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SCM: ADF Property Programs

1. The minimum value of the electron phonon coupling for a mode to be taken into account in the calculation The default value is zero Together with the MODES option this provides a way to significantly reduce the total number of Franck Condon factors As with the MODES option always check if the results do not change too much QUANTA 11 12 The maximum number of vibrational quanta to be taken into account for both states Franck Condon factors will be calculated for every permutation of up to and including 11 12 quanta over the vibrational modes optional TRANSLATE Move the center of mass of both geometries to the origin optional ROTATE Rotate the geometries to maximize the overlap of the nuclear coordinates Only a few keys from the TAPE21 file are used for the calculation of the Franck Condon factors Disk space usage can be significantly reduced by extracting just these keys from the TAPE21 file before further analysis The following shell script will extract the keys from the KF file specified by the first argument and store them in a new KF file specified by the second argument using the cpkf utility 33 bin sh cpkf 1 2 Geometry nr of atoms Geometry xyz GeometrySnr of atomtypes Geometry fragment and atomtype index Geometry atomtype Geometry mass Freg Frequencies FreqsNormalmodes Result TAPE61 After a successful calculation fcf produces a TAPE61 KF file All results are stored in
2. ADF Property Programs ADF Program System Release 2009 01 Scientific Computing amp Modelling NV Vrije Universiteit Theoretical Chemistry De Boelelaan 1083 1081 HV Amsterdam The Netherlands E mail support scm com Copyright 1993 2009 SCM Vrije Universiteit Theoretical Chemistry Amsterdam The Netherlands All rights reserved Table of Contents ADF Property Programs siii 1 Table Of Contents sissies 2 GeneralintroducioN cda da 4 CPE NMR spin spin couplifigs ria E A ARE iia 5 Ann ia sacaase sanncdaeddasccaadsaannadeceandeanassaanaascsaaaieadis 5 Theoretical and technical aspeciS vassrdnaan sai 5 Further technical aspects and current limitatioNS ooonconnonnnnncnnconnnnnnonccnononccnnnnnnnnnnnnos 6 Bug fix in case more than 1 perturbing atom and DSO or PSO sess 7 Running CPL 7 putear ERE TAREA em tm ton ote eritis 7 WEIMAR UE switches cubas 9 NMRECUPLINO SDK cT 10 GGA REY I 12 Practical ASDOCUtS iniciada 12 Norme UT ee aia 12 Restan insistas iaa 13 How to avoid the unnecessary computation of many SCF cycles ssssssss 13 Computing individual terms in the coupling tensor sssee 14 Twa bond atndtrioresbDondoouplimas un 0 2 ee 14 Principal axis system the whole coupling tensor n unse 14 IReferenGes rana 15 EPR g tensor NMR
3. Implementation of a hybrid DFT method for calculating NMR shieldings using Slater type orbitals with spin orbital coupling included Applications to 1870s 195pt and C in heavy metal complexes Journal of Physical Chemistry A online 24 J Autschbach Magnitude of Finite Nucleus Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin Spin Coupling Constants ChemPhysChem published online 2009 25 J Autschbach Two component relativistic hybrid density functional computations of nuclear spin spin coupling tensors using Slater type basis sets and density fitting techniques Journal of Chemical Physics 129 094105 2008 Erratum Journal of Chemical Physics 130 209901 2009 26 D L Bryce and J Autschbach Relativistic hybrid density functional calculations of indirect nuclear spin spin coupling tensors Comparison with experiment for diatomic alkali metal halides Canadian Journal of Chemistry 87 927 2009 36 Keywords CLGEPR 17 EPRGTENSOR 22 NMRCOUPLING 9 10 37 Index A tensor 16 C6 coefficient 30 C8 coefficient 30 C10 coefficient 30 CPL Diamagnetic orbital term 6 CPL Fermi Contact term 6 CPL Paramagnetic orbital term 6 CPL Spin Dipole term 6 dispersion coefficients 30 EPR 16 16 ESR 16 16 g tensor 16 16 GIAO formalism 20 long range dispersion interaction 30 NICS 19 28 NMR chemical shift 25 NMR shielding tensor 25 NMR spin spin couplings 5 38 NSSC
4. With other words the different matrix elements of these shielding tensors are printed Finally DEBUG and BIGDEBUG invokes the calculation and output of various test parameters etc that are of interest for debugging only and can be ignored otherwise see the code for details 20 EprSize completely analogous to Size for EPR g tensors respectively Default same as Size if EPR is input specified the keys are obsolete otherwise Grit The argument is a real number PSMAL Only those matrix elements M of the paramagnetic shielding are printed for which the absolute of M is greater then psmal times the isotropic shielding at this nucleus E g CRIT 0 1 prints only matrix elements if they are at least 10 of the isotropic shielding in magnitude Default psmal 0 00001 The keyword is not relevant if the SIZE is specified as MINIMAL or SMALL It is ignored in this case Format This keyword refers to the format that is used for some of the output d format or f format Possible arguments are F the default or D The f format is easier to read and thus the default The D format gives a few more digits and might sometimes be useful for this reason PrincipalAxisRep The total shielding tensor is being symmetrized and transformed into its principal axis representation The given keyword regulates the step It has the two possible arguments PRINT default and NOPRINT NOPRINT suppresses the diagonalization Antisymmetr
5. and their orbital energies Both in turn depend on the density functional or Kohn Sham potential that has been chosen for the ADF run and the basis set quality It is difficult to give a general advice here concerning the NSSCCs So far we have found that the use of GGAs improves the NSSCCs with respect to experiment in most cases in comparison to LDA Different GGAs often yield very similar results Further in particular for those cases for which the OP term is large or even dominant both standard LDAs and GGAs sometimes do not provide an accurate enough description of the orbitals and deviation of the CPL results as compared to experiment can be substantial Future developments of density functionals might be able to cure these problems For the time being we recommend that you base the CPL run on different choices of density functionals in the ADF run and investigate the convergence of the result with respect to basis set and integration accuracy Note that CPL itself uses the VWN functional by default to determine the first order perturbed MOs There are enough indications to believe that this is a reasonable approximation for NMR purposes In ADF2009 01 the first order potential of the PBE family of GGA functionals and the first order potential of the hybrid PBEO functional can be used See Refs 25 26 for applications of such first order potentials However other hybrid functionals and Hartree Fock can not or should not be used in combinatio
6. below for the detailed description Additional keys and subkeys may be recognized but are not intended for general use Input description The calculation of the NMR shielding tensor s ESR EPR g tensor is invoked with a block type key CLGEPR If this block key is not present the program will attempt to read the input from the block key NMRSHIELDING Thus you just put the lines CLGEPR END 17 into the input to start the calculation of the shieldings with some default settings that are described below Note that th e word shielding refers in the following generally to any of NMR shielding ESR EPR g tensor Cases where this statement is not true should be recognizable from the context The availab End le subkeys are abbreviations in brackets CLGEPR uclei NUCL NUCOPTIONS AToms NUCL Ghosts GHOST CalcVirtDia CALCV oParamagneticShielding NOPARA Output OUTP ixOccupations NoMixOccupations MIXOCC NOMIXOCC EprGTensor EPRGT Output Ghosts and EprGTensor are block type subkeys Output and EprGTensor have a number of possible arguments of their own see below A disabled subkey is Tape An undocumented subkey is Testlt used occasionally for debugging NUCLEI The optional subkey NUCLEI NUCL has as arguments either ALL NONE or some integer numbers The default is ALL unless EPRGT is specified in which case the def
7. coefficients A schematic example taken from the set of sample runs for the usage of DISPER is the following Step1 run ADF for say the HF molecule In the input file you specify the RESPONSE data block RESPONSE axWaals 8 Compute dispersion coefficients up to C8 ALLTENSOR This option must be specified in the ADF calc for a subsequent DISPER run ALLCOMPONENTS Must also be specified for DISPER End At the end of the run copy the local file TENSOR to a file tensorA For simplicity we will now compute the dispersion coefficients between two HF molecules Therefore copy tensorA to tensorB Now run DISPER without any other input It will look for the local files tensorA and tensorB and compute corresponding dispersion coefficients to print them on standard output The output might look something like this DISPER 2000 02 RunTime Apr04 2001 14 14 13 kkkkkkkkkk C COEFFICIENTS kkkkkkkkkk n LA KA LB KB L coefficient Y coefficient P 6 00 0 0 0 28 29432373 28 29432373 620002 7487547697 3 348533127 8000 0 0 416 1888455 416 1888455 800202 0 4323024202E 05 0 1933315197E 05 8 2 0 0 0 2 402 3556946 179 9389368 8 2 0 2 0 4 0 4238960180E 05 8 4 0 0 O 4 36 67895539 12 22631846 8 4 0 2 0 6 0 2000286301E 05 The n value in the first column refers to the long range radial interaction The case n 6 refers to the usual dipole dipole type interaction related to a 1 R8 depen
