrometer you used and
65. e dimensional carbon spectrum the chemical shifts of all 1 C nuclei are known For every pair of bonded carbon atoms the 2D spectrum contains a four line pattern restricted to two small regions indicated by a pair of rectangles as shown in Figure 39 Each rectangle contains two of four transitions com prising the spectrum of a coupled two spin system The spectral lines are derived from a double quantum coherence and are antiphase rather than both positive as in normal 1D spectra Each doublet encloses the chemical shift frequency of one of the bonded carbons on the horizontal chemical shift axis In the second dimension the double quantum fre quency DQF axis all four transitions appear at a frequency that is the sum of the two chemical shifts In Figure 39 four transitions can be found two with shift frequencies of the methine carbon at approximately J 2 where J is the carbon carbon scalar coupling constant and two at approximately 2 for the methylene carbon All four transitions have a DQF of approximately v vg A similar bond pattern between the methylene B and 2 13 01 66 Part I Lecture Notes methyl C carbons also exists but no bond pattern is found between the methine A and methyl C carbons 15 3 Heteronuclear Chemical Shift Correlation This experiment produces a 2D spectrum with the F axis labelled by the chemical shift of one nucleus e g 613 o and the F axis labelled by that of another nucleus e g
66. e hypercomplex so you must use the appropriate commands to analyze the data Make a 2D contour plot with the cor responding 1D spectra along the appropriate axes The macro plhx cor is useful for this The command dpcon creates a screen display that is a true contour plot like the one produced by the pcon com mand rather than a color intensity map as is produced by the dcon or dconi commands The dpcon command gives better definition of the contours as they will appear on a printer but it can take a rather long time to compute this display so use it with caution Experiment first with a highly expanded portion of the spectrum so that the com putation time will not be excessive The various display and plotting commands have lots of options to control how the spectra are dis played or plotted these can be found in the on line manuals Learning to properly work up and plot high quality 2D data takes practice Read the manual and practice as much as you can Using the results from your COSY or DQCOSY data make as many assignments as possible in your HMQC and HMBC spectra 2 13 01 Laboratory 10 Heteronuclear Two Dimensional J Spectroscopy 127 Laboratory 10 Heteronuclear Two Dimensional J Spec troscopy In previous 2D experiments such as COSY and HETCOR correlations were made between two chemical shifts connected by some interaction such as scalar coupling in J spectroscopy the emphasis is on interpretation of multiplet s
67. e spinner turbine with a tissue Skin oil from your hands will accumulate and cause the sample not to spin The lineshape sample is chloroform in acetone d Before inserting the sample in the spinner turbine be sure that the sample tube and spin ner turbine are clean Before releasing the sample into the upper bar rel be sure there is sufficient air to support the sample at the top of the barrel then click the insert button to lower the sample into the probe Click close to close the acqi window explib This command will display a list of the experiments currently exist ing in your home directory You have your own copy of the experi ment files that cannot be changed by other users The experiments will be just as you left them when you last logged out Notice the size of the experiments Do not leave unneeded experiments especially large ones in your home directory Archive the data you want to keep and delete the experiment using delexp cexp n where n can be 1 through 9 but must not be the same as for one of the already existing experiments This creates a new experiment file where you can perform data acquisition without disturbing whatever is in the other experiments Caution exp5 is used by some com mands as buffer space for the results It is best to avoid this one until you are very familiar with the software jexpn Join experiment n that you just created Click the following buttons in sequence Main Menu File S
68. eaks that partially or completely cancel each other Full analysis of the coupling constants will not be required for this experiment but the resolution in your spectrum will be sufficient to permit this if you wish to do it on your own 7 0 1 PROCEDURE a You will need two experiment files for this procedure one for your 1D reference spectrum and another for your 2D data b Insert the sample provided by your instructor set up the spectrome ter for protons acquire a spectrum and narrow the sweep width to a practical minimum You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the dilute sample because the signal is too strong from the concentrated sample for this proton experiment Shim the magnet as necessary to obtain good line shape After the spectral width has been minimized acquire a spectrum using a 90 de gree pulse width and nt 16 Decrease the gain if error messages such as ADC OVERFLOW or RECEIVER OVERFLOW occur This procedure will prevent similar problems from disrupting the 2D data acquisition C Join the second experiment and move the parameter set from your setup spectrum to this file with the mp command 2 13 01 116 Part II Laboratory Experiments d dqcosy This macro makes all the changes to the parameter set necessary to run the DQCOSY experiment but all the values may not be appro priate for your experimen
69. ear species e g one can observe 13C while irradiating IH or homonuclear if they are the same e g one can irradiate a particular proton while observing the effect on the rest of the proton spectrum A commonly used notation for these two experiments is 13C H and H H respectively The term decoupling stems from the fact that when a spin is irradiated the fine structure or splittings of all the other spins in the coupling network which are due to scalar coupling with the irradiated spin are collapsed so that the splitting pattern appears as if the irradiated spin were not coupled to the others The intensities of the remaining resonances however may be substantially different from those expected in a spin system created by removing the irradiated spin and considering only the remaining spins These intensity dif ferences are called the nuclear Overhauser effect NOE The NOE arises as a consequence of the T type relaxation occurring in the spin system As an example of these principles let us examine the equation of motion for a proton coupled to a carbon 13 nucleus 11 1 Equation of Motion for a Two Spin System Figure 21 shows a the energy level diagram of a single spin 1 2 with only one re laxation pathway available in contrast to b a system of two spins 1 2 with four energy lev els and six possible relaxation pathways Using the density matrix formalism one can show that the z components of the magnetization evolve acc
70. eflect the offsets you have entered The values entered for tn dn tof and dof determine the observe frequency and the decoupler frequency This is why the probe cannot be correctly tuned until a su command has been executed the probe does not necessarily receive the correct frequencies until this command is completed The load parameter controls whether or not the values of the shims are also sent to the acquisition computer all other acqui sition parameters are always transferred In this case since we have set load to y the values of the shims are transferred and loaded into the shim DAC s Whenever you type a go ga or au the spectrome ter will automatically precede the acquisition with a su to recognize any changes you may have made to the acquisition parameters The su command automatically sets load to n after it completes the transfer It is advisable to always keep load set to n unless you are specifically loading standard shims Otherwise you may accidental ly enter an experiment containing nonoptimal shims and transfer these to the shim DAC s replacing the set you have carefully opti mized Click acqi in the menu bar and then click lock in the acqi window Lock the spectrometer to the acetone in the sample as you were shown in the demo Tune the probe Be gentle the probes are fragile and expensive more than 20 000 each if they have to be returned to the factory for repair they are usually gone for
71. egres sion using 7 M 0 and M co as adjustable parameters This is the way the spectrometer software does it We will not go into the details of the algorithm here Experimentally 7 is dependent upon several factors these include temperature solvent viscosity and the presence of paramagnetic impurities Note that molecular oxy gen O is paramagnetic therefore dissolved oxygen can decrease the measured value of T This may be undesirable in cases where one is trying to accurately measure dipolar re laxation or NOE See Section 6 on page 15 and Section 12 on page 45 for additional de tails 2 4 1 PROCEDURE a Eject the 40 Dioxane sample and insert the sample supplied by you instructor for this laboratory session b Lock tune the probe shim the magnet and obtain a decoupled spec trum 2 13 01 Laboratory 2 Observation of Carbon 13 ment Tune the probe and shim the magnet as before Obtain a spectrum using nt 1 and a large spectral width sw 50000 at first then nar row the spectral width using the movesw command so as to include just the peaks from the compound and about 500 Hz of signal free region on each end of the spectrum np 16384 Change the number of data points to 16384 and note the automatic change in acquisition time at Problem 34 Explain why at changed dp y fn 32768 dm y pw90 x Enter x the value for the 90 degree pulse you determined in part 2 When the spectr
72. en the closest approach of M to the negative z axis is 20 because B must bisect the vertex angle of the cone traced out by M as it precesses Problem 10 on page 13 The time required will be shorter because the precession is controlled by B ef and Bow is larger than B so the precession is faster The phase will be different because the cone does not intersect the xy plane exactly on the x axis The strength of the B field is at most a few tens of kilohertz while the carbon 13 is many megahertz off resonance Thus B eff is essentially colinear with the positive z axis and cannot perturb the spins The vertex angle of the cone is essentially zero Problem 11 on page 15 Differentiating the proposed solution gives AM __ ase a M C di Comparing this form with the given equations may be identified with 1 7 in the firs two equations and with 1 7 in the third The constant C is clearly zero in the first two cases and M in the third The constant A must be identified with the usual constant of integra tion and can be evaluated by noting that at 0 A M C Hence one cannot know pre cisely what A is until the value of M at 0 is specified Problem 12 on page 15 In this case see Figure 5 one can define the effective field to be 2 13 01 148 Part III Appendices Substituting this equation into Equation 15 yields dM _ M de a aM sap aB dt di T dM _ M Mo dt T Problem 13 on page
73. ene or methyl resonances An example of this treatment is shown in Figure 28 for menthol 0 5 Intensity A 9 in degrees Figure 27 Cs SA er mb Jr 70 9 Figure 28 2 13 01 52 Part I Lecture Notes The DEPT experiment can also be used as a convenient method for calibrating the proton pulse width Usually in experiments of this type proton pulses are applied using the decoupler transmitter Since the decoupler pulses B gt essentially always have a different calibration factor than the observe pulses B4 it is necessary to have an indirect method of calibrating B with the instrument set up as it will be when the experiments which will use the calibration are done This can be accomplished by observing a methylene resonance us ing a DEPT pulse sequence with 6 set to nominally 90 degrees Then adjusting the proton pulse width one can observe the methylene resonance to pass through a null as the proton pulse passes through exactly 90 degrees If the calibration point is completely unknown a rough calibration can be achieved by setting 0 to a nominal 45 degree value and searching for a maximum intensity as a function of the proton pulse width This calibration can be used in numerous other one and two dimensional experiments where decoupler pulses are required 2 13 01 14 Fundamental Concepts of Two Dimensional NMR 53 14 Fundamental Concepts of Two Dimensional NMR Before disc
74. eriment INADEQUATE is one of the most elegant 2D structure elucidation tech niques A single spectrum has the potential to reveal the complete carbon skeleton of a molecule The method depends on creation of double quantum coherence in a spin system consisting of two bonded BC nuclei At natural abundance for 5C 1 1 about one mol ecule in ten thousand will have two 5C nuclei participating in a particular bond Thus the method will be very insensitive compared to the more routine experiments observing car bon in molecules with only one 13C nucleus The pulse sequence for this experiment is shown in Figure 38 The first three pulses constitute the preparation part of the sequence they simply create double quantum coher ence which is then allowed to evolve during f Since no double quantum state is available for an isolated 1 C the molecules with only one 5C do not contribute to the double quan tum coherences The last 90 degree pulse brings the double quantum coherence back to sin gle quantum antiphase magnetization which is detected as a function of t The magnetization that was in the double quantum coherence during the evolution is amplitude modulated at the double quantum frequency as a function of t Broadband proton decou pling is applied during the entire experiment so proton carbon couplings need not be con sidered To get a satisfactory spectrum one must suppress the signals from the one hundred times more numerous molecules
75. eriments might be useful in solving research problems Give examples relevant to your own research if you can 2 13 01 99 100 Part II Laboratory Experiments 2 13 01 Laboratory 4 Observation of a Less Common X Nucleus 101 Laboratory 4 Observation of a Less Common X Nucleus In this session you will have the opportunity to observe a nucleus other than the common ones protons fluorine carbon and phosphorus that are NMR active Experi ments involving these four do comprise the bulk of present day NMR data nevertheless data from the numerous other NMR active nuclei can often be useful You will be given a choice of which nucleus you wish to observe from the list given below The list is not ex haustive but has been selected based upon natural abundances and relative sensitivities to be practical to complete in one laboratory period without isotopic enrichment Most elements occur naturally in more than one isotopic form The fraction of a nat ural sample of an element that is a given isotope is termed the natural abundance of that isotope The natural abundance of some isotopes varies substantially depending on the source of the sample Only isotopes which have a nonzero nuclear spin can be detected by NMR The natural abundances of NMR active isotopes vary widely For some elements such as hydrogen fluorine and phosphorus the natural abundance of one NMR active iso tope is essentially 100 For example the natural abund
