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1. D D 01 28 2009 16 22 46 __A 02 07 2009 09 02 06 __A 02 07 2009 09 03 20 Z AOMix manual pdf __A 01 28 2009 16 24 40 E aomix p 1 exe 372kB A 01 18 2009 10 24 12 F AOMix p11 exe 384kB __A 02 07 2009 09 05 56 r1 aomix p9 exe 380kB _ A 01 21 2009 13 29 54 E AOMix S exe 584kB A 02 07 2009 09 05 20 1 AOMix exe 424kB _ A 02 07 2009 09 10 48 AOMIX642 EXE 91kB _ A 02 07 2009 09 08 20 5 aomixpar txt 2kB __A 01 29 2009 16 40 56 fe NH3BH3 eda out 252kB _ A 02 17 2007 22 21 30 Program Files 257 682 bytes in 1 files G AOMix 2009 pack gt AOMix exe NH3BH3 eda out g we LA Prop Gl com o view dca Z copy Move a s Drive G 476 937 MB total 153 841 MB free mmm 1 s Drive G 476 937 MB total 1 AOMix reads the orbital information directly from output files of common quantum chemistry software packages and produces ASCII text files which contains molecular orbital energies symmetries percentages of contributions from fragments of the molecule atoms groups of atoms groups of orbitals etc overlap populations HF and DFT wave functions DOS plot data etc The default scheme for the population analysis of HF DFT calculations is MPA if the overlap matrix is included in an output file You can select SCPA as an alternative method by adding the SCPA keyword to aomixpar txt Keyword AOMix Keyword description execution SCPA standard Specifies SCPA as a method f
2. If you run AOMix and experience a problem please check sample input and output files http www sg chem net download to make sure that you run your calculations correctly and also read the FAQ page http www sg chem net NP faq php When new versions of the quantum chemical software packages Gaussian Jaguar Q Chem etc are released there can be changes in output file formatting and or modifications in keyword functionalities These changes can affect AOMix execution In this situation please 84 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 inspect your output files from the new version of the software and if possible compare them with output files from the old version of the software If after reading the AOMix manual and the FAQ webpage you cannot resolve your problem contact the AOMix developer with the detailed description of your problem Abbreviations AF Anti ferromagnetic AO Atomic orbital BS Broken symmetry BSSE Basis set superposition error CDA Charge decomposition analysis CMO Canonical molecular orbital COOP Crystal orbital overlap population identical to OPDOS CS Closed shell CT Charge transfer DFT Density functional theory DOS Density of states ECP Effective core potential EDA Energy decomposition analysis ESP Electrostatic potential FMO Frontier molecular orbital FO Fragment molecular orbital GP Gross population HF Hartree Fock HOFO Highest occupied fragment
3. After setting up the fragment list file start the AOMix program by execute the AOMix exe command with names of the output file and fragment list file as shown in the example below AOMix exe BH3CO log fragments txt For correct execution of the program ensure that your output files contain all necessary data To make sure that this is the case use the following settings Use only SINGLE POINT CALCULATION OUTPUT FILES for AOMix processing Don t use geometry optimization job files ADF calculations with no core use the symmetry nosym keyword ADF output file functions should contain energies and coefficients of all molecular orbitals For this the following keywords need to be included in an ADF input file Eprint sfo eig ovl End The TITLE field must be present in output files because it is used as an identifier for the results section 48 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 DFTB calculations DFTB Files detailed out eigenvec out oversqr dat are required in addition to a standard output file which includes the DFTB program header GAMESS US calculations use RUNTYP ENERGY and NPRINT 3 in the CONTRL input section Gaussian e forabinitio DFT calculations e for ZINDO calculations use a single point job with the keywords P POP FULL SCF TIGHT and IOp 3 33 1 use a single point job with P IOp 5 33 2 HyperChem calculatio
4. FORMAT P 0 1 2 FO option The number defines the cutoff limit for the LONG FORM of AOMix FO output files So if some LCFO MO coefficients went missing in the LONG FORM of your AOMix FO output this is not a software bug 64 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 After the LONG FORM AOMix prints the compositions of all occupied and unoccupied molecular orbitals in terms of occupied and unoccupied fragment orbitals MO compositions in terms of fragment molecular orbitals charge transfer CT and electronic polarization PL terms FO contributions to all occupied molecular orbitals Occupied FO 390 4 680 5 Unoccupied FO 21 1 8 0 Sum 411 5 688 5 FO contributions to all unoccupied molecular orbitals Occupied FO 9 6 19 5 Unoccupied FO 1678 9 2292 0 Sum 1688 5 2311 5 PL 1 PL 2 1 6 CT 2 51 CT 1 gt 2 11 5 net charge transfer 0 23 e If molecular symmetry is present in a calculation AOMix prints a summary for each set of molecular orbitals of given irreducible representation AOMix also prints contributions of each fragment molecular orbital to all occupied molecular orbitals OMOs and unoccupied molecular orbitals UMOs For example FR ORB OCCUP SUM over OMOs SUM over UMOs 2 8 1 99 908 0 091 2 9 1 91 108 8 902 2 10 1 100 000 0 000 2 11 1 100 000 0 000 2 12 0 5 779 94 222 2 13 0 5 787 94 213 2 14 0 0 171 99 828 Here the
5. S Px Py Pz Q QO000000000 WWWWNHNNNRPRPR PR 0 0 0 20 0 0 0 0 0 0 20 36236 13668 07705 00000 36094 13627 07715 00000 36904 00029 15833 00000 0 08866 15871 00000 20123 09761 17237 00000 48305 01904 00765 00000 26975 39441 06608 10536 00000 43173 04994 07771 00000 04042 22765 00073 00000 0 0 0 O 0 0 O 0 0 0 0 0 17211 18388 24226 00000 17441 18252 23894 00000 35945 00235 16561 00000 Atomic orbitals 1 4 are on atom 1 carbon atomic orbitals 5 8 are on 30592 01395 21133 00000 30181 00357 20795 00000 00208 36219 00344 00000 01444 06777 05029 00408 12659 11025 05886 07823 17658 00491 00158 00552 00852 01688 06322 00288 02118 27837 numbers 08809 29675 13282 00000 09679 29442 13844 00000 04514 00604 31819 00000 atom 2 carbon and atomic orbitals 9 12 are on atom 3 carbon Note that unlike the majority of the other programs HyperChem and MOPAC DO NOT PRINT ATOMIC ORBITAL NUMBERS in the LCAO MO output only ATOM NUMBERS Thus if you want to analyze MOs in terms of contributions from specific atomic orbitals you have to find their lis numbers in the LCAO MO output by counting orbitals manually 45 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Unless a user want to treat all atom
6. 0 025 respectively Note 1 Automatic breakdown into atomic spdf contributions is limited to the cases with 5d 7f basis sets basis sets with 5 d functions and 7 f functions If the basis set has 6 Cartesian d functions and 10 Cartesian f functions AOMix will skip the spdf analysis Note 2 Overlap populations and DOS plot data are generated only if NF x 13 this is done to limit the size of AOMix output files 50 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Note 3 For Gaussian calculations AOMix will generate two scripts AOMix cube win bat for MS Windows and AOMix cube bat for Linux UNIX for cube file generation These AOMix scripts will be helpful to generate cube files for visualization of molecular orbitals spin density and the electrostatic potential The example of the UNIX script AOMix cube bat is shown below touch temp fchk rm temp fchk formchk temp chk cubegen 0 potential temp fchk C9H17CuNA4S2 ESP cub 0 h cubegen 0 spin temp fchk C9H17CuN4S2 spin cub 0 h cubegen 0 MO 78 temp fchk C9H17CuN4S2 A 78 HOMO 2 cub 0 h cubegen 0 MO 79 temp fchk C9H17CuN4S2 A 79 HOMO 1 cub 0 h cubegen 0 MO 80 temp fchk C9H17CuN4S2 A 80 HOMO 0 cub 0 h cubegen 0 MO 81 temp fchk C9H17CuN4S2 A 81 LUMO 0 cub 0 h cubegen 0 MO 82 temp fchk C9H17CuN4S2 A 82 LUMO 1 cub 0 h cubegen 0 MO 83 temp fchk C9H17CuN4S2 A 83 LUMO 2 cub 0 h cubegen 0 MO 374 temp fchk C9H17CuN4S2 B 77 HOMO 2 cub 0 h cubegen 0 MO
7. OP 0 36 0 18 1 1 L 5 S 0 43 0 24 OP 0 02 0 00 In the above example the HOMO of the complex orbital 11 with the eigenvalue of 12 718 eV is a mixture of 94 9 HOMO of Fragment 1 and 3 6 LUMO 1 and 1 4 HOMO 1 of Fragment 2 The overlap integral between the HOMO of Fragment 1 and LUMO 1 of Fragment 2 is 0 24 while the overlap population for this FO pair in the HOMO is 0 05 indicating bonding interaction between HOFO 1 and LUFO 1 2 The overlap integral between the HOMO of Fragment 1 and HOMO 2 of Fragment 2 is 0 06 while the overlap population for this FO pair is 0 02 Examples of orbital interaction diagrams from AOMix are presented in this manual on the www sg chem net website and in References If time will permit the author will add additional educational examples for the analysis of chemical bonding in different systems in the near future 77 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 2 2 1 1 0 0 A 3i S 2 1 Lumo 2 O 82 4s C 18 4p Cu 5 3 D c oO a 4 4 5 Oo 5 Lumo HoMo 9 49 3d C NN oll 7 HOMO 1 Q 6 HOMO Z 7 7 8 ET Y 8 L Z z CuL CuL SC F SC F B Spin orbital interaction diagram illustrating the coupling of the metal and thiolate fragments in the CuL SC F complex the AOMix FO calculation at the BSLYP TZVP level MOs with a and a symmetries are shown in red and blue respectively molecular orbitals of the ML and
8. 3 527 0 000 6 F 0 904 0 000 7 EF 0 904 0 000 8 F 0 904 0 000 Condensed Fukui Functions in Molecules 23 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Fukui functions are the common descriptors of site reactivity They are defined as the derivative of the electron density with respect to the total number of electrons N in the system at the constant external potential v r apr f at L Since chemists are mostly concerned with properties associated with atoms and or molecular fragments functional groups etc rather than properties associated with points in space condensed Fukui functions were define In a finite difference approximation they can be expressed by the following equations fi p QN D o CN condensed Fukui function for a nucleophilic attack f P N p N D condensed Fukui function for an electrophilic attack fi Lo QN D o QCN D 2 condensed Fukui function for a radical attack where k are sites atoms molecular fragments for nucleophilic electrophilic and radical agents and p are their gross electron populations A high value of f implies a high reactivity of that site k Besides the type of condensed Fukui function whose value is highest at a particular site predicts the type of attack that predominates at that site It is possible to evaluate the condensed Fukui functions using AOMix from single point calculations directly without res
9. Fr 1951 C79 2 Chatt J Duncanson L A J Chem Soc 1953 2929 3 Dapprich S Frenking G J Phys Chem 1995 99 9352 9362 s Frenking G Frohlich N Chem Rev 2000 100 717 774 Gorelsky S I Ghosh S Solomon E Journal of the American Chemical Society 006 128 278 290 16 Gorelsky S Solomon E Theoretical Chemistry Accounts 2008 129 57 65 7 Mayer Chem Phys Lett 2004 393 209 212 Reed A E Weinhold F J Chem Phys 1983 78 4066 4073 98 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 19 Reed A E Weinstock R B Weinhold F J Chem Phys 1985 83 735 746 20 Reed A E Curtiss L A Weinhold F Chem Rev 1988 88 899 926 21 Haslingerova Czech J Phys 1977 B27 1389 1393 22 Hoffmann R Solids and Surfaces A Chemist s View of Bonding in Extended Structures VCH Publishers New York 1988 23 Glassey W V Hoffmann R J Chem Phys 2000 113 1698 1704 24 Segal M D Phys Rev 1996 54 16317 16320 25 Mayer I Chem Phys Lett 1983 97 270 274 26 Borisova N P Semenov S G Vestn Leningrad Univ 1976 98 27 Natiello M A Medrano J A Chem Phys Lett 1984 105 180 28 Mayer Theor Chim Acta 1985 67 315 322 29 Mayer Int J Quantum Chem 1986 29 73 30 Mayer Int J Quantum Chem 1986 29 477 31 Mayer I Chem Phys Lett 1984 110 440 32 S
10. J Am Chem Soc 2007 129 14570 14571 49 Giambiagi M Giambiagi M S d Silva C D d S Figueiredo A P d Phys Chem Chem Phys 2000 2 3381 3392 50 Li X Kuznetsov A E Zhang H F Boldyrev A Wang L S Science 2001 291 859 861 51 Fukui K Yonezawa T Shingu H J Chem Phys 1952 20 722 725 Fukui K Yonezawa T Nagata C Shingu H J Chem Phys 1954 22 1433 1442 53 Fukui K Theory of Orientation and Stereoselection Springer Verlag Berlin 1975 Fukui K Science 1982 218 747 754 55 Chemical Reactivity and Reaction Paths Klopman G Ed John Wiley amp Sons New York 1974 56 Makedonas C Mitsopoulou C A Eur J Inorg Chem 2006 590 598 57 Gorelsky S I MO Description of Transition Metal Complexes by DFT and INDO S In Comprehensive Coordination Chemistry Il McCleverty J A Meyer T J Eds Elsevier Amsterdam 2004 Vol 2 pp 651 660 58 Zhou B Kral mer T Thompson A L McGrady J E Goicoechea J M Inorg Chem 2011 50 8028 8037 99 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 59 Hughbanks T Hoffmann R J Am Chem Soc 1983 105 3528 3735 60 Ghosh S Gorelsky S I Chen P Cabrito I Moura J J G Moura l Solomon E J Am Chem Soc 2003 125 15708 15709 61 Lever A B P Gorelsky S Struct Bonding Berlin 2004 107 77 114 62 del Rio D Galindo
11. LUMO LUMO 1 etc A closed shell reference state is used here for simplicity OOPBOs can also be used to evaluate effects of electron population of unoccupied molecular orbitals Automatic calculation of OOP bond orders for frontier orbitals has been implemented in the AOMix software Keyword and its possible and AOMix Keyword description default values execution OOPS ER 10 20 40 standard OOPBO 10 turns on calculation of OOP bond orders for 10 HOMOs and 10 LUMOs OOPBO 20 turns on calculation of OOP bond orders for 20 HOMOs and 20 LUMOs OOPBO 40 turns on calculation of OOP bond orders for 40 HOMOs and 40 LUMOs 19 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Multi center bond orders There are systems in which three center two electron interactions contribute to bonding These interactions can be evaluated by using 3 center bond orders The 3 center bond orders Bagcfor closed shell species are 94945 Buc gt gt gt _ PS PS CPS ae A be B ceC For open shell species Biga Bizot B c where Boge gt gt gt P S 4 P S P S and ae A be B ceC Bh Y S S P S PS acA be B ceC These indices can be used to identify the 3 center orbital interactions in molecules The Basc indices of 3 center bonds are positive with the maximum theoretically possible value of 8 MM 27 0 296 AOMix will print a and B
12. Label other command to show a desired attribute such as the HOMO composition Figure 2 or atomic spin densities as atomic labels In addition you can use the Render By Attribute tool to color atoms or change their sizes based on the attribute Importing 2 center attribute data PB READER In UCSF Chimera 2 center parameters between pairs of atoms are referred to as pseudobonds PB Pseudobonds are lines drawn between atoms to signify connections other than standard bonds The PseudoBond Reader Tools Depiction PseudoBond Reader allows Chimera users to create pseudobonds connecting arbitrary pairs of atoms Apply the PseudoBond Reader to visualize Mayer bond orders from AOMix atom chimera BO txt Bond order depiction e g line style and color can be controlled with PseudoBond Panel under the Tools General controls A user can also apply the PseudoBond Reader to visualize internuclear distances from AOMix atom chimera BD txt See the FAQ page http www sg chem net NP fag php for more details Keyword AOMix Keyword description execution PSEUDOBONDS X X color standard Assigns the print format threshold value and color to bond orders in UCSF Chimera PseudoBond attribute files By default bond orders are depicted in blue color and only those that are higher than 0 1 the default threshold value are written to AOMix atom chimera BO txt You can change the default values by using the PSEUDOBONDS
13. energy surfaces of the Cu cluster the Nyis Cu Scys 2Cu Nyis cluster and B Mayer bond order Bag between the two Cu atoms of Cu as a function of the Cu Cu distance Most single chemical bonds can be considered as being formed by a pair of electrons occupying a two center molecular orbital Multiple bonds double or triple are formed by two or three pairs of electrons occupying two or three molecular orbitals respectively Orbital occupancy perturbed Mayer bond orders To evaluate contributions of individual occupied MOs to bonding between different atoms orbital occupancy perturbed OOP Mayer bond orders are introduced B as Y Y OS OS DS S ae A be B 18 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 New total and spin density matrix elements P and P respectively are calculated for the system with the original set of MOs but one electron is taken out from a given molecular orbital Scheme 2 and then these orbital occupancy perturbed OOP density matrices are used to calculate OOP bond orders B 5 d H Tr H H H H H H H H H H H T H H H Reference X HOMO X HOMO 1 X HOMO 2 X LUMO X LUMO 1 Electronic State Scheme 2 Reference electronic state and corresponding occupancy perturbed states in which an electron is removed from one occupied molecular orbital HOMO HOMO 1 HOMO 2 etc or added to an unoccupied molecular orbital
14. 1 column is the fragment number the 2 column is the fragment molecular orbital number the 3 column indicates the initial FO occupancy 1 for occupied FOs and 0 for unoccupied FOs and the last two columns show the contributions to all occupied molecular orbitals and unoccupied molecular orbitals respectively FO contributions 96 to all occupied MOs printed in the 4 column SUM over OMOs are equal to FO occupations in the complex FO occupation in the complex FO contribution to all OMOs 100 65 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 So in the above example the a spin LUMO orbital 12 of fragment 2 contributed 5 78 to the the a spin occupied molecular orbitals of the complex or putting it another way the a spin LUMO of fragment 2 has the 0 058 occupancy in the complex the a spin HOMO 2 orbital 9 of fragment 2 contributed 8 90 to the the a spin unoccupied molecular orbitals of the complex and has the 0 911 occupancy in the complex This information and the MO FO matrix are very helpful for analyzing polarization and charge transfer interactions between fragments Blas GWE Unoccupied MOs Unoccupied MOs A A B A A B Occupied MOs ET MOs l EB dur Unoccupied MOs Unoccupied MOs A B A B B Occupied MOs Lee Scheme 5 Compositions of occupied and unoccupied molecular orbitals of A B in terms of Occupied MOs occupied and unoccupied molecular orbitals of f