8. either the formal frozen core support or a faster implementation will ever be done The term is activated by specifying SOO subsubkeyword within the EPRGT subkey of the EPR keyblock ie 23 CLGEPR EprGTensor SOO SubEnd END Additionally the following keywords to be given at the top level of the EPR input file can be used to controls certain technical aspects of the calculation NOGSOOSCREENING This keyword will disable screening of the contributions in the 6D numerical integral For large molecules gt 20 atoms this keyword will make the G SOO contribution scale as O N 2 instead of O N It should not change calculated G SOO contributions by more than a few parts per million GSOODETAILED Calculate and print contributions from gauge dependent paramagnetic and diamagnetic currents Using this option will defeat the screening to a large extent and slow down the calculation GSOOSPINWEIGHTS w_alpha w_beta Specifies the weights of the alpin alpha and spin beta currents in the self interaction corrected total current For spin doublet radicals the default is GSOOSPINWEIGHTS 0 0 2 0 Specifying 1 0 1 0 will disable self interaction correction PROXCELLS number Number of cells used for constructing proximity grid PROXBUF number Size of the memory buffer in 50 byte units which will be used for sorting the proximity grid References The original implementat
9. have been translated and or rotated with respect to each other To remove the six translational and rotational degrees of freedom we can center the equilibrium positions around the center of mass and rotate one of the states to provice maximum overlap The latter is included with the zero order axis switching matrix B implemented according to 19 When we have obtained the displacement vector it is trivial to calculate the dimensionless electron phonon couplings They are given by A F 2 7k Here 2trw h is a vector containing the reduced frequencies 20 When the displacement vector k the reduced frequencies F and I and the Duschinsky rotation matrix J L BoL have been obtained the Franck Condon factors can be calculated using the two dimensional array method of Ruhoff and Ratner 20 There is one Franck Condon factor for every permutation of the vibrational quanta over both states Since they represent transition probabilities all Franck Condon factors of one state which respect to one vibrational state of the other state must sum to one Since the total number of possible vibrational quanta and hence the total number of permutations is infinite in practice we will calculate the Franck Condon factors until those sums are sufficiently close to one Since the number of permutations rapidly increases with increasing number of vibrational quanta it is generally possible to already stop after the sum is greater than about two thirds
10. is MRCOUPLING END This represents a minimal input file for CPL The NMRCOUPLING key hosts all optional keys that are relevant for the NSSCCs themselves In addition to the mandatory NURCOUPLING key CPL recognizes the following input switches GGA See the separate section for this key which influences the first order potential that is used RESTART restart_file restart the computation from file restart_file This is the TAPE13 produced during a CPL run By default TAPE 13 is deleted after a successful completion of CPL As with ADF restarts you can not use the name TAPE 13 for restart file but you have to rename it e g to tape13 restart SAVEFILE TAPE13 keep the restart file even after a successful completion of CPL TAPE13 is currently the only file that is meaningful as a parameter to SAVEFILE NMRCOUPLING subkeys The available switches within a NMRCOUPLING END block control the computation of the NSSCCs By default the program will evaluate the FC coupling contribution for the first nucleus being the perturbing nucleus and all remaining nuclei responding Please note that the ordering of atoms in CPL is generally different from the ADF input The ordering of atoms is the one being stored in TAPE21 and it is grouped by fragment types In case you are in doubt about the ordering of atoms you can run CPL for a few seconds It will print a list of atoms with their coordinates The ordering is currentl
11. tensor of electron paramagnetic resonance spectroscopy using Gauge Including Atomic Orbitals and Density Functional Theory Journal of Physical Chemistry A 101 3388 1997 9 S Patchkovskii and T Ziegler Calculation of the EPR g Tensors of High Spin Radicals with Density Functional Theory Journal of Physical Chemistry A 105 5490 2001 10 S Patchkovskii J Autschbach and T Ziegler Curing difficult cases in magnetic properties prediction with self interaction corrected density functional theory Journal of Chemical Physics 115 26 2001 11 S K Wolff and T Ziegler Calculation of DFT GIAO NMR shifts with inclusion of spin orbit coupling Journal of Chemical Physics 109 895 1998 12 S K Wolff T Ziegler E van Lenthe and E J Baerends Density functional calculations of nuclear magnetic shieldings using the zeroth order regular approximation ZORA for relativistic effects ZORA nuclear magnetic resonance Journal of Chemical Physics 110 7689 1999 13 V P Osinga S J A van Gisbergen J G Snijders and E J Baerends Density functional results for isotropic and anisotropic multipole polarizabilities and C6 C7 and Cg Van der Waals dispersion coefficients for molecules Journal of Chemical Physics 1997 106 p 5091 14 A van der Avoird P E S Wormer F Mulder R M Berns Topics in Current Chemistry 93 1 1980 15 C J Pickard and F Mauri First Principles Theory of the EPR g Tensor in Solids Defects in Qua
12. the Fcf section firstmode lastmode the first and last vibrational mode taken into account the minimum value of the electron phonon coupling maximum level or maximum number of vibrational quanta in maxl1 maxl2 both states whether the TRANSLATE and ROTATE options were specified in the input mass atomic mass vector m nmodes number of vibrational modes with a non zero frequency E OTE PAE rotation matrix J meo calculation of the Franck Condon factors lambda1 lambda2 lambda2 electron phonon couplings for both states And electron phonon couplings for both states And couplings for both states A and A apt mz em number of oe emer of maxl1 maxl2 quanta over maot mape maxp2 oe emer vibrational modes lo ground state to ground state overlap integral lo 0 ground state to ground state overlap integral loo state to ground state overlap integral lo 0 frequencies of every permutation of the vibrational quanta for both states maxp1 by maxp2 Franck Condon factor matrix fcfsum1 fcfsum2 average sum of the Franck Condon factors for both states In addition to producing a binary TAPE61 file fcf also writes the frequencies displacement vectors and electron phonon couplings for both states to the standard output translate rotate freq1 freq2 34 References 1 J Autschbach and T Ziegler Nuclear spin spin coupling constants from regular approximate density functional c
13. 5 01 the bugs in the NMR module are fixed that gave problems in the ADF2004 01 and older versions Input options The whole input file for NMR uses one block key NMR with several optional sub keys each having a series of options NMR Out OutOptions 25 Calc CalcOptions UlK UlKOptions Nuc NucOptions Atoms AtomsOptions Ghosts GhostsOptions Analysis AnalysisOptions End OUT Out OutOptions The sub key Out controls printed output Its options specify the details by their optional presence The following OutOptions are recognized Default ISO All Implies all the other options except for ISO which may be specified in addition ISO Isotropic shielding constants Tens Shielding tensors Eig Eigenvectors U1 The U1 matrix F1 The first order change in the Fock matrix 1 The first order change in the Overlap matrix AOP The paramagnetic AO matrix 7 the matrix in the representation of elementary atomic basis functions AOD The diamagnetic AO matrix AOF The Fermi contact AO matrix REFS Literature references INFO General information CALC Calc CalcOptions The sub key Calc controls what is actually calculated The following options are available Default ALL All Implies all of the other options to this key Para The paramagnetic part Dia The diamagnetic part FC 26 The Fermi contact part in case of the Pauli Hamiltonian SO The Fermi contact part in case of the ZOR
14. A Hamiltonian Note that in case of the ZORA Hamiltonian default the scaled ZORA method is used If the sub key Calc is used but not the option ALL then the plain ZORA method is used For chemical shifts only compare results with the same options U1K UIK UlKOptions The sub key U1K determines which terms are included in the calculation of the U1 matrix first order changes in MO coefficients Options Default none Best The best recommended options for each relativistic option are included for this sub key All Implies all the other options to this key MV The mass velocity term Dar The Darwin term ZMAN The Spin Zeeman term Note for chemical shifts only compare results with the same options NUC Nuc NucOptions The sub key Nuc determines for which nuclei the chemical shifts are computed If this sub key is omitted from the NMR block the calculations are carried out for all nuclei Else you may use this options by simply typing Nuc in the NMR block without any further data this means for no nuclei at all Alternatively you may type the index of the atom s you want to see analyzed Default all nuclei are calculated i e as for omitting this sub key Example NUC 2 1 The numbers refer to the internal numbering of the nuclei as it appears somewhere early in the general ADF output This internal numbering is also the internal NMR numbering but it is not necessarily the same as the input ordering U
15. C 5 nuclear spin spin coupling constant 5 nuclear independent chemical shift 19 28 Q tensor 16 reduced spin spin coupling constant 5 SICOEP 23 spin spin coupling constant 5 van der Waals 30
16. NSSCCs the coupling between any pair of nuclei in the molecule can be computed See Ref 4 for an example Principal axis system the whole coupling tensor CPL evaluates the complete 3x3 coupling tensor with respect to the Cartesian input coordinate system Depending on the orientation of the molecule and the local symmetry the coupling tensor has in fact often only a small number of independent components CPL evaluates the principal components by the following procedure the 3x3 matrix is transformed into the basis of the eigenvectors of its symmetric part This diagonalizes the symmetric part of the coupling tensor A set of eigenvectors principal axis system is also printed 14 References 1 J Autschbach T Ziegler J Chem Phys 2000 113 936 2 J Autschbach T Ziegler J Chem Phys 2000 113 9410 3 J Autschbach T Ziegler J Am Chem Soc 2001 123 3341 4 J Autschbach T Ziegler J Am Chem Soc 2001 123 5320 24 J Autschbach ChemPhysChem published online 2009 25 J Autschbach J Chem Phys 2008 129 094105 J Chem Phys 2009 130 209901 26 D L Bryce and J Autschbach Can J Chem 2009 87 927 See also N F Ramsey Phys Rev 91 303 1953 Dickson R M Ziegler T J Phys Chem 1996 100 5286 Khandogin J Ziegler T Spectr Acta A 1999 55 607 D L Bryce R Wasylishen J Am Chem Soc 122 3197 2000 ADF User s manual SCM Vrije Universite