76. et Di rectory More VNMR Now click on stdtests in the file list it will be highlighted then click Change Click the file name correspond ing to the probe you are using and click Change Click last_h11shp fid in the file list then Return then Load This retrieves the last line shape test run by one of the NMR staff If you wish you can type wft to see what the line shape looked like at that time Using this technique you can navigate to and load any fid file into the current experiment load y su 2 13 01 81 82 Part II Laboratory Experiments When a fid file is saved all the parameters values in effect at that time including all the shim values are saved with it The spectrom eter has two computers One is called the host and is used for han dling the screen keyboard and peripherals as well as doing computations such as Fourier transforms this is the Sun workstation you are now using The other is called the acquisition computer and is located inside the spectrometer console This computer actu ally controls the spectrometer making the pulses and delays digitiz ing the FID etc su tells the host to transfer the acquisition parameters that you have entered to the acquisition computer Among other things it sends the appropriate pulse sequence code and checks which nuclei will be observed and decoupled and sends the appropriate frequencies to the acquisition processor The fre quencies correctly r
77. ety in handling samples and chemicals in the NMR laboratories d What to do when the system doesn t respond normally e Sample Sample preparation tube quality sample tube positioning Read Appendix 2 on page 141 2 13 01 80 Part II Laboratory Experiments f Probes Probe observe and decoupler channel tuning range sticks probe filter and cable arrangements g Locking and shimming Finding a deuterium lock signal manual and computer shimming loading standard shims Read Appendix 1 on page 137 h Data acquisition starting stopping monitoring an acquisition while in progress For this experiment acquisition parameters will be given to you Later you will learn how to create and modify the parameters to suit your purposes i Phasing and plotting use of manual and automatic phase adjust ment use of remote printers and plotters j Saving data and transferring it to permanent archival storage See Chemistry NMR Laboratory Application Note No 1 Data Ar chiving Copies are available in the spectrometer rooms and the document can be viewed on the web at http www chem utah edu chemistry facilities nmr app1 html 1 2 Pertinent Parameters and Commands The following parameters and commands are frequently used Most of them may be accessed from the menu buttons as well as by command line entry Study any that you are not familiar with in the User s Manual prior to doing this experiment acqi axis cexp
78. experiment and using the result in a feed back sys tem This is called an NMR lock Additional details concerning locking and shimming may be found in the vnmr manual Getting Started Chapter 6 It is common practice to make up samples for proton NMR spectroscopy in solvents with most usually greater than 99 5 of the protium replaced by deuterium so that the strong proton signals from the solvent will not interfere with those from the solute of inter est Having done this one can use the deuterium NMR signal to produce the required field frequency lock This type of lock is called an internal lock and is the most common type used for high resolution liquids NMR Deuterated solvents are almost universally used for NMR samples even when a nucleus other than H is being observed The fluorine 19 reso nance is also used but less frequently It has been found to be of great value when very low temperature liquid NMR studies are being carried out using low freezing point freon type solvents or when the spectrometer is set up to observe deuterium It is generally not practi cal to observe and lock on deuterium simultaneously The lock nucleus can also be con tained in an ampule external to the sample of interest This is termed an external lock and is much less commonly used for high resolution liquids work While searching for an NMR lock signal using the acqi window you are actually doing an NMR experiment varying the field with the z0 kn
79. fer to Section 11 on page 41 for a discussion of the NOE and its relationship to the dipole dipole relaxation mecha nism How can the NOESY correlations be used In a protein for example two protons that reside in two different amino acids widely separated in the polypeptide chain may show a NOESY correlation indicating that the chain is folded such that they are close to each other through space In a given protein there may be dozens or even hundreds of NOE SY correlations Such correlations taken together with other known structural constraints can provide enough data to fully determine the three dimensional structure of the protein This information is very valuable because proteins generally do not perform their biologi cal function unless they are properly folded and knowing the way they are folded is essen tial to understanding how they function In this experiment we will be dealing not with proteins but with smaller molecules In this case the NOESY correlations can be used to determine the geometry of stereo cen ters distinguish between cis and trans isomers distinguish between axial axial and axial equatorial relationships in cyclohexyl rings etc The intensities of the cross peaks in a NOESY spectrum of a small molecule are generally only one or two percent as large as the corresponding diagonal peaks and of opposite phase Thus if the diagonal peaks are phased for pure negative absorption the cross peaks will be phased f
80. ffecting the pulse sequence The display can be modified in various ways if time permits look up this com mand in the on line manual to see how Note that pulses are being applied in the proton channel Thus at this point it is necessary to determine a value for pp and pplvl so that you can correctly set the proton pulse widths This is done using the pp cal macro Join or create a new experiment and move your 1D carbon 13 pa rameters there then type ppcal This sets up a special pulse se 2 13 01 109 110 Part II Laboratory Experiments quence for calibrating the proton pulse Note that you cannot use the proton pulse calibration determined while observing protons because the path of the radio frequency en ergy through the spectrometer is different when applying pulses through the decoupler channel than when they are applied through the observe channel and the strength of the B field may be differ ent 1 Read the help file that is printed by the macro and modify the param eters as needed Check with your instructor as to the maximum pplvl that can be used with your spectrometer and probe Set up the pp ar ray from 0 to 40 microseconds to start with then enter a more appro priate array if necessary when you have a better idea what the 90 degree pulse is You may want to make an array with smaller steps near the 90 degree pulse value to get a more accurate determination Save the data for your report j pp x mult
81. g the in version recovery T sequence For quick approximations since 7 7 for nonviscous isotropic liquids the rela tion 1 UTOE 54 where L is the full width of the line at half maximum in Hz can be used to set a lower limit on 7 Since many other factors such as magnet inhomogeneity and unresolved scalar cou pling can broaden lines it is only a lower limit and can be in error by orders of magnitude in some cases 2 13 01 90 Part II Laboratory Experiments The intensity of the line as a function of t is given by t M t M c0 M 0 mes 2 55 1 As d2 i e f is increased from a value much smaller than T to a value much greater than T the intensity of a line in the spectrum will start out negative pass through zero and as ymptotically approach a maximum value The value of d2 at which the intensity is zero let us call it fun is related to T by T Tull _ Tull 56 l In2 0 693 This gives a much better approximation to T than the line width but is still fairly crude Problem 32 Derive Equation 56 T is more accurately determined by plotting In M c M t vs t M co is the am plitude corresponding to the maximum signal i e t is infinite and M t is the signal am plitude at each value of t The slope of the line gives the value of 1 7 Problem 33 Show that the slope of the log plot does give T The most accurate way to calculate T is to do a three parameter nonlinear r
82. ghtly different arrangements for doing this There are two main types of probes Broadband probes are designed such that the X observe coil is located closest to the sample for maximum sensitivity and the proton decoupler coil is located further away since proton sensitivity is not as much an issue for decoupling Indirect detection or HX probes are constructed with the proton coil close to the sample for best proton sensitivity and the X coil further away The probes are redundant in that the HX probe can be used to observe an X nucleus and decouple H or the broadband probe used to observe H and de couple X but in both cases signal to noise and resolution will not be optimal 2 2 1 PROCEDURE a Log in and perform the checklist 2 13 01 86 Part II Laboratory Experiments b Check with your instructor to make sure the correct probe is in stalled Gi Insert and lock the carbon 13 sensitivity sample Do not use the doped sensitivity sample the purple one This sample contains 40 dioxane 60 benzene d d Tune the probe observe channel and decoupler channel Your in structor will teach you how to do this for the particular probe you are using Mishandling of the probe tuning adjustments can damage the probe If you are not perfectly sure of what you are doing get help e Retrieve the latest carbon lineshape test for the probe you are using from the stdtests directory load the shims and parameters from this file then lo
83. gned to a particular pw array element when you display the array Adjust the vertical scale vs and vertical position vp as needed so that all the spectra are on scale If the first few spectra indicate that the range of pw is not correct for the value of tpwr you are using abort the acquisition and readjust the array so as to obtain a little more than one full cycle of the sine wave l Archive the data m Now reset your parameters so that the dioxane line is about 10 000 Hz off resonance Repeat the pulse width calibration to see what ef fect being off resonance has Archive this data Include in your re port diagrams to show where Bui is in the two cases and how this influences your pulse width calibration n When you make hard copy for your laboratory report try both pap and ppa to add a parameter list to your spectrum and note the differ ences 2 4 Determination of a Carbon T The method used to determine 7 in this session will be inversion recovery The pulse sequence is shown in Figure 22 of the lecture notes The delay d1 allows the mag 2 13 01 Laboratory 2 Observation of Carbon 13 89 netization to come to thermal equilibrium The 180 degree pulse p1 then places the mag netization along the negative z axis assuming no off resonance or B inhomogeneity effects The magnetization relaxes toward thermal equilibrium due to T spin lattice or longitudinal relaxation processes for some period of time t con
84. gnetic so dissolved oxygen does contribute to relaxation 6 2 4 Spin Rotation Interactions For small molecules rotating rapidly and undergoing collisions with other mole cules interaction of the magnetic field produced as the molecule rotates with the nuclear magnetic moment can produce relaxation For most organic molecules this effect is negli gible Dissolved CO would be an example where it would be non negligible This mech anism becomes more important as the temperature is increased in contrast to other mechanisms which vary inversely with temperature 2 13 01 20 Part I Lecture Notes 6 2 5 Quadrupolar Interactions If a nucleus has a quadrupole moment deuterium for example and is in an unsym metrical electronic environment this can produce a fluctuating field that causes relaxation Since carbon 13 and protium have no quadrupole moment this mechanism is often unim portant for structural organic chemistry 6 2 6 Scalar Interactions Just as for dipole dipole and quadrupolar interactions scalar interactions or J cou plings depend on molecular orientation and the values we see in liquid spectra are averages over all orientations Likewise the modulations involved can produce relaxation However this effect is usually negligible in organic molecules 2 13 01 7 The CW NMR Experiment 21 7 The CW NMR Experiment Now suppose one turns on a B field along the x direction of the rotating frame The equ
85. h scales the tallest peak in the spectrum to the value of vs in millimeters Center the dioxane peak as you did before in the S N test and adjust vs so 2 13 01 88 Part II Laboratory Experiments the peak is about 1 3 full screen in height Adjust the phase so as to have a pure absorption signal then DO NOT adjust the phase in sub sequent steps h dl 5 This is a relaxation delay of 5 seconds which allows for the magne tization to return to thermal equilibrium before the next pulse The calibration will not be accurate if d1 is set too small 1 Check the standard spectrum book to see what the nominal width of the 90 degree pulse should be Type array and answer the questions so as to have pw arrayed with about 50 values between 0 and 450 degrees The array values will be displayed when the command completes The array may be redisplayed by typing da anytime Check to see that the array is correct Individual values in the array may be changed or elements added to the array as follows for exam ple pw 51 45 Try this to add one more value to your pw array j ga Start the acquisition The amplitudes of the dioxane peak should trace out a little more than one full cycle of a sine curve If the curve is not smooth or not sinusoidal this is usually an indication of probe arcing Try again with a lower value of tpwr k You can monitor the acquisition in progress using the dssh and ds n commands where n is the spectrum number assi