15. 25148 0 24811 2 21397 C 0 13818 0 16800 0 01251 o 0 38420 0 20138 0 91730 The results of the calculation are written to the output file BH3CO log 1 fragment BHs the Gaussian input file P HF 6 31G d NoSymm Pop Full IOp 3 33 1 SCF Tight Fragment 1 BH3 01 B 0 90571 0 71072 1 31687 H 0 83756 1 90583 1 19882 H 2 00975 0 24811 1 19883 H 0 25148 0 24811 2 21397 The results of the calculation are written to the output file fragm1 log pha fragment CO the Gaussian input file P HF 6 31G d NoSymm Pop Full I0p 3 33 1 SCF Tight Fragment 2 CO 0 0 13818 0 16800 0 01251 0 38420 0 20138 0 91730 onar The results of the calculation are written to the output file fragm2 log Since the atomic coordinates in the above calculations do not correspond to the standard input orientation in Gaussian the NoSymm keyword in the Gaussian input files is needed Step 3 If you are using non Latin MS Windows version execute the US command in the Windows command prompt 60 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Step 4 Start the AOMix program with the FO execution option make sure that the output files for the molecular fragments fragm1 log and fragm2 log are present in the AOMix directory Steps 1 and 2 AOMix exe BH3CO log FO The above line corresponds to the instruction when a user starts AOMix exe in the command prompt If you prefer to start AOMix exe from a desktop the
16. 7 79 e 8 92 occupied unoccupied orbital gap 3 41eV 129 HOMO 11 2 b1 70 30 128 HOMO 1 11 31 e 72 28 127 HOMO 2 11 31 e 72 28 The one electron excitations have the following MLCT characters HOMO gt LUMO 0 1 70 8 62 HOMO gt LUMO 2 70 0 70 HOMO 1 2 LUMO 0 1 72 8 64 HOMO 1 2 LUMO 2 72 0 72 If the excited state is formed by more than one one electron excitation then the metal CT character of this excited state is expressed as a sum of CT characters of each participating excitation i gt j CTM Y Cf 96 M M 3 4 3 where C ij are the appropriate coefficients of the th eigenvector of the Cl matrix 34 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 So one can very effectively use the MO compositions in terms of fragment orbital contributions to probe the nature of electronic transitions 35 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Charge decomposition analysis CDA 1314 is one of the two methods that are The CDA method of Frenking and co workers currently implemented in the AOMix program and can be used to evaluate fragment to fragment donation and back donation in molecular systems In CDA it is also possible to calculate so called repulsion and residue terms rj and Aj respectively Scheme 3 Electron Donation and Back donation and Repulsion and Residue Terms Fragment 2 unoccu
17. A Resa l Carmona E Angew Chem Intl Ed 2005 44 1244 1247 63 Platas Iglesias C Esteban Gomez D Enriquez Perez T Avecilla F de Blas A Rodriguez Blas T norg Chem 2005 44 2224 2233 64 Gorelsky S l Lever A B P Can J Anal Sci Spectr 2003 48 93 105 65 Kitaura K Morokuma K Int J Quantum Chem 1976 10 325 340 66 Ziegler T Rauk A Theoret Chim Acta 1977 46 1 10 67 Grimme S J Comput Chem 2006 27 1787 1799 68 Pettersen E F Goddard T D Huang C C Couch G S Greenblatt D M Meng E C Ferrin T E J Comput Chem 2004 25 1605 1612 69 Rusanova J Rusanov E Gorelsky S l Christendat D Popescu R Farah A A Beaulac R Reber C Lever A B P Inorg Chem 2006 45 6246 6262 70 llango S Vidjayacoumar B Gambarotta S Gorelsky S Inorg Chem 2008 47 3265 3273 71 Gorelsky S Lapointe D Fagnou K J Am Chem Soc 2008 130 10848 10849 72 Sarangi R Gorelsky S Basumallick L Hwang H J Pratt R C Stack T D P Lu Y Hodgson K O Hedman B Solomon E J Am Chem Soc 2008 130 3866 3877 73 Albright T A Burdett J K Whangbo M H Orbital Interactions in Chemistry John Willey amp Sons New York 1985 74 Senthilkumar K Grozema F C Guerra C F Bickelhaupt F M Siebbeles L D A J Am Chem Soc 2003 125 13658 13659 75 Senthilkumar
18. AOMix manual www sg chem net Updated on July 23 2015 Electron donation between fragments lt 0 00le for any omitted MO ALPHA ORBITALS 1 gt 2 2 gt 1 HOMO 9 2 0 000 0 001 HOMO 7 4 0 001 0 013 HOMO 6 5 0 003 0 041 HOMO 5 6 0 020 0 038 HOMO 2 9 0 027 0 171 HOMO 1 4 10 0 044 0 001 HOMO O 4 11 0 044 0 001 TotalALPHA BETA 0 181 0 471 Repulsion and residue Delta terms between fragments ALPHA ORBITALS 1 lt gt 2 Delta HOMO 9 4 2 0 000 0 000 HOMO 7 4 4 0 003 0 000 HOMO 6 4 5 0 116 0 001 HOMO 5 4 6 0 107 0 000 HOMO 2 9 0 370 0 001 HOMO 1 4 10 0 019 0 HOMO O 4 11 0 019 0 TotalALPHA BETA 0 335 0 002 FRAGMENT POPULATIONS calculated in the AO and FO basis sets the final test ALPHA ORBITALS BETA ORBITALS TOTAL ALPHA BETA SPIN Fragm AO FO AO FO AQ gt FO AO gt FO 1 4 115 4 115 4 115 4 115 8 230 8 230 0 000 0 000 25 6 885 6 885 6 885 6 885 13 770 13 770 0 000 0 000 Initially one would expect that the difference between the amount of donation and back donation between fragments should be equal to the net charge transfer between fragments However in the CDA this is not the case For the above example the BH3CO molecule CT 2 1 CT 12 0 471 0 181 0 29 e which is only fairly close to the net charge transfer 0 23 e For many complexes the situation is much worse the
19. Duncanson model For ab initio and DFT wave functions AOMix uses the CDA method of Frenking and co workers and the extended CDA ECDA 5 which includes evaluation of charge transfer and polarization contributions Methods to Derive Atomic Orbital Contributions to Molecular Orbitals Electronic structure calculations yield the electronic energy and the wave function of a molecular system in a particular electronic state The wave function itself is usually too complicated to provide a simple physical picture of the system One needs to define simplified notions and characteristics of the wave function in order to gain insight into the electronic structure of molecules and to predict chemical reactivity and other properties Within the LCAO MO formalism the wave function for the i eigenstate of the molecule ion can be written as NBF y y o 3 1 1 asl for an atom localized basis set ya If the MOs are obtained with semiempirical zero differential overlap ZDO methods then the overlap between any two different basis functions Sap lt Xa Xb gt 3 1 2 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 is neglected and the contribution of the atomic orbital AO v to the i MO is equal to the square of the corresponding LCAO coefficient Ca and the electron population of atom A equals to 2n e 8 1 3 acA where the index a runs over all AOs localized on atom A n are MO occupation numbe
20. Fe 0 000000 0 000000 0 018179 C 1 821462 0 000000 0 090291 Cc 1 821462 0 000000 0 090291 C 0 000000 1 503897 0 976361 C 0 000000 1 503897 0 976361 0 0 000000 2 460510 1 620978 O 0 000000 2 460510 1 620978 0 2 968878 0 000000 0 160975 0 2 968878 0 000000 0 160975 Fe 0 LANL2DZ keke oc O 6 31G ckok ck Fe 0 LANL2DZ the Gaussian input file for Fragment 2 P B3LYP 6 31G d 5D SCF Tight Pop Full IOp 3 33 1 NOSYMM Fragment 2 C2H4 01 Cc 0 000000 0 704147 2 039071 Cc 0 000000 0 704147 2 039071 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 Note that the 5D keyword is in the above Gaussian input files necessary to avoid the mismatch in numbers of basis functions due to different 5D 6D settings in different basis sets Construction of orbital interaction diagrams Orbital interaction diagrams are constructed easily from AOMix FO output files For molecular systems with no symmetry AOMix FO will create files AOMix MO FO alpha dat and AOMix MO FO beta dat which contain orbital interaction plot data for a and B spin orbitals respectively For molecular systems with symmetry AOMix FO will create files AOMix MO FO alpha I dat and AOMix MO FO beta l dat for orbitals of each irreducible representation For example for H3B CO complex which has Cs symmetry AOMix FO will create files 74 Dr S I Gorelsky AOMix manua
21. Gorelsky AOMix manual www sg chem net Updated on July 23 2015 While the SOFTWARE has been tested for accuracy and proper functioning the author disclaims any responsibility for the accuracy or correctness of the SOFTWARE or for its use or application by Licensee The author is licensing the SOFTWARE to Licensee on an AS IS basis and makes no representation or warranty either expressed or implied of any kind and hereby disclaims any warranties representations or guarantees of any kind as to the SOFTWARE including but not limited to any warranties of merchantability adequacy or suitability of the SOFTWARE for any particular purpose or to produce any particular result and any warranties of freedom of infringement of any patents copyrights trade secrets or other rights of third parties The author shall not have any liability to Licensee or any other person arising out of the use of the SOFTWARE by Licensee for any reason including but not limited to inadequacy or unsuitability of the SOFTWARE for any particular purpose or to produce any particular result or the infringement of any patents copyrights trade secrets or other rights of third parties for any latent defects therein or the failure of the authors to provide Licensee with any modifications or changes in the SOFTWARE No liability is accepted for any limitations in the mathematical methods and algorithms used within the program The information in this document is provid
22. K Grozema F C Guerra C F Bickelhaupt F M Lewis F D Berlin Y A Ratner M A Siebbeles L D A J Am Chem Soc 2005 127 14894 14903 76 Senthilkumar K Grozema F C Bickelhaupt F M Siebbeles L D A J Chem Phys 2003 119 9809 9817 77 Schafer A Huber C Ahlrichs R J Chem Phys 1994 100 5829 5835 78 Godbout N Salahub D R Andzelm J Wimmer E Can J Chem 1992 70 560 571 79 Boys S F Bernardi F Mol Phys 1970 19 553 80 Noodleman L J Chem Phys 1981 74 5737 81 Noodleman L Lovell T Han W G Liu T Torres R A Himo F In Comprehensive Coordination Chemistry Il McCleverty J A Meyer T J Eds Elsevier Amsterdam 2004 Vol 2 pp 491 510 82 Noodleman L Lovell T Han W G Li J Himo F Chem Rev 2004 104 459 508 83 Horvath S Gorelsky S I Gambarotta S Korobkov Angew Chem Int Ed 2008 47 9937 9940 84 Jones C J O Hare D Chem Commun 2003 2208 100
23. S are not equal to zero SCPA and MMPA are not equivalent and provide different numerical answers for MO compositions Nonetheless MO compositions computed by all three methods are usually consistent and do not differ too much This is because the overlap populations between fragments are much lower than the net populations Scheme 1 at least for a majority of occupied molecular orbitals Appreciable differences between MPA MMPA and SCPA results may occur when molecular orbitals are either strongly bonding or antibonding MOs with large overlap populations 10 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 LIGAND X Net Population Net Population Metal X Oveslap Population z METAL Net Population Scheme 1 Electron population analysis for transition metal complexes The gross electron population of the molecular fragment is equal to a sum of the net population and the appropriate overlap populations L wdin Population Analysis L wdin population analysis LPA in based on the S P S formula with a parameter a being set to 1 2 In the L wdin approach nonorthogonal AOs are transformed to an orthogonal set The transformed orbitals a are given by Ls FE Y In LPA the a 5 and gross electron populations associated with fragment A are GP gt S p S acA aa and aa GP 5 S p s acA GP GP GP The spin density is gi
24. difference between the calculated amounts of donation and back donation is very different from the net charge donation between fragments This is because the terms donation and back donation in the CDA method do not include only charge transfer interactions but rather an overall reorganization of electronic density including both charge transfer between fragments and electronic polarization of fragments 62 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 MO compositions in terms of fragment orbital contributions LCFO MO coefficients are written to AOMix MO FO alpha txt and AOMix MO FO beta txt for a and B spin orbitals respectively These files will also include the FO overlap matrix if a user has instructed AOMix CDA to print this matrix Here is part of the LONG FORM of AOMix MO FO alpha txt output for the H3B CO complex BH is fragment 1 and CO is fragment 2 It contains the MO compositions in terms of percentage contributions of fragment orbitals MO 1 2 3 4 5 6 7 8 HOMO 7 HOMO 6 HOMO 5 HOMO 4 HOMO 3 HOMO 2 HOMO 1 HOMO E eV 44 37 26 31 21 04 18 59 18 59 14 11 11 07 11 07 Total 0 34 39 18 36 03 1 30 1 30 43 41 95 45 95 45 SumOFO 0 19 35 82 36 03 1 24 1 24 26 42 95 35 95 35 SumUFO 0 15 3 36 0 00 0 06 0 06 16 99 0 10 0 10 FOF OC 9 a 11 0 19 35 82 36 03 0 00 0 00 26 42 0 00 0 00 21 0 00 0 00 0 00 0 03 1 22 0 00 95 13 0 23 3 1 0 00 0 00 0 00 1 22 0 03 0 00 0 234 9
25. is 0 200 and to mix 20 0 0 200 of B spin orbital 21 of fragment 2 with B spin orbital 16 of fragment 1 the overlap between these two fragment orbitals is 0 400 40 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Working with AOMix Execution environment of the AOMix software is controlled by the parameter file aomixpar txt You can modify the execution parameters to tune the program to your particular tasks See the keyword descriptions in this manual To start the AOMix program using the default fragment setting all atoms orbitals are individual fragments 1 place the output file s which you want to process in the same directory with the AOMix executable files and 2 execute the AOMix exe command with a name of the output file to be processed in the command prompt For example AOMix exe BH3CO 1log Here the output file to be processed is BH3CO log Do not use empty spaces in file names such as BH3CO output log because the AOMix software cannot process such names If you are using non Latin MS Windows version such as Chinese Japanese or Korean execute the US command in the Windows command prompt before you start AOMix exe 41 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Recommendation you can use file manager programs such as FAR manager http www farmanager com download php or WinNC httpz www winnc com to select and enter output file n
26. it is available and can be applied by using the MMPA keyword in the AOMix parameter file aomixpar txt Keyword AOMix Keyword description execution MMPA standard Specifies MMPA as an additional method to MPA for population analysis for ab initio DFT calculations Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 SCPA An alternative way to partition electron density in molecules was proposed by Ros and Schuit SCPA In this method the overlap populations are not considered and the contribution of yato the i MO is assumed to be equal to 2 C i 2 k where k runs over all AOs 3 1 11 This method does not suffer from the same problems as MPA and MMPA because Eqn 3 1 11 guarantees that orbital populations derived will be only positive and will not be in excess of two However SCPA still suffers from a problem of basis set dependence It has been incorrectly stated in some papers that the MMPA equation Eqn 3 1 10 can be after some rearrangement transformed to the SCPA equation Eqn 3 1 11 In a general case Equation 3 1 10 cannot be reduced to Equation 3 1 11 except in one special case SCPA is only equivalent to MMPA when the molecular orbitals of the system are represented as linear combinations of just two atomic orbitals with non zero overlap V CX t Cu 3 1 12 In a general case of many electron many orbital systems where the majority of overlap integrals
27. k a where NF is a number of fragments In AOMix FO calculations a possible number of fragments NF varies from 1 to 4000 For calculations with NF 1 AOMix calculates the MO compositions of a molecule in terms of the MOs of the same molecule in some other electronic state defined in a fragm1 log calculation Thus this option can be used to find the MO compositions of cation A in terms of the MOs of a neutral molecule A 55 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Lt a MO Relaxation EMO Resin gt Relaxation Koopmans State Final State Koopmans State Final State Veuve 2 a or the Koopmans state Scheme 4 Analysis of the electronic relaxation process after the ionization from the B spin HOMO dashed red area using the contributions from the occupied MOs OMOs shown in blue the RAMO shown in red and the other unoccupied MOs UMO shown in pink of the Koopmans state as the basis The population of the unoccupied RAMO when going from the Koopmans state to the final state is presented by a red dashed arrow adopted from Ref 5 Alternatively you can analyze MO compositions of molecule A in an excited state in terms of the MOs of a molecule A in the ground state or to compare MO descriptions obtained using different levels of theory such as HF and DFT For details please see Ref For systems with the number of fragments greater than 1 AOMix will use C
28. manual www sg chem net Updated on July 23 2015 EXAMPLE 1 Building the wave function of the BH3CO molecule from the wave functions of BH and CO 1 fragment BHs the Gaussian 09 input file P HF 6 31G d NoSymm Pop Full 1IOp 3 33 1 SCF Tight Fragment 1 BH3 01 B 0 90571 0 71072 1 31687 H 0 83756 1 90583 1 19882 H 2 00975 0 24811 1 19883 H 0 25148 0 24811 2 21397 on fragment CO the Gaussian 09 input file P HF 6 31G d NoSymm Pop Full I0p 3 33 1 SCF Tight Fragment 2 CO 1 0 13818 0 16800 0 01251 0 38420 0 20138 0 91730 ooo 3 Place the fragment output files in the AOMix directory If you are using non Latin MS Windows version execute the US command in the Windows command prompt 4 Start the AOMix exe program with the FO keyword and run it with fragment output files from Step 2 AOMix exe FO For Gaussian calculations AOMix generates a AOMix fragment wave gjf file that contains the wave function AO coefficients after the 5E16 8 Fortran format line which is constructed from the converged wave functions of the fragments As in regular AOMix calculations the anti ferromagnetic spin coupling scheme can be added if necessary by the use of the FLIP ix keyword in the aomixpar txt file This keyword instructs AOMix to exchange swap a spin and f spin orbitals for fragment i After AOMix execution modify the keywords of the newly created AOMix fragment wave file to suit your needs The following
29. molecular orbital HOMO Highest occupied molecular orbital LCAO Linear combination of atomic orbitals LCFO Linear combination of fragment orbitals LPA L wdin population analysis LUFO Lowest unoccupied fragment molecular orbital LUMO Lowest unoccupied molecular orbital MO Molecular orbital MPA Mulliken population analysis MMPA Modified Mulliken population analysis NBF Number of basis functions NF Number of fragments NP Net population NPA Natural population analysis OFO Occupied fragment molecular orbital OMO Occupied molecular orbital OOP Orbital occupancy perturbed OOPBO Orbital occupancy perturbed bond order OP Overlap population OPDOS Overlap population density of states OS Open shell PB Pseudobond PDOS Partial density of states PUHF Projected unrestricted Hartree Fock method 85 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 RHF Spin restricted Hartree Fock method QC Quantum chemistry SCPA c population analysis TD DFT Time dependent density functional theory TDOS Total density of states TOP Total overlap population UFO Unoccupied vacant fragment molecular orbital UMO Unoccupied vacant molecular orbital UHF Spin unrestricted Hartree Fock method ZDO Zero differential overlap 86