17. OD term is computationally very cheap since only integrals involving the electron density have to be evaluated The next expensive term is the OP term For this contribution the first order perturbed MOs have to be computed With the available density functionals in ADF the OP term does not cause a change in the Kohn Sham potential and the first order MOs can be computed directly i e without an iterative procedure This is equivalent to the approach that has been implemented in the NMR code for ADF Both the FC and the SD terms induce electron spin density to first order as a perturbation Equivalent to the iterative solution of the unperturbed Kohn Sham equations the first order MOs depend on that first order spin density which in turn depends on the first order MOs Therefore in order to evaluate the FC and SD NSSCC contributions the CPL program carries out a SCF cycle In the scalar or non relativistic case the computational cost for the FC term is comparable to an ADF single point calculation with a local density functional The evaluation of the SD term is more expensive The current implementation utilizes the CPL spin orbit code to compute the combined FC SD contribution and therefore leaves some room for future speed ups In most cases the SD term yields a negligible NSSCC and the much faster code for the scalar or non relativistic FC term can be used However it is very important to include the SD term in the computation if coupling
18. References 5 G Schreckenbach and T Ziegler J Phys Chem 99 606 1995 7 G Schreckenbach and T Ziegler Int J Quant Chem 61 899 1997 11 S K Wolff and T Ziegler Journal of Chemical Physics 109 895 1998 12 S K Wolff T Ziegler E van Lenthe and E J Baerends J Chem Phys 110 7689 1999 21 J Poater E van Lenthe and E J Baerends J Chem Phys 118 8584 2003 22 M Krykunov T Ziegler and E van Lenthe Int J Quant Chem 109 1676 2009 23 M Krykunov T Ziegler and E van Lenthe submitted 29 DISPER Dispersion Coefficients The DISPER program was originally written by V Osinga 13 The original documentation was written by S J A van Gisbergen Van der Waals dispersion coefficients The program DISPER computes Van der Waals dispersion coefficients up to C10 for two arbitrary closed shell molecules ADF itself can already compute some Ce and Ca coefficients between two identical closed shell molecules These coefficients describe the long range dispersion interaction between two molecules It requires previous ADF TDDFT calculations for the polarizability tensors at imaginary frequencies for the two interacting molecules Each such ADF calculation produces a file TENSOR if suitable input for ADF is given The TENSOR files must be renamed tensorA and tensorB respectively and must be present as local files for DISPER The DISPER program takes no other input and prints a list of dispersion
19. TORE options END GGA key GGA GGA Use first order GGA potential instead of the first order VWN potential Should only be used for the PBE family of GGA exchange correlation functionals and for the hybrid functional PBEO See Refs 25 26 for applications of calculating spin spin couplings with PBEO However other hybrid functionals and Hartree Fock can not or should not be used in combination with For consistency reasons of the first order potential one should use the keyword USESPCODE in the ADF calculation An example input for ADF for the hybrid PBEO would then contain USESPCODE XC hybrid PBEO End Practical Aspects Minimal input The default settings for CPL are invoked by the simple minimal content of the input file NMRCOUPLING END This is equivalent to 12 NMRCOUPLING NUCLEI 123 45 67 8 up to number of atoms SCF CONVERGE le 4 ITERATIONS 25 FC END Restarts CPL is restartable after the computation of each the complete set of FC or FC SD and OP matrix elements and after their transformation to the MO basis Further in spin orbit runs or in scalar or non relativistic computations involving the SD term CPL is restartable after each SCF cycle As with ADF restarts you need to supply a proper input file for a restarted computation and the restart file TAPE13 which needs to be renamed Changing the input of a calculation for a restart is not supported In re
20. The remaining one third will be distributed over so many Franck Condon factors that their individual contributions are negligible 32 In the limiting case of one vibrational mode with the same frequency in both states the expression for the Franck Condon factors of transitions from the ground vibrational state to an excited vibrational state are given by the familiar expression 2 llo e A2 n Input The input for fcf is keyword oriented and is read from the standard input fcf recognizes several keywords but only two have to be specified to perform the calculation All input therefore contains at least two lines of the following form STATES statel state2 QUANTA 11 12 STATES statel state2 The filenames of two TAPE21 files resulting from a numerical or analytical frequency calculation The calculations must have been performed on the same molecule i e the type mass and order of occurrence of all the atoms or fragments has to be the same in both files optional MODES first last The first and last mode to be taken into account in the calculation If this option is omitted all modes are taken into account This option can be used to effectively specify and energy range for the Franck Condonf factors When using this options always check if the results electron phonon couplings ground state to ground overlap integral average sum of Franck Condon factors etc do not change too much optional LAMBDA lambda
21. alculations Formalism and scalar relativistic results for heavy metal compounds Journal of Chemical Physics 113 936 2000 2 J Autschbach and T Ziegler Nuclear spin spin coupling constants from regular approximate relativistic density functional calculations Il Spin orbit coupling effects and anisotropies Journal of Chemical Physics 113 9410 2000 3 J Autschbach and T Ziegler Solvent Effects on Heavy Atom Nuclear Spin Spin Coupling Constants A Theoretical Study of Hg C and Pt P Couplings Journal of the American Chemical Society 123 3341 2001 4 J Autschbach and T Ziegler A Theoretical Investigation of the Remarkable Nuclear Spin Spin Coupling Pattern in NC 5Pt TI CN T Journal of the American Chemical Society 123 5320 2001 5 G Schreckenbach and T Ziegler The calculation of NMR shielding tensors using GIAO s and modern density functional theory Journal of Physical Chemistry 99 606 1995 6 G Schreckenbach and T Ziegler The calculation of NMR shielding tensors based on density functional theory and the frozen core approximation International Journal of Quantum Chemistry 60 753 1996 7 G Schreckenbach and T Ziegler Calculation of NMR shielding tensors based on density functional theory and a scalar relativistic Pauli type Hamiltonian The application to transition metal complexes International Journal of Quantum Chemistry 61 899 1997 8 G Schreckenbach and T Ziegler Calculation of the G
22. anisotropies are to be evaluated In the case where the NSSCC computation is based on spin orbit coupled relativistic two component ZORA MOs the SD term causes only a marginal increase in computational time as compared to the FC term alone Generally in this case the computational cost for the FC term is already approximately one order of magnitude higher than in the scalar or non relativistic case since the 3 x y z components of the spin density with respect to 3 components of the perturbation respectively have to be determined self consistently The additional presence of the SD term only shows up in a somewhat more costly evaluation of the matrix elements of the perturbation operator However CPL spends most of its computational time in the SCF cycle Therefore in spin orbit computations the computation of the FC SD terms is the default The OP term has to be evaluated self consistently too in this case and is added as a perturbation in the SCF cycle upon request We use the terminology perturbing and responding nucleus within the CPL output The perturbing nucleus is the one for which the first order MOs have to be computed self consistently while the NSSCC is then determined by these first order MOs and the FC SD and OP matrix elements of the second responding nucleus For the OD term this distinction makes no sense but is used in the output for reasons of consistency Experimental NSSCCs between two nuclei A a
23. ault is NONE This subkey specifies for which nuclei the NMR shielding is calculated The input line NUCLEI ALL keeps the NMR default in this case the shielding is calculated at all nuclei in the molecule The keyword NONE specifies that no nuclei are desired Obviously at least one ghost has to be chosen in this case or EPRGT have to be specified the program aborts otherwise cf subkey Ghosts Alternatively the numbers of the desired nuclei can be specified Example NUCLEI 2 1 The numbers refer to the internal numbering of the nuclei as it appears somewhere early in the general ADF output This internal numbering is also the internal NMR numbering but it is not necessarily the same as the input ordering Use the subkey ATOMS to specify the nuclei according to this input ordering in the ADF calculation Note that th e number of nuclei has not a very significant consequence for the total CPU time since the CPU intensive parts of the NMR calculations are mostly independent of it However the length of the output file does depend on the number of NMR nuclei ATOMS This subkey ATOMS specifies for which nuclei the NMR shielding is calculated Default all nuclei are calculated i e as for omitting this sub key Example ATOMS 2 1 18 The numbers refer to the input ordering in the ADF calculation Use the subkey NUCLEI to specify the nuclei according to the internal NMR numbers of the atoms GHOSTS The s