86. he plcosy macro Discuss in your report how the information from the contour plot can be used to assign the spectrum 2 13 01 113 114 Part II Laboratory Experiments 2 13 01 Laboratory 7 Double Quantum Filtered Homonuclear Correlation Spectroscopy DQCOSY 115 Laboratory 7 Double Quantum Filtered Homonuclear Cor relation Spectroscopy DQCOSY The DQCOSY experiment is essentially similar to the COSY experiment in that scalar coupling networks are mapped out However it is particularly well adapted to being run as a hypercomplex phase sensitive experiment Read the introductory material for the COSY experiment Laboratory 6 on page 111 if you have not already done so A phase sensitive variant of the COSY experiment exists but has the disadvantage that the peaks along the diagonal are in dispersion mode when the cross peaks are in ab sorption mode Thus the intense tails of the diagonal can interfere with interpretation of the cross peaks The phase sensitive DQCOSY experiment can be phased so that all the peaks including the diagonal are in pure absorption either positive or negative With a phase sen sitive display and reasonable digital resolution it becomes evident that the cross peaks have antiphase character with respect to the direct couplings but not for the indirect or pas sive couplings See Derome beginning on page 217 for an excellent discussion of how to interpret these patterns Beware of antiphase p
87. he sample still does not spin try a standard sample If the standard does not spin consult one of the NMR staff If the standard spins the problem is with your tube and a different one should be used Never use any kind of sample container not explicitly designed for NMR use as a sample tube without approval from the laboratory manager Spin rates should be on the order of 15 25 Hz for 5 mm sam ple tubes With samples properly prepared as described below vortexing of the sample is 2 13 01 142 Part III Appendices not a problem With 10 mm sample tubes spin rates greater than 15 Hz will form a vortex that penetrates into the coil region of the probe and destroys magnetic field homogeneity Sample volumes should be kept constant from sample to sample and should be 50 mm in height from the bottom of the tube to the meniscus A volume of 0 7 mL will produce the correct height in standard 5 mm NMR tubes Accurately adjusting the volume of your research sample to equal that of the standard sample used to obtain the standard shims will make it significantly easier to shim on your research sample beginning from the standard shim settings The increase in solute concentration by making a short sample usually turns out not to be a significant advantage because the best lineshape is difficult to achieve The ideal sample would be a perfect sphere but since this is practically unachievable a cylinder that extends from well below the receiver coi
88. hese results for the case where B is along the z axis note that if then B y7 0 and M is stationary in the rotating frame This condition is termed resonance Without dwelling on the details of the electronics one can say that an NMR spectrometer has the capacity to transform the signals from the probe laboratory frame to equivalent signals in a frame rotating at y 2 13 01 4 The Rotating Frame 11 Laboratory Frame x Rotating Frame Figure 5 2 13 01 12 Part I Lecture Notes 5 The Effects of Radio Frequency Fields Pulses 5 1 On Resonance Pulses Recall that when a sample is placed in a magnetic field the magnetization goes af ter some time to thermal equilibrium with no transverse components and consequently no NMR signal in the coil How can one perturb the magnetization away from thermal equi librium so as to produce transverse components which can be detected Using the same coil shown in Figure 5 one can apply an oscillating voltage to the coil so as to create an oscillating magnetic field in the sample This oscillating field can be decomposed into two counter rotating fields One or the other of these fields will always be rotating in the same sense as the precession of the nuclear spins The form of this rotating field is B B cos 1 sin o t i 13 Problem 6 Show that the sum of two counter rotating fields is an oscillating field If all three of the frequencies the oscilla
89. hly correct but probably can be further optimized You may want to experiment with other weighting func tions later on the workstation f time The program will calculate and display the approximate total exper iment time If everything is set up correctly this should not be more than ten or twenty minutes g go h wft2d While the acquisition is in progress you may transform the partially completed 2D FID and observe how the resolution in the vj dimen sion increases as more increments are collected i foldt 2 13 01 Laboratory 6 Homonuclear Correlation Spectroscopy COSY This command folds the transformed spectrum about the diagonal and has the effect of helping to eliminate f noise and spurious peaks in the spectrum The foldt command requires that sw sw1 full This command will set the chart parameters to display the contour plot so as to fill the screen dconi Learn how to use this program to display vertical and horizontal traces and projections and make expansions Save both the 1D and 2D data sets Arrange for a session on the workstation Learn to use the interactive weighting program wti and get some additional practice with the features of the dconi program Make a contour plot with the 1D ref erence spectrum plotted on the top and side with proper chemical shift scales Be sure the chemical shifts in the 1D spectra align prop erly with those of the 2D spectrum You may want to look up t
90. ical Shift Correlation HMQC HMBC 123 Laboratory 9 Indirect Detection of Heteronuclear Chemical Shift Correlation HMQC HMBC In contrast to the HETCOR experiment which uses the X nucleus BC in this case as the observed nucleus the HMQC Heteronuclear Multiple Quantum Correlation exper iment acquires proton FID s detecting the carbon frequencies indirectly This method has the advantage that protons can be detected with substantially greater sensitivity per nucleus than is possible for carbon or other X nuclei of lower gyromagnetic ratio There are several drawbacks to this method 1 It is necessary usually to cover a rather wide spectral region in the indirectly detected dimension which requires many tf increments to achieve high resolution However it should be noted that often modest resolution is sufficient 2 If the X nucleus is of low abundance 1 1 natural abundance for 13C for example the pro ton signals from molecules with no BC must be suppressed 3 If decoupling is required it is more difficult to decouple over the broad chemical shift range of BC than over the comparatively narrow one for protons In spite of these obstacles the HMQC experiment has become widely used and modern spectrometers are capable of doing it well The determination of the structure of molecules often requires the use of several dif ferent kinds of information Like a jigsaw puzzle each puzzle piece alone does not give a clear pic
91. icate scalar coupling between the two multiplets whose chemical shifts define the position of the peak The peaks along the diagonal simply replicate the 1D spectrum The pulse sequence used is shown in Figure 37 The COSY pulse sequence is deceptively simple a full expla nation of how it works is beyond the scope of this treatment but some idea can be had by considering an AX spin system where both A and X are protons The first 90 degree pulse creates transverse magnetization in both A and X which then evolves under scalar coupling as we have seen before in the heteronuclear case The second 90 degree pulse transfers po larization from A to X and from X to A in somewhat the same way as the simultaneous pulses on protons and carbon did in the DEPT experiment The magnetization precesses at the rate dictated by the chemical shift of the source nucleus during t but that dictated by the destination nucleus during ft Thus the correlation is produced 90 905 Figure 37 2 13 01 15 Chemical Shift Correlation Experiments 63 The phase cycling normally used is as follows 0 1 2 3 53 0 1 2 3 53 The receiver follows the usual CYCLOPS sequence The inner loop produces quadrature detection in the F domain while the outer one suppresses quadrature images 15 2 Carbon Carbon Homonuclear Correlation the 2D INADEQUATE Ex periment The 2D version of the Incredible Natural Abundance Double Quantum Transfer Ex p
92. ill have m 1 2 than have m 1 2 on a 7 05 Tesla spectrometer m 4 18 ai __ AE hay hyBo l 45 m 4 Figure 1 2 13 01 Part I Lecture Notes Answer kT 4 14X10 erg AE 1 99 x 107 erg AE 4 8x10 5 _ exo A 0 999952 e A kT 5x10 8 2 6 24 2 13 01 2 Net Magnetization and Nuclear Precession 5 2 Net Magnetization and Nuclear Precession 2 1 Classical Equation of Motion of a Magnetic Dipole The classical equation of motion for a magnetic moment p in an external field B is given by dp uxB 1 p X 1 where p is the angular momentum For nuclear spins p and pare related by the gyromag netic ratio y according to p 7p 2 Eliminating p between Equation 1 and Equation 2 one obtains du y uxB 3 q 77 xB 3 Note that the time rate of change of y is always perpendicular to p and B See Figure 2 2 2 Magnetization of an Ensemble of Spins Now suppose one has an ensemble of moments w each making an angle 0 with the external field the external field direction will be taken to be the z direction but ran domly distributed with respect to their components in the xy plane When nuclear spins are treated quantum mechanically they distribute in just this way if they are placed in a mag netic field for a sufficient length of time The dipoles will have identical magnitudes but a D u 1 2 1 2 Figure 2 2 13 01 6 Part I Lectu
93. in channel which has no compensating signal in quadrature in the lower gain channel Consider the consequences of altering the phase of successive pulses in an ordinary one pulse FT experiment as shown in Figure 12 according to 90 90 90_ 90_ Figure 36 shows the FID s obtained Table I shows how the FID s can be combined to yield a final FID nominally the same as that resulting from four 90 pulses Note however that both the 2 13 01 14 Fundamental Concepts of Two Dimensional NMR 59 Amplitude Figure 35 Table I Pulse and receiver phases for quadrature image suppression Receiver Phase Pulse phase Real Imaginary x y x y X y X y X y x y real and the imaginary part of the summed FID uses each receiver channel in a symmetric way so that any difference in gain between the two channels will be compensated exactly 2 13 01 60 Part I Lecture Notes Receiver Channel tn fn Mann Jen ro Figure 36 2 13 01 14 Fundamental Concepts of Two Dimensional NMR 61 This example serves as an introduction to numerous other phase cycles used in pulsed NMR spectroscopy 14 5 Pulsed Field Gradients Pulsed field gradients PFG can in many cases be used as an alternative to phase cycling This is done by applying a pulse of current to a coil that causes a large inhomoge neity in the Bg field It is as if for example the z gradient of the shims were to be misa
94. intensity ratios as a normal FT spec trum Thus they can be easily interpreted or decoupled to produce a simpler spectrum in the usual way By adjusting the width 6 of the final proton pulse one can produce spectra which identify various types of spin systems Figure 27 shows how CH CH and CH spin systems respond to the tip angle of the final proton pulse with all other parameters of the pulse sequence kept constant For 0 90degrees only methine carbons appear in the spec trum For 0 135 degrees methine and methyl carbons are positive while methylene car bons are negative Of course quaternary carbons never appear because there is no source of polarization for them These two spectra plus an ordinary proton decoupled FT spectrum to pick up the quaternary carbons provide sufficient information to determine the number of directly bonded protons for each carbon in the spectrum One additional DEPT spectrum with 45 degrees yields three independent pieces of information so that appropriate lin ear combinations of the three spectra can yield subspectra containing only methine meth 2 13 01 13 Polarization Transfer INEPT and DEPT 49 l de z e y y x x INEPT 90 x 180 x 90 y i H 1 4J 1 4J a 2 Se d b 180 x 90 x 180 to Figure 25 2 13 01 50 Part I Lecture Notes SV a x x x DEPT 0 x 180 x 8 y Decouple Figure 26 2 13 01 13 Polarization Transfer INEPT and DEPT 51 yl
95. ion is left along the y axis The magnetization as a function of time subsequent to the pulse has the form M Me sin o 21 M me cos o t The NMR signal FID detected by the spectrometer is of course proportional to this mag netization see Figure 12 It is convenient to define a complex FID as f t M iM 22 Mx Figure 12 2 13 01 24 Part I Lecture Notes A Fourier transform FT is then performed on this FID according to F o fee 23 resulting in F o oh SR I 24 2 1 0 0 T 1 0 0 T Comparing Equation 24 with the results of the cw experiment Equation 20 the real part of F corresponds to the absorption mode signal and the imaginary part to the dispersion mode Figure 12 shows a complex FID and the corresponding FT spectrum is identical to that shown in Figure 11 Problem 15 What would be the difference between a FID from a resonance above the rotating frame in frequency as opposed to one whose frequency is less than that of the rotating frame by the same amount If one has a spectrum with many lines a pulse may be applied to simultaneously excite all of the lines and a FID collected containing the spectral information from all the resonances A Fourier transform can then be performed to produce a spectrum containing all the information that by cw methods would require slowly sweeping through each res onance and recording the result 2 1
96. is Sometimes low sensitivity can be circumvented by using pulse sequences that are able to take advantage of the scalar cou pling of an insensitive nucleus to a more sensitive nucleus such as IH This process is re ferred to as polarization transfer and is the basis for several 1D and 2D NMR experiments Problem 44 Independent of relative sensitivity considerations re laxation effects can have a great influence on the ease with which spectra can be taken of insensitive nuclei Discuss how T and T might affect your ability to get a spectrum of such a nucleus a if T and 7 are both very long b if T is very long and T is very short and c if T and T are both very short Note that T cannot be very short and 7 very long because this would imply that the magnetization recovers to thermal equilibrium along the z axis before the xy magnetization has relaxed to zero yielding a net magneti zation greater than Mo which is impossible 4 1 New Commands and Parameters The following commands and parameters should be studied for this experiment in addition to the ones you have already learned tn dn spcfrq movetof 4 2 Outside preparation ALL OF THE FOLLOWING SECTION MUST BE COMPLETED BEFORE YOU ARRIVE FOR YOUR INSTRUMENT SESSION Table I Relative receptivity of some common isotopes isotope Ry 19F 0 83 AID 6 6 10 HB 0 13 170 1 08 10 DN 3 8 10 2 13 01 Laboratory 4