30. not usually cause failures in calculations of MPA derived MO compositions CDA and bond orders However basis sets with very diffuse functions such as 6 311 G may cause unrealistic results The indicators of this problem are 1 negative MO contributions from fragments in the MO composition analysis using MPA or MMPA 2 MOocontributions from fragments that are greater than 10096 in the MO composition analysis using MPA or MMPA negative partial DOS values large negative charge donation and back donation values between fragments using CDA and 5 large negative 2 center bond order indices If you encounter any of the above and your basis set contains diffuse functions you will need to check your population results with a well behaving basis set The TZVP basis set is recommended for population analysis calculations It is a high quality basis set with enough flexibility to produce accurate results for structures thermochemistry and electronic structure analysis As a more economic alternative the DZVP basis set can be used When you run AOMix FO calculations it is important to remember about the basis set superposition error BSSE effects Usually the BSSE is discussed for calculations of energies of formations but it is also relevant for construction of MO FO interaction diagrams It is clear that the BSSE is expected to be particularly significant when small inadequate basis sets are used These do not provide an
31. out of 1 of orbital B of fragment 2 with orbital B of fragment 1 The overlap between these two fragment orbitals is 0 425 38 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Let s apply this keyword to evaluate orbital contribution of HOMO NH to LUMO BHs3 charge transfer to the bonding in the BH4NHs adduct FO Contributions to occupied and unoccupied MOs The sixth column in the output below indicates the FO occupancies 100 in the molecule Fr Orb Initial E eV Symmetry FO Contribution to Occupancy gt OMOs gt UMOs 1 1 HOFO 4 1 422 70 na 100 00 0 00 1 2 HOFO 3 1 30 95 na 98 91 1 09 1 3 HOFO 2 1 17 09 na 100 00 0 00 1 4 HOFO 1 1 17 09 na 100 00 0 00 1 6 LUFO 0 6 07 na 0 11 99 89 1 7 LUFO 1 0 8 84 na 0 26 99 74 1 8 LUFO 2 0 8 84 na 0 26 99 74 2 1 HOFO 3 1 207 32 na 99 99 0 01 2 2 HOFO 2 1 19 07 na 98 75 1 25 2 3 HOFO 1 1 13 16 na 99 79 0 21 2 4 HOFO 1 13 16 na 99 79 0 21 2 6 LUFO 1 0 8 35 na 0 03 99 97 2 7 LUFO 2 0 8 35 na 0 03 99 97 2 8 LUFO 3 0 8 93 na 0 61 99 39 From the above AOMix FO results AOMix MO FO alpha txt we can see that HOFO NH3 and LUFO BHs make the largest charge transfer contributions to the bonding in the BH3NH3 adduct The HOMO of the NH fragment fragment 1 is orbital 5 The LUMO of the BH fragment fragment 2 is orbital 5 The overlap between the HOMO NH3 and LUMO BHs is 0 425 these data can be found in AOMix MO FO alpha txt and AOMix M
32. spin components of Basc for open shell species An example of a 3 center 2 electron bond is the cyclic H3 ion H os44 A H H where the 3 center bond order index 25 is 0 296 at the HF 6 31G level A B C 3 CENTER bond order index value gt 0 01 Diborane BHs and the CoHy H and C5 H H4O complexes are also systems with two electron 3 center chemical bonds In BsHe the Baye index is 0 24 at the HF 6 31G level In the C H H3O complex with the Tethyiene On interaction the Benc index is 0 224 at the BSLYP TZVP 20 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 level For systems with no 3 center bonds the Bygc indices have values near zero The 3 center bond orders can be used to identify agostic interactions 33 4d 11 5s Pd Figure 2 adapted from Fig 1 in Ref 5 The transition state for the concerted metallation deprotonation reaction pathway Select H atoms have been removed for clarity Relevant two center bond orders red distances black and NPA derived atomic charges a u blue are shown The 3 center covalent interaction and charge transferred CT from the C H bond to the metal based acceptor orbital are shown at right There are systems in which 4 5 and 6 center interactions can be at play These interactions can be evaluated by using 4 5 and 6 center bond orders this option is activated by the MULTI CENTER keyword in aomixpar
33. than 30 numbers in each line If a fragment list requires more than 30 numbers use several lines so that each line does not contain more than 30 numbers see EXAMPLE 3 below The above two formats can be used jointly For instance the following instructions tell AOMix to group atomic orbitals 1 5 10 50 60 62 and 70 80 into the first fragment and orbitals 2 3 4 6 9 and 63 69 into the second fragment 2 1 5 010 50 60 62 0 70 80 1 My first fragment 234069 0 63 69 1 My second fragment Note that there should be no duplication in fragments two different fragments cannot contain the same basis functions AOMix automatically checks for duplications and will exit with an error message if it detects duplication 46 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 If the partitioning is not complete if it does not include all atoms or orbitals in all fragments AOMix will find omitted orbitals atoms and will include them as an additional fragment named Leftovers HOW TO SPECIFY USER DEFINED FRAGMENTS EXAMPLE 1 A list of atomic orbitals 3 fragments 3 0122 1 Ru atom 0 23 40 0 77 130 0 155 162 1 Quinine O 41 76 0 131 154 1 NH3 ligands These instructions tell AOMix to group atomic orbitals 1 22 into the 1 fragment the Ru atom atomic orbitals 23 40 77 130 and 155 162 into the 2 fragment the quinine ligand and atomic orbitals 41 76 and 131 154 into the 3 fragment the
34. therefore provide the same information as given by the main AOMix output file a population analysis per orbital but they enable an easy graphical representation and are particularly useful when there are many one electron levels in a given molecular system You can obtain a simple view of the character of the molecular orbitals in a certain energy range One can also find out in which Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 molecular orbitals certain basis functions or fragment orbitals give large contributions and whether such contributions are bonding nonbonding or anti bonding with respect to particular bonds of fragment pairs The following options are available for DOS computations e total Density of States TDOS e partial Density of States PDOS showing contributions of molecular fragments to TDOS e overlap population Density Of States OPDOS between molecular fragments OPDOS plots are also known in the literature as Crystal Orbital Overlap Population COOP diagrams Typographical Conventions in This Manual The talics font is used for program names and variables The Bold Italics font is used for file names The Bold Courier New fontis used for program input and output examples The Elephant font is used to indicate the AOMix keywords The Bold Verdana font is used to indicate keywords of other program packages such as Gaussian 03 Jaguar etc Software Requirem
35. with Fe CO and CH as fragments when using a mixed all electron basis set TZVP for Fe and 6 31G d for the other atoms with pure d functions 5D the input file for the Fe CO 4 C2H4 P B3LYP GEN 5D SCF Tight Pop Full IOp 3 33 1 The Fe CO 4 C2H4 complex the molecule is in standard orientation NOSYMM is not necessary 0 1 Fe 0 000000 0 000000 0 018179 C 1 821462 0 000000 0 090291 c 1 821462 0 000000 0 090291 Cc 0 000000 1 503897 0 976361 c 0 000000 1 503897 0 976361 Oo 0 000000 2 460510 1 620978 0 0 000000 2 460510 1 620978 Oo 2 968878 0 000000 0 160975 0 2 968878 0 000000 0 160975 0 000000 0 704147 2 039071 C 0 000000 0 704147 2 039071 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 Fe 0 TZVP kkk OCHO 6 31G kk the input file for Fragment 1 P B3LYP GEN 5D SCF Tight Pop Full IOp 3 33 1 NOSYMM Fragment 1 Fe CO 4 01 Fe 0 000000 0 000000 0 018179 Cc 1 821462 0 000000 0 090291 c 1 821462 0 000000 0 090291 c 0 000000 1 503897 0 976361 e 0 000000 1 503897 0 976361 0 0 000000 2 460510 1 620978 Oo 0 000000 2 460510 1 620978 0 2 968878 0 000000 0 160975 Oo 2 968878 0 000000 0 160975 Fe 0 TZVP kkk oco 6 31G kkkk 72 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 P B3LYP 6 31G d 5D SCF Tight Pop Full IOp 3 33 1 NOSYMM Fragment 2 C
36. with one fragment the a and B spin electron conservation is not a limitation to study orbital interactions between open shell radicals See the OPEN SHELL FO CALCULATIONS section below If this is not the case your QC software removed near linearly dependent functions from the orbital set this is done to stabilize SCF convergence AOMix FO requires that Number of canonical orbitals NBF You can force Gaussian to turn off the projection of basis functions to obey the Number of canonical orbitals NBF condition by adding the IOp 3 3222 keyword to the route In other QC packages typically one can employ another keyword with the same function Refer to the corresponding software manuals to determine the appropriate action The necessary and highly recommended keywords for preparing output files of QC software packages for AOMix FO calculations QC package Calculation keywords in Step 1 Calculation keywords in Type of a whole molecule Step 2 calculation molecular fragments GAMESS US Use RUNTYP ENERGY same as for a whole ab initio DFT COORD UNIQUE and NPRINT 3 in molecule calculation the CONTRL input section Gaussian 98 09 P POP FULL IOp 3 33 1 ZP POP FULL ab initio DFT NoSymm SCF Tight IOp 3 33z1 NoSymm SCF Tight Gaussian 98 09 P IOp 5 33 2 NoSymm P IOp 5 33z2 ZINDO keyword NoSymm Jaguar 7 x isymm 0 ipvirt 1 ip102 8 same as for a whole 57 Dr S I Gorelsky AOMix
37. 000 0 006 0 117 0 000 0 001 0 028 OP 3 amp 5 0 003 0 000 0 000 0 000 0 001 0 000 0 027 0 059 0 000 0 000 OP 4 amp 5 0 004 0 001 0 002 0 001 0 000 0 003 0 167 0 000 0 000 0 017 Positive OP4s values represent a bonding interaction large negative OP4s values correspond to an anti bonding interaction and OP4g 0 indicates no bonding between the fragments AO contributions 2 c4 c5 S45 0 01 to overlap populations can be printed to AOMix output files by using the OP CONTRIBUTIONS keyword Keyword and its possible and AOMix Keyword description default values SGT OP CONTRIBUTIONS ON standard The keyword instructs AOMix to print contributions to overlap populations Currently it OFF only works if NF 2 14 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 For example Alpha MO 8 OP contributions gt 0 01 4 19 Ca 0 4093 Cb 0 5523 Sab 0 1150 2 Ca Cb Sab 0 052 23 Ca 0 4093 Cb 6021 Sab 0 1709 2 Ca Cb Sab 0 084 4 0 8 19 Ca 0 4348 Cb 0 5523 Sab 0 3178 2 Ca Cb Sab 0 153 8 23 Ca 0 4348 Cb 0 6021 Sab 0 5781 2 Ca Cb Sab 0 303 Bond Orders In AOMix four types of bond order indices are available for the analysis of covalent bonding between molecular fragments 1 2 center generalized Wiberg indices calculated from the canonical MOs in the AO basis 2 2 center Wiberg indices calculated in the L wdin basis 28 31 and 3 2 ce
38. 000E 04 00000E 05 00000E 05 00000E 05 00000E 00 31000E 03 00000E 00 00000E 00 10000E 03 00000E 00 00000E 05 11000E 03 o 1o0 toonmo mpiiwWHiu 3 2 0 71072 1 31687 1 90583 1 19882 0 24811 1 19883 0 24811 2 21397 0 16800 0 01251 0 20138 0 91730 00000E 04 1 50000E 04 0 00000E 00 0 00000E 00 00000E 05 0 00000E 00 0 00000E 00 3 80000E 04 00000E 05 0 00000E 00 0 00000E 00 0 00000E 00 00000E 05 1 00000E 05 7 00000E 05 1 00000E 05 00000E 05 0 00000E 00 6 30000E 04 0 00000E 00 80000E 04 8 40000E 04 0 00000E 00 0 00000E 00 00000E 05 6 00000E 05 0 00000E 00 0 00000E 00 94670E 01 2 11400E 02 2 03000E 03 0 00000E 00 61000E 03 5 90000E 04 0 00000E 00 0 00000E 00 26000E 03 4 26000E 03 0 00000E 00 0 00000E 00 00000E 05 2 00000E 04 0 00000E 00 0 00000E 00 90000E 03 0 00000E 00 0 00000E 00 7 80000E 04 87 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 APPENDIX Il For Gaussian and GAMESS US calculations AOMix provides a method to use the converged wave functions of fragments to generate a guess wave function for a whole molecular system This option can be very helpful to 1 generate a high quality initial guess for multi fragment molecular systems and 2 to setup open shell calculations of anti ferromagnetically AF coupled systems 7 EXAMPLE 1 a pentalene bridged V V complex where the two ions are separated by 2 54A and anti ferromagnet
39. 250 AOMix could not find the LCAO MO data in the output file you selected Make sure that LCAO MO coefficients are included in the output file 251 There was a problem while reading the LCAO MO data Inspect your output file 255 AOM ix could not find the LCAO MO data for beta spin orbitals in the output file 260 AOMix could not find the overlap matrix Make sure that the overlap matrix is included in your output file 261 There was a problem when reading the overlap matrix Inspect your output file 287 Output files for less than 2 fragments were found CDA calculations require at least 2 fragments with the output file names fragm1 log and fragm2 log Make sure that the output files for fragments are present in the AOMix directory 288 There is only one fragment in the fragment list and this fragment represents the entire molecule This is not allowed Make sure that there will be at least 2 fragments in your calculation 289 Number of fragments is incorrect Make corrections to your fragment list file 290 Number of fragments exceeds the AOMix limit 291 292 The wrong fragment list specification Fix your fragment list file 293 You cannot use a list of atoms to process this output file Specify molecular fragments as a list of atomic orbitals 295 There is a duplication in the fragments Fix your fragment list file 296 The wrong fragment list specification Fix your fragment list file
40. 2H4 0 d fe 0 000000 0 704147 2 039071 C 0 000000 0 704147 2 039071 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 CDA example 4 The following example shows how to setup Gaussian 09 calculations for the AOMix FO analysis of the Fe CO 4 C2H4 complex with Fe CO and CH as fragments when using a mixed basis set with ECP LanL2DZ for Fe and 6 31G d for the other atoms and with pure d functions 5D the Gaussian input file for the Fe CO 4 C2H P B3LYP GEN 5D SCF Tight Pop Full IOp 3 33 1 Pseudo Read The Fe CO 4 C2H4 complex the molecule is in standard orientation NOSYMM is not necessary 01 Fe 0 000000 0 000000 0 018179 G 1 821462 0 000000 0 090291 G 1 821462 0 000000 0 090291 C 0 000000 1 503897 0 976361 C 0 000000 1 503897 0 976361 0 0 000000 2 460510 1 620978 0 0 000000 2 460510 1 620978 0 2 968878 0 000000 0 160975 0 2 968878 0 000000 0 160975 C 0 000000 0 704147 2 039071 C 0 000000 0 704147 2 039071 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 H 0 910796 1 252234 2 262845 Fe 0 LANL2DZ keke OCHO 6 31G ckck ck Fe 0 LANL2DZ the Gaussian input file for Fragment 1 P B3LYP GEN 5D SCF Tight Pop Full IOp 3 33 1 Pseudo Read NOSYMM 73 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Fragment 1 Fe CO 4 01
41. 375 temp fchk C9H17CuN4S2 B 78 HOMO 1 cub 0 h cubegen 0 MO 376 temp fchk C9H17CuN4S2 B 79 HOMO 0 cub 0 h cubegen 0 MO 377 temp fchk C9H17CuN4S2 B 80 LUMO 0 cub 0 h cubegen 0 MO 378 temp fchk C9H17CuN4S2 B 81 LUMO 1 cub 0 h cubegen 0 MO 379 temp fchk C9H17CuN4S2 B 82 LUMO 2 cub 0 h In the above script AOMix instructs the cubegen program from the Gaussian package to create cube files for electrostatic potential spin density for open shell species and 6 frontier orbitals a and B spin HOMO 2 HOMO 1 HOMO LUMO LUMO 1 LUMO 2 from a spin unrestricted calculation in which temp chk was a Gaussian checkpoint file For convenience cube files names for example C9H17CuN4S2 B 82 LUMO 2 cub include molecular formula spin A a spin MO B B spin MO and MO number By default the generate script will include five HOMOs and five LUMOs If you want the script to include more orbitals use CUBE 10 then the script will include 10 HOMOs and 10 LUMOs CUBE 20 then the script will include 20 HOMOs and 20 LUMOs or the CUBE ALL keyword then the script will include all molecular orbitals Keyword and its possible and AOMix Keyword description default values execution standard The keyword instructs the program to create a CUBE OFF 5 10 15 20 25 30 ALL ESP script for the Gaussian cubegen utility X is a number of frontier occupied and unoccupied orbitals to be included in the script the ESP sub keywo
42. 5 13 40 0 13 3 04 0 00 0 00 0 00 15 98 0 00 0 00 5 0 0 03 0 33 0 00 0 00 0 00 1 02 0 00 0 00 Total 99 66 60 82 63 97 98 70 98 70 56 59 4 55 4 55 SumOFO 99 66 60 58 63 68 98 62 98 62 56 53 1 33 1 33 SumUFO 0 00 0 23 0 29 0 08 0 08 0 05 3 21 3 21 FOF OC 11 99 624 0 24 0 03 0 00 0 00 0 00 0 00 0 00 21 0 03 50 344 47 52 0 00 0 00 0 01 0 00 0 00 31 0 00 0 00 0 00 98 61 0 01 0 00 0 05 1 28 41 0 00 0 00 0 00 0 01 98 61 0 00 1 28 0 05 5 1 0 01 10 00 16 13 0 00 0 00 56 524 0 00 0 00 6 0 0 00 0 00 0 00 0 00 0 08 0 00 3 21 0 00 7 0 0 00 0 00 0 00 0 08 0 00 0 00 0 00 3 21 8 0 0 00 0 23 0 29 0 00 0 00 0 05 0 00 0 00 The signs after the FO contributions in the above Table indicate the signs wave function phase factors of the LCFO MO coefficients Ca NF ye 2 Ye k a From the above table for example it can be seen that the HOMO of BH3CO is composed of 95 1 HOFO BH 3 2 LUFO 1 CO 1 3 HOFO 2 CO and HOMO 2 of BH3CO is composed of 26 4 HOFO 2 BH3 16 0 LUFO BH 56 5 HOFO CO The LCFO MO coefficients Ca can be also printed to AOMix FO output files by using the LCFO ON keyword in the aomixpar txt file 63 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Keyword and its possible and AOMix Keyword description default values execution LCFO ON OFF FO option The keyword controls printing of t
43. 50 204 0 0000 0 0019 0 0040 0 0029 HOFO 4 522 449 LUFO 7 50 202 0 0000 0 0007 0 0015 0 0033 HOFO 4 522 449 LUFO 8 51 902 0 0000 0 0011 0 0014 0 0005 HOFO 4 522 449 LUFO 9 51 901 0 0000 0 0022 0 0008 0 0002 HOFO 4 522 449 LUFO 10 70 486 0 0008 0 4367 0 4352 0 1864 HOFO 4 522 449 LUFO 11 99 830 0 0144 7 5542 7 55217 3 0513 HOFO 3 28 624 HOFO 4 669 764 0 0000 0 0814 0 0816 0 0034 HOFO 3 28 624 HOFO 3 30 324 0 0169 0 7321 20 7321 0 4972 HOFO 3 28 624 HOFO 2 12 900 0 0589 21 9990 21 9991 1 2228 HOFO 3 28 624 HOFO 1 9 052 0 0029 0 1092 0 1093 0 0546 HOFO 3 28 624 HOFO 0 9 054 0 0043 0 1623 0 1622 0 0808 HOFO 3 28 624 LUFO 0 1 049 0 2803 8 3694 8 3692 4 1593 81 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Practical Recommendations Electron population analysis and the related concepts bond orders valence indices etc are extremely useful for the wave function analysis However one has to remember that 1 Resulting quantities are not quantum mechanical observables 2 Results are dependent on the quality of the basis set What makes this dependence problematic is that the improvement in basis set resulting in lowing of the total electronic energy can make results of the population analysis MPA in particular worse or even completely unrealistic My experience with different basis sets shows that basis sets such as 6 31G 6 311G TZV and TZVP do