24. ble integration precision for many applications We do not recommend to use an ACCINT parameter smaller than 4 for obtaining meaningful results and encourage to use higher settings whenever possible 2 The basis set NSSCCs are sensitive chemical probes and therefore flexible basis sets have to be employed in order to yield a valid description of the MOs that determine the NSSCCs We have found that it is imperative to use at least basis set TZ2P V from the ADF basis set database Additional polarization functions in the valence shell may be necessary Furthermore the FC perturbation usually requires additional steep 1s functions i e with exponents much higher than the nuclear charge for a proper description In the relativistic heavy element case the use of additional steep basis functions as compared to the ZORA TZ2P basis is mandatory The use of steep functions is only of high importance for those nuclei for which the NSSCC is to be evaluated In ADF2009 01 some basis sets suitable for NSSCCs has been added to the ADF basis set directory in the directory ADFRESOURCES ZORA jcpl For elements not available in this directory we suggest to use basis TZ2P as a starting point and to add some 1s basis functions and appropriate fit functions with higher exponents in order to improve the accuracy of the FC term This is especially important for the heavy NMR nuclei For the nuclei for which NSSCCs are to be evaluated it is necessary to use all
25. calculation of the paramagnetic shielding of atoms since the occupation numbers are not all equal see also the key MixOcc The key doesn t have any argument The default is obviously that this feature be not used A warning is given to the user if this switch is set for molecules OUTPUT The subkey OUTPUT is a block type subkey Possible arguments are abbreviations in brackets Output Size EprSize Criteria CRIT Format PrincipalAxisRep PRINCIP AntisymmetricTensors ANTISY PrintMat PrintM SumUpOccVir SUMUP RelativisticShielding RELATIVIST SubEnd Many of those are not necessary for most cases All of the keywords in detail Size regulates the amount of information about the NMR shielding that is printed and sometimes calculated Possible arguments are abbreviations in brackets MINIMAL MIN SMALL SMAL LARGE LARG DEBUG BIGDEBUG BIGDEB Default is small If MIN is specified then only the isotropic shielding constant and its contributions as well as the total shielding tensor are printed for the different nuclei For SMALL the default also the dia and paramagnetic shielding tensors are shown in the output If LARGE is specified then the different contributions to the paramagnetic shielding tensor are printed according to our GIAO formulation Furthermore the dia and paramagnetic shieldings are analyzed with respect to the occupied and virtual orbitals of the unperturbed molecule
26. chemical SOIL 16 Compatibility and features c cccccccececcsccecsescccteceeecccterescccttesessceteeeassacievansastieraeastcoereesstieress 16 Comparison to related functionality in the ADF package eene 16 Summary of the input options rire repro oon t Erro Rr EE eR x MESE EP PER ER ET Trank IS YEAR ROO Eran ranita 17 ln pub SS CUA GON cca ics scp a ic EE NI ET ME 17 Na E annehmen 18 ATOM saa AA 18 ROSS aii A LI 19 CAUCUIRTDIA conri ive 19 NOPAR A arsenal lio 20 INI P 20 MixOccupations4 INNOMIXOGOUDSUORS saisie ton eit cet m oen EIE HE 22 EPRETENSOR anne na aaa aces ee tei eae 22 SICHER nennen dl T T 23 The spin other orbit term in the g tensor uussrressnnssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 23 EL m 24 NMR chemical shift isisisi is 25 DEVE ACCU Ma 25 Input opHoORS ee NM E caer er E 25 OUT ansehen ter sates du ERE DE Ded dn PE RS 26 CAU ita dida di 26 A NO 27 A A A 27 ATOMS net AAN 27 Ciel in energie 28 ANALYSIS uam er I eek 29 Referentes JPERPEREEREENEDESEHNEUERENEEEEEPENEUEEUBEREEEFEESEREEEPLEETEUEFEEEENTELUSUPERCELELEREEEFTEUSERDERITTEREEEEPURGEFERELTEREEFEN 29 DISPER Dispersion Coefticients rrt icono apnea Fiona etin bna na aaa EX RR AR aan dan 30 Van der Waals dispersion coefficients e ccceeeeeeeeeeeeeneeeeeeeeeeeeeeneeeaneeseeeeeeseneeeeeeanes 30 FCF Franck Go
27. dence in the dispersion energy The n 7 case relates to a dipole quadrupole polarizability on one system and a dipole dipole polarizability on the other this is not symmetric The n 8 term may contain contributions from a quadrupole quadrupole polarizability on one system in combination with a dipole dipole polarizability on the other as well as contributions from two dipole quadrupole polarizabilities 30 Terms which are zero by symmetry are not printed In the example above this is the case for all n 7 terms because the systems apparently are too symmetric to have a nonzero dipole quadrupole polarizability The best known and most important coefficients are the isotropic ones determining the purely radial dependence of the dispersion energy They are characterized by the quantum numbers 6 0000 0 or 8 0 0 0 0 0 etc Other combinations of quantum numbers refer to different types of angular dependence The complete set determines the dispersion energy for arbitrary orientations between the two subsystems A and B The complete expressions are rather involved and lengthy We refer the interested reader to the paper 13 which contains a complete description of the meaning of the various parts of the output as well as references to the earlier literature which contain the mathematical derivations In particular a useful review which was at the basis of the ADF implementation is given in 14 Of particular significance is Eq 8 of the JCP pap
28. e Fock and the hybrid potentials can not or should not be used in combination with NMR chemical shift and EPR g tensor calculations Comparison to related functionality in the ADF package The ADF package contains already other possibilities to calculate NMR properties and ESR EPR properties namely the stand alone NMR program and the ESR option within the ADF program The stand alone NMR program calculates the NMR shielding tensors of closed shell molecules not only for the non relativistic and scalar relativistic Pauli Hamiltonian but also for the spin orbit coupled Pauli Hamiltonian and scalar relativistic and spin orbit coupled ZORA Hamiltonian using a TAPE21 from a self consistent ADF calculation Only in the spin orbit coupled cases the ADF calculation should use SYMMETRY NOSYM See ADF user s guide Starting from ADF2009 01 this stand alone NMR program can also be used in combination with hybrids which is not possible with the EPR NMR program However the analysis of the different orbital contributions to the shielding tensor can be done much more extensively in the EPR NMR program described here The ESR option within the ADF program can calculate the EPR g tensor if spin orbit coupling is included either at the Pauli or ZORA level If the calculation is spin restricted there must be exactly one unpaired electron which means it can then calculate only low spin g tensors with an effective spin of 1 2 If the calculation is spin unr
29. elding contributions The arguments are PRINT the default for relativistic calculations and NOPRINT which is obviously the default for non relativistic calculations MixOccupations NoMixOccupations The subkeys MixOccupations NoMixOccupations MIXOCC NOMIXOCC Our GIAO formulation of the shielding does not allow for broken non integer occupation numbers that are used in ADF for partially filled degenerate orbitals The reason is that we use the S Matrix for the occupied occupied contributions to the paramagnetic shielding which in turn avoids degenerate perturbation theory Hence the program aborts when these broken occupation numbers occur key NoMixOcc the default This default can be overwritten key MixOcc in which case we use the occupied occupied U matrix instead of the S matrix but only for combinations of occupied MOs that do not have equal occupation numbers This is mostly an experimental feature EPRGTENSOR Subkey EprGTensor invokes the calculation of the EPR or ESR g tensor and its contributions The key is a block type subkey and most of the arguments are not really required Those arguments are abbreviations in brackets EprGTensor EPRXC X Alpha par XCCutOff XCCUT KinCorrection KINCORR SOO Skip SubEnd Disabled arguments include TestPot and TestPar The other keywords in detail EPRXC regulates which XC potential to use for the exchange in the effective ESR potentia
30. electron basis sets This is not a restriction due to the implementation but we have found that with the available frozen core basis sets the flexibility of the basis in the vicinity of the nuclei is not sufficient It is possible to use frozen core basis sets if you add enough basis functions in the core region such that the basis approaches the flexibility of at least a double zeta all electron basis there 1 In that sense the savings in computational time due to usage of a frozen core basis are not as pronounced as in standard ADF computations Unless reliable frozen core basis sets for the NSSCC computation are available we strongly discourage the use of frozen core basis sets with the CPL program 3 The finite size of a nucleus typically the isotropic J couplings are reduced in magnitude by about 10 to 15 96 for couplings between one of the heaviest NMR nuclei and a light atomic ligand and even more So for couplings between two heavy atoms see Ref 24 However one should have really large basis sets with tight basis functions to observe this effect in calculations see the previous point about basis sets The basis sets in the directory SADFRESOURCES ZORA jopl are suitable for finite nucleus calculations A finite size of the molecule can be set in the ADF program with the key NUCLEARMODEL NuclearModel Gaussian 4 The density functional the results of the CPL code depend mostly on the shape of the MOs that have been determined by ADF