97. ition as shown in Figure 8 This is called a correlation function The Fourier transform of a correlation function is called a spectral density func 2 13 01 6 Relaxation Bloch s Equation 17 o tauc 104 14 10 25 tauc 10 12 tauc 10 10 2 w Longer Correlation Time D A E 1 5 2 dl Shorter Correlati 0 5 0 2 x 2 ci E Z Xx x amp amp x Xx Frequency tion The amplitude of a spectral density function at a certain frequency controls the relax ation rate Figure 9 shows examples of spectral density functions for several different correlation times The area under each spectral density curve is the same Figure 10 shows relaxation times as a function of correlation time Note how the spin lattice rate reaches a maximum then declines while the spin spin rate continues to increase Thus small mole cules in nonviscous media show long relaxation times and narrow lines because they are tumbling rapidly This is called motional narrowing or extreme narrowing Note also that T 7 in this region By contrast large molecules viscous media or solids are character ized by long spin lattice relaxation times but wide lines because the spin spin relaxation times are growing ever shorter Actually the spin spin relaxation rate reaches a limit when all molecular tumbling stops as in many crystalline solids at low temperature This effect is not shown in the figure The maximum of the spin lattice
98. l to well above it is a reasonable al ternative Short samples produce artifacts in the lineshape that are difficult or impossible to shim out Special cells and probes are available to deal with very limited sample amounts You may want to discuss your problem with one of the NMR staff when you encounter this situation Samples should be inserted into the spinner turbine using the depth gauge provided Accurate positioning of the sample in the coil is as important as correct sample height for maintaining good homogeneity without excess labor for shim adjustment Standard sets of shims and shim settings recalled from previously collected data will be of much greater val ue when samples are prepared in a consistent fashion 2 13 01 Appendix 3 Solutions to Problems 143 Appendix 3 Solutions to Problems The following are solutions to the problems in the lecture notes Problem 2 on page 6 M p dM d du rare DL L Lru xB En x y MxB dt Problem 3 on page 6 Simply write the cross product in determinant form then expand the determinant in minors of the first row i j k dM q Mx B rM M M B B B fe pe fe DK B B B B B B 7 M B M B Ji M B M B j M B M B k which leads directly to Equation 7 Problem 4 on page 8 Simply eliminate all terms involving B or B from Equation 7 to yield Equation 8 Now differentiate Equation 9 with respect to time to yield
99. le to see bond patterns Since signals can occur only near the chemical shifts that you know from the 1D spectrum it works well to examine about a two ppm wide strip in the chemical shift direction in the vi cinity of each 1D shift while maintaining full spectral width in the double quantum direction Look for the characteristic antiphase dou blets When you find one look for its mate at the same double quan tum frequency Continue this process for all the lines in the 1D spectrum g Save your data for later analysis 2 13 01 Laboratory 12 Through Space Correlations NOESY 131 Laboratory 12 Through Space Correlations NOESY Read the introductory material for the COSY and DQCOSY experiments Labora tory 6 on page 111 and Laboratory 7 on page 115 if you have not already done so The NOESY experiment is essentially similar to the COSY and DQCOSY experi ments in its form and data processing protocols The NOESY two dimensional FID is hy percomplex and is processed essentially the same way as was the DQCOSY data in Laboratory 7 on page 115 It differs however in that dipole dipole relaxation is the inter action to be exploited rather than scalar coupling Since the dipole dipole mechanism acts through space not through bonds correlations indicate that the correlated nuclei are close through space whether or not they are close through intervening bonds The acronym NOESY stands for Nuclear Overhauser Effect Spectroscopy Re
100. lei They usually are only one data point wide no matter how long the acquisition time is and have random phase Because of the random phase they will usually become less prominent with time averaging They may come in clusters that look a little like multiplets The spectrometer manufacturers generally try to exclude glitches from the regions where commonly observed nuclei resonate but it is impossible to exclude them from all regions where less commonly observed nuclei are found Be aware that line broadening and other convolution functions can cause glitches to appear to be more than one data point wide With weak signals you may need to time average to see a convincing resonance When you have enough signal to noise you should be able to see an exponentially decaying FID using df 4 4 PROCEDURE a Do not attempt this step without assistance unless you have been trained to install probes Install a probe appropriate for the nucleus you have chosen Check that the instrument is operating properly by running either a carbon 13 or proton lineshape test as appropriate for the probe b Calculate the approximate Larmor frequency for the nucleus you 2 13 01 Laboratory 4 Observation of a Less Common X Nucleus 105 have chosen Set tn and verify that the spectrometer frequency is close to the one you calculated Set up reasonable parameters for ac quisition considering the properties of the nucleus you will observe Remember to execute an
101. lets is usually eliminated 16 1 Heteronuclear J Spectra The classical case for heteronuclear J spectra is the display of Joy in F while ob serving BC Remember however that the technique can be used for other pairs of nuclei as well There are two ways to do this experiment The gated decoupler method is the sim plest to implement but leads to scaling of the coupling constants by a factor of 1 2 Figure 41 shows the pulse sequence for this method Problem 29 The other method for heteronuclear J spectroscopy leaves the decoupler off during all of t and places a 180 degree proton pulse simultaneous with the 180 degree carbon pulse Make a diagram of this pulse sequence similar to Figure 41 and explain how it works Why are the coupling constants not scaled by a factor of 1 2 16 2 Homonuclear J Spectra Figure 42 shows the pulse sequence for homonuclear J spectroscopy Problem 30 Add vector diagrams to Figure 42 showing how the magnetization evolves for an AX spin system Show the effects of chemical shift and scalar coupling Discuss how the sequence works What is refo cussed and what is not refocussed Since there is no analog of broadband decoupling in a homonuclear system the sca lar couplings appear in both domains Hence the multiplets appear along a line tilted at 45 degrees If the rectangular data matrix is distorted into a parallelogram with angles of 45 2 13 01 16 Homonuclear and Heteronuclear J Spectra
102. ling experiments of the type described here These 2D experiments are often replacing the 1D counterparts now even for routine analyses However it is useful to understand the principles involved in the 1D experiments and sometimes when a single piece of information is all that is re quired the 1D experiment is preferable 3 1 New Commands and Parameters In addition to the ones you have already learned the following new commands and parameters will be used in this experiment rts gamah2 h2cal dof dm dmm dmf dlp sd sda homo int li dli ins axis rl rfp split 3 2 Homonuclear Single Frequency Decoupling Single frequency decoupling as its name implies involves irradiation of the sample with a coherent single frequency at the chemical shift of one of the nuclear species in the sample Since it is a second irradiation in addition to B4 it is called B When the B power is much greater than the scalar couplings the scalar couplings are effectively removed from the spectrum Consequently these scalar couplings disappear from the multiplet pattern of any nuclei that are scalar coupling partners of the one being irradiated thus identifying the partners The term homonuclear means that both coupling partners are of the same nuclear species e g lH IH This is the one we will do 19F4 19R 31p 3 p etc The heteronu clear case will be dealt with in the next section This technique may be used to track down the origi
103. lity tube only z1 and z2 will change much from sample to sample or even from week to week If you seem to be experiencing dramatic changes in the other shims chances are something else is wrong that can t be fixed by merely adjusting the shims If you don t immediately get good results on your unknown sample go to a standard lineshape sample If you can t get an adequate spectrum of a lineshape standard you can t hope to get a good spectrum of an unknown Conversely if you do get a good standard spectrum you will usu ally get a good spectrum of an unknown 2 13 01 140 Part III Appendices 2 13 01 Appendix 2 Sample Preparation 141 Appendix 2 Sample Preparation The importance of proper sample preparation can not be over emphasized The stan dard samples used in these exercises for spectrometer performance checks were made with high purity solvents and solutes and high quality sample tubes Paramagnetic impurities including dissolved oxygen should be rigorously excluded from a sample for best results The levels of dissolved oxygen encountered by preparing samples in ambient atmosphere are not of much concern when chemical shifts and coupling constants are the object of the experiment but if any sort of relaxation or NOE data is desired oxygen must be excluded Paramagnetic ions can have a dramatic effect on your spectrum even at very low concen trations This is especially true if the ions tend to complex with the compound of
104. ment manager to arrange for training and checkout if this has not already been completed It is best to perform the experiments in sequence if one is inexperienced with NMR techniques because each successive experiment presumes familiarity with the techniques used in preceding laboratory sessions Also the directions for the experiments become less explicit as one progresses through the course under the presumption that the student is be coming familiar with various procedures and does not need explicit instructions Once the techniques have been mastered the various experiments may be used as guides for analyz ing other samples 2 13 01 78 2 13 01 Part II Laboratory Experiments Laboratory 1 Proton Line shape Proton Resolution 79 Laboratory 1 Proton Line shape Proton Resolution Before beginning this laboratory you should have completed the basic checkout This laboratory will serve as a review of that checkout and expand upon the skills gained in the checkout training In this laboratory particular aspects of the spectrometer such as safety procedures to protect vulnerable components basic disk operations such as reboot ing the system software accounting and log in procedures location of the various compo nents that make up an NMR spectrometer and basic operations such as locking probe installation and tuning and shimming the magnet will be reviewed You should become very familiar with these procedures so that
105. n of a coupling present in a multiplet or to simplify a multiplet pattern to determine the value of a particular scalar coupling 3 2 1 PROCEDURE a Log on to the system and perform the checklist Check with your instructor to be sure the correct probe is installed b Insert sample labeled PHENETOLE set up a proton experiment tune the probe lock and shim the magnet starting from the best pro ton line shape shims you have obtained previously The rts com mand may prove useful c Run a preliminary spectrum with a sweep width sufficient to insure 2 13 01 96 Part II Laboratory Experiments that no lines are aliased Be sure the solvent parameter is set correct ly np should be at least 32 K points fn should then be 32 K or larg er or set fn n Set dn and tn to protons d Decrease the spectral width to a more appropriate value and take an other spectrum Be sure you are adequately digitizing the FID movesw and df should be useful e Reference your spectrum to TMS using the center line of the solvent multiplet as a secondary standard nl and rl should be useful f Expand the region containing the triplet and the quartet of the phene tole and make a hard copy for later comparison with the decoupled spectrum Be sure to display a scale in ppm under the spectrum and print the parameters You may want to save this display using s1 Be sure to archive the data in case you want it again later Learn how to crea
106. n of sodium dichloroacetate in 90 H 0 10 D20 9 3 2 Digitization in Time The S H unit is triggered at precisely equal intervals of time by a signal derived from the same master frequency from which all other frequencies in the spectrometer are derived Both M and M are sampled simultaneously Figure 15 shows schematically how the S H works DIGITIZATION 5 w D E o a a 5 10 15 20 Figure 14 2 13 01 28 Part I Lecture Notes The spectral width S over which resonances can be accurately sampled is given by S F 26 where N is the number of complex samples of the FID The number of points parameter on most spectrometers is 2N counting one for the real and one for the imaginary part of the FID and A is the total time during which the FID is sampled the acquisition time The spectral width encompasses the range S 2 from the frequency of the transmitter The interval between data points in the FID will be A N 1 S and the separation in the spectrum will be S N 1 A Problem 17 Assuming that two adjacent lines are narrower than 1 A how close to each other can they be and still be detected as separate lines Suppose that this separation were due to a scalar coupling what error limits should you report for the coupling constant Amplitude AIN 2A N 3A N 4A N Time Figure 15 2 13 01 9 The Anatomy of a Free Induction Decay 29 If the computer memory is capable of
107. nspin ning gradients are the ones involving x or y Because the shim coils cannot be made per fectly a change in one gradient will affect the optimum value of others For example the z4 gradient contains a considerable component of z2 so that whenever z4 is adjusted z2 must be readjusted to compensate Hence it is necessary to cycle through sets of gradients until all are simultaneously maximized Additionally the lock phase may need to be reop timized as the lineshape improves You will find that there are as many methods used to shim a magnet as there are operators Shimming magnets requires some experience as well as training It is difficult to write down exactly how to shim a magnet just as it is to explain how to hit a golf ball straight down the fairway Certain basic principles can be explained then you just have to do it until you can do it well A page indicating how misadjustment of var ious shims affects the lineshape is posted near each spectrometer Be careful not to take these diagrams too literally because different magnets behave differently but the general principles are correct Remember also that these diagrams represent gross missetting of a single gradient If several gradients are misset the result can be more difficult to interpret Trust standard shim settings Under normal circumstances with a sample containing no paramagnetic materials that completely fills the coil 50 mm liquid height in the tube in a high qua