44. 613 0 611 1 224 0 00169 0 558 0 557 1 115 0 00065 4 1 0 380 0 381 0 761 0 00122 0 419 0 420 0 839 0 00081 5 1 0 397 0 404 0 801 0 00659 0 159 0 161 0 320 0 00254 6 1 0 024 0 024 0 048 0 00040 0 062 0 063 0 126 0 00105 LPA derived atomic charges are rather sensitive to the basis set see Table 1 A good point of LPA is that it does not give negative populations or orbital populations greater than 2 WARNING if a 6D 10F basis set a basis set with 6 Cartesian d functions yx dyy dzz dy dz dyz or and 10 Cartesian f functions are used in calculations LPA exhibit a rotational dependence can predict non equal populations for equivalent atoms and thus in this situation should not be used for the analysis 12 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Table 1 The charge of the carbon atom in the CO molecule at the B3LYP level of theory Basis Set 6 31G 6 31 G 6 311G 6 311 G 6 311 G 3df TZVP MPA 0 63 0 66 0 50 0 46 1 03 0 55 LPA 0 20 0 35 0 06 0 09 0 46 0 24 NPA 1 04 1 04 1 00 0 99 1 02 0 95 a each basis set was set to use the 5D polarization functions on C and O The structure of CO was optimized at the B3LYP 6 311G level Rc o 1 1605 A In the above calculations LPA derived charge of the carbon atom in CO displays largest variation from 0 46 to 0 36 a u NPA gerived charges show very little variation Overlap P
45. 7 0 047 1v 3 2 372 0 281 0 281 0 140 0 140 0 103 0 103 1v 4C 2 266 0 391 0 391 0 195 0 195 0 124 0 124 1v 5C 2 314 0 349 0 349 0 174 0 174 0 068 0 068 1V 6c 2 375 0 301 0 301 0 150 0 150 0 069 0 069 1v 12C 2 321 0 401 0 401 0 201 0 201 0 070 0 070 1v 13C 2 149 0 514 0 514 0 257 0 257 0 103 0 103 1v 14C 2 222 0 487 0 487 0 244 0 244 0 356 0 356 Alpha MO 51 52 53 54 55 56 57 58 59 60 HOMO 4 HOMO 3 HOMO 2 HOMO 1 HOMO LUMO LUMO 1 LUMO 2 LUMO 3 LUMO 4 Energy eV 15 69 14 06 13 58 13 21 13 15 11 18 7 76 7 66 STS 7 12 Symmetry al a2 b1 a2 al b1 al b2 a2 al FRAG 1 0 52 0 00 0 00 0 00 0 39 0 80 0 60 0 66 0 00 60 97 FRAG 2 13 43 26 05 68 09 66 98 81 13 21 60 69 317 73 24 0 70 0 31 FRAG 3 82 90 72 92 29 91 30 66 15 88 76 48 4 13 11 49 99 23 2 08 FRAG 4 0 33 0 66 1 41 1 957 0 03 0 87 19 94 0 00 0 05 13 74 FRAGE 5 2 82 0 37 0 59 0 98 2 57 0 26 5 96 14 61 0 01 27 06 oP 1 amp 2 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 OP 1 amp 3 0 005 0 000 0 002 0 000 0 005 0 016 0 020 0 017 0 000 0 303 OP 1 amp 4 0 000 0 000 0 001 0 000 0 001 0 016 0 036 0 000 0 000 0 229 OP 1 amp 5 0 004 0 000 0 002 0 000 0 002 0 005 0 009 0 020 0 000 0 078 oOP 2 amp 3 0 037 0 023 0 024 0 067 0 107 0 061 0 163 0 481 0 003 0 005 OP 2 amp 4 0 003 0 021 0 042 0 037 0 000 0 011 0 767 0 001 0 000 0 020 OP 2 amp 5 0 014 0 008 0 021 0 016 0 055 0 009 0 206 0 523 0 000 0 008 OP 3 amp 4 0 004 0 002 0 004 0 007 0
46. 82 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 accurate description and lack the necessary flexibility Thus recommend the use of basis sets such as TZVP to run AOMix FO calculations and to build MO interaction diagrams The large flexible triple zeta basis sets minimize the BSSE to a small negligible value Limitations for AOMix FO calculations Max number of fragments Max number of orbitals basis functions 4000 4000 Additional keywords in the AOMix parameter file aomixpar txt All lines with a hash symbol in this file are treated as comments and will be ignored by the program Keyword and its possible and AOMix Keyword description default values execution SPDF ALL OFF standard SPDF ALL instructs AOMix to print S P D F NOSINGLE or a list of etc orbital contributions for all atoms or fragments fragments up to 20 integer numbers in a list SPDF NOSINGLE instructs AOMix to print S P D F etc orbital contributions for all atoms or fragments except those with one type of orbitals typically these are hydrogen atoms SPDF 1 15 31 45 instructs AOMix to print S P D F orbital contributions for atoms fragments 1 15 31 and 45 NETPOP ON OFF standard The keyword controls printing of net orbital populations OP ON OFF standard The keyword controls printing of overlap Eu populations FO ALWAYS standard The keyword instructs AOMix to turn o
47. 999 Note that this AOMix functionality has been tested for only closed shell systems using all electron basis sets In EDA one can define the following contributions to the electronic interaction energy between two fragments in a molecule electrostatic energy Egs exchange repulsion energy Pauli repulsion Egx and orbital interaction energy E Ein Egs Egy Eor The electrostatic energy and exchange repulsion energy can be combined together into a single term E steric As a result E Egon E nt steric orb and E orb AOMix allows to evaluate E steric using Gaussian calculations In order to proceed with such calculations a user has to setup a new Gaussian calculation using the converged wavefunctions of two fragments see Appendix Il After the corresponding GUESS CARDS input file is prepared by AOMix with the FO execution option a Gaussian calculation of the whole complex using this input file will have to be executed The orbital interaction term E is be readily extracted from the electronic energy values in the 1 and the last SCF cycles E E last SCF E st SCF For example for the interaction between the BH3 and NH3 fragments in the BH3NH3 adduct AOMix FO reports 37 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 The molecule the sum of fragments test 0 00000 OK Electronic energy a u Whole molecule Sum of fragments Fragmen
48. AOMIx version 6 88 Software Manual Wave function Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 AOMix is a user friendly comprehensive package for the molecular orbital analysis AOMix calculates percentage contributions of different molecular fragments atoms ligands groups of atomic orbitals basis functions groups of fragment molecular orbitals etc to molecular orbitals from output files generated by different computational chemistry packages and produces data tables in the ASCII text format with relevant MO information condensed Fukui functions etc In addition it generates total partial and overlap population density of states DOS plots and can be used for MO composition analysis in systems with many fragments It also calculates the MO compositions in the basis of fragment molecular orbitals FOs occupation numbers for FOs and atomic orbitals AOs and if the number of fragments is greater than 1 the amounts of electron donation back donation between molecular fragments charge decomposition analysis CDA electronic polarizations of fragments and generates plot data for MO interaction diagrams In addition it can be used for Morokuma s energy decomposition analysis EDA and to generate a guess wave function of multi fragment molecular systems from the wave functions of fragments The software calculates total and free valence indices of fragments 2 center Wiberg L wdin and Maye
49. BITALS and ATOMS The molecule in the ADF output has to be guilt from atomic fragments EXAMPLE OF THE LCAO MO OUTPUT FROM Gaussian 98 03 09 191 13 C 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 14 15 1S 2S 3S 4PX APY 4PZ 5PX 5PY 5PZ 6D 0 6D 1 6D 1 6D 2 6D 2 1S 2S 1S 2S I I ot oOooooooo oooooo0o0o0oo9c o 00110 00290 00845 00000 01065 01577 00000 00241 00146 00096 00000 00017 00011 00000 405999 00010 405999 00010 OOOoOooo0o0000050500000000 00000 00000 00000 03074 00000 00000 00129 00000 00000 00000 00295 00000 00000 00284 02475 00412 02475 00412 OOOoOOooococococoo I I 1 OoOoOOoOoooo 44 available available available available available available available available available available available 01488 0 00262 0 01567 03439 0 00783 0 03699 06530 0 00508 0 08224 00000 0 00000 0 00000 01379 0 21671 0 01171 13845 0 03374 0 28372 00000 0 00000 0 00000 03258 0 03023 0 04244 00053 0 00159 0 01050 00478 0 01128 0 00719 00000 0 00000 0 00000 01295 0 00131 0 02599 00075 0 00406 0 00041 00000 0 00000 0 00000 00957 0 01148 0 00726 00272 0 01142 0 00497 00957 0 01148 0 00726 00272 0 01142 0 00497 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Atomic orbitals 191 204 are on atom 13 carbon atomic orbita
50. DA and ECDA The latter allows separate evaluation of charge transfer and polarization contributions see below AOMix can process Hartree Fock HF correlated and DFT wave functions from ADF GAMESS Gaussian Jaguar and Q Chem calculations and semiempirical ZDO wave functions from Gaussian ZINDO HyperChem Spartan ZINDO and CNDO INDO calculations Fragment list files which are needed for AOMix calculations with non standard user defined fragments are not needed for AOMix FO calculations because the fragments are defined by the fragment calculations fragmX log see below 56 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 The AOMix FO analysis can be used for both spin restricted and spin unrestricted calculations In addition it can process mixed type calculations such as for example a whole molecule is treated at the spin unrestricted level while one or all of molecular fragments are treated at the spin restricted level The requirements for AOMix FO calculations are Number of basis functions in the molecule Y number of basis functions of all molecular fragments Number of a spin electrons in the molecule X number of a spin electrons of all molecular fragments Number of D spin electrons in the molecule Y number of fi spin electrons of all molecular fragments Number of canonical orbitals number of basis functions NBF These requirements does not apply for calculations
51. Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 APPENDIX Anyone who has been running large size QM calculations knows how important it is to be able to restart your calculations from the converged wave functions Usually this is achieved by using checkpoint files If you did not keep these files or you have switched from one operating system to other and forgot to keep formatted checkpoint files you have to re run calculations from scratch to obtain converged wave functions Keeping the checkpoint files is not necessary anymore AOMix can recover converged wave function from an output file To activate this option include the GUESS CARDS keyword in the aomixpar txt file Keyword AOMix Keyword description execution GUESS CARDS standard If the keyword is included in aomixpar txt AOMix will generate a Gaussian input file that contains the converged wave function as an initial guess Then run AOMix as you would run it for standard AOMix calculations For Gaussian calculations AOMix will generate the AOMix guess cards gjf file that contains the atomic coordinates of the whole molecule and the complete initial guess data after the 5E16 5 Fortran format line that represents the converged wave function For example chk BH3CO P HF 6 31G d SCF Tight GUESS CARDS BH3 CO Hn 90571 83756 400975 25148 13818 38420 oommmuo OOONOO 5E16 5 1 00000E 05 10
52. FE HE HE E TE FE FE FE FE FE HE HE E TE FE FE FE FE FE HE HE E TE HE HE FE FE HE HE HE E TE TE HE HE HE aE E E E HE 1st parameter peak shape Possible values 0 Gaussian 1 Lorentzian 2 pseudo Voigt 2nd parameter band width at half height Default value 3000 0 cm 1 UV VIS 0 3000 0 AOMix reads calculated excitation energies and oscillator strengths of electronic transitions from a Gaussian TD DFT output file and produces a data file UV Vis spectrum dat containing the absorption spectrum curve in the following format 1st column Energy 10 cm 2nd column Wavelength nm 3rd column Molar absorptivity cm L mol A user can import this data file using any available software MS Excel Quattro Pro Origin SigmaPlot KaleidaGraph etc to create a figure with the UV Vis spectrum 95 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 By using AOMix you fully agree with the following LICENSE AGREEMENT GRANT OF LICENSE The author S l Gorelsky grants a nonexclusive nontransferable license to use the AOMix program and its additional modules the SOFTWARE according to the terms and conditions herein An academic single user license permits a user to run the SOFTWARE on a computer by a single academic user An academic research group license permits users from the same research group to run the SOFTWARE on their computers at one academic institution department only A
53. NHs ligands EXAMPLE 2 A list of atoms 3 fragments 3 1 2 Ru atom 2308 13 0 26 29 2 Quinine 04701425 2 NH3 ligands These instructions tell AOMix to treat atom 1 as the 1 fragment the Ru atom group atoms 2 3 8 13 and 26 29 into the 2 fragment quinone and group atoms 4 7 and 14 25 into the 3 fragment the NH ligands EXAMPLE 3 A list of atoms 2 fragments If fragments contain many atoms orbitals a user can use multiple lines to specify the numbers For example 2 1 5 0 10 50 60 62 O 70 80 90 92 95 97 99 100 103 108 109 112 1000 1100 0 1200 2000 2 My first fragment 0 2001 3000 2 My second fragment 47 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 These instructions tell AOMix to group atoms 1 5 10 50 60 62 70 80 90 92 95 97 99 100 103 108 109 112 1000 1100 and 1200 2000 into the first fragment and atoms 2001 3000 into the second fragment EXAMPLE 4 A list of atoms and atomic orbitals 4 fragments 4 0 1 12 1 s p orbitals of Ru atom 0 13 22 1 d orbitals of Ru atom 2308 13 0 26 29 2 Quinone ligand 0470 14 25 2 NH3 ligands These instructions tell AOMix to group atomic orbitals 1 12 into the 1 fragment s p orbitals of Ru atom atomic orbitals 13 22 into the on fragment d orbitals of Ru atom atoms 2 3 8 13 and 26 29 into the 3 fragment quinone ligand and atoms 4 7 and 14 25 into the 4 fragment the NH ligands
54. O FO beta txt output files from an AOM n run with the FO option If we mix 12 0 of the LUMO of BH into the HOMO of NH we turn on o donation of 0 24 electrons from NHs to BHs see the Figure below This 88 HOMO NH3 12 LUMO BHs mixing contributes 13 9 kcal mol to the electronic interaction energy in the BH3NH3 adduct This number is obtained as a difference between the two E 1st SCF values from the Gaussian output files obtained from the AOMix generated Gaussian input files with the initial guess wavefunction data with and without the application of the mixing keyword Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 12 HOFO NH 88 LUFO BH Py o b Co LUFO BH H4N BH 88 HOFO NH 12 LUFO BH For analysis of orbital interactions in open shell species using the spin unrestricted MO treatment two keywords MIXING and MIXINGBETA can be used as shown in the example below MIXING 15 20 0 060 0 100 MIXING 17 22 0 100 0 200 MIXINGBETA 16 21 0 200 0 400 The MIXING keyword applies to a spin orbitals and the MIXINGBETA keyword applies to B spin orbitals The keywords instruct AOMix FO to mix 6 096 0 060 of a spin orbital 20 of fragment 2 with a spin orbital 15 of fragment 1 the overlap between these two fragment orbitals is 0 100 to mix 10 09e 0 100 of a spin orbital 22 of fragment 2 with a spin orbital 17 of fragment 1 the overlap between these two fragment orbitals
55. O composition shown in blue represents the condensed Fukui function for an electrophilic attack f and the LUMO composition shown in red represents the condensed Fukui function for a nucleophilic attack UL 25 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 For the HOMO the contributions of the carbon atoms at the a and B positions are 17 1 and 7 8 respectively For the LUMO the contributions of the carbon atoms at the a and f positions are 17 096 and 7 896 respectively These contributions indicate that electrophilic nucleophilic and radical since f 2 f f 2 attacks at the a carbon atom of naphthalene should be more effective than those at the B carbon atom You can also refer to a recent paper of Makedonas et al as an example of the analysis of the reactivity of Metal diimine dithiolato complexes using the Fukui functions and AOMix Overlap matrix between a and B spin molecular orbitals In a spin unrestricted wave function the a and B spin molecular orbitals are not necessarily orthogonal to one another only within each set either a MOs or B MOs are all of the molecular orbitals mutually orthogonal to one another Thus there are cases of interest where it is relevant to evaluate the overlap integrals between a and B spin MOs ot o7 the so called mutual overlap matrix These overlap integrals are useful for evaluating the matching degree of corresponding a
56. OMix is used to calculated the MO compositions gross fragment populations and the overlap populations between fragments in addition AOMix will also print the net populations the first sum in Eqn 3 1 7 if the NETPOP ON keyword is present in aomixpar txt Keyword and its possible and AOMix Keyword description default values execution NETPOP ON OFF standard The keyword controls printing of net orbital populations There are deficiencies in MPA 1 MPA orbital populations can have non physical negative values or be in excess of two The fragment contributions can exceed 100 or be less than 0 when analyzing the MO compositions 2 MPA derived populations are sensitive to a basis set particularly as the basis set is enlarged to get higher accuracy and includes diffuse functions see Table 1 The reason for these two problems is the imbalance of the overlap populations and the net atomic populations This imbalance is due primarily to the arbitrary equal distribution of the overlap population between atoms involved When O c c S is greater than ca the contribution of the a AO to the MO b a becomes negative Clearly this is likely to happen when the coefficient cx is small but the overlap integral S4 and the coefficient cj are large This is a typical situation for high energy unoccupied MOs from calculations that use extended or unbalanced basis sets In this case it is not reasonable to split
57. SC F fragments are shifted by 4 0 eV and 4 5 eV respectively Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 2 2 1 1 76 sp 0 d 2 Cl 79 sp 2 d 2 56 sp 24 d 18 CI 0 0 4 4 LUFOH 36 sp 47 d 8 Cl a D SE L a 2 gt 7 sp 77 d 8 Cl D 1 D c 3 b 3 LU S LUFO Q 4 4 O Ru HOFO 1 sp 62 d 37 CI 5 60 d 40 Cl 5 HOFO 1 ack donation 1 sp 92 d 5 Cl 6 HOFO 2 6 88 93 Cl HOFO c NE f HOFO 1 AGS DZ L SS OS HOFO 2 AN Ru NH Cl SA IZ X 9 BQDI gt Ru NH Cl BQDI The orbital interaction diagram illustrating the coupling of the Ru NH3 Cl and BQDI fragments in the Ru NH3 Cl BQDI complex with Czy symmetry the AOMix FO calculation at the B8LYP LanL2DZ level molecular orbitals of the Ru NH3 2Cl and BQDI fragments are shifted by 0 7 eV and 0 7 eV respectively 79 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 In the above figure donation from the BQDI ligand to the Ru NH3 2Cl fragment can be clearly seen LUFO and LUFO 1 of Ru NH3 2Cl interact with HOFO 1 and HOFO 2 of the BQDI ligand respectively black and red lines corresponding to orbitals of b and a symmetry and strong back donation from the Ru NH3 2Clo fragment to the BQDI ligand is present too the HOFO of Ru NH3 2 Cl is mixing with the LUFO of the BQDI ligand green lines As a result the AOMix CDA results for this complex are Electron don