31. er mentioned above as it defines the meaning of the calculated coefficients CnAKALB KBL as printed above For highly symmetric systems a different convention is sometimes employed It is based on Legendre polynomials hence the P in the final column instead of on the spherical harmonics the Y in the column before the last The P coefficients are defined only for those coefficients that are nonzero in highly symmetric systems and never contain additional information with respect to the Y coefficients They are defined Eq 14 in the mentioned J Chem Phys paper in terms of the Y coefficients by Cab 1 k e 99 9 o 1 Because the quality of the dispersion coefficients is determined by the quality of the polarizabilities that are the input for DISPER it is important to get good polarizabilities from ADF For that it is important in the case of small systems to use an asymptotically correct XC potential several choices are available in ADF such as SAOP or GRAC and a basis set containing diffuse functions We refer to the ADF User s Guide for details 31 FCF Franck Condon Factors fcf is an auxiliary program which can be used to calculate Franck Condon factors from two vibrational mode calculations 18 fcf requires an ascii input file where the user specifies the TAPE21 files from two adf vibrational mode calculations carried out for two different electronic spin or charge states of the same molecule These calculat
32. es document Spin orbit coupling NMR calculations on systems computed by ADF with Spin Orbit relativistic effects included must have used NOSYM symmetry in the ADF calculation NMR can also be combined with ADF ZORA calculations The NMR program reads from TAPE21 the relativistic option that is used in the ADF calculation and will use the same relativistic option in the NMR calculations SAOP TAPE10 Important ADF2004 01 or later use SAVE TAPE10 in the ADF calculation for special exchange correlation potentials like SIC or SAOP since the NMR program does not know how to calculate SIC SAOP or other model potentials On TAPE10 the SCF potential is written which is read in by the NMR program The use of the model SAOP potential leads to isotropic chemical shifts which are substantially improved over both LDA and GGA functionals and of similar accuracy as results with a self interaction corrected functional SIC see 21 SAOP is computationally expedient and routinely applicable to all systems requiring virtually the same computational effort as LDA and GGA calculations NICS The Nucleus Independent Chemical Shift NICS can be calculated at any point in the molecule Hybrids Starting from ADF2009 01 Hartree Fock and the hybrid potentials can used in combination with NMR chemical shielding calculations see Refs 22 23 Bug fix ADF2005 01 off diagonal part shielding tensor Bug fix off diagonal part shielding tensor In the ADF200
33. estricted the collinear approximation must be used There may be more than one unpaired electron which means that one can calculate high spin g tensors The EPR NMR program can also calculate the g tensor at the unrestricted level and can also calculate high spin g tensors The EPR NMR program can calculate contributions from the spin other orbit term to the g tensor which is not possible with the ESR option in ADF With the ADF program it is also possible to calculate more EPR parameters namely the nuclear magnetic dipole hyperfine interaction A tensor and the nuclear electric quadrupole hyperfine interaction Q tensor see the ADF user guide and the keywords ESR and QTENS respectively 16 Summary of the input options The program recognizes the following input keys CLGEPR Nuclei ALL n Atoms lees Ghosts xl yl zl PERA Subend CalcVirtDia CALCV NoParamagneticShielding NOPARA Output Size Minimal Small Large Debug Bigdebug EprSize Minimal Small Large Debug Bigdebug Criteria psmal Format F D PrincipalAxisRep Print Noprint AntisymmetricTensors PrintMat Bl SF COEF SumUpOccVir RelativisticShielding Print Noprint Subend ixOccupations NoMixOccupations MIXOCC NOMIXOCC EprGTensor EPRXC X Alpha par XCCutOff n KinCorrection On Off SOO SubEnd END Not all combinations of the input parameters and SCF options used to create TAPE21 are allowed or required See
34. eus has been chosen as the perturbing one and which as the responding one convergence has to be good enough though Suppose you want to compute the NSSCCs in the water molecule with O being nucleus no 1 In that case NUCLEI 1 2 3 NUCLEI 2 3 yields the same O H and H H coupling constants as the input NUCLEI 2 1 NUCLEI 1 3 NUCLEI 3 2 but with less computational effort due to the fact that only 2 instead of 3 SCF cycles will be performed The example chosen here is trivial but in other cases it can be worthwhile to consider different sequences of computations Alternatively you can use the ATOMPERT and ATOMRESP subkeys ATOMPERT 1 2 ATOMRESP 2 3 13 which will calculate the spin spin coupling of the nuclei 1 2 1 3 and 2 3 skips 2 2 since the nuclei are the same which are the same O H and H H couplings as before Note the numbers of the nuclei for the subkeys ATOMPERT and ATOMRESP refer to the input ordering in the ADF calculation whereas the numbers of the nuclei for the subkey NUCLEI refer to the internal CPL numbers of the atoms Computing individual terms in the coupling tensor As we have mentioned before the FC OP and OD terms can be calculated individually but not the SD term In case the SD input option is given the FC SD contribution is evaluated instead This is NOT equal to the sum of the individual FC and SD contributions since there is a cross term between these t
35. icTensors This key allows the printing of the antisymmetric part of the total shielding tensor The antisymmetric part is usually not accessible for experiment Thus the default is the argument NOPRINT The other recognized argument is PRINT PrintMat This keyword invokes the printing of the respective matrices Arguments any of B1 SF COEF The default is no printing Bl B1 refers to the first order B coefficients of the frozen core approximation It is irrelevant in all electron calculations COEF COEF refers to the first order coefficients of the magnetic wave functions i e the S matrix occupied occupied and the U matrix occupied virtual SF SF finally means the constituting matrices of the U coefficients the first order S matrix occupied virtual and the first order F matrix occupied virtual This keyword is probably of interest for debugging only SumUpOccVir 21 invokes the additional output of the occ vir matrix elements summed up per occupied MO over all the virtuals This is only relevant for Large Ouput and ignored otherwise Default turned off No arguments are required This keyword is sometimes quite useful since it gives a quick overview as to which occupied orbitals have a significant contribution to the paramagnetic shielding Also it doesn t cost any CPU time and not much space in the output file RelativisticShielding Print key for the output of the direct scalar relativistic shi
36. ion is documented fairly thoroughly in Georg Schreckenbach s Ph D thesis University of Calgary 1996 which is available at http www scm com Doc publist html as well as in the following papers Georg Schreckenbach and Tom Ziegler 5 J Phys Chem 1995 99 606 NMR all electron formulation 6 Int J Quantum Chem 1996 60 753 frozen core approximation 7 Int J Quantum Chem 1997 61 899 scalar relativistic method 8 J Phys Chem A 1997 101 3388 ESR g tensor S Patchkovskii et al 9 S Patchkovskii T Ziegler J Phys Chem 2001 A105 5490 High spin EPR g tensor 17 S Patchkovskii R S Strong C J Pickard and S Un J Chem Phys 2005 122 214101 spin other orbit term g tensor There are also various application papers published These papers illustrate some of the concepts and functionality that is described here 24 NMR chemical shift The NMR program was originally written by G Schreckenbach and later adapted and extended by S K Wolff Introduction The utility program NMR computes NMR chemical shifts It has been developed in the Theoretical Chemistry group of the University of Calgary 5 7 11 12 NMR requires an ASCII input file and a TAPE21 result file from an ADF calculation on the molecule to be analyzed The ADF result file must be present with name TAPE21 in the directory where you execute NMR A few sample runs are contained in the ADF distribution package See the Exampl
37. ions can be either numerical or analytical The number of vibrational quanta that have to be taken into account for both states in the evaluation of the Franck Condon factors have to be specified fcf produces a binary KF file TAPE61 which can be inspected using the kf utilities Furthermore fcf writes the frequencies vibrational displacements and electron phonon couplings for both states too the standard output including any error messages Introduction Franck Condon factors are the squares of the overlap integrals of vibrational wave functions Given a transition between two electronic spin or charge states the Franck Condon factors represent the probabilities for accompanying vibrational transitions As such they can be used to predict the relative intensities of absorption or emission lines in spectroscopy or excitation lines in transport measurements When a molecule makes a transition to another state the equilibrium position of the nuclei changes and this will give rise to vibrations To determine which vibrational modes will be active we first have to express the displacement of the nuclei in the normal modes k L m Boxo x o Here k is the displacement vector L is the normal mode matrix m is a matrix with the mass of the nuclei on the diagonal B is the zero order axis switching matrix and xo is the equilibrium position of the nuclei For free molecules depending on symmetry constraints the geometries of both states may