108. nuclear Correlation the 2D INADEQUATE Experi ment 63 15 3 Heteronuclear Chemical Shift Correlation 66 16 Homonuclear and Heteronuclear J Spectra UV 68 16 1 Heteronuclear Spectrum ententes 68 1623 Homonucl ar Spectral use 68 17 A Basic Pulsed Fourier Transform Spectrometer i 71 17 1 Generating Bo The Magnet ili iena 72 17 2 Generating B the observe transmitter ie 72 17 3 Detecting the Nuclear Induction Signals the Receiver 12 17 4 The Data Processing and Spectrometer Control System IMS COMDUICE SENS SE RS a a as 72 17 5 Maintaining a Constant Field Frequency Ratio the Lock System 12 17 6 Generating B gt o the Decotplet moi ara ian 12 17 7 Controlling the Sample Temperature the Variable Temperature System atea aaa 12 17 8 Coupling All the Other Subsystems to the Sample the Probe 72 LES Bibliostapiy Es lacune a alal il te cie ue nn 73 Part II Laboratory Experiments P rt MOUTON rele 77 Laboratory 1 Proton Line shape Proton Resolution 79 LT Demonstraion srl lei eae Ne eae ek 79 1 2 Pertinent Parameters and Commands 80 1 3 Setting Up Shimming the Line Shape Test 80 Laboratory 2 Observation of Carbon 13 0isg20ie8 nisin ai 85 2 1 New Commands and Parameters sila a ae a Aes 85 2 2 Observation of an X Nucleus 22 pct aaa 85 2 3 Calibr
109. ob while periodically pulsing the sample using the lock transmitter The trace on the screen is the deuterium FID following each pulse The field is adjusted until the resonance condition is achieved At a field of 7 05 Tesla for example this occurs at 46 05 MHz The lock signal when off resonance appears as a sinusoidal trace The frequency of this sinusoid is the difference between the lock transmitter frequency and the Larmor frequency of the deuterium One must adjust z0 until this difference is near zero Thus as resonance is approached fewer cycles of the FID are seen but with greater amplitude Signals far from resonance will be of low amplitude with many cycles visible When z0 is adjusted to the on resonance condition the feedback system can be activated by pressing the lock on button The signal then ceases to oscillate 2 13 01 138 Part III Appendices at all and any drift in frequency or field will be compensated to maintain a constant ratio Adjust the lock phase for maximum lock level When searching for a lock signal high values for both lock power and gain may be used Locking on a signal under these conditions may result in an unstable oscillating lock signal This is sometimes referred to as a breathing lock It is caused by saturation of the lock nuclei as a consequence of too much lock power When this occurs slowly reduce the lock power and increase the lock gain if necessary until the oscillations stop
110. of the repetition rate 2 13 01 34 Tip Angle degrees 150 100 50 Pulse Repetition Rate t T1 Figure 17 2 13 01 Part I Lecture Notes 10 Digital Filters and Convolution 35 10 Digital Filters and Convolution In the context of NMR spectroscopy digital filters are computational algorithms that reject unwanted signals or noise and allow desirable signals to pass through to the final spectral display Filters can also alter line shapes with either desirable or undesirable re sults These undesirable results are generally caused by unintentional digital filtering 10 1 The Convolution Theorem In preparation for discussion of digital filters it is necessary to understand the Fou rier convolution theorem Suppose one has three functions of time a t b t and c t such that c t a 1 b 1 35 then if A B and C are the Fourier transforms of each of the correspond ing time functions it can be shown that C do A B o 36 Of course these computations must be done on sampled functions as has been discussed previously Figure 18 illustrates how the convolution operation works in the frequency do main for two lines of equal width In the computer the calculation would actually be done by multiplying the FID s corresponding to the two lines together and transforming the prod uct to give the convolved spectrum Due to the computational efficiency of the FFT this can be
111. ometer sets up the 7 experiment it will use this val ue to set pw to a 90 degree pulse and p1 to a 180 degree pulse ai Problem 35 Why must one use absolute intensity in this experi dotl This is a macro to set up a T experiment The macro will look at the value in pw90 copy it to pw double it and enter it as a value for p1 then will determine what value to use for the equilibration delay d1 and the values to put in the d2 array by asking you what values are expected for the minimum and maximum 7 s and how long you want the experiment to last Use the following Minimum 0 1 sec ond Maximum 5 seconds and a total experiment time of 0 5 hours da This will display the array for d2 that the macro determined for you Problem 36 Explain why the values in the array are reasonable choices based on your answers to the questions in the dot1 macro dg Note the value for the relaxation delay d1 calculated by the macro Problem 37 Explain why this value is a reasonable choice dps 2 13 01 91 Part II Laboratory Experiments This will display the pulse sequence showing the pulses and delays It should look similar to Figure 22 This command can be used any time to verify that the pulse sequence variables are set up correctly Parameters other than the default pulses and delays can be viewed See the command and parameter reference manual for details k Add appropriate text for this experiment I ga Start
112. onuclear Correlation Spectroscopy COSY 111 Laboratory 6 Homonuclear Correlation Spectroscopy CO SY The COSY experiment yields much the same information as a homonuclear decou pling experiment in that scalar coupling networks are mapped out However a single COSY spectrum encompasses all the information which could be obtained from irradiating each multiplet in the spectrum and observing the changes in the other multiplets In simple molecules this information could possibly be obtained more easily with a series of homo nuclear decoupling experiments and in general where a few 1D experiments would give the needed information it is more efficient to obtain it that way However as molecules being investigated become larger and more complex the COSY experiment can become the only reasonable way to get the needed data Among other problems it is difficult to maintain ad equate selectivity of the homonuclear decoupling so that in congested areas of the spectrum the irradiation will affect not only the multiplet of interest but also those nearby The COSY experiment on the other hand will frequently unsort even overlapping multiplets In addition to the standard COSY pulse sequence used in this experiment there also exist related pulse sequences such as double quantum COSY DQCOSY and phase sensi tive COSY COSYPS To keep the acquisition time reasonable the 2D experiment run dur ing this session will be preformed under fairly low resol
113. or positive absorption If a COSY response is also possible between two protons because they are close through bonds one will often see the COSY cross peak superimposed on the NOESY cross peak One must be careful not to misinterpret a COSY response as a NOESY correlation For this rea son it is useful to run a COSY for comparison with the NOESY spectrum 2 13 01 132 Part II Laboratory Experiments 12 0 1 PROCEDURE a You will need two experiment files for this procedure one for your 1D reference spectrum and another for your 2D data b Insert the sample provided by your instructor set up the spectrome ter for protons acquire a spectrum and narrow the sweep width to a practical minimum You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the dilute sample because the signal is too strong from the concentrated sample for this proton experiment Shim the magnet as necessary to obtain good line shape After the spectral width has been minimized acquire a spectrum using a 90 de gree pulse width and nt 16 Decrease the gain if error messages such as ADC OVERFLOW or RECEIVER OVERFLOW occur This procedure will prevent similar problems from disrupting the 2D data acquisition c Join the second experiment and move the parameter set from your setup spectrum to this file with the mp command d noesy This macro makes all the changes to
114. ording to e fr i 44 dt M t Pu Mi t M co 2 13 01 42 where and Also note that 1 Perrino IC 1 Py W 2Wy W 1H 1 o W W Ticu M co 24 M o0 Yc Part I Lecture Notes 45 46 47 48 If the proton is strongly irradiated the scalar coupling manifested in the carbon spectrum disappears immediately and after several T s the proton transitions saturate i e M 350 2 n Q B 4 Pigi ae I Su n sf wi wr SNS i I 1 a a Figure 21 2 13 01 11 Decoupling and the Nuclear Overhauser Effect 43 Problem 24 Show that under decoupling the steady state solution of the equation of motion is ME 1 nc ME 49 where Vy0O Norn ED 50 Under proton decoupling the equation of motion for the 13C magnetization becomes dM t Pe M0 1 eu MSE 51 This means that the C magnetization evolves just as though the proton is not there except that it evolves toward the NOE enhanced value rather than toward the usual thermal equi librium If the relaxation is purely dipolar then p 20 and n 2Thus the carbon mag netization will be enhanced by a factor of 1 n 3 If other relaxation mechanisms are important the factor will be less than three It is the factor 1 7 which is generally re ferred to as the NOE The same principles apply to other nuclear
115. pairs besides protons and carbon 13 but note that if the gyromagnetic factors have opposite sign as would be the case for protons and nitrogen 15 then the NOE would be negative and line intensities would be decreased from their thermal equilibrium values even becoming zero or negative Problem 25 What would be the NOE for a gt N IH experiment un der purely dipolar relaxation Draw a schematic DN spectrum of forma mide showing intensities to scale with and without proton decoupling Ignore the long range coupling to the formyl proton 11 2 Homonuclear Decoupling The discussion above applies equally well to a system of two nonequivalent pro tons Problem 26 What would the maximum NOE be for two protons 2 13 01 44 Part I Lecture Notes Since the dipolar relaxation mechanism depends critically on the through space dis tance between the interacting nuclei it is possible in certain cases to determine internuclear distances using proton proton NOE s This technique is coming to be widely used for de termining structure in macromolecules such as proteins 11 3 Broadband Decoupling The usual way to run BE spectra is with all the protons decoupled To accomplish this it is in general necessary to simultaneously irradiate protons of varying chemical shifts This is done by modulating the decoupler rf transmitter so as to spread the power over the necessary band of frequencies For a number of years this was done b
116. quence produces signals that are positive with the usual intensity patterns hence the name Distortionless Character istic of both methods is the fact that unlike the NOE the enhancement is independent of the sign of y The pulse repetition rate is governed by the T of the sensitive nucleus which is usually shorter than that of the observed nucleus hence one can use shorter relaxation delays with a resultant decrease in the total experiment time The most common source of polarization is IH but nuclei such as F and 3 P are also used To be useful for this pur pose a nucleus must have high natural abundance and a large value of Y The INEPT and DEPT pulse sequences were invented as tools for enhancement of insensitive nuclei but they are currently far more commonly used for differentiating be tween CH CH and CH moieties in a molecule Consult the lecture notes section 13 on page 48 for details of the pulse sequence and how the signal intensities for the various CH moieties depend on the width of the final proton pulse This dependence can also be used to calibrate the decoupler pulse This calibration will be useful for 2D experiments which you will perform later 2 13 01 108 Part II Laboratory Experiments In this laboratory session you will learn three ways to find out about various aspects of spectrometer operation 1 on line manuals 2 the dps command and 3 pulse se quence source code Study the use of e
117. r Multiple Bond Correlation 2 13 01 124 Part II Laboratory Experiments 9 0 1 PROCEDURE a If necessary change the probe to an appropriate indirect detection probe Load appropriate shims and verify line shape as needed b For these 2D experiments it is necessary to know the calibration of carbon pulses applied through the decoupler channel This calibra tion is difficult to accomplish using natural abundance compounds so a standard sample containing carbon 13 enriched methyl iodide is provided Obtain 1D coupled carbon spectrum of the provided standard sample this can be done through the decoupler coil of your indirect detection probe Note that the chemical shift of methyl io dide is upfield from TMS Determine the value of tof that will place the methyl iodide quartet exactly at the center of your spectrum Record this value of tof for later use Ignore the other peaks in the spectrum These compounds are used for other calibrations Gi Obtain a proton spectrum of the standard sample and place the me thyl iodide peaks near the center of the spectrum The methyl iodide signals are the three equally spaced peaks of about equal intensity Ignore the other peaks The center peak is from carbon 12 methyl io dide and the outer peaks are the doublet from the carbon 13 methyl iodide Calibrate the proton 90 degree pulse d pwxcal This macro sets up a simple magnetization transfer experiment Set all the parameters appropriatel
118. r coupling continues to evolve Since the scalar coupling continues to evolve during the entirety of r the scalar couplings develop their full value in contrast to the gated decoupler method where they evolve during only half of t and develop only half of their actual value 2 13 01 160 Part III Appendices 2D J Spectrum reparation Evolution Detection l 80 x ecouple Decouple H x 80 x Problem 30 on page 68 The only difference between this experiment and the heteronuclear case is that it is impossible to do broadband decoupling during acquisition Thus scalar coupling is present in both F and F but chemical shifts are present only in F The vector diagrams shown 2 13 01 Appendix 3 Solutions to Problems 161 for the previous problem are completely relevant The chemical shift is refocussed but the scalar coupling is not Since the 180 degree pulse is nonselective it inverts both doublets of the proton AX spin system just as the simultaneous pulses on protons and carbon did in the heteronuclear case 2 13 01 162 Part III Appendices 2 13 01