58. UMOs of the A B complex in terms of occupied and unoccupied molecular orbitals of fragments A and B OFOs and UFOs The FO contributions are color coded to help in reading this scheme adapted from Ref 67 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 By analyzing the MO compositions in terms of occupied and unoccupied fragment molecular orbitals it is possible to separate electronic polarization and charge transfer donation interactions If for example the BH3CO adduct one has MO compositions in terms of fragment molecular orbitals charge transfer CT and electronic polarization PL terms FO contributions to all occupied molecular orbitals Occupied FO 390 4 680 5 Unoccupied FO 21 1 8 0 Sum 411 5 688 5 FO contributions to all unoccupied molecular orbitals Occupied FO 9 6 19 5 Unoccupied FO 1678 9 2292 0 Sum 1688 5 2311 5 PL 1 PL 2 1 6 CT 2 51 CT 1 2 11 5 net charge transfer 0 23 e then the difference in electronic polarization contributions PL 1 PL 2 is 1 6 orbital and the difference in charge transfer contributions CT 1 2 CT 2 1 is 11 5 orbital which in a case of doubly occupied orbitals corresponds to a net charge transfer of 2 0 11520 23 e This extended CDA analysis is especially helpful in connection with the energy decomposition analysis EDA of Kitaura Morokuma and Ziegler where the interaction energy between mole
59. a spin orbitals or each of the AOMix MO FO beta l dat files for B spin orbitals as plain text files in your favorite graph software 2 Create a line plot or a line plot with multiple XY pairs in case of a symmetrical molecule and for each imported AOMix MO FO dat file define the 1 Column from each AOMix MO FO dat file as X and the 2 Column as Y If a molecule has symmetry and you can import and plot data for each irreducible representation by selecting appropriate AOMix MO FO dat files and using different color to highlight different orbital symmetries Most likely you may want to re scale the Y axis to focus your plot on the MO energy region near the HOMO LUMO gap The orbital interaction plot is ready The aomixpar txt file can be used to define the non default parameters for creating orbital interaction diagrams To set new parameters edit the line after the AOMix FO line HEHEH AOMix FO HPHH I E E HE H B E E ERE ERE ERE ERE E HE FE EE FE FE FE HE FE HE HE FE HE HE HE G 4 0 0 0 0 0 If the above line is modified to be say 3 0 1 55 1 41 AOMix will connect all MO FO pairs for which the FO contributions are greater than 3 0 and it will shift the FO energies of Fragment 1 and Fragment 2 by 1 55 eV and 1 41 eV respectively The option of adjusting the MO energies of fragments is useful for constructing orbital interaction diagrams for complexes containing ions The SHORT FORM of an AOMix FO output will print the recomme
60. ailable in Cerius Accelrys Inc and CAChe Fujitsu Inc Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Processing Capabilities of AOMix Software Calculation type AOMix standard run run using the FO option ADF DFT DFTB DFT GAMESS US HF DFT Gaussian HF DFT ZINDO HyperChem HF DFT O 2 Semiempirical Jaguar HF DFT MOPAC2009 Semiempirical ORCA HF DFT Q Chem HF DFT Spartan HF DFT Semiempirical Turbomole HF DFT ZINDO Semiempirical CNDO INDO Semiempirical SCPA MPA and MMPA are available O SCPA is available MPA and MMPA are not available in the current version Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Procedures for the electron population analysis in AOMix Mulliken population analysis MPA modified Mulliken population analysis MMPA c population analysis SCPA L wdin population analysis LPA ecce CUTE umm the MO analysis in terms of the contributions from fragment molecular orbitals and charge decomposition analysis CDA CDA has been devised to analyze molecular interactions in systems which can be described as donor acceptor complexes The electronic changes associated with the formation of a molecule consisting of two or more fragments are partitioned in terms of the Dewar Chatt 11 12
61. al www sg chem net the input file for Fragm P UB3LYP TZVP SCF Tight Pop Full Fragment 1 HC 4 the input file for Fragm 0 000000 0 000000 0 000000 0 000000 ent 1 0 000000 0 000000 ent 2 0 000000 0 000000 0 000000 0 000000 Updated on July 23 2015 1 661837 0 599005 0 599005 1 661837 IOp 3 33 1 NoSymm 0 000000 0 000000 1 661837 0 599005 P UB3LYP TZVP SCF Tight Pop Full I0p 3 33 1 NoSymm Fragment 2 CH 4 mao 0 000000 0 000000 0 000000 0 000000 0 599005 1 661837 the above example shows the Gaussian 09 input files for the AOMix FO calculation In this situation you want to couple the a spin FOs of the 1 fragment with the f spin FOs of the 2 fragment anti ferromagnetic spin coupling The anti ferromagnetic spin coupling scheme is added in AOMix by the use of the FLIP ix keyword in the aomixpar txt file This keyword instructs AOMix to exchange swap a spin and f spin orbitals for fragment i Keyword and its possible and AOMix Keyword description default values eee Ne FLIP amp FO option Exchanges swaps a and B spin molecular orbitals for a selected molecular fragment i 1 NF FLIP 1x applies the orbital swap to Fragment 1 etc FLIP 2x applies the orbital swap to Fragment 2 A user can apply this keyword to as many fragments as necessary For example FLIP 2x 4x applies the orbital swa
62. alculates continuous DOS data in a yoyo 10 eV gt E Lumo 10 eV energy region using Gaussian functions with half widths of 0 5 eV If you want to specify an energy range explicitly un comment the ENERGYRANGE keyword and enter the desired lower and upper energy values eV for DOS calculations see the example below Keyword AOMix Keyword description execution ENERGYRANGE standard The keyword instructs the program to use user E1 E defined energy range from E1 to E2 eV for DOS calculations The default values for E1 and E2 are yoyo 10 eV and i uyo 10 eV respectively In addition the Lorentzian model and the pseudo Voigt model a convolution using both the Gaussian and Lorentzian functions with the weighting factors w and 1 w respectively are available You can change the continuous DOS convolution settings by modifying the corresponding parameters in the aomixpar txt file Hat TE FE HE HE FE FE HE FE FE E FE FE HE HE FE FE E FE FE E a FE HE HE EEE FE FE EE HE FE FE EE EE ERE ERE EE EE EE EE EE E H E Td Density of States DOS convolution parameters Td FE HE FE FE HE FE HE HE E HERE E HERE E HERE EE FE FE ERE E ERE E HERE E ERE E ERE EE FE aE HE HE FE HE HE a HE HE FE Ea aE E a a EE E lst DOS parameter Peak Shape Possible values 0 Gaussian 1 Lorentzian 2 pseudo Voigt 2nd parameter Print Window Default value 10 0 eV 3rd parameter Width at Half Height Default value 0 5 eV 4th param
63. ames in the command line In WinNC it is done by selecting an appropriate file name in the directory list window see the screenshot below t WinNc 4 6 Left Fies Commands Extra Options Help Right G AOMix 2009 pack a aomix 2009 pack 3 a g c 2d 2f sea 3 D C3 EXAMPLES CDA SUB DIR D 01 28 2009 16 22 46 7 AOMix CDA exe 764kB A 02 07 2009 09 02 06 EI AOMix L exe 660kB A 02 07 2009 09 03 20 Z AOMix manual pdf 1j488kB __A 01 28 2009 16 24 40 7 aomix p1 exe 372kB __A 01 18 2009 10 24 12 E AOMix p 11 exe 384kB A 02 07 2009 09 05 56 aomix p9 exe 380kB _ A 01 21 2009 13 29 54 AOMix S exe 584kB A 02 07 2009 09 05 20 F1 AOMix exe 424kB A 02 07 2009 09 10 48 AOMIX642 EXE 91kB _ A 02 07 2009 09 08 20 a aomixpar txt 2kB A 01 29 2009 16 40 56 NH3BH3 eda out 252kB A 02 17 2007 22 21 30 Program Files 257 682 bytes in 1 files G AOMix 2009 pack gt AOMix exe i Q wn l Prop Com amp View a Edi Copy Move d lt Drive G 476 937 MB total 153 842 MB free Bs Drive G 476 937 MB total 1 and then pressing the Ctrl Enter buttons at the same time 42 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 8 WinNc 4 6 Left Files Commands Extra Options Help Right di dcoseegW ge ig C9 AOMix 2009 pack G3 a g Peed st wa Y Name Extensi Size Attr Date Time
64. and B spin orbital pairs as can be see from the following section of the AOMix output AOMix atom txt Matching Alpha and Beta Spin Molecular Orbitals Alpha MO Closely matching beta spin MO overlap integral between the two 1 Occ 1 Occ 1 00 2 Occ 2 Occ 1 00 3 Occ 3 Occ 1 00 4 Occ 4 Occ 1 00 89 Occ 89 Occ 0 85 90 Occ 90 0 83 91 91 1 00 In the above example the a HOMO a spin orbital 90 is closely related to the B LUMO the overlap integral between the two spin orbitals is 0 83 while the a LUMO a spin orbital 91 is identical to the 8 LUMO 1 the overlap integral is 1 00 An example of usage of this data is provided in Ref 26 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 A user can select to print the full mutual overlap matrix by using the PROJECTION FULL keyword in the aomixpar txt file to print a portion of the mutual overlap matrix that includes only the occupied MOs the PROJECTION OCCUPIED keyword or to skip this step PROJECTION OFF The last is the default option Keyword and its AOMix Keyword description possible and default values execution PROJECTION FULL standard The keyword controls printing of the overlap matrix between a and B spin MOs OCCUPIED OFF If AOMix is instructed using the PROJECTION keyword to print the full or partial MO overlap matrix v w for a spin unrestricted wave funct
65. annigrahi A B Kar T Chem Phys Lett 1990 173 569 572 33 Kar T Marcos E S Chem Phys Lett 1992 192 14 20 34 Gorelsky S Basumallick L Vura Weis J Sarangi R Hedman B Hodgson K O Fujisawa K Solomon E Inorg Chem 2005 44 4947 4960 35 Solomon E Gorelsky S I Dey A J Comput Chem 2006 27 1415 1428 36 Sizova O V Skripnikov L V Sokolov A Y Journal of Molecular Structure Theochem 2008 870 1 9 37 Sizova O V Skripnikov L V Sokolov A Y Sizov V V Int J Quantum Chem 2009 109 2581 2590 38 Gorelsky S Xie X Chen Y Fee J A Solomon E J Am Chem Soc 2006 128 16452 16453 39 Ponec R Yuzhakov G Cooper D L J Phys Chem A 2003 107 2100 2105 40 Johnston H S Adv Chem Phys 1960 85 131 41 Johnston H S Parr C J Am Chem Soc 1963 85 2544 42 Gorelsky S J Chem Theory Comput 2012 8 908 914 43 deGiambiagi M S Giambiagi M Fortes M D Theochem J Mol Struct 1997 391 44 Ponec R Mayer I J Phys Chem A 1997 101 1738 1741 45 Bochicchio R C Ponec R Lain L Torre A J Phys Chem A 1998 102 7176 7180 46 Ponec R Torre A Lain L Bochicchio R C nt J Quantum Chem 2000 77 710 715 47 Brookhart M Green M L H Parkin G Proc Natl Acad Sci U S A 2007 104 6908 6914 48 Lafrance M Gorelsky S l Fagnou K
66. ation between fragments Ru gt BQDI BODI gt Ru b2 orbitals 0 000 0 140 al orbitals 0 025 0 156 b1 orbitals 0 100 0 001 a2 orbitals 0 000 0 000 Total over OMOs 0 110 0 289 Total ALPHA BETA 0 220 0 579 Since no charge donation occurs via the MOs with a symmetry these orbitals play no role in covalent bonding between the metal fragment and the BQDI ligand Calculation of charge transfer integrals and site energies to analyze charge electron hole transport properties The site energies and charge transfer integrals can be obtained by utilizing AOMix FO calculations namely the possibility to exploit the molecular fragment orbitals as a basis set in calculations on a system consisting of two or more fragments With the each DFT program the eigenvector matrix C is obtained by solving the Kohn Sham equation h sC SCE with E the diagonal matrix containing the eigenvalues of the orbitals of the composite system consisting of two or more fragments The eigenvector matrix C and the overlap matrix S are defined in terms of the fragment orbitals on the individual fragments rather than in terms of the atomic orbitals The matrix elements of the Kohn Sham Hamiltonian in this basis set T i j can be obtained by using the relation hys SCEC This procedure allows direct calculations of the charge transfer integrals including their signs Keyword AOMix Keyword description execution FO OVERLAP ON FO The keyword contro
67. cond column the PDOS for the first fragment the third column the PDOS for the second fragment etc For continuous DOS data files the last column is the TDOS the sum of PDOSs for all fragments All PDOS and TDOS values in continuous plots are scaled by 1 2 For a spin unrestricted calculation AOMix prints PDOS TDOS data for a spin molecular orbitals first and then the corresponding values for B spin molecular orbitals Column 1 orbital energy units eV Column 2 PDOS contribution of Fragment 1 to TDOS a spin orbitals 31 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Column NF 1 PDOSne contribution of Fragment NF to TDOS a spin orbitals Column NF 2 TDOS a spin orbitals Column NF 3 PDOS contribution of Fragment 1 to TDOS f spin orbitals Column 2 NF 2 PDOSuyc contribution of Fragment NF to TDOS f spin orbitals Column 2 NF 3 TDOS p spin orbitals So if a calculation is performed using the spin unrestricted method and the molecule has 2 fragments AOMix X DOS txt will contain Column 1 orbital energy units eV Column 2 PDOS contribution of Fragment 1 to TDOS a spin orbitals Column 3 PDOS contribution of Fragment 2 to TDOS a spin orbitals Column 4 TDOS a spin orbitals Column 5 PDOS contribution of Fragment 1 to TDOS f spin orbitals Column 6 PDOS contribution of Fragment 2 to TDOS f spin orbitals Column 7 TDOS p spin orbitals By default AOMix c
68. corrections to energy from DFT calculations 9 E E E DFT D KS DFT disp where Exs prer is the usual self consistent Kohn Sham energy as obtained from the chosen DFT level of theory and Ej is an empirical dispersion correction of Grimme 2006 If a calculation involves a structure with elements from H to Xe the value of Ej is automatically calculated and printed in the AOMix atom txt output file For example for a DFT calculation with the PBE functional AOMix atom txt will contain an entry DFT D Correction S Grimme J Comput Chem 2006 vol 27 1787 1799 PBE value Dispersion correction to the SCF energy is 102 1 kJ mol 24 38 kcal mol 52 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 This functionality is currently only available for processing Gaussian and Jaguar output files Visualization of AOMix calculated properties using UCSF Chimera UCSF Chimera http www cgl ucsf edu chimera is a very advanced extensible graphical package for visualization of structures and properties of both simple and very complex molecular structures Keyword and its AOMix Keyword description possible and default values execution CHIMERA ON OFF standard The keyword controls printing of Chimera attribute files If AOMix is executed with the keyword CHIMERA ON and each atom defined as a fragment the program will generate a Chimera readable atomic attribute file AOMix ato
69. cular fragments is divided in the following components 1 ES the classical electrostatic interaction of the occupied FO of fragment A with those of another fragment B this interaction does not result in any orbital mixing between different FOs 2 EX the exchange interaction the interaction between OFO of fragments A and B that causes the exchange repulsion 3 PL the electronic polarization mixes the OFOs and UFOs within each fragment intra fragment excitations PL interactions can be further split into two types initial polarization and induced polarization The initial polarization is the polarization before CT and the induced polarization is the polarization after CT 4 CT the charge transfer covalent bond interaction which causes electron delocalization between fragments by mixing the OFOs of fragment A with the UFOs of 68 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 fragment B charge donation from fragment A to fragment B the OFOs of fragment B with the UFOs of fragment A charge donation from fragment B to fragment A In addition to the LONG FORM you can use the SHORT FORM section of AOMix FO output files to see the MO compositions in terms of fragment molecular orbitals The SHORT FORM includes information about all occupied MOs and up to 50 lowest unoccupied MOs The short form lists up to eight FOs with largest LCFO MO coefficients and each contribution is greater than 196 F
70. culations As a result the geometry specification of an entire molecule must follow this order fragment 1 atoml xl yl zl atom2 x2 y2 z2 atom3 x3 y3 z3 fragment 2 atom4 x4 y4 z4 atom5 x5 y5 z5 fragment 3 atom6 x6 y6 z6 atom7 x7 y7 z7 58 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Etc In this example atoms 1 3 belong to Fragment 1 atoms 4 5 form to Fragment 2 and all remaining atoms form Fragment 3 Step 2 Calculate MOs of molecular fragments using atomic coordinates in Step 1 Output files for molecular fragments are outputs of single point calculations They must contain the LCAO MO and overlap matrices A fragment can be a single molecule a single ligand or a group of molecules a group of ligands IMPORTANT The atom order and xyz atomic coordinates in fragments must match those in an entire molecule If a default setting in your QC package is to rearrange atoms or and reorient a molecule when it starts a calculation you should disable such software features using appropriate keywords such as NoSymm in Gaussian The atom order requirement does not apply to HyperChem calculations where the program puts all hydrogen atoms at the end of the molecule specification AOMix deals automatically with H atom reordering when processing HyperChem output files Fragment file names are pre defined as described below For correct AOMix execution output files from your electronic struct
71. ed AS IS and is subject to change without notice A user may copy distribute this manual in any medium provided that this document is presented distributed in its complete form 97 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Acknowledgements Many thanks to all AOMix users who contributed to the development of the AOMix package by testing it using different QM applications and packages and trying to push the software to its limits This has been essential to make AOMix a well tested and behaved product as it is today CONTACT INFORMATION Dr S Gorelsky Centre for Catalysis Research and Innovation University of Ottawa Ottawa Ontario CANADA K1N 6N5 E mail software sg chem net S I Gorelsky 1997 2015 References Mulliken R S J Chem Phys 1955 23 1833 1840 Mulliken R S J Chem Phys 1955 23 1841 1846 Mulliken R S J Chem Phys 1955 23 2338 2342 Mulliken R S J Chem Phys 1955 23 2343 2346 Stout E W Politzer P Theoret Chim Acta 1968 12 379 386 Christoffersen R E Baker K A Chem Phys Lett 1971 8 4 9 Grabenstetter J E Whitehead M A Theoret Chim Acta 1972 26 390 Gorelsky S Lever A B P J Organomet Chem 2001 635 187 196 Ros P Schuit G C A Theoret Chim Acta Berl 1966 4 1 12 0 Lowdin P O Adv Quantum Phys 1970 5 185 199 1 Dewar M J S Bull Soc Chim
72. ed shell acA be B ceC deD eeE species and a and B spin components of BAgcpe printed for open shell species Boycos 2 22 2 2 P S P S P S P S P S and acA be B ceC deD eeE Bhronn 9 22 2 2 P S P S PS P S P S ae A be B ceC deD eeE 22 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 can be evaluated by using AOMix to identify the 5 center interactions in molecules The 6 center bond orders Bagcper are defined in the analogous way For benzene CgH at the B3LYP TZVP level of theory A B c D E F 6 CENTER bond order index value 0 001 1c 2c 3C 4C 5C 6c B ABCDEF 0 084 Total and free valence indices of atoms or fragments In addition to bond orders and fragment and orbital populations AOMix calculates the total and free valences of fragments The total valence of atom A fragment A is defined as V 2 23 PS gt PS PS aeA a beA Its free valence is the difference between the total valence V4 and the sum of the bond orders formed by it F V M Bap gt P S PS B BzA a be A From the above equation it is clear that the free valence index F4 vanishes for all closed shell Systems PP 0 As an example atomic total and free valence indices are shown below for the NH3BF3 molecule Atom Total and Free Valences V F 1 N 3 355 0 000 2 H 0 942 0 000 3 po 0 942 0 000 4 H 0 942 0 000 5 B