38. it Amsterdam The Netherlands G Schreckenbach S K Wolff T Ziegler Modeling NMR chemical shifts ACS Symposium Series Washington DC 1999 15 EPR g tensor NMR chemical shift The EPR NMR part of this User s Guide is adapted from a document originally written by G Schreckenbach and later updated by S Patchkovskii the two main authors of this program Compatibility and features The stand alone EPR NMR program is compatible with ADF 2000 and the more recent versions For ADF 2000 or more recent only a TAPE21 from a self consistent ADF calculation is required on input The program will also accept TAPE10 which will make the calculation somewhat faster In either case the SCF calculation used to create TAPE21 must be done with the SYMMETRY NOSYM keyword Important ADF2004 01 or later use SAVE TAPE10 in the ADF calculation for special exchange correlation potentials like SIC or SAOP since the EPR NMR program does not know how to calculate SIC SAOP or other model potentials On TAPE10 the SCF potential is written which is read in by the EPR program The program supports calculations of NMR shielding tensors of closed shell molecules and EPR g tensors of open shell molecules Low spin and high spin EPR g tensors can be calculated Both non relativistic and scalar Pauli Hamiltonians are supported Spin orbit and ZORA are not supported A detailed breakdown of the orbital contributions can be provided on output Hartre
39. l Georg Schreckenbach s Ph D thesis p 124 Note that this does not influence the XC potential that is used elsewhere in the calculation Currently implemented argument X Alpha X ALP It is possible to specify the X alpha parameter to be used as a positive real number after the keyword The default for the whole keyword is EPRXC X Alpha 0 7 XCCutOff 22 A numerical cutoff to be used with the EPR exchange potential It avoids numerical instabilities but has no influence on the results otherwise The default turns out to be sensitive and should not be changed it depends on the number of integration points and the number of electrons Alternatively one can specify a real number CUTFF the EPR exchange potential is set to zero if its value is smaller then 10 CUTFF in the given integration point KinCorrection This keywords includes or excludes the use of the isotropic kinetic energy to the g tensor Arguments are ON default and OFF SOO This keywords includes the spin other orbit term in the calculation of the G tensor G SOO Note the calculation of this term takes a long time See also the separate section on the spin other orbit term Skip This key allows one to exclude various contributions from the calculation of the g tensor that might be useful to see their respective importance see e g the EPR paper tables 7 and 8 Possible arguments are any of NucDerivative NUCDER CoreDerivative COREDER ValDe
40. lear spin spin coupling there are four terms contributing to the NSSCC between two nuclei A and B the paramagnetic and diamagnetic orbital terms OP and OD respectively and the electron spin dependent Fermi contact FC and spin dipole term SD In the literature the OP and OD terms are often named PSO and DSO for paramagnetic and diamagnetic spin orbital In the more general ZORA formulation very similar operators are responsible for the NSSCC therefore we use the same terminology for the individual contributions In general the interpretation of the results for a heavy atom system is basically equivalent to a non relativistic situation In most cases the FC term yields the most important contribution to the NSSCC However many exceptions are known for which one or each of the other terms can be non negligible or even dominant We therefore suggest that you always check at least for a smaller but similar model system or by using a smaller basis set which of the four terms are negligible and which are dominant By default the CPL program computes the FC coupling between the first and all other nuclei of the molecule respectively Other couplings or the computation of the OP OD and SD terms can be requested by input switches see the Running CPL section of this document for details All contributions to the NSSCC are evaluated with the help of the numerical integration scheme implemented into ADF In general the computation of the
41. n with NMR spin spin coupling calculations 5 Modeling the experimental setup computing such sensitive numbers as NMR chemical shifts and in particular NSSCCs can result in substantial deviations from experimental data The simple reason might be that the isolated system that has been computed at zero temperature is not at all a good approximation to the system that has been studied experimentally We 3 4 and other authors have found that in particular solvent effects can contribute very substantially to the NSSCC In case you are comparing CPL results to experimental data obtained in strongly coordinating solvents we suggest that you consider solvent effects as a major influence We have found that even weakly coordinating solvents can cause sizeable effects on the NSSCCs for coordinatively unsaturated metal complexes Other sources of errors can be the neglect of vibrational corrections to the NSSCCs usually in the range of a few percent If the parameters of the underlying ADF computation are carefully chosen and the density functional is able to provide an accurate description of the molecule under investigation it is possible to compute NSSCCs by means of DFT with very satisfactory accuracy please note that for properties as sensitive as NSSCCs agreement with experimental results within about 10 error can be regarded as quite good Further chemical trends will be correctly reproduced for a related series of molecules in most cases Howeve
42. nctional The Xa potential is available as an alternative but usually leads to less accurate results In ADF2009 01 the first order potential of the PBE family of GGA functionals and the hybrid PBEO functional can be used Currently only spin restricted computations for systems with an even number of electrons are supported Further the calculation does not make use of symmetry and must be based on an ADF run with input SYMMETRY NOSYM Non Aufbau configurations are not supported The atom input list must not contain dummy atoms With the present version of CPL the SD term and the FC SD cross term cannot be evaluated separately Either the sum of FC SD cross terms or the FC term individually are computed CPL is restartable after various time consuming steps of the computation In ADF2009 01 the hybrid PBEO functional can be used in combination with NMR spin spin coupling calculations see the documentation for the extra keys that are needed However other hybrid functionals and Hartree Fock can not or should not be used in combination with NMR spin spin coupling calculations In ADF2009 01 the effects of a finite size of a nucleus on the spin spin couplings can be calculated A finite size of the nucleus can be set with the NUCLEARMODEL key in the input for the ADF calculation Bug fix in case more than 1 perturbing atom and DSO or PSO In the ADF2006 01b version a bug in the CPL module is fixed that gave problems in ADF2006 01 and olde
43. nd B are usually reported as J A B in Hertz From a computational point of view the so called reduced NSSCCs K A B are more convenient for comparisons CPL outputs both The J s are set to zero in case the nuclear magneto gyric ratio of one of the nuclei A or B is not available at run time Further technical aspects and current limitations In order to facilitate the future computation of rather large molecules all matrix elements of the perturbation operators FC SD and OP are evaluated in the Slater AO basis that is specified as input in the CREATE runs of ADF The AO matrix elements are further transformed to the basis of MOs and the calculation proceeds within the MO basis This allows for a convenient analysis of the results in terms of contributions from individual occupied and virtual MOs Such an analysis can be requested by input The matrix elements themselves as well as the first order contributions to the potential are evaluated by numerical integration The CPL code which is parallelized can use multiple processors for these steps of the computation The accuracy setting for the numerical integration is of high importance to obtain accurate matrix elements Furthermore the basis set being employed needs to be flexible enough to describe the perturbation correctly This means usually that modified basis sets have to be used in particular for heavy element calculations The first order potential is currently approximated by the VWN fu
44. ndon Factor Sui ias 32 nrod hio Maniana 32 MOUT e n T p EM Osee EE ER RUIN 33 Result TABEOT1 se RS ida AX RR 34 References gas ASI I ICI I ILI LIT 35 ucl 37 Index ao 38 General introduction This document describes some programs that can be run after earlier ADF calculation s have produced the required result file s such as TAPE21 The ADF program itself also enables the calculation of various molecular properties excitation energies and hyper polarizabilities to name a few that are not mentioned here Please consult the ADF User s Guide to check for information on the property in which you are interested if the underlying document does not contain the required information The documentation of the ADF program also includes information on ADF utilities Many of these also use ADF result files but these executables perform more technical tasks than the programs described here such as visualization and handling of the output There is some overlap in functionality between programs in the ADF suite regarding the NMR and ESR properties Each implementation has its own merits and deficiencies The differences are mentioned in the appropriate places in the documentation in order to let the user decide which option is most suitable for his problem CPL NMR spin spin couplings The original version of this part of the User s Guide was written by Jochen Autschbach primary author of the CPL c
45. ode Introduction The CPL code of the Amsterdam Density Functional program system allows the user to calculate Nuclear Spin spin Coupling Constants NSSCCs 1 2 NSSCCs are usually observed in NMR Nuclear Magnetic Resonance spectroscopy and give rise to the splitting of the signals of the NMR spectrum in multiplets They contain a wealth of information about the geometric and electronic structure of the compound being investigated The calculation needs a standard TAPE21 ADF output file CPL reads also an input key and optional settings from stdin usually from an input file Technical parameters such as the maximum memory usage can be set here as well One of the key features of the program is its ability to treat heavy nuclei with the ZORA relativistic formalism We refer the reader to the literature for details about our implementation 1 2 Please use the information printed in the output header of the CPL program in order to provide references of this work in scientific publications The development of the CPL program started in 2000 CPL provides the main functionality in order to evaluate NSSCCs based on DFT as well as a number of additional features in order to provide an analysis of the results Several analysis features for the coupling constant have been added see the CONTRIBUTIONS sub key Please report bugs or suggestions to SCM at support scm com Theoretical and technical aspects Within the non relativistic theory of nuc