119. r run ning the vnmr software and configured with the required probes and hardware options may be used A switchable broadband probe is sufficient for all the experiments Various other probes such as broadband indirect detection four nucleus or proton fluorine may be sub stituted for performing individual experiments This will be discussed in greater detail in each experiment This laboratory manual is not intended to replace the Varian User s Manuals All the manuals are available on line Paper manuals are no longer distributed in quantity by Vari an The paper manuals found in the spectrometer rooms generally pertain to older versions of the software but the on line manuals will always be the proper versions for the installed software Pertinent sections of these manuals may be consulted prior to each session on the instrument if you are unfamiliar with commands and parameters used Vnmr and the man uals are accessible from many workstations and personal computers in the department These may also be used for examining your data and preparing reports after your sessions on the spectrometer Hard copy may be sent to several alternative printers Check with one of the NMR staff if you don t know a convenient place to get access These experiments presume that the student has completed the basic instrument checkout and has a basic knowledge of how to interpret one dimensional proton and car bon 13 spectra Contact the analytical instru
120. rconducting Solenoids Field Homogeneity Adjustment the Shim System Generating B the observe transmitter Crystal Controlled Oscillator Frequency Synthesizer Phase Shifters Gating Circuits Attenuators Power Amplifiers 17 2 6 1 Linear vs Tuned Amplifiers 17 2 6 2 Pulse vs Continuous Amplifiers Detecting the Nuclear Induction Signals the Receiver Preamplifiers Mixers Analog Filters The Data Processing and Spectrometer Control System the Computer Maintaining a Constant Field Frequency Ratio the Lock System Generating B the Decoupler Controlling the Sample Temperature the Variable Temperature Sys tem Coupling All the Other Subsystems to the Sample the Probe 2 13 01 Bibliography 73 Bibliography The following titles can serve as a basis for additional independent study The var ious headings indicate the level of preparation necessary to understand the material Introductory a A E Derome Modern NMR Techniques for Chemistry Research Permamon Press 1987 b T C Farrar Pulse Nuclear Magnetic Resonance Spectroscopy The Farragut Press 1987 c Horst Friebolin Basic One and Two Dimensional NMR Spectros copy VCH 1991 d R K Harris Nuclear Magnetic Resonance Spectroscopy Pitman Pub Inc 1983 e J K M Sanders B K Hunter Modern NMR Spectroscopy A Guide for Chemists Oxford University Press New York 1987 f D Shaw Fourier Transform NMR Spe
121. re Notes few more will have a positive z component rather than a negative one This corresponds to the excess of nuclear spins having m 1 2 over those having m 1 2 See Figure 2 Summing over all the w one has Lu Mo M is usually referred to as the thermal equilibrium magnetization 2 3 Nuclear Precession Rather than the thermal equilibrium distribution described above suppose that the w are arbitrarily distributed such that Lu M 5 then it is easy to show that dM y7 MxB 6 q MB 6 Problem 2 Derive Equation 6 Problem 3 Write the above vector equation in component form and show that dM Ta y M B E M B dM aa y M B M_B 7 dM a MB M B Figure 3 illustrates the evolution of M according to Equation 6 or Equation 7 when B is in the z direction and M is in the yz plane at time t 2 13 01 2 Net Magnetization and Nuclear Precession Figure 3 2 13 01 8 Part I Lecture Notes 3 Detection of Precessing Magnetization In the case where B Byk B k and M t 0 Moi Mi the equation of motion for M reduces to a y M B i M B j 8 Problem 4 Satisfy yourself that the above equation is correct and prove that a solution of this equation is M t My cos ot i Mo sin o j 9 where YBo Now if a coil is wrapped around the sample as in Figure 4 an oscillating voltage will be induced in the coil by the oscillating magnetization in the s
122. ree FID s At this point you can continue on a workstation if necessary h Use the appropriate commands to weight transform and plot your data These data are not hypercomplex so you must use the appro priate commands to analyze the data Make a 2D contour plot with the corresponding 1D spectra along the appropriate axes The macro plhxcor is useful for this The command dpcon creates a screen dis play that is a true contour plot like the one produced by the pcon command rather than a color intensity map as is produced by the dcon or dconi commands The dpcon command gives better defini tion of the contours as they will appear on a printer but it can take a rather long time to compute this display so use it with caution Ex periment first with a highly expanded portion of the spectrum so that the computation time will not be excessive The various display and plotting commands have lots of options to control how the spec tra are displayed or plotted these can be found in the on line manu als 2 13 01 Laboratory 8 Heteronuclear Chemical Shift Correlation Spectroscopy HETCOR 121 Learning to properly work up and plot high quality 2D data takes practice Read the manual and practice as much as you can Using the results from your COSY or DQCOSY data make as many assignments as possible in your HETCOR spectrum 2 13 01 122 Part II Laboratory Experiments 2 13 01 Laboratory 9 Indirect Detection of Heteronuclear Chem
123. se this program to display vertical and horizontal traces and projections and make expansions Save both the 1D and 2D data sets Arrange for a session on the workstation Find all the NOESY cross peaks and see what they tell you about the stereo configuration of your molecule If desired you can get some additional practice with the features of the wti and dconi programs Make a contour plot with the 1D reference spectrum plotted on the top and side with proper chemical shift scales Be sure the chemical shifts in the 1D spectra align properly with those of the 2D spectrum You may want to look up the plcosy macro it can be used just as you did in the COSY or DQCOSY experiments 2 13 01 133 134 Part II Laboratory Experiments 2 13 01 Part Ill Appendices These appendices are designed to supplement the spectrometer User Manual More detail can be found there on many of the items discussed in these appendices Spectrometer commands and parameters are given in bold type for easy identification Appendix 1 Locking and Shimming the Spectrometer 137 Appendix 1 Locking and Shimming the Spectrometer 1 1 Obtaining Lock If a high field NMR spectrometer is to produce satisfactory results the ratio of the field strength Bo to the frequency must remain constant to within about one part in 10 often for hours or even days at a time for long time averaging This extraordinary sta bility can be achieved by doing an NMR
124. shift less relaxation agents such as chromium III acetylacetonate Cr acac 3 have been used to produce integrable carbon spectra but will not be described here The suppressed NOE experiment consists of gating the decoupler off during a delay period before the observe pulse then switching it on during the acquisition Decoupling happens immediately whereas the NOE builds up at a rate controlled by T and thus does not affect the amplitude of the resonances The opposite experiment to that described above is a coupled spectrum with NOE This type of spectrum is obtained by allowing the NOE to build up with the decoupler on during some time period before the observe pulse then switching it off during the acqui sition time Coupling information is present in the FID as soon as the decoupler is turned off but the intensities of the resonances are those characteristic of the NOE enhanced spec trum This is often the method of choice to obtain coupled carbon spectra because of the increased signal to noise afforded by the NOE 3 4 1 PROCEDURE a Use the PHENETOLE sample as before Set up and obtain a broad band decoupled DE spectrum Now set nt 16 d1 30 sec and use ai Create a decoupler mode array by typing dm yyy nny nnn yyn Acquire the four spectra b The rest of this experiment can be done at a workstation if you wish Learning to use the integration tools may be a bit time consuming In
125. su before attempting to tune the probe In stall the correct quarter wave cable on the preamp for the nucleus you will be observing If needed install the correct fixed capacitor or inductor stick in the probe then tune Search for a signal considering all the hints that were given in the previous section d Narrow the spectral width if necessary and acquire a well digitized spectrum of reasonable signal to noise e Reference your spectrum to a known chemical shift if possible If not explain why not f If time allows run a 90 degree pulse width calibration and T Does this information suggest any changes in the parameters you used above g Your discussion of this experiment should include as many aspects of the particular nucleus as possible for example chemical shift and referencing coupling constants relaxation characteristics etc Be sure to discuss how these characteristics influence optimum choice of spectrometer operating parameters Did you make appropriate choices for the spectra you obtained How would you do things dif ferently if you need to observe this nucleus in the future If the spec trum you obtained has more than one resonance explain their origins and determine the values of any coupling constants Learn how to use dll and to print the line list Also learn to use dpf and ppf 2 13 01 106 Part II Laboratory Experiments 2 13 01 Laboratory 5 Distortionless Enhancement by Polarization Tr
126. t Note the new parameters in both dg and dg1 Critically examine the parameters and make any alterations you think are appropriate Each increment must complete the full phase cycle as required by the pulse sequence to obtain satisfactory results Find out what the minimum phase cycle is from the on line manuals or the pulse sequence source code Be sure pw is set to the correct 90 degree pulse width Since signal to noise will normally not be a problem on this sample it is acceptable to saturate the spins substan tially use a d1 of 0 6 sec Note that hs the homospoil parameter is set to yn Because we will be pulsing very rapidly this is needed to destroy any excess transverse magnetization before the next FID is generated This will disturb the lock so you must turn up the lock power and gain high enough so that lock is not lost The lock will still work sufficiently well that we will get good data Make sure d2 is zero and set sw1 equal to sw as determined in the set up proton spectrum Set np to 1024 and ni to 512 Set fn in both dimensions to 2 K The delay d2 is the rt delay It is incremented by the program and the increment is calculated from sw1 This is not an ordinary ar ray such as you used when you measured T s and cannot be dis played it is referred to as an implicit array e time The program will calculate and display the approximate total exper iment time If everything is set up correctly this should be
127. t can be extracted from peak intensities measured from a series of such spectra taken as a function of t in much the same way as was described for the T4 measurement 12 3 Measurement of T gt by the Carr Purcell Meiboom Gill Method If the spins diffuse into a region of different magnetic field during t this constitutes a stochastic process then the refocussing will not accurately represent spin spin relaxation processes This problem can be largely overcome by the pulse sequence of Figure 24 The series of 180 y pulses repeatedly refocuses the magnetization In this case only the diffu sion happening during 27 effectively reduces the echo amplitude By making 7 short enough the effects of diffusion can be made insignificant The second half of each echo can be taken as an FID Fourier transformed and analyzed as before With the pulse se 90 x 180 y T gt lt T t4 2T Figure 23 2 13 01 12 Multiple Pulse Experiments Spin Echoes Measurement of T and T 47 Figure 24 quence as written in Figure 24 pulse imperfections in the 180 degree pulses tend to accu mulate But merely by alternating the phase of successive y pulses this can largely be eliminated Problem 28 This experiment will work also if the train of 180 de gree pulses is not phase shifted with respect to the initial 90 degree pulse How will the results of the experiment differ in this case Why is this not a better wa
128. t as follows Click the right mouse button anywhere in the background window A menu will pop up click On line Manuals with the left mouse button If the appropriate menu item is not present you can start the on line manual reader by typing vnmr_ihelp at any unix prompt Once the reader displays the list of available manuals select VNMR Command and Parameter Reference then click D in the alphabet list at the left side of the display Select dept in the list at the left side of the window you may need to scroll the list This brings up a brief description of the dept macro Among other things you will note an item that says See also User Guide Liquids NMR Since there is no hypertext link you have to go back to the main menu by clicking the to menu item in list at the left side of the window This takes you back to the menu where you can select User Guide Liquids The list at the left of the window is a hypertext table of contents for this manual click on the small triangle to the left of In dex Select D in the sublist that opens up then find dept in the 2 13 01 Laboratory 5 Distortionless Enhancement by Polarization Transfer DEPT main window which now displays the relevant section of the index You may have to scroll to find the correct entry Click on the hyper text page number to go to the corresponding page in the manual Your browser is now pointed at the sec
129. t the signal from the protons of water is much reduced Why The water molecules diffuse rapidly in the liquid compared to the large protein mol ecules Thus the water molecules at the end of the delay have on average moved to some other place in the sample with a different z coordinate and do not correctly rephase while the protein molecules do have the same z coordinate as before and rephase just fine By choosing the correct delay between the gradient pulses the strong signal from water can be suppressed leaving the desired proton resonances of the protein Numerous other applications for pulsed field gradients have been published This brief discussion serves only to give the flavor of what can be done 2 13 01 62 Part I Lecture Notes 15 Chemical Shift Correlation Experiments A large class of 2D experiments produces correlations between chemical shifts The correlations occur as a consequence of some interaction between the nuclei whose chemical shifts are correlated Various interactions such as scalar coupling dipolar coupling NOE and chemical exchange have been exploited by means of clever pulse sequences to yield structural and other information Some examples will be discussed to illustrate how this can be done 15 1 Homonuclear Shift Correlation COSY The COSY experiment yields a 2D spectrum with both F and F labelled by the chemical shift of the nucleus observed most often protons Off diagonal peaks ind