73. ents MS Windows NT 2000 XP for all QM software MS Windows 7 Vista for processing ADF DFTB GAMESS US Gaussian Jaguar Q Chem and Turbomole output files only Supported operating systems AOM Nx also can be run under Linux using WINE http www winehq org Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 AOMix processes output files from the following programs 2 ADF Scientific Computing amp Modelling NV Only calculations with no SGM core functions do not confuse core functions with core orbitals please refer to the ADF user manual for details http www scm com CNDO INDO Dr J R Reimers U of Sydney Australia DFTB Density Functional based Tight Binding Plus DFTB joe itii http www dftb plus info GAMESS US GAMESS including WinGAMESS PC GAMESS and Firefly http classic chem msu su gran gamess G Gaussian 98 Gaussian 03 Gaussian 09 Gaussian Inc A http www gaussian com EA HyperChem HyperCube Inc Ja guar Jaguar 7 x Schrodinger Inc MOPAC2009 Dr J J P Stewart Stewart Computational Chemistry MOPAC http openmopac net ORCA ORCA Department of molecular theory and spectroscopy Max Planck Institute for Chemical Energy Conversion Muelheim Ruhr Germany IB CHEM Q Chem 3 2 4 0 Q Chem Inc Spartan Wavefunction Inc Turbomole 6 5 COSMOlogic GmbH ZINDO ZINDO M C Zerner Quantum Theory Project U of Florida USA ZINDO is av
74. eta MO Energy eV ATOM dca Net pop S orbitals p orbitals d orbitals ATOM 2N Net pop s orbitals p orbitals d orbitals T11 7 HOMO 7 53 112 LIS 114 115 HOMO 4 HOMO 3 1 30 1 19 2 82 3 25 2 94 3 07 0 00 0 00 0 25 0 49 2 56 2a TI 0 21 22 97 0 14 23 49 0 00 0 00 0 12 22 89 0 09 0 08 8 49 6 47 Updated on July 23 2015 35 58 0 37 37 70 0 31 1 90 0 00 2 55 0 09 31 13 0 27 16 42 29 In this table the gross and net populations refer to pages 7 8 for the definitions are printed for each fragment it is followed by s p d orbital contributions In the above example the gross and net populations in the LUMO for the Cu atom fragment 1 are 48 696 and 54 796 respectively The Cu atom character in the LUMO 48 696 the gross population comes from the d and p orbitals their contributions to the LUMO are 47 596 and 1 196 respectively At the end of the AOMix output for all non closed shell singlet calculations contributions to the spin density are printed ATOM 1Cu 2N 3N 4N 5N 6N 7N 0 gt p S 0 0 0 0 0 0 0 025 000 001 052 002 052 002 In the above example for the 1Cu atom fragment 1 the atomic spin density 0 471 comes almost entirely from the difference 0 503 in the d orbital occupation and slightly altered by spin polarization of the s and p orbitals their contributions to the atom spin density are 0 006 and
75. eter Data sampling step Default value 0 05 eV 5th parameter the gaussian weighting coefficient in the pseudo Voigt function Default value 0 50 This parameter only Se c cb che cb choc 32 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 applies if the peak shape parameter is 2 pseudo Voigt DOS 0 10 0 0 5 0 05 0 50 lst parameter must be an integer parameters 2 5 must be real numbers ENERGYRANGE 20 0 10 0 AOMix writes the OPDOS data to the following files AOMix MPA OPDOS txt a continuous line plot and AOMix MPA OPDOS line txt a bar line plot The data structure of these files is the same as the order of overlap populations in AOMix output files NF Order of columns in OPDOS data files AOMix MPA OPDOS ixt and AOMix MPA OPDOS line txt 2 Energy eV OPDOS 2 a and OPDOS if this is a spin unrestricted calculation 3 Energy eV OPDOS a OPDOS a OPDOSz3 a and OPDOS 4 f OPDOS 8 OPDOS B if this is a spin unrestricted calculation 4 Energy eV OPDOS a OPDOS a OPDOS a OPDOS a OPDOS a OPDOSs4 a and OPDOS 2 8 OPDOS 4 B OPDOS 4 8 OPDOSz3 8 OPDOS 8 OPDOSs3 B8 if this is a spin unrestricted calculation Charge transfer character of electronic transitions Typically one interprets features in electronic spectra of transition metal complexes as metal centered MC metal t
76. example shows the AOMix fragment wave gjf file for the BH3CO molecule P HF 6 31G d SCF Tight Guess Cards NOSYMM POP FULL NPA 1IOp 3 33 1 The spin restricted wave function from the molecular fragments Frag 1 AE 4 BE 4 BH3 92 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Frag 2 AE 7 BE Ty CO 01 B 0 90571 0 71072 1 31687 H 0 83756 1 90583 1 19882 H 2 00975 0 24811 1 19883 H 0 25148 0 24811 2 21397 Cc 0 13818 0 16800 0 01251 Oo 0 38420 0 20138 0 91730 5E16 8 1 9 96240000E 01 2 36300000E 02 0 00000000E 00 2 00000000E 05 1 02000000E 03 1 15100000E 02 0 00000000E 00 0 00000000E 00 1 80000000E 04 5 00000000E 05 5 00000000E 05 9 60000000E 04 0 00000000E 00 0 00000000E 00 3 00000000E 05 1 20000000E 04 2 29000000E 03 1 20000000E 04 2 29000000E 03 1 20000000E 04 2 29000000E 03 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 0 00000000E 00 For GAMESS US calculations AOMix will generate the AOMix fragment wave dat file that contains the wave function AO coefficients after the VEC line that is constructed from the converged wave functions of the fragments Copy the VEC section of the AOMix fragment wave dat file to your GAMESS input file for the whole m
77. he LCFO MO matrix THE LCFO MO MATRIX 1 2 3 4 5 6 7 8 1 1 0 043 0 2 1 0 000 0 3 1 0 000 0 40 0 035 0 5 0 0 017 0 6 0 0 000 0 7 0 0 000 0 11 0 998 0 21 0 018 0 3 1 0 000 0 41 0 000 0 5 1 0 011 0 6 0 0 000 0 7 0 0 000 0 8 0 0 001 0 000 048 HOMO 5 HOMO 4 HOMO 3 HOMO 2 HOMO 1 HOMO 21 04 18 59 18 59 14 11 11 07 11 07 Fragment 1 mI I I EI L I I I I I I I L I I L I I I I I 0 600 0 000 0 000 0 514 0 000 0 000 0 000 0 016 0 110 0 000 0 975 0 048 0 000 0 110 0 016 0 000 0 048 0 975 0 002 0 000 0 000 0 400 0 000 0 000 0 005 0 000 0 000 0 101 0 000 0 000 0 000 0 024 0 004 0 000 0 001 0 031 0 000 0 004 0 024 0 000 0 031 0 001 Fragment 2 s S 0 018 0 000 0 000 0 002 0 000 0 000 0 689 0 000 0 000 0 009 0 000 0 000 0 000 0 993 0 011 0 000 0 023 0 113 0 000 0 011 0 993 0 000 0 113 0 023 0 402 0 000 0 000 0 752 0 000 0 000 0 000 0 006 0 028 0 000 0 179 0 001 0 000 0 028 0 006 0 000 0 001 0 179 0 054 0 000 0 000 0 023 0 000 0 000 Note In order to produce concise output files AOMix prints LCFO MO coefficients in the LONG FORM only if they are no less than the threshold value the default value is 0 196 a user can increase it to 1 by using the FORMAT P 0 keyword or decrease it to 0 01 by using the FORMAT P 2 keyword in the AOMix parameter file Keyword and its possible and AOMix default values execution Keyword description
78. he given symmetry type In this manner the bond order may be broken down into the contributions from the different symmetry orbital character contributions Baz x B 5 T T If molecular symmetry is present AOMix attempts to resolve the bond order contributions Bag and Bas d for each irreducible presentation For example for a molecule with Ca symmetry AOWMix prints e Bag for a spin orbitals with a symmetry BaAg a e Bag for a spin orbitals with a symmetry Bas a2 e Bag for a spin orbitals with b symmetry Bag bi e Bag for a spin orbitals with b symmetry BAg b e and Bas B4g a B4g a7 Bag bi Bag b For example here is the symmetry bond order components for the Cu S bond atoms 1 and 28 respectively in the Cu L SCgFs complex C symmetry with two irreducible representations a Symmetry Contributions to Bond Orders Resolved contributions to 2 PA S PA S that are larger than 0 01 FRi FR2 a a 1Cu 28S 0 35 0 03 16 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Resolved contributions to 2 PB S PB S that are larger than 0 01 FRI FR2 a a 1Cu 28S 0 36 0 33 Thus the results from the AOMix calculations can deliver local information on the chemical bonding between molecular fragments and the symmetry decomposition with respect to I makes it possible to resolve
79. ic orbitals or all atoms as individual fragments an auxiliary ASCII text file has to be created to specify molecular fragments AOMix will read the fragment information from this file This auxiliary file must be created using the following format Line 1 NF 1 2 3 etc Line 2 orbitals atoms in the 1 fragment followed by 1 or 2 Line 3 the name of the 1 fragment or a blank line Line 4 orbitals atoms in the 2 fragment followed by 1 or 2 Line 5 the name of the 27 fragment or a blank line etc The atom orbital list statements are not restricted to one line for each fragment As many lines as necessary can be used to list all relevant atoms orbitals see EXAMPLE 3 below in this section Fragment names are limited to one line per fragment If you do not want to assign any name to a fragment the name line should be blank DON T USE TAB s AS DELIMITERS IN FRAGMENT LIST FILES The program may not see them as valid delimiters and this may lead to unpredictable program execution Use only blank space characters and commas as delimiters Fragments can be specified using the following formats The first format is to have a list of numbers N No Ns etc N N N N Ns Ny X The numbers can be in an arbitrary order The second format is to specify a range from N to N3 to be included in a fragment 0 N N X If Xis 1 then this is a list of atomic orbitals If Xis 2 then this is a list of atoms Do not list more
80. ically coupled to yield a ground state wave function with Siotai 0 V Cp CsHe 2 Figure A Il Spin density of the broken symmetry state for V Cs5Hs o CsHe open shell singlet from the PBE TZVP calculation The initial guess wave function was generated from the fragment wave functions by AOMix 88 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 C3 o N o Electronic Energy kcal mol o o N o O1 1 0 0 5 V V Bond Order 0 0 20 22 24 26 28 30 32 34 V V Distance A Figure A III Potential energy surfaces and metal metal bond order profiles calculated for the for the BS singlet black lines the OS singlet after the spin projection correction has been applied black lines with circles CS singlet gray triplet red pentet blue and septet green electronic states of V CsHs 2Pn at the PBE TZVP and PBE D TZVP levels of theory dashed and solid lines respectively All electronic energies are referenced to the energy of the BS singlet A dotted vertical line indicates a value of the V V distance from the X ray structure 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 EXAMPLE 2 Mn O L s cations where the AF interactions between the high spin Mn ions S 2 dominate at low Mn N O Mn dihedral angle values producing a spin frustrated group state The way to employ AOMix for initial guess wave function calculations is a
81. ion Y the expectation value of S is computed v Is Iv XE sz abes E ut we i j where ng and ng are the numbers of a spin and B spin electrons respectively Total partial and overlap population density of states plots If the number of fragments in a calculation is less than 14 AOMix generates total TDOS partial PDOS and overlap population OPDOS density of states plots The main use of the DOS plots is to provide a pictorial representation of MO compositions and their contributions to chemical bonding through the OPDOS plots which are also referred in the literature as Crystal Orbital Overlap Population COOP diagrams The total density of states TDOS at energy E is written as TDOS E E amp 27 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 where the summation index i goes over all one electron energy levels Thus the integral of TDOS E over an energy interval E41 to Eo gives the number of one electron states in that energy interval In DOS calculations with AOMix the function can be substituted by Lorentzians Gaussians or pseudo Voigt functions F TDOS E gt F E e In order to find out how much a given fragment A an orbital an atom a group of orbitals or a groups of atoms contributes to one electron levels at certain energies one may weigh a one electron level with the fragment character C4 These fragment characters are dete
82. keyword in the aomixpar txt file PSEUDOBONDS 2 0 3 red The above line will instruct AOMix to assign red color to bond orders and print them to AOMix atom chimera BO txt using the X XX output format with the 0 3 threshold value all bond order indices with values less than 0 3 will be omitted The figure below shows the Mayer bond orders in anthracene at the B3LYP TZVP level of theory 54 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 AOMix created atom bond attribute files can be edited using any text editor such as Notepad before importing them to UCSF Chimera to suit user s needs Using fragment molecular orbitals AOMix FO calculations AOMix with the FO execution option can be most helpful for the analysis for chemical 15 16 35 48 69 72 bonding in molecules However a user must understand how to select appropriate fragments to describe the chemical bonding in a given system There are many books for example Ref 5979 describing this topic in considerable detail You can find additional information in the papers quoted in this manual In addition for GAMESS and Gaussian calculations AOMix FO can be used to generate a guess wave function of multi fragment molecular systems from the wave functions of fragments See APPENDIX II for details MOs of a molecular system can be expanded as linear combinations of the MOs of fragments gr the LCFO MO expansion NF p New
83. l www sg chem net Updated on July 23 2015 AOMix MO FO alpha a1 dat and AOMix MO FO alpha e dat which will contain interaction diagrams for orbitals with a and e symmetry respectively see Figure below Orbital Interactions between BH and CO in BH CO AM1 calculation AOMix CDA ef 98 39 6 37 S 8 8 S gt 10 10 D D C 12 12 Lu O 14 14 16 16 18 18 20 20 22 22 24 24 26 26 BH BH CO CO Orbital interaction diagram for the H3B CO molecule which is formed by BH and CO the AM1 calculation orbitals with a symmetry are shown in blue orbitals with e symmetry are shown in red In the current version AOMix reads symmetry information from the QM output files Gaussian Jaguar HyperChem etc Some irreducible representations such as a and e include the symbol which cannot be included in file names AOMix will replace the symbol with the X symbol in the AOMix MO FO dat file names By default AOMix connects MO FO pairs for which corresponding contributions are greater than 496 It is possible to change the value of this parameter You can use any graph 75 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 software of your choice SigmaPlot 2000 Excel etc to create orbital interaction diagrams from AOMix FO output files To create the orbital interaction plot 1 Import each of the AOMix MO FO alpha l dat files for
84. lar orbitals of the complex containing the tetrahedral Cu S cluster The OPDOS Cu S plot on the right indicates which molecular orbitals are bonding non bonding or anti bonding with respect to Cu S bonds The OPDOS data are presented in two formats a line plot red and a continuous Gaussian band shape plot black In some cases it is convenient to use line plots to show DOS data In other cases it is more helpful to present DOS data in a continuous format such as shown below Density of States DOS Spectrum of Ru NH BQDI B3LYP LanL2DZ calculation total contribution from Ru atom contribution from BQDI ligand contribution from NH3 ligands HOMO 2 1 i HOMO Partial and Total DOS Energy eV 30 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Overlap Population Density of States Plot N O Molecule BP86 6 311G calculation OPDOS Energy eV More examples of the TDOS and PDOS plots are given in Refs examples of the OPDOS plots are given in Refs 5506269 The AOMix program writes TDOS PDOS plot data to AOMix X DOS line txt a bar line plot and AOMix X DOS txt a continuous line plot where X is the population scheme used MPA MMPA SCPA A user can import data from these files using his her favorite graph plotting software Origin Sigmaplot Excel etc The data structure of these TDOS PDOS plot files afrom AOWMix is the first column is energy eV the se
85. lmost identical to regular AOMix FO calculations 1 Build your molecular system as in the following order fragment 1 atoml xl yl zl atom2 x2 y2 z2 atom3 x3 y3 z3 fragment 2 atom4 x4 y4 z4 atom5 x5 y5 z5 fragment 3 atom6 x6 y6 z6 atom7 x7 y7 z7 Etc 90 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 2 Calculate the MOs of molecular fragments using atomic coordinates in Step 1 Output files for molecular fragments are outputs of single point calculations They must contain the LCAO MO and overlap matrices IMPORTANT The atom order and xyz atomic coordinates in fragments must match those in an entire molecule If a default setting in your QC package is to rearrange atoms or and reorient a molecule when it starts a calculation you should disable such software features using appropriate keywords such as NoSymm in Gaussian 98 03 09 Fragment file names are pre defined as described below For correct AOMix execution output files from your electronic structure package Gaussian and GAMESS must be named as follows Output for l Output File Name Fragment 1 fragm1 log Fragment 2 if present fragm2 log Fragment 3 if present fragm3 log Fragment 99 if present fragm99 log Let s take the BH43CO complex as an example and define BH and CO as two fragments Then the input structures for the single point calculations must be given as shown below 91 Dr S I Gorelsky AOMix
86. ls 205 206 are on atom 14 hydrogen and atomic orbitals 207 208 are on atom 15 hydrogen Note that if the number of orbitals is greater than 999 the Gaussian output will look like this 997 998 999 kkk kk kkk KkK KkK kkk KkK kkk KkK KkK k kkk KkK 117 0 118 H 119 H 1S 25 2PX PY PZ N Uu o0 KX Bod od BW WW Wd t3 tg gr N Bs oO 158 28 15 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00153 00157 00900 03250 02568 01522 01543 04850 03569 00001 00125 00000 00135 00344 01024 05947 00169 02293 0 0 0 0 0 0 0 0 0 0 01285 07079 00035 08764 14132 08717 04160 12485 22263 01147 00983 00847 00209 00388 02248 15626 12149 27698 0 0 0 O 0 20222 0 0 0 0 0 0 0 0 0 0 0 0 0 00334 05159 05751 00535 03181 11174 01519 08798 00853 00432 02461 01908 00551 06354 06432 08394 06610 0 01941 00858 00048 04061 07398 01109 00101 04233 01036 00508 0 0 0 0 0 0 0 00332 01637 00488 00235 02228 00795 06407 15275 0 0 m 0 0 0 AOMix will process such output with no problem the software does not use orbital printed in the first column by Gaussian EXAMPLE OF THE LCAO MO OUTPUT FROM HyperChem 0 0 0 0 0 0 0 0
87. ls printing of LCFO MO and FO overlap matrices charge transfer integrals 80 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 LCFO ON and the site energies If AOMix FO calculations are performed with the keywords OVERLAP ON and LCFO ON in aomixpar txt the AOMix program will print the site energies and charge transfer integrals see AOMIx MO FO alpha txt and if it is a spin unrestricted calculation AOMIx MO FO beta txt output files Overlap and charge transfer integrals see 10 1021 ja037027d 10 1021 ja054257e Fragment 1 Fragment 2 T S C E C 1 1 2 Sij Site energy Site energy Overlap T 4 2 T 1 3 T1i4T33 FO T i i eV FO T j 3 eV S i j ev ev ev HOFO 4 522 449 HOFO 4 669 764 0 0000 0 0095 0 0096 0 0116 HOFO 4 522 449 HOFO 3 30 324 0 0005 0 2030 0 2070 0 1310 HOFO 4 522 449 HOFO 2 12 900 0 0043 2 1695 2 1748 1 1521 HOFO 4 522 449 HOFO 1 9 052 0 0000 0 0118 0 0082 0 0066 HOFO 4 522 449 HOFO 0 9 054 0 0000 0 0193 0 0160 0 0100 HOFO 4 522 449 LUFO 0 1 049 0 0304 15 7455 15 7485 7 9468 HOFO 4 522 449 LUFO 1 21 089 0 0221 11 5548 11 5531 5 5290 HOFO 4 522 449 LUFO 2 29 949 0 0131 6 8204 6 8254 3 2216 HOFO 4 522 449 LUFO 3 33 064 0 0000 0 0219 0 0228 0 0116 HOFO 4 522 449 LUFO 4 33 060 0 0001 0 0368 0 0342 0 0193 HOFO 4 522 449 LUFO 5 39 257 0 0181 9 4433 9 4443 4 3652 HOFO 4 522 449 LUFO 6