46. pects section for instructions how to estimate the FC SD cross term The option NOFC will disable both the FC and SD computation SCF ITERATIONS 25 NOCYCLE CONVERGE 1e 4 Settings related to the SCF cycle that is carried out by CPL Valid options are with default values if applicable ITERATIONS 25 maximum number of iterations NOCYCLE perform no cycle equivalent to ITERATIONS 0 CONVERGE le 4 convergence criterion an input of e corresponds approximately to a convergence of log e digits i e the results will be converged to about four significant digits by default The measurement for the convergence is based on the sum S of the magnitudes of all occupied virtual matrix elements of the induced first order exchange potential Note that the actual convergence criterion being used in the computation is e times S of the first cycle i e the convergence criterion is set relative to the initial value of S XALPHA Use first order Xalpha potential instead of VWN potential default This will usually decrease the accuracy for couplings involving hydrogen and does not have a large effect for couplings between heavier nuclei not default The key is mainly intended to ensure compatibility with our previously published results CONTRIBUTIONS le19 LMO SFO LMO2 SFO2 11 Print contributions from individual orbitals to the FC and OP term of the NSSCCs that are larger in magnitude than a cer
47. pensive part in the calculation Note the numbers refer to the input ordering in the ADF calculation Use the subkey NUCLEI to specify the nuclei according to the internal CPL numbers of the atoms GAMMA nnuc gamma Input a non default magneto gyric ratio of g gamma for nucleus no nnuc in units of rad T s Note that one should include the the typical 107 factor CPL normally uses the g value of the most abundant NMR active isotope for a nucleus of a given charge by default With the GAMMA keyword you can override this value or supply a value if CPL does not know about it A list of g s that is used in the 10 computation is printed in the output You have to provide the GAMMA key for each nucleus you want to specify DSO Compute the diamagnetic orbital term for each NSSCC that is requested not default PSO SD FC Compute the paramagnetic orbital term for each NSSCC not default Compute the SD term for each NSSCC This is only default for spin orbit ADF runs The output will contain the sum of the FC and SD contributions Please note that requesting this option results in a greatly increased computational cost in scalar or non relativistic runs The option NOSD will turn the SD computation off in spin orbit runs and has no effect otherwise Compute the FC contribution to the NSSCCs This is the default option Please note that it is currently not possible to compute the SD term without the FC term Consult the practical as
48. r due to the inherent approximate character of the density functionals currently available with ADF and necessary basis set limitations great care should be taken that the results are reliable CPL assumes Aufbau configurations Please make sure that there are no empty orbitals with energies below the highest occupied MO HOMO In addition the SYMMETRY NOSYM key has to be used in the ADF computation It is currently not possible to use dummy atoms in the ADF input if the TAPE21 is intended to be used for a subsequent CPL computation Main input switches With the ADF output TAPE21 present in the current working directory the CPL code is invoked by SADFBIN cpl lt input file where input_file contains the input for CPL We have tried to ensure some backward compatibility with older ADF versions such as ADF 1999 and ADF 2 3 Normally you will use the ADF suite that contains the CPL code of the same version CPL tries to detect if the TAPE21 belongs to an older version of ADF and exits with an error message in case it is not able to process this file For ADF 2 3 you have to supply also the TAPE10 of ADF 2 3 in addition to TAPE21 specify SAVEFILE TAPE10 in the ADF input file We provide this option for testing purposes however this functionality is not supported and we do not recommend to run CPL on top of the output of an older ADF version input_file must contain at least one block type input key in order to start the CPL run The input key
49. r versions The problem in ADF2006 01 and older versions is In case there is more than 1 perturbing atom and the DSO or PSO term is calculated only the results of the spin spin couplings for the first perturbing atom are correct but the results of the other spin spin couplings may be incorrect Running CPL Input file for CPL TAPE21 In order to run the CPL code you need the general ADF output file TAPE21 being present in the directory where CPL is running Most of the computation s specific settings will be taken from TAPE21 such as the integration accuracy the basis set the density functional being employed nuclear coordinates and so on That also means that nearly all of the aspects that affect the quality of CPL s results are already determined in the input for the ADF run Five aspects are of particular importance here 1 The numerical integration accuracy the perturbation operators are large in the vicinity of the nuclei Therefore you have to make sure that the integration grid is fine enough in the atomic core regions We have found that INTEGRATION 6 in the ADF input yields high enough integration accuracy for the CPL code in most cases In case you can not afford such a high integration accuracy throughout we suggest the use of the INTEGRATION block key to assure that the integration parameter equals 6 at least in the atomic core regions INTEGRATION ACCINT 4 0 or higher ACCSPH 6 0 END This should yield a reasona
50. rivative VALDER XCDerivative XCDER KinCorrection KINCORR Specifying these arguments excludes the derivative of the nuclear core electronic valence electronic or exchange potentials arguments NUCDER COREDER VALDER or XCDER respectively from the effective potential to be used for the g tensor Specifying XCDER here is equivalent to the argument NONE of the keyword EPRXC Finally Skip KinCorr excludes the kinetic energy correction from the g tensor and is equivalent to the keyword KinCorr OFF SICOEP In case of SICOEP or any other model potential in ADF use SAVE TAPE10 in the adf calculation and use TAPE10 as input for the NMR EPR program On TAPE10 the SCF potential is written which is read in by the NMR EPR program The spin other orbit term in the g tensor The spin other orbit contribution to the g tensor is computed as suggested by Pickard and Mauri 15 with the modification for high spin case proposed by Patchkovskii and Schrekenbach 16 The theory and implementation of this part of the code in the EPR module of the ADF package is explained in detail in 17 The G SOO contribution is implemented for the all electron case only The implementation uses a 6 dimensional numerical integration and is therefore quite slow However it should still be possible to do 100 atoms or so with a TZP basis set on a single CPU PC Given the very small magnitude of the SOO corrections it is rather unlikely that
51. rtz Physical Review Letters 88 86403 2002 16 S Patchkovskii and G Schreckenbach in Calculation of NMR and EPR parameters M Kaupp M B hl V G Malkin Editors Wiley Weinheim 2004 33 17 S Patchkovskii R S Strong C J Pickard and S Un Gauge invariance of the spin other orbit contribution to the g tensors of electron paramagnetic resonance Journal of Chemical Physics 122 214101 2005 18 J S Seldenthuis H S J van der Zant M A Ratner and J M Thijssen Vibrational Excitations in Weakly Coupled Single Molecule Junctions A Computational Analysis ACS Nano 2 1445 2008 19 G M Sando and K G Spears Ab Initio Computation of the Duschinsky Mixing of Vibrations and Nonlinear Effects Journal of Physical Chemistry A 105 5326 2001 20 P T Ruhoff and M A Ratner Algorithms for computing Franck Condon overlap integrals International Journal of Quantum Chemistry 77 383 2000 21 J Poater E van Lenthe and E J Baerends Nuclear magnetic resonance chemical shifts with the statistical average of orbital dependent model potentials in Kohn Sham density functional theory Journal of Chemical Physics 118 8584 2003 22 M Krykunov T Ziegler and E van Lenthe Hybrid density functional calculations of nuclear magnetic shieldings using Slater type orbitals and the zeroth order regular approximation International Journal of Quantum Chemistry 109 1676 2009 23 M Krykunov T Ziegler and E van Lenthe
52. se the subkey ATOMS to specify the nuclei according to this input ordering in the ADF calculation Note that the number of nuclei has a significant consequence for the total CPU time ATOMS Atoms AtomsOptions 27 This subkey ATOMS specifies for which nuclei the NMR shielding is calculated Default all nuclei are calculated i e as for omitting this sub key Example ATOMS 2 1 The numbers refer to the input ordering in the ADF calculation Use the subkey NUC to specify the nuclei according to the internal NMR numbers of the atoms GHOSTS The subkey GHOSTS is a block type subkey The format is Ghosts xxl yyl zzl xx2 yy2 zz2 SubEnd With this key the user can specify ANY point s within the molecule at which the shielding is to be calculated whatever the physical meaning of this shielding is One can think of those points as neutrons within the molecule There is a publication by P Schleyer et al using a similar feature J Am Chem Soc 118 6317 1996 They call it NICS Nucleus Independent Chemical Shift Note that the NICS value is minus 1 times the isotropic part of the shielding tensor that is calculated at these points xxl yyl zzl real numbers that specify the Cartesian coordinates of ghost 1 etc The coordinates have to be specified in the same units as any other input ADF subkey Units That is you use Angstrom for the ghosts if you did so for the atomic coordinates or bohr otherwise The same