130. te a subdirectory in your archive and place all the data from this experiment in it g Expand the region containing the quartet until you can place a cursor accurately at the center of the multiplet The split command may be useful h Use sd to set the decoupler frequency to the cursor position Write down the value of dof you will use this offset later for heter onuclear single frequency decoupling i homo y We want to do homonuclear decoupling Setting the decoupler mod ulation mode dmm to is not operationally necessary but should be done to remind you that you are doing cw decoupling j dpwr 28 k Run a preliminary spectrum then increase or decrease the value of dpwr as needed to the lowest power that will totally collapse the high field triplet Make an array of dof over a range of 10 Hz around your original value and observe the effect Try 2 Hz steps to begin then 0 2 Hz steps in the vicinity of the best value Was your original value the optimum one Be sure to save the data for your report l Make a hard copy of the best decoupled spectrum just like the one you made for the coupled spectrum m If time permits repeat the above procedure irradiating the triplet 3 3 Heteronuclear Single Frequency Decoupling The principles involved in heteronuclear decoupling are precisely the same as in homonuclear decoupling The difference is that the observed isotope will be different from 2 13 01 Laborator
131. tegrate the methyl and methylene regions in the first two spectra Learn to use the menu buttons to control the integration and estab lish integral resets The de drift correction and be baseline correc tion commands can be used as needed to help the signal free regions to integrate to zero as they should Be sure the spectrum is 2 13 01 Laboratory 3 Decoupling and the NOE correctly phased before applying these corrections d Display the second spectrum expanded to show the integral of the methylene and methyl carbons Set ins 1 and place the cursor with in the integral region of the methylene Use the macro setint to nor malize this integral to one Use dli to list the integrals With the NOE suppressed the integral of the methyl should also be one within ex perimental error Now display the first spectrum and note the inte grals of the methyl and methylene The values of these integrals are your measured NOE values for these two carbons e Learn to use the various display and plot commands for integrals such as dli pir pirn setint f Determine the signal to noise ratio for the methyl and methylene multiplets using spectra three and four Problem 43 Explain why your integrals of the first spectrum ob tained above give the values of the NOE for the methyl and methylene car bons Is the increase in signal to noise from the third to the fourth spectrum consistent with your measured NOE Discuss how the various exp
132. the parameter set necessary to run the NOESY experiment but all the values may not be appropri ate for your experiment Note the new parameters in both dg and dg1 Critically examine the parameters and make any alterations you think are appropriate It may be useful to display the pulse sequence using dps The mix parameter is the most critical one for this experiment This is the time during which the NOE is allowed to build up before it is measured The cross peak intensities increase with increased mix values up to about T of the protons then decreases exponentially to zero as mix is increased further If time permits run a quick T mea surement on your sample and use about 0 1 to 0 5 times T for mix Otherwise ask your instructor for an appropriate value There will probably not be time to do so during this session but an array of val ues of mix may be run to determine the rate at which the NOE grows The closer two protons are the faster the NOE will build up so that internuclear distances can be at least roughly estimated from the initial slope of the buildup curve However with only one value of mix one can still conclude from the presence of a NOESY cross peak that two protons are within a few Angstroms of each other For example cis protons generally will give a NOESY cross peak trans protons will not Each increment must complete the full phase cycle as required by the pulse sequence to obtain satisfactory results Find out
133. the solvent lines Make sure that the magnet is well shimmed and that the decoupler is set up correctly and well calibrated The S N in the 2D spectrum will be rather poor and any degradation of the lines due to poor shimming or poor de coupling may cause your data to be partially uninterpretable You should be able to obtain a line width of about 0 3 Hz with good line shape for most small molecules Check the 90 degree pulse calibra tion also b Move the parameters to another experiment and execute the inadqt macro This macro as supplied by Varian sets many parameters to nonoptimal values for our purposes Make the following changes np 32768 This should give an at of about 3 s if sw is set correctly sw1l sw Be sure pw is set to a carefully calibrated 90 degree pulse dl n nt 16 ni 64 dp y Gi If everything is set up correctly you should be able to use the time macro to verify that the acquisition will require less than 3 hr 2 13 01 130 Part II Laboratory Experiments d Start the acquisition with go e While the acquisition is progressing you can Fourier transform the partially completed data using wftida and wft2da Be sure to set fn and fn1 appropriately Use wti to set up the convolution functions Gaussians work quite well for this data set You may want to set pmode full Look up the pmode parameter and learn what it does f When the 2D FID is about half complete you should begin to be ab
134. ting field One the rotating frame and the Larmor frequency are made equal then the equation of motion has the form dM MxB 14 a MxB 14 Problem 7 Convince yourself that Equation 14 follows from those given previously This equation says that the magnetization will precess about the direction of the rf field at arate YB A typical value of vj might be 25 KHz This means that a complete rotation of the magnetization through 360 degrees would take 40 us Suppose however that we turn on the rf transmitter for only 10 us delivering a pulse of energy to the sample which precesses the magnetization through 90 degrees and leaves it in the xy plane As shown in Figure 6 by controlling the duration and phase the phase controls the orientation of B with respect to the rotating frame axes of the rf pulse the magnetization can be placed anywhere one desires 2 13 01 5 The Effects of Radio Frequency Fields Pulses 13 Problem 8 Make a figure similar to Figure 6 showing how the magnetization could be placed along the x or y axes 5 2 Off Resonance Pulses If then B ef has a component in the z direction because the fictitious field from the rotating frame transformation does not perfectly cancel By As shown in Figure 7 By is the sum of B and this off resonance field The magnetization then pre cesses about B and not about B The magnetization traverses the surface of a cone with
135. tion of the manual relating to the DEPT experiment Study these pages to learn more about how to run DEPT on the Varian spectrometer You can iconify this window by clicking the dot button in the upper right corner of the window and bring it back to refer to it by double clicking on the icon This general procedure can be used to look up anything in the man uals printon dg printoff This prints a hard copy of the dg window for reference dept This is the macro you just looked up in the on line manuals which loads in the proper pulse sequence and modifies or creates other per tinent parameters for the DEPT experiment The macro assumes that you have already set up to run a normal carbon spectrum so be sure the current experiment contains the parameters you used to acquire the carbon 13 spectrum as outlined above The macro prints a help file in the text window of VNMR You can ignore this if you wish since we have already looked up the infor mation in the on line manuals printon dg printoff This prints a hard copy of the dg window after execution of the dept macro so that you can note the changes the macro made to the pa rameter set you used for your decoupled carbon spectrum Problem 45 Compare the listings of parameters before and after ex ecution of the dept macro and explain all the differences you find g dps This displays a diagram of the pulse sequence showing the values of all the parameters directly a
136. to make a second sam ple using some more interesting compound 4 3 General Considerations Nominally correct frequencies for most isotopes are coded into the vnmr software The tables containing these data are located in vnmr nuctables These are just ASCII files You can take a look at them with an editor if you wish to see which nuclei are included Based on the type of spectrometer you are using vnmr will choose the correct file from the nuctables directory Then setting tn will get you in the correct frequency range for your nucleus If the chemical shift dispersion of your chosen nucleus is large wide sweep widths may have to be used The maximum allowable sweep width on the Inova spectrometers is 500 kHz on the older models it is generally 100 kHz However you need to consider the spectral width you can reasonably expect to cover with the B field strength you have available Refer to Section 5 2 on page 13 You may need to use more than one value of tof if a very wide range of chemical shifts needs to be checked When a signal is found move the spectral window to put your signal s in the center of the spectrum and narrow the spectral width to include just the signals of interest Increase the acquisition time to ad equately digitize the FID if necessary Verify that the signals are not aliased and are true NMR signals not glitches Glitches are spikes that can occur in the spectrum and are from electronic sources not from nuc
137. tour plot can be used to assign the spectrum 2 13 01 118 Part II Laboratory Experiments 2 13 01 Laboratory 8 Heteronuclear Chemical Shift Correlation Spectroscopy HETCOR 119 Laboratory 8 Heteronuclear Chemical Shift Correlation Spectroscopy HETCOR The determination of the structure of molecules often requires the use of several dif ferent kinds of information Like a jigsaw puzzle each puzzle piece alone does not give a clear picture but when all the pieces are assembled properly the picture becomes clear If one begins with a 1D proton and a 1D carbon spectrum of the molecule to be studied some things can be inferred about the structure but the picture is by no means complete The DEPT data from Laboratory 5 tells us how many protons are attached to each carbon One can add the proton proton correlation from Laboratory 6 or 7 to show which protons are near each other through bonds but still not everything is known about the structure In this laboratory session we will determine which proton is attached to which carbon Thus what ever we have learned about the protons can be correlated with the carbons The reverse is also true the greater chemical shift dispersion for carbon and for many other X nuclei as well in conjunction with spreading of the peaks into the second dimension permits the as signment of proton resonances in complicated congested spectra in cases where assignment of the 1D proton spectrum is impossible
138. trolled by the parameter d2 which will be an arrayed parameter to permit monitoring of the full relaxation curve The amplitude of the partially relaxed magnetization is then measured by application of a 90 degree pulse pw to tip the magnetization into the xy plane where it will produce an FID as a function of t during the acquisition time at A critical aspect of this experiment is allowing enough time between the end of the acquisition and the next 180 degree pulse d1 for complete re establishment of the thermal equilibrium magnetization to occur Since the 7 relaxation is exponential 5 7 s are needed to recover about 99 of the thermal equilibrium magnetization A priori you do not know how long this delay must be since this is what you are determining in a 7 experiment you must therefore put in a best guess This relaxation delay may need to be only a few milliseconds for quadrupolar nuclei or many minutes for a highly isolated spin 1 2 nucleus It is difficult to generalize but a guess for a T for protons in small organic molecules would be 1 10 seconds while carbons would range from 1 100 seconds You should also realize that if there is more than one nuclear spin in a molecule and this is almost always the case relaxation can be nonexpo nential For proton decoupled C spectra relaxation is almost always close to exponential but in coupled spin systems it need not be Problem 31 Draw and explain vector diagrams describin
139. tructure Pulse sequences for heteronuclear and homonuclear J spectroscopy however both refocus chemical shifts but display scalar coupling For the former chemical shift and scalar coupling can be made completely orthogonal by decoupling protons during ty Homonuclear J spectroscopy on the other hand does not completely separate the two because broadband decoupling cannot be preformed during t but can be made to appear so after appropriate data manipulations Magnet inhomogeneity effects are also refocussed so that natural line widths free of inho mogeneity broadening can be obtained if the data are acquired with sufficient digital reso lution This permits resolution of couplings that would be impossible in a 1D spectrum Severe overlap of multiplets resulting from scalar coupling can make the interpretation of 1D experiments difficult if not impossible 10 0 1 PROCEDURE a You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the concentrated sample for this experiment For this session set up three experiments two for 1D spectra and a third for the 2D data In one experiment run a minimum spectral width 13C spectrum of the more concentrated sample with full proton decou pling and 32 K data points In another experiment use the same ac quisition parameters modified so as to collect a proton coupled LG spectrum with NOE as was performed in Labor