88. m chimera txt and two pseudobond attribute files AOMix atom chimera BO txt and AOMix atom chimera BD txt Those contain the following data AOMix atom chimera txt 1 center attributes such as MPA LPA and NPA derived spin densities total and free valences of atoms NPA derived charges atomic contributions to the frontier orbitals 10 HOMOs and 10 LUMOs which also represent the condensed Fukui functions AOMix atom chimera BD txt internuclear distances as 2 center pseudobond attributes AOMix atom chimera BO txt Mayer bond orders as 2 center pseudobondQ attributes If AOMix is executed with user defined fragments and NF is the number of fragments the program will generate attribute files AOMix frNF chimera txt and AOMix frNF chimera BO txt These two files contain same type data as AOMix atom chimera and AOMix atom chimera BO However a user can only use AOMix frNF chimera txt and AOMix frNF chimera BO txt with UCSF Chimera if user defined fragments are individual atoms Importing 1 center attribute data 53 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Define Render by Pawel pente To import AOMix calculated ATOMIC 1 center attribute data to your UCSF Chimera session open the structure file for your molecule Then use the Define Attribute tool Tools Structure Analysis Define Attribute to import the data from AOMix atom chimera txt then you should employ the Actions
89. manual www sg chem net Updated on July 23 2015 ab initio DFT ip18 2 numd 6 iacc 2 molecule calculation in the amp gen input section HyperChem QuantumPrintLevel 1 same as for a whole ZDO calculations molecule calculation MOPAC use the keywords VECTORS EIGEN and same as for a whole ZDO calculations ALLVEC molecule calculation ORCA Q Chem 3 x use the keywords same as for a whole calculations PRINT_ORBITALS 99999 molecule calculation IPRINT 200 NO_REORIENT TRUE SYMMETRY_DECOMPOSITION 0 SYMMETRY_IGNORE 1 ZINDO use the keyword MOS in the OUTPUT input same as for a whole ZDO calculations section molecule calculation a This keyword is only necessary if the specified molecular geometry is not in the standard orientation If you are doing AOMix FO calculations for the first time it can useful to run one or two sample AOMix FO calculations The AOMix FO input and output examples are provided for several QM packages and can be downloaded from http www sg chem net download FIVE STEPS FOR AOMIX FO CALCULATIONS Steps 1 and 2 are performed using a QC package see APPENDIX II if you want to use AOMix to construct the wave function of a molecular systems from the wave functions of the fragments Step 1 Calculate MOs of an entire molecule An output file is a regular output file for AOMix calculations The atom sequence is critical and should not be changed in fragment cal
90. n 1 start AOMix exe 2 when prompted by the software enter the file name which corresponds to the calculation of a complete molecular system for example BH3CO Log and the FO keyword The AOMix program runs several checks before starting the FO calculation a the program verifies the wave function of the whole molecule b the program verifies the wave functions of the fragments and c the program verifies the overlap matrix of the molecule and its fragments If any of these checks fails make sure that you setup your calculations in Step 1 and 2 see above correctly After the main calculation AOMix runs a final check it compares and prints fragment populations calculated in the AO and FO basis sets These populations should be identical Here is an example FRAGMENT POPULATIONS calculated in the AO and FO basis sets the final test ALPHA ORBITALS BETA ORBITALS TOTAL ALPHA BETA SPIN Fragm AO FO AO FO AO FO AO FO 13 4 115 4 115 4 115 4 115 8 230 8 230 0 000 0 000 2 6 885 6 885 6 885 6 885 13 770 13 770 0 000 0 000 If fragment populations calculated in the AO and FO basis sets are different AOMix will print a warning message At the end of the AOMix run you should see the message Normal Termination AOMix FO Output Donation back donation repulsion and residue terms that are printed in the AOMix FO txt file are computed using the CDA scheme 61 Dr S I Gorelsky
91. n the FO calculation even when the FO keyword is absent in the execution command line NOSYMM all types If the keyword is included in aomixpar txt the use of symmetry is turned off CORE X FO option Include MOs within the X eV range in the MO X must be a real number 50 0 interaction plot 100 0 200 0 etc Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 AOMix Error Codes AOM ix performs multiple checks during calculations and may stop when they detect an error or give you a warning massage The list error codes is shown in the table below Error Error description code 1 A data formatting problem Inspect your output file 100 One or more of the AOMix executable files are missing Make sure that you have downloaded the complete AOMix package with all executable exe files 201 The output file does not match the format of the quantum chemical package 202 AOMix could not determine the quantum chemical package 208 AOM ix could not find the TITLE line in your output file 220 AOMix could not find the number of electrons in the output file 239 AOMix cannot process ADF calculations with core basis functions Please use the all electron basis sets without core functions 240 AOMix could not find the number of orbitals in the output file 242 Number of orbitals exceeds the program limit 243 Number of canonical orbitals is not valid
92. nded MO energy shifts for each fragment They appear in the format like this HOMO 7 4 44 373 eV 99 6 H 4 2 VShift 1 41 eV HOMO 8 3 205 70 eV 100 0 H 3 1 VShift 1 55 eV Here the recommended shift values are 1 55 eV for Fragment 1 and 1 41 eV for Fragment 2 If the FO OVERLAP ON keyword is included in the aomixpar txt file Keyword and its possible and AOMix Keyword description default values execution FO OVERLAP ON OFF FO option The keyword controls printing of the FO overlap matrix 76 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 the SHOFT FORM of the AOMix FO output will include the overlap integrals S wie wi and overlap populations 2c c S7 where the are the LCFO MO coefficients from al al NF they cw expansions V aiV ak k ALPHA SPIN ORBITALS Mol Orbital Compositions in terms of dominant FO contributions FO Overlap integrals S ab and overlap populations OP 2 c ai c bi S ab LUMO 0 12 3 161 eV Fr 1 7 1 L 1 3 0 H 0 1 9 L 2 Fr 2 46 7 L 1 S 0 32 0 24 0 09 OP 0 07 0 10 0 01 40 0 L 0 S 0 09 0 06 0 32 OP 0 02 0 02 0 04 HOMO O 11 12 718 eV Fr 1 94 9 H 0 Fr 2 3 6 L 1 S 0 24 OP 0 05 1 4 H 1 S 0 06 OP 0 02 HOMO 1 10 12 718 eV Fr 1 94 9 H 1 Fr 2 3 6 L 0 S 0 24 OP 0 05 1 4 H 2 S 0 06 OP 0 02 HOMO 2 9 15 102 eV Fr 1 57 3 H 2 14 5 L 0 Fr 2 25 9 H 0 S 0 35 0 62
93. ns use QuantumPrintLevel 1 Jaguar 7 x calculations use the keywords ipvirt 1 ip102 8 ip18 2 and numd 6 in the amp gen input section MOPACO calculations use the keywords VECTORS EIGEN and ALLVEC ORCA calculations use the keywords 9 ooutput Print P Basis 2 Print P Overlap 1 Print P MOs 1 end Q Chem 3 x calculations use the keywords PRINT ORBITALS 99999 and IPRINT 200 Spartan calculations For processing use output files instead of spartan files Turbomole calculations use the t2aomix script in the Turbomole package ZINDO calculations use the keyword MOS in the OUTPUT input section 3 The nosym keyword is only necessary for symmetric molecules b Do not confuse the core functions and core orbitals please refer to the ADF user manual for details c Use Turbomole default format 4D20 14 for the MO output It is known that in all types of orbital based population analysis schemes the numerical values of calculated electron populations and related indices bond orders MO compositions etc generally depend on the quality of the basis set used For this reason it is always prudent to analyze the basis set dependence especially when using Pople type basis sets with diffuse functions such as 6 311 G of any calculated parameter 49 Dr S I Gorelsky AOMix manual www sg chem net Here is an example of the AOMix MO composition output B
94. nter Mayer indices calculated from canonical MOs in the AO and FO basis 4 3 4 5 and 6 center Mayer type bond order indices calculated from the canonical MOs in the AO basis AOM n is very flexible about how a user can define fragments it is possible to obtain bond orders between atoms groups of atoms groups of orbitals etc The latter option is especially useful when you are interested to perform symmetry decomposition of bond orders see below Generalized Wiberg bond order indices Bag are Bas gt gt PS p PS ae A beB and the Mayer bond orders Bag are Bas 9 Y PS PS P S P S ae A be B where P and P are total density and spin density matrices respectively The above equation for the Mayer bond orders can be re written using the Mayer bond orders for a and p spin orbitals B s 23 M P S P S and acA be B 15 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Bas 2 P S P S ae X beY Thus the total Mayer bond orders are Bas Bag Bas 2 gt gt P S P S P S PS acA be B For the closed shell spin singlet state calculations P P and as a result Bag Bas and Bag Bag In a general case with P z PP the generalized Wiberg and Mayer bond orders are not equal It is also possible to define components of bond orders by performing the summation 34 37 only for orbitals of t
95. o ligand charge transfer MLCT ligand to metal charge transfer LMCT ligand to ligand charge transfer LLCT metal to metal charge transfer MMCT intraligand or ligand centered LC transitions etc However such descriptions are only appropriate in the weak metal ligand coupling limit where pure excited states are most rigorously defined When the metal ligand coupling is high the MOs are of mixed metal ligand character and descriptions of electronic excitations such as pure MC MLCT LMCT LLCT or LC become very approximate 33 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 For characterization of the electronic transitions as partial CT transitions the following definition of the CT character can be used CT M 100 P M P M 3 4 1 where P M and PM are electronic densities on the metal in the electronic ground state and the l th excited state respectively Positive CT M values correspond to MLCT transitions negative CT M values to LMCT transitions This definition Eqn 3 4 1 can be re written using the AO contributions to the MOs For the HOMO x LUMO y excitation the metal CT character is CT M e M uowox M Lumosy 3 4 2 For example here are the frontier MOs of the Ru terpy complex from B3LYP LanL2DZ calculations MO Number Eigenvalue eV Contribution Symmetry Fragment Ru terpy 132 LUMO 2 7 66 a2 0 100 131 LUMO 1 7 79 e 8 92 130 LUMO
96. of both the Gaussian and Lorentzian functions elw 0 50 civ f exp 2 773 I 1 2 I 1 2 1 032 7 f 025A I Aiz a 0254 55 l 3 where molar absorptivity molar extinction coefficient is given in units of mol L cm The sums in Eqns 1 3 include all allowed electronic transitions with energies w expressed in cm half bandwidths A 2 expressed in cm and oscillator strengths f So the total integrated intensity under an absorption profile obtained from Eqns 1 3 is equal to a sum of the oscillator strengths 4 32x10 e do gt f 4 I A Gaussian shape can be chosen for spectroscopic bands with inhomogeneous line broadening such as charge transfer absorption bands of large polyatomic molecules in solution A Lorentzian shape can be chosen for spectroscopic bands with homogeneous line broadening for more details please refer to J Steinfeld Molecules and Radiation An Introduction to Modern Molecular Spectroscopy The MIT Press Cambridge MA 1981 pages 22 24 94 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 A user can control the simulation of the UV Vis spectrum by modifying the corresponding parameters for the UV VIS keyword in the aomixpar txt file Hat H aH EH EH HE HE ERE FE FE FE FE FE HE HE E a FE FE FE FE FE HE HE E aE aE a aE EE EH E E E E HHH UV Vis spectrum convolution parameters HHH Hat FE HE HE E HE FE FE FE HE
97. olecule calculation For spin unrestricted calculations you should always include NORB zx keyword in the GUESS section to make sure that GAMESS can correctly read all a and B spin orbital coefficients For more details please refer to two example sets provided in the EXAMPLES directory with the AOMix executables Currently this AOMix functionality to build wave functions of multi fragment molecular systems from fragment wave functions can be used for Gaussian and GAMESS US calculations only In future releases similar functionality can be added for use with other quantum mechanical packages if they allow the same functionality as Guess Cards in Gaussian or the GUESS MOREAD keyword the GUESS section and the VEC data section in GAMESS 93 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 APPENDIX Ill For a Gaussian output file that contains the results of TD DFT calculations AOMix program reads excitation energies and oscillator strengths of electronic transitions and generates a data plot file with an electronic absorption spectrum the same functionality as the SWizard program http www sg chem net swizard The absorption spectrum is calculated as a sum of Gaussian or and Lorentzian bands using the following equations Gaussian Model elw c f exp 2 719 9 I 12 1 1 2 J a 1 Lorentzian Model elw cx f 0 25A s I I Aas 0 POZA ar Pseudo Voigt Model a convolution
98. opulations and Chemical Bonding The 2c c terms where a e atom A and b e atom B are the overlap populations between the two atoms with atomic orbitals 7 and p respectively of the i MO The total overlap population TOP between atoms A and B in a molecule is calculated by adding together overlap populations for orbitals centered on these two atoms TOPs M n gt gt 2c 6 S 3 2 1 i acA be B where Cai is the LCAO MO coefficient of ya on atom A cy is the coefficient of vy on atom B both in the MO and S is the overlap integral for these two AOs The overlap populations OP concept can be extended to the analysis of the bonding between the central atom and the ligands in transition metal complexes or other large molecules In AOMix Equation 3 2 1 is applied to user defined fragments which can be individual atoms groups of atoms or an atomic orbital or groups of orbitals OP spi 9 2c 6 S 3 2 2 ae A beB 13 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 TOP4s 9 n OPa 9 n 9 3 2e 6 S 3 2 3 i ae A beB The TOP4g and OP4s values are printed in the AOMix output files 2 CENTER BOND ORDERS BETWEEN FRAGMENTS B AB and its components 2 PA S PA S and 2 PB S PB S and TOTAL OVERLAP POPULATIONS TOPs Wiberg Mayer bond orders gt 0 01 Overlap populations A B d A B P S P S B AB B alpha B beta TOP alpha TOP beta 1v 2C 2 306 0 360 0 360 0 180 0 180 0 04
99. or a given MO FO components are printed in the order of decreasing importance LUMO 0 9 0 117 eV 79 1 L 1 2 16 5 L 0 2 2 7 H 0 1 HOMO 0 8 11 072 eV 95 1 H 0 1 3 2 L4 1 2 1 3 H 2 2 HOMO 1 47 11 072 eV 95 1 H 1 1 3 2 L 0 2 1 3 H 1 2 HOMO 2 146 14 111 eV 56 5 H 0 2 26 4 H 2 1 16 0 L 0 1 1 0 L 1 1 To save space the notation in the SHORT FORM section of AOMix FO outputs is H 3 1 HOFO 3 of Fragment 1 L 0 1 LUFO of Fragment 1 H 0 2 HOFO of Fragment 2 L 1 2 LUFO 1 of Fragment 2 etc Open shell calculations If you study orbital interactions between open shell fragments you may have a situation when using the default AOMix settings you will not be able to complete calculations because of non conservation of the number of a and p spin electrons a NF NF g olecule niragmenti neee niragmenti a B B i i For instance if you want to study orbital interactions between two CH radicals forming the CH2 molecule you have the following situation the CH molecule closed shell has 7 a spin and 7 p spin electrons however each CH radical in the quartet spin state has 5 a spin and 2 p spin electrons adding to a total of 10 a spin and 4 p spin electrons in the default spin coupling scheme ferromagnetic CDA example 2 EE the input file for the whole molecule P B3LYP TZVP SCF Tight Pop Full IOp 3 33 1 The HC CH molecule 0 1 69 Dr S I Gorelsky AOMix manu
100. or population analysis instead of MPA for ab initio DFT calculations 43 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Unless you want to treat all atomic orbitals or all atoms as individual fragments two default settings for AOMix you have to specify fragments You can do so by identifying which atoms or atomic orbitals basis functions should be included in a particular fragment The option to specify fragments as a list of atomic orbitals gives you the greatest flexibility thus it is available for processing output files from all software packages Using this ORBITAL option you can separate s p d f orbital contributions by appropriately defined fragments for AOMix calculations For convenience you can also specify fragments as a list of atoms However this option is not available for all software packages see the Table below QC Program ADF DFTB GAMESS US Gaussian 98 03 09 ab initio Gaussian 98 03 09 ZINDO HyperChem Jaguar MOPACO9 ORCA Reimers CNDO INDO Q Chem Spartan Turbomole ZINDO Option to specify molecular fragments as a list of ORBITALS available available available available available available available available available available available available available available ATOMS available available available available available available available available available available available Both OR
101. orting to additional calculations involving the systems with N 1 and N 1 electrons as an example see Ref 2 fi X C tc eS where i LUMO ack b a a 2 f EX Ca tc gt Cy Sas where i HOMO aek L b a Because for systems with non degenerate HOMO and LUMO the above two expressions represent the fragment contributions in the MPA framework to the LUMO and the HOMO 24 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 respectively the condensed Fukui functions are calculated automatically when compositions of molecular orbitals are evaluated This formulation is suitable if the two frontier orbital description the HOMO and the LUMO is sufficient for describing the reactivity of a particular molecular system This description however is not suitable for systems with high density of states near the HOMO LUMO gap such as transition metal systems It is easy to see that the condensed Fukui functions must be non negative owing that all fragment contributions to MOs must be non negative Note also that the condensed Fukui functions just like the fragment contributions to MOs are normalized and fi f fy 1 2 As an example let s consider naphthalene Ci 9Hg Figure 3 shows the compositions of the HOMO and the LUMO of the molecule HOMO 0 0 Figure 3 The MPA derived composition of the HOMO and the LUMO of naphthalene at the BSLYP 6 31G level The HOM