53. set of coordinates has to be specified as point charges with charge zero using the key EFIELD This is necessary in order to allow the appropriate distribution of integration points around the ghosts E g if you want to have two ghosts with the coordinates xx1 yy1 zz1 and xx2 yy2 zz2 then you must also have in the input the key EFIELD as follows EFTELD xxl yyl zzl 0 0 XX2 yy2 zz2 0 0 END the last number is the charge at these coordinates zero Eventually this step should be programmed internally but for now the procedure outlined above works No check is done to verify whether those point charges are taken care of or not but their omission leads to unpredictable results Only Cartesian coordinates are possible for ghosts even if the atoms were originally specified using internal coordinates This shouldn t be a problem though e g one could start an ADF run of the molecule of interest and get very soon the Cartesian coordinates of the atoms in the output This run would then be aborted and restarted with the ghosts specified as desired The ghosts are numbered in the output as NNUC 1 NNUC 2 where NNUC is the total number of nuclei in this molecule Default no ghosts 28 ANALYSIS Analysis AnalysisOptions The sub key Analysis controls the MO analysis After the word sub key Analysis you type an integer which then specifies that the first so many MOs are to be analyzed Default no Analysis
54. started runs the program will automatically continue at the latest possible point before the execution stopped and changing the input between restarts can cause inconsistencies that may lead to a crash Unless you are computing a very large molecule the most likely need for a restart will probably occur during a computation of the FC SD SCF cycle We have already mentioned that this is a very time consuming part of the computation and for this reason CPL can be restarted after each completed SCF cycle The convergence of the results should not be affected by a restart You can e g use this in order to complete a lengthy CPL computation in case you have tight time limits in your queuing system or after a power loss How to avoid the unnecessary computation of many SCF cycles As already mentioned once the first order MOs with respect to the perturbation by one of the nuclear spins have been determined the NSSCC between this and all other nuclei can be computed rather quickly For each nucleus that participates in at least one of the coupling constants to be determined the matrix elements of the FC SD and OP operators have to be evaluated once unless the computation of the respective terms is disabled You can use this information in order to minimize the number of nuclei for which an SCF cycle has to be performed This can lead to a great speedup of the computation The final result the NSSCC between A and B does not depend on which nucl
55. tain threshold The threshold refers to the reduced coupling constant K in SI units not default Additionally an analysis in terms of Boys localized MOs see User s Guide and SFOs At present either each key LMO SFO LMO2 SFO2 can be used individually or grouped as LMO SFO2 or SFO2 LMO If you need all analyses or different combinations it is recommended to restart the CPL calculation from TAPE13 and to specify 0 iterations in the SCF This way the only additional computational cost should be the analysis itself The equation and an application for the analyses due to the LMO and SFO keys is described in the papers Autschbach J Igna C D Ziegler T A theoretical investigation of the apparently irregular behavior of Pt Pt spin spin coupling constants J Am Chem Soc 2003 125 1028 1032 and Guennic B L Matsumoto K Autschbach J On the NMR properties of platinum thallium bonded complexes Analysis of relativistic density functional theory results Magn Res Chem 2004 42 S99 S116 The other analysis is based on the same equation as in Khandogin J Ziegler T A density functional study of nuclear magnetic resonance spin spin coupling constants in transition metal systems Spectrochim Acta 1999 A 55 607 624 In order for the LMO based analyses to work the MO LMO transformation matrix needs to be stored on TAPE21 In the ADF input you can achieve this with the option STORE to the LOCORB key i e LOCORB S
56. ubkey GHOSTS is a block type subkey The format is Ghosts xxl yyl zzl xx2 yy2 zz2 SubEnd With this key the user can specify ANY point s within the molecule at which the shielding is to be calculated whatever the physical meaning of this shielding is One can think of those points as neutrons within the molecule There is a publication by P Schleyer et al using a similar feature J Am Chem Soc 118 6317 1996 They call it NICS Nucleus Independent Chemical Shift Note that the NICS value is minus 1 times the isotropic part of the shielding tensor that is calculated at these points xxl yyl zzl real numbers that specify the Cartesian coordinates of ghost 1 etc The coordinates have to be specified in the same units as any other input ADF subkey Units That is you use Angstrom for the ghosts if you did so for the atomic coordinates or bohr otherwise The same set of coordinates has to be specified as point charges with charge zero using the key EFIELD This is necessary in order to allow the appropriate distribution of integration points around the ghosts E g if you want to have two ghosts with the coordinates xx1 yy1 zz1 and xx2 yy2 zz2 then you must also have in the input the key EFIELD as follows EPFIELD xxl yyl zzl 0 0 XX2 yy2 zz2 0 0 END the last number is the charge at these coordinates zero Eventually this step should be programmed internally but for now the procedure outlined abo
57. ve works No check is done to verify whether those point charges are taken care of or not but their omission leads to unpredictable results Only Cartesian coordinates are possible for ghosts even if the atoms were originally specified using internal coordinates This shouldn t be a problem though e g one could start an ADF run of the molecule of interest and get very soon the Cartesian coordinates of the atoms in the output This run would then be aborted and restarted with the ghosts specified as desired The ghosts are numbered in the output as NNUC 1 NNUC 2 where NNUC is the total number of nuclei in this molecule Default no ghosts CALCVIRTDIA The subkey CALCVIRTDIA invokes the calculation of the diamagnetic integrals for a specified number of virtual orbitals The argument is an integer number NVDIA NVDIA is the number of virtual orbitals for which those integrals are desired Example 19 CalcVirtDia 12 results in the calculation and output of these integrals for the first 12 lowest energy virtuals of each spin Default NVDIA 0 The program aborts if the specified number is bigger than the total number of virtuals that this molecule has for the given basis set NOPARA The subkey NOPARA suppresses the calculation of the paramagnetic shielding completely This can be useful if single atoms are considered Then the paramagnetic shielding must vanish by symmetry On the other hand the program would crash in the
58. wo Due to computational simplicity and efficiency CPL evaluates either the matrix elements for the FC operator or the combined ones for FC SD The final result therefore contains either FC only or FC SD plus the cross terms Only the latter in addition to the OP and OD contributions should be compared to experimental results We will implement the computation of the individual SD term in a future version of CPL in order to assist the analysis of the CPL results Likewise in a spin orbit based relativistic computation there exists a cross term between the spin dependent FC and SD terms and the OP term In the scalar or non relativistic limit this contribution is always zero With the PSO option present CPL computes the FC SD and OP terms including all cross contributions Even though the output suggests that the individual OP and FC SD terms are printed they contain additional cross terms if spin orbit coupling is large You can run CPL with the options NMRCOUPLING NOFC NOSD PSO END in order to evaluate the individual OP contribution s In a second run you can then compute just the FC SD contributions The differences between these two CPL runs and a third one with all three terms present yields the relativistic FC SD OP cross term Two bond and more bond couplings CPL does not discriminate between one bond and two bond couplings etc in any technical sense Even though we 1 4 have validated the code mostly for one bond
59. y the same as required the NMR program in the ADF program system On the other hand note that for the subkeys ATOMPERT and ATOMRESP the number of the atoms refer to the input ordering in the ADF calculation Available subkeys are NMRCOUPLING NUCLEI npert nrespl nresp2 ATOMPERT npertl npert2 npert3 ATOMRESP nrespl nresp2 nresp3 GAMMA nnuc gamma DSO PSO SD FC SCF ITERATIONS 25 NOCYCLE CONVERGE 1e 4 XALPHA CONTRIBUTIONS 1E19 LMO SFO LMO2 SFO2 END NUCLEI npert nrespl nresp2 Use nucleus no npert as the perturbing nucleus and nuclei nresp1 nresp2 etc as responding nuclei You can supply more than one NUCLEI keys in which case CPL evaluates the first order MOs for each perturbing nucleus that is specified and computes the NSSCCs between all specified responding nuclei For each NUCLEI line in the input CPL has to perform an SCF cycle Note for the numbers of the atoms the internal CPL numbering should be used ATOMPERT npertl npert2 npert3 ATOMRESP nrespl nresp2 nresp3 ATOMPERT use nucleus no npert1 npert2 etc as the perturbing nuclei ATOMRESP use nucleus no nresp1 nresp2 etc as the responding nuclei You can supply more than one ATOMPERT and or ATOMRESP key CPL computes the NSSCCs for all pairs of combinations of perturbing atoms and responding atoms For each perturbing atom CPL has to perform an SCF cycle which is the ex

SCM: ADF Property Programs

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