140. ture but when all the pieces are assembled properly the picture becomes clear If one begins with a 1D proton and a 1D carbon spectrum of the molecule to be studied some things can be inferred about the structure but the picture is normally not complete The DEPT data tells us how many protons are attached to each carbon One can add the proton proton correlation from COSY or DQCOSY spectra to show which protons are near each other through bonds but still not everything is known about the structure In this laboratory session we will determine which proton is attached to which carbon Thus whatever we have learned about the protons can be correlated with the carbons The reverse is also true the greater chemical shift dispersion for carbon and for many other X nuclei as well in conjunction with spreading of the peaks into the second dimension permits the assignment of proton resonances in complicated congested spectra in cases where assignment of the 1D proton spectrum is impossible The upfield region of the proton spectrum is often very crowded but the corresponding region of the carbon 13 spectrum is usually well resolved In the first section of this experiment the one bond scalar interaction is used to re veal which proton is bonded to which carbon In the second section the multiple bond scalar interactions are used to reveal which carbons are nearby to a given proton This latter ex periment is often referred to as HMBC Heteronuclea
141. u should explore the effect of the various shims on the line shape Next time you might not be so lucky When your best spectrum has been collected add text make hard copy and archive the data as you did above Many newer spectrometers can produce good line shape even with out sample spinning This is often desirable for running 2D and other more complex experiments Turn off the spinning Now adjust the xl and yl shims for maximum lock level Acquire label plot and archive another spectrum This will allow you to judge if this spec trometer can be used with nonspinning samples later on at 1 5 This changes the acquisition time to 1 5 seconds What effect do you think this will have on the spectrum of chloroform ga Collect another spectrum with the new acquisition time Note any change in line shape Document the three line shape parameters as you did above Make plots and archive the data No matter how well shimmed the magnet is you cannot obtain the best resolution unless you have adequate acquisition time to produce a well digitized line All these hard copies should be included and discussed in your re port for this laboratory Make a permanent archive of your data on CDR Your instructor will help you if needed Shut down the spectrometer and log out observing all the protocols you were taught during the demonstration 2 13 01 Laboratory 2 Observation of Carbon 13 85 Laboratory 2 Observation of Carbon 13
142. u have a proton spectrum with two lines in it Each line represents one proton in your molecule One line has a 7 of 10 seconds the other 1 second A spectrum is run with an acquisition time of 1 second and a D1 of 4 seconds Based on what you have learned in this ex periment what will happen to the intensities of these lines What will hap pen when you integrate the spectrum and try to count protons Now suppose the 7 s of the two protons are equal with one of them reso nating at 5 ppm which is nearly on resonance The second proton is at 10 ppm which is far enough off resonance so that B differs appreciably from B If one collects a spectrum using a 90 degree pulse calibrated correctly for the 5 ppm proton will the integrals of the two resonances be equal Why or why not Hint you may want to review Section 5 2 Discuss how one would need to set up the spectrometer to ensure that accu rate integrals would be obtained in a proton spectrum if B is not adjustable Hint Consider what happens for pulses much less than 90 degrees 2 13 01 93 94 2 13 01 Part II Laboratory Experiments Laboratory 3 Decoupling and the NOE 95 Laboratory 3 Decoupling and the NOE In this laboratory exercise some of the effects obtainable with the use of the decou pler will be demonstrated It should be noted that 2D experiments exist which give the same information in one experiment as would be obtainable from many decoup
143. uality of your spectra If the system will not lock using sample with a strong lock signal it is usually be cause the lock phase is too far from the correct value Change the phase by about 90 degrees and try again With a weak lock it is sometimes necessary to lock on a standard sample with a strong lock set the lock phase correctly then return to the original sample Once locked the signal can be accurately phased by maximizing the lock amplitude as a function of the lock phase It is also possible to have the computer perform these operations automatically using the lock command but you should learn to do it manually because manual locking is usually faster and more reliable The computer algorithm does not always work for weak lock signals 2 13 01 Appendix 1 Locking and Shimming the Spectrometer 139 If you have trouble locking and shimming on your sample the best strategy is to put in either a proton or a carbon 13 lineshape sample and see if you can achieve lineshape about as good as that of the stored standard spectra If you can the problem is most likely with your sample or tube If you cannot you should seek help from one of the NMR staff 1 2 Shimming the Magnet A superconducting magnet differs from permanent and electromagnets in that the direction of the field is parallel to the long axis or spinning axis of the sample tube rather than perpendicular to it Thus the spinning gradients are the z axis shims and the no
144. ure 22 shows a pulse sequence which permits quantitative measurement of this process by producing a series of partially relaxed spectra By varying the time between the 90 and 180 degree pulses the partially relaxed z magnetization is projected on the y axis Fou rier transformation of the resulting FID and measurement of the peak intensities then pro duces a set of data for each peak in the spectrum which can be analyzed to obtain the value of T See Equation 55 Problem 27 We have considered previously Figure 7 the inade quacy of a 180 degree pulse when B differs appreciably from B i e when the line is too far off resonance If the 180 degree pulse is replaced by 180 x 90 x t Figure 22 2 13 01 46 Part I Lecture Notes a pulse sandwich of the form 90 x 180 y 90 x describe how this situa tion will be improved 12 2 Hahn Spin Echoes Figure 23 shows another pulse sequence which permits the measurement of 7 At 27 dephasing due to magnet inhomogeneity is reversed and the magnetization in said to refocus or form a spin echo The concept of refocussing of magnetization is critical to an understanding of two dimensional experiments True 7 processes which are stochastic or random in nature do not refocus so the amplitude of the magnetization is reduced but only by these stochastic processes The second half of the echo can be Fourier transformed to produce a spectrum in the usual way The value of T g
145. ussing specific 2D experiments some fundamental concepts character istic of all 2D experiments will prove useful 14 1 The Generic 2D Pulse Sequence Four time periods characterize a 2D experiment as shown in Figure 29 Each of the four periods can take a variety of forms depending on the experiment but some fairly typ ical examples can be given Preparation frequently consists of just waiting long enough for the spins to be sufficiently close to thermal equilibrium or some steady state condition then perhaps applying a 90 degree pulse to produce transverse magnetization or coherence Thus prepared the magnetization is allowed to evolve often with some refocussing pulses so as to exhibit some desired characteristic of the spin system as a function of t4 The mix ing period can be used to enhance certain aspects of the evolving magnetization i e to fil ter out just the information the experimenter wants and convert it into the single quantum coherence which can be detected by the spectrometer During detection the carefully pre pared transverse magnetization is sampled as a function of fy Systematic incrementation of t with sampling of the resulting transverse magnetization as a function of t for each t4 in crement yields a two dimensional FID as illustrated in Figure 30 The form of the 2D FID is 5 t t HEA onion T 2 ay 52 2 1 TL Preparation Evolution Mixing Detection optional Figure 29 2 13 01
146. ution conditions in both dimensions hence the ability to resolve correlated peaks in heavily congested areas of the 2D spectrum will be greatly diminished and will not demonstrate the full potential of this type of experiment but you should realize that even small proteins have been successfully analyzed by these methods Although quantitative coupling information is present in the COSY spectrum and coupling patterns can be observed with high enough digital resolu tion it is generally better to use the phase sensitive DQCOSY experiment for this purpose See Laboratory 7 on page 115 6 0 1 PROCEDURE a You will need two experiment files for this procedure one for your 1D reference spectrum and another for your 2D data b Insert the sample provided by your instructor set up the spectrome ter for protons acquire a spectrum and narrow the sweep width to a practical minimum You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the dilute sample because the signal is too strong from the concentrated sample for this proton experiment Shim the magnet as necessary to obtain good line shape highest 2 13 01 112 Part II Laboratory Experiments possible resolution is not required for this experiment After the spectral width has been minimized acquire a spectrum using a 90 de gree pulse width nt 16 Decrease the gain if error messages such
147. y then array the carbon pulse from zero to 50 microseconds Ask your instructor what power is accept able for the probe you are using Phase the first spectrum to give pos itive peaks The center peak will remain constant throughout the array The two outer peaks will decrease and pass through a null when the carbon pulse is 90 degrees If necessary reset the array and reacquire the data to accurately determine the carbon 90 degree pulse e Now you will need four experiments one for your reference proton spectrum one for the reference carbon spectrum a third for the HMQC data and a fourth for the HMBC data For both carbon and proton use the smallest sw that is practical without peaks aliasing from outside the spectral window or if peaks must be aliased e g solvent peaks adjust sw and tof so that the aliased peaks will appear in a region free of signals of interest You will normally be provided a concentrated sample for carbon 13 experiments and a more dilute one for proton experiments Be sure to use the dilute sample because the signal is too strong from the concentrated sample for this proton experiment f Acquire the 1D proton spectrum 2 13 01 Laboratory 9 Indirect Detection of Heteronuclear Chemical Shift Correlation HMQC HMBC i Join a second experiment and retrieve the 1D carbon spectrum that you acquired in Laboratory 5 If you don t have this you will need to acquire a reference carbon spectrum using the
148. y 3 Decoupling and the NOE 97 the decoupled one Some common combinations are BC H 31p lH ISN tH 1K 3 p Problem 41 Why would a lH Boy or lH SN experiment be of marginal utility at natural abundance Hint think about the isotope distri bution in the molecules How many different isotopimers will there be and what will each one contribute to the proton spectrum There are 2D exper iments which can overcome this limitation What is the most important property such a 2D experiment would have to have 3 3 1 PROCEDURE a Use the PHENETOLE sample as above tune the probe to 13C and obtain a broadband proton decoupled spectrum If you need to you can discuss with your instructor reasonable values for sw at np d1 pw dn dof dm dmm fn and Ib Use at least 64 K data points Ob tain the current correct values for dmf and dpwr for the instrument you are using from the standard spectrum book for your spectrome ter b Reference your spectrum to TMS using the solvent line display a scale in ppm add appropriate text and archive the data c dmm c dof x where x is the decoupler offset that you made note of when you were doing homonuclear decoupling This will change the decoupler modulation mode from waltz modulation w to coherent single fre quency c d Rerun the spectrum with the new decoupler parameters and enough transients to obtain good signal to noise You will probably need to decrease the decoupler
149. y to measure 77 2 13 01 48 Part I Lecture Notes 13 Polarization Transfer INEPT and DEPT The magnetization generated in a sample depends on the yof the nucleus involved so a high ynucleus such as 1H develops greater magnetization in a constant field than for example DN or PC Ifa high ynucleus and a low ynucleus are coupled by scalar coupling magnetization can be transferred from the high to the low ynucleus thus increasing the sen sitivity with which the low ynucleus can be detected 13 1 INEPT Figure 25 shows the pulse sequence used for the INEPT Insensitive Nucleus En hanced by Polarization Transfer experiment Vector diagrams show the evolution of the magnetization at key points The principle problem with this method is that antiphase mul tiplets are generated which cancel to produce zero intensity when decoupling is applied An additional refocussing step can be added to the pulse sequence to overcome this problem but the DEPT pulse sequence also solves this problem and has other positive attributes as well 13 2 DEPT Figure 26 shows the DEPT Distortionless Enhancement by Polarization Transfer pulse sequence and vector diagram Since DEPT depends on the properties of double quan tum coherence to achieve its effect the vector diagrams are not completely satisfactory but do provide some sense of what is happening to the magnetization Scalar coupled multiplets produced by DEPT are enhanced but have the same
150. y using pseu do random noise for modulation but more recently other techniques have been developed which use the available power more effectively The current best such technique for 13C IH experiments seems to be the WALTZ modulation sequence of Freeman It is im portant to minimize the amount of power used for broadband decoupling Since the power is on continuously it can heat the sample in much the same way as a microwave oven heats food Using WALTZ modulation it is generally possible to decouple over the full proton chemical shift range using power levels of the order of one watt in a five or ten millimeter sample 2 13 01 12 Multiple Pulse Experiments Spin Echoes Measurement of T and T 45 12 Multiple Pulse Experiments Spin Echoes Measure ment of T and T gt In the preceding section the consequences of subjecting the nuclear spins to a single radio frequency pulse were outlined but the great variety of data available from NMR ex periments is obtained principally from subjecting the spins to multiple pulses of various phases and amplitudes separated by carefully chosen delays Many of the principles in volved can be illustrated using a simple two pulse sequence to measure the value of T and To 12 1 Measurement of T by Inversion Recovery We have seen previously Equation 16 how the z component of the magnetization relaxes exponentially back to thermal equilibrium whenever it is disturbed from that state Fig

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