102. p to Fragments 2 and 4 70 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Going back to the C2H example After application of the FLIP 2x keyword the second CH fragment has 2 a spin and 5 p spin electrons Thus NF NF gu Sa ng eue io ieee and the number of a and f spin electrons in the whole molecule is correct fragment fragment HA ARTF S9 Ql LOR N MELIANA LN B3LYP TZVP ENS NI ase p j j NN LL NSC 5 4 3 f p IN NP Ja 5 Iz M AM ix E 10 Jo AN Jo 6 Orbital interaction diagram for the HC CH molecule which is formed by two CH radicals at the B3LYP TZVP level a spin orbitals are shown in blue p spin orbitals are shown in red AOMix FO calculations with mixed basis sets AOMix can process calculations with mixed basis sets but one has to ensure that the number of d orbitals in each shell five vs six remains the same in the whole molecule and fragment calculations In Gaussian 98 03 09 this can be done by using the 5D keyword for calculations with five d functions pure d functions and the the 6D keyword for calculations with six d functions Cartesian d functions per shell 71 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 CDA example 3 The following example shows how to setup Gaussian 09 calculations for the AOMix FO analysis of the Fe CO 4 C2H4 complex
103. pied FOs Fragment 1 Fragment 3 unoccupied FOs unoccupied FOs Fragment 3 Fragment 1 occupied FOs occupied FOs Fragment 2 E r23 occupied FOs Scheme 3 Charge decomposition analysis for a molecular system with three fragments In the CDA method the terms donation and back donation do not mean only charge transfer interactions they rather correspond to an overall reorganization of electronic density including both charge transfer and electronic polarization Thus the difference between the amount of donation and back donation between fragments is not equal to the net charge transfer between fragments Stronger electronic polarization of fragments will produce a greater deviation between the difference between the amount of donation and back donation and the net charge transfer Thus in cases with large electronic polarization of fragments it is recommended to use ECDA see the AOMix FO section 36 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 in this manual where fragment polarization contributions are taken into account and separated from charge transfer interactions Along the same line the repulsion values in CDA Scheme 3 correspond to the repulsion after polarization i e electron density rearrangement not the repulsion between pristine fragments Energy decomposition analysis EDA AOMix can be used for energy decomposition analysis EDA of Morokuma and Ziegler 9
104. r and 3 4 5 and 6 center bond orders between molecular fragments which can be defined as atoms groups of atoms or groups of atomic orbitals and performs the L wdin population analysis The software can be also used for recovery of the initial guess as the converged wave function and the analysis of spin unrestricted MO calculations the program projects B spin molecular orbitals on to o spin molecular orbitals and prints the overlap matrix a v calculations y Finally AOMix can be used to evaluate dispersion energy corrections to DFT AOMix helps to analyze the nature of the chemical bonding in molecular systems and to monitor changes in the electron density distribution upon the electron excitation Let s say there is a band in an absorption spectrum of a molecule or an ion at 400 nm which is assigned to a HOMO LUMO 2 electron excitation What does it tell about properties of this molecule ion what do we know about the nature of the corresponding excited state What will happen with this molecule ion after the photoexcitation AOMix helps to answer these questions using the molecular orbital decomposition analysis and various density of states DOS plots The main use of DOS plots is to provide a pictorial representation of MO populations The orbital character is determined by the Mulliken population analysis MPA or another available population analysis procedure such as SCPA per molecular orbital The DOS plots
105. ragments A and B adapted from Ref 1 No charge transfer between fragments A and B and no electronic polarization of fragments this case corresponds to a molecule with no covalent interaction between fragments 66 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 2 Polarization of fragment A PL A in presence of fragment B this mixes the OFOs and UFOs of fragment A no charge transfer between A and B and no polarization of fragment B 3 Charge transfer from fragment A to fragment B CT A B mixing the OFOs of fragment A with the UFOs of fragment B no polarization of A and B and 4 Charge transfer from fragment A to fragment B CT A B mixing the OFOs of fragment A with the UFOs of fragment B larger charge transfer from fragment B to fragment A CT B A mixing the OFOs of fragment B with the UFOs of fragment A and no polarization of A and B In a general case there is some electronic polarization of both fragments PL A and PL B charge donation from A to B CT A B and charge donation from B to A CT B 4A UFOs A Unoccupied MOs A A B B Occupied MOs PL OFOs B PL A CT A to B OFO A in unoccupied MOs A B PL A CT B to A UFO A in occupied MOs A B PL B CT B to A OFO B in unoccupied MOs A B PL B CT A to B UFO B in occupied MOs A B Scheme 6 Compositions of occupied and unoccupied molecular orbitals OMOs and
106. rd indicates that the script will include the command to generate the CUBE file for the electrostatic potential 51 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Note 4 Calculation of bond orders between fragments only be done if fragments are defined as e alist of atoms or orbitals or e each atom is a fragment Note 5 If 6d 10f basis sets basis sets with 6 Cartesian d functions and 10 Cartesian f functions are used in calculations LPA exhibit a rotational dependence can predict non equal populations for equivalent atoms and thus in this situation should not be used Note 6 Auser can select to print eigenvalues and eigenvectors of the overlap matrix and the s and S matrices by using the S EIGV ON and LOWDIN ON keywords in the aomixpar txt file Keyword and its possible and AOMix Keyword description default values execution S EIGV ON OFF standard the S EIGV ON and LOWDIN ON keywords turn on printing of all eigenvalues and eigenvectors of the overlap matrix and the S and S matrices if the keyword is absent or commented the program will print six lowest eigenvalues LOWDIN OFF ON standard LOWDIN ON Instructs the program to perform ALWAYS LDA if the number of orbitals is 500 or less LOWDIN ALWA YS Instructs the program to perform LPA for all calculations Dispersion correction for DFT calculations AOMix can be used to calculate dispersion
107. rmined by means of MPA or SCPA Thus for the partial density of states one gets PDOS E Y C F E amp j A sum of PDOS E for all fragments gives TDOS E TDOS E V PDOS E A The overlap population density of states for fragments A and B is OPDOS E S OP F E amp The integration of the OPDOSAg E function over all populated levels gives the total overlap population 7OPA4g between fragments A and B Er TOP OPDOS EME Positive OPDOS E regions represent energy regions where A B bonding levels are located and negative OPDOS E regions represent energy regions where A B anti bonding level are located Thus OPDOS functions enable one to ascertain bonding characteristics of electronic levels in a given energy range with respect to any pair of molecular fragments Since calculation 28 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 of the OPDOS functions requires the overlap populations OP4s OPDOS plots are only calculated for non ZDO calculations with MPA as a method for the electron population analysis 4 10 Orbital Energy eV 2s A 16 18 80 3s S 0 10 20 30 40 50 04 0 2 00 02 04 S orbital contribution OPDOS Cu S 29 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 In the above example two DOS plots are shown The PDOS plot on the left indicates the sulfur atom character in the molecu
108. rs and the index runs over all MOs This is no longer the case if the overlap integrals 3 1 2 are non zero which is generally the case To analyze wave functions with non zero overlap it s necessary to include the overlap populations 2c_ S in the calculations Several schemes were proposed in the literature to deal with the overlap populations These methods are described below Mulliken Population Analysis The most popular and widely used procedure is Mulliken population analysis MPA In MPA the overlap population is split equally between two atoms so the net contribution of 7 to the i MO is equal to 356 6 87 8 1 4 b and the gross atomic population of atom A is GP n Y Y ce 3 1 5 acA k where the index a runs over all AOs localized on the atom A k runs over all AOs of the molecule n 2 1 0 are MO occupation numbers and i runs over all MOs MPA can be utilized for the analysis of the MO compositions in terms of the contributing fragments Contribution of fragment A to the th MO is given by 9o 100 9 Y ce S 3 1 6 acA k The above expression can be re written in the following form Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 hai Y 2 68 gt Yes 3 1 7 aeAaeA acA be A The first sum so called net fragment populations contains only contributions from fragment A and the second sum contains contributions from the overlap populations A
109. site license permits users from the licensed institution to run the SOFTWARE on computers owned by this institution The licensee has no ownership rights in the software or in any copyrights for the software or documentation through this license A user shall not 1 Modify translate reverse engineer decompile or disassemble the SOFTWARE 2 Sell rent lease or transfer all or part of the SOFTWARE or any rights granted hereunder to any person 3 Remove any proprietary notices labels or marks from the SOFTWARE or Documentation A user shall include a proper reference in any publications and conference presentations where you utilized or reported the data which you obtained using the SOFTWARE For example The electronic structure was analyzed using the AOMix program 1 2 1 S I Gorelsky AOMix Program for Molecular Orbital Analysis version 6 X University of Ottawa 2013 htip www sg chem net 2 S l Gorelsky A B P Lever J Organomet Chem 2001 635 187 196 COPYRIGHT Title and copyrights to this SOFTWARE and accompanying materials and any copies made by a user remain with the author This Agreement is effective until terminated A user may terminate this Agreement at any time by destroying all copies of Software This Agreement will be terminated without advanced notice if a user fails to comply with any provision of this Agreement Upon Termination a user must destroy all copies of Software 96 Dr S I
110. t 1 Fragment 2 E SCF 82 611817 82 535557 from CARDS E orb 47 9 kcal mol 1 82 552583 56 184287 26 368297 Interaction energy between the fragments without the BSSE correction Delta E SCF 1 612 eV 37 17 kcal mol 1 E n between the BH and NH fragments in the BH3NH3 adduct at the HF 6 31G level of theory is 37 17 kcal mol E 0 kcal mol S 47 9 kcal mol 82 611817482 535557 a u and E is 10 7 steric Additional information can be extracted about orbital contributions to the electronic interaction energy by using the MIXING keyword with four numbers in the aomixpar txt file Keyword AOMix Keyword description execution MIXING M N x xx y yy FO option If the keyword is included in aomixpar txt AOMix will generate the Gaussian input file that contains the wave function built from fragment wave functions and in which orbital M of fragment 1 and orbital N of fragment 2 were mixed together see the EDA section for details MIXINGBETA M N x xxx FO option If the keyword is included in aomixpar txt AOMix YYYY will generate the Gaussian input file that contains the wave function built from fragment wave functions and in which B spin orbital M of fragment 1 and B spin orbital N of fragment 2 were mixed together see the EDA section for details In this example MIXING B 5 0 120 0 425 the MIXING keyword instructs AOMix FO to mix 12 096 0 120
111. the o rr and 6 contributions Table 2 Two center Mayer bond orders for selected small molecules at the B3LYP TZVP level Single bonds H2 1 00 Na 1 00 K2 0 99 F 0 90 Cl 0 97 Br 1 00 Aromatic C C bonds C H 1 42 Double bonds H2C CH 1 97 O spin triplet ground state 1 74 Triple bonds HC CH 3 12 No 2 69 P5 2 90 Bond order indices can be used for the analysis of the electronic structure of intermediate structures in reaction paths Several reports have been published in which bond orders were utilized for the interpretation of reaction pathways by monitoring the variation of bond orders along a reaction path or internuclear distance so called bond order profiles These studies indicate that 1 the breaking of existing chemical bonds is synchronized with the formation of new chemical bonds and or strengthening of remaining ones the bond order conservation rule 9 2 the position of the transition state is localized in the vicinity of the inflection point on the bond order profile 3 the inflection point in the bond order profile see Figure 1B occurs if there is a change in the ground state wave function 17 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 0 1 266 2 2 24 2 6 2 8 3 0 3 2 Cu Cu Distance R Cu Cu Bond Order Figure 1 adapted from Fig 3 in Ref 9 A The ground state and the first excited state potential
112. the overlap populations equally rather it would be better to assign a smaller portion of 20 059 45 to Xa and the greater portion to Xo Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Modified Mulliken Population Analysis One approach to address some of the MPA deficiencies is to divide the overlap populations in a way that better reflects the non equivalent sharing of electrons between non equivalent atoms Stout and Politzer suggested that the overlap populations are to be split between atoms A and B based on the ratio of the corresponding LCAO MO coefficients Cx and Cpi 2 ai for atom A 3 1 8 Cai tC c for atom B 3 1 9 Cai tC This method is known as the modified Mulliken population analysis MMPA and is available for use in AOMix In MMPA the contribution of ya to the i MO is equal to e 2 2c S cis s 3 1 10 bza ai T Cpi Even though this method should divide the overlap population between atoms less arbitrarily Eqn 3 1 10 itself does not guarantee that orbital populations derived will not have non physical negative values or be in excess of two The major drawback of MMPA is that the orbital compositions and electron populations obtained with MMPA Equation 3 1 10 are invariant neither to unitary transformations among degenerate molecular orbitals nor to unitary transformations of basis orbitals and thus MMPA is not particularly useful Nevertheless
113. txt Keyword and its possible and AOMix Keyword description default values Seen MULTLCENTER OFF 3 4 Standard MULTI CENTER 3 turns on calculation of 3 5 6 center bond order indices MULTI CENTER 4 turns on calculation of 3 and 4 center bond order indices MULTI CENTER 5 turns on calculation of 3 4 and 5 center bond order indices MULTI CENTER 6 turns on calculation of 3 4 5 and 6 center bond order indices 21 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 The multi center interactions are present in molecular systems with significant electron delocalization effects such as aromatic hydrocarbons 4 center bond orders B4scp B gcp b3 x b3 PS PS PS PS printed for closed shell species aeA beB ceC deD and a and B spin components of Basco printed for open shell species Bisco gt gt gt 2 P S P S P S P S and acA be B ceC deD Biso 2 2 2 2 P S P S P S P S ae A beB ceC deD can be evaluated by using AOMix to identify the 4 center interactions For example for the metal aromatic cluster ion AL with Dy symmetry d AI Al 2 58 the Bagcp index of the 4 center Al interaction is positive A B Cc D 4 CENTER bond order index value gt 0 01 1Al 2A1 3Al 4Al B ABCD 0 114 5 center bond orders Bagcpe Bascor Yo gt PS PS PS PS PS printed for clos
114. ure package ADF Gaussian GAMESS etc except Turbomole must be named as follows Output File Name Whole molecule Any name with the log out extension except fragm log Fragment 1 fragm1 log Fragment 2 if present fragm2 log Fragment 3 if present fragm3 log Fragment 99 if present fragm99 log IMPORTANT File names fragm1 log fragm9999 log are reserved for fragment output files This name scheme is implemented to make it easier to run AOMix FO calculations with a large number of fragments For a molecule with two fragments three outputs files should be prepared for processing molecule log fragm1 log and fragm2 log for a molecule with 3 fragments 4 outputs files should be prepared for processing molecule log fragm1 log fragm2 log and fragm3 log etc When you want to obtain the MO composition for a molecule using another molecule as a reference 2 outputs files should be prepared for processing molecule log and fragm1 log a reference molecule 59 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 Let s take the BH43CO complex as an example and define BH and CO as two fragments Then the input structures for the single point calculations must be given as shown below CDA EXAMPLE 1 the BH3CO complex the Gaussian input file P HF 6 31G d NoSymm Pop Full IOp 3 33 1 SCF Tight BH3 CO 01 B 0 90571 0 71072 1 31687 H 0 83756 1 90583 1 19882 H 2 00975 0 24811 1 19883 H 0
115. ven by 11 Dr S I Gorelsky AOMix manual www sg chem net Updated on July 23 2015 SP GP GP The AOMix program will print the a B and gross electron Mulliken and L wdin populations and spin densities for each fragment a B and gross electron Mulliken and L wdin populations and spin densities of each atomic orbital I m I I I l l I ll l l ll ll l ll ll ll GROSS POPULATIONS OF ATOMS MULLIKEN LOWDIN 4 Symb ALPHA BETA TOTAL SPINDENS ALPHA BETA TOTAL SPINDENS 1 Cu 14 682 14 211 28 893 0 47150 14 624 14 125 28 749 0 49982 2 N 3 512 3 512 7 023 0 00017 3 549 3 550 7 099 0 00041 3 N 3 552 3 553 7 105 0 00073 3 497 3 498 6 995 0 00045 4 N 3 513 3 443 6 956 0 07057 3 563 3 505 7 068 0 05763 5 N 3 542 3 543 7 085 0 00085 3 490 3 490 6 981 0 00010 6 N 3 513 3 443 6 956 0 07057 3 563 3 505 7 068 0 05763 T N 3 542 3 543 7 085 0 00085 3 490 3 490 6 981 0 00010 8 C 3 107 3 107 6 214 0 00018 3 018 3 018 6 037 0 00006 9 C3 3 001 3 001 6 002 0 00009 3 074 3 074 6 148 0 00007 SSSS SSS SS SSSSSS S S GROSS ATOMIC ORBITAL POPULATIONS zzzzzzzzzzzzzzz MULLIKEN LOWDIN AO FR ALPHA BETA TOTAL SPINDENS ALPHA BETA TOTAL SPINDENS 1 1 1 000 1 000 2 000 0 00000 0 998 0 998 1 997 0 00000 2 1 1 000 1 000 2 000 0 00001 0 999 0 999 1 999 0 00000 3 1 0

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