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1. Fragment 1 Fragment 3 unoccupied FOs unoccupied FOs Fragment 1 Fragment 3 occupied FOs occupied FOs h Fragment 2 FA r12 123 occupied FOs Scheme 2 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 CDA section 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 2 correspond to the repulsion after polarization i e electron density rearrangement not the repulsion between pristine fragments Page 31 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Energy decomposition analysis AOMix CDA coupled with Gaussian 98 03 calculations can be used for Morokuma
2. Page 80 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Electronic Energy kcal mol V V Bond Order z 0 0 i 2 568 22 24 26 28 30 32 V V Distance A Figure A III Upper Potential energy surfaces and lower Mayer V V bond orders for electronic states of different spin multiplicity of V Cp 2 CgH as a function of the V V internuclear distance the PBE TZVP calculations The way to employ AOMix CDA for initial guess wave function calculations is almost identical to regular AOMix CDA calculations 1 Build your molecular system as in the following order fragment 1 atoml x1 yl al 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 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 Page 81 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 Fragment file n
3. total contribution from Ru atom contribution from BQDI ligand contribution from NH3 ligands HOMO 2 1 i HOMO Partial and Total DOS Energy eV Page 26 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 7 8 The AOMix S program writes continuous TDOS PDOS plot data to AOMix S x DOS line txt and continuous TDOS PDOS plot data to AOMix S X DOS txt where X is the population scheme used MPA MMPA SCPA The data structure of these TDOS PDOS plot files is the first column is energy eV the second 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 S exe 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 Column NF 1 PDOSye contribution of Fragment NF to TDOS a spin orbitals Page 27 of 89 Dr S I Gorelsky AOMix manual ww
4. made by you remain with the author Page 85 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 This Agreement is effective until terminated You may terminate this Agreement at any time by destroying all copies of Software This Agreement will terminate immediately without notice from the author if you fail to comply with any provision of this Agreement Upon Termination you must destroy all copies of Software 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 re
5. Accelrys Inc and CAChe Fujitsu Inc Processing of these output files is achieved by using AOMix prep exe only Other computational chemistry packages can be added to the above list Contact the AOMix author about it Page 3 of 89 Dr S I Gorelsky AOMix manual www sg chem net Available options for AOMix and its modules Updated on August 14 2008 Software Calculation type AOMix AOMix AOMix S AOMix CDA AOMix L prep ADF DFT GAMESS US HF DFT Gaussian 98 HF DFT Gaussian 03 ZINDO F F A F HyperChem HF DFT 0 0 O O Semiempirical Jaguar 3 x 6 x HF DFT MOPAC Semiempirical Q Chem 2 x HF DFT Q Q Q Q Chem 3 x HF DFT Spartan HF DFT 0 0 Semiempirical Turbomole 5 HF DFT ZINDO Semiempirical CNDO INDO Semiempirical SCPA MPA and MMPA are available O SCPA is available MPA and MMPA are not available Q SCPA is available MPA and MMPA are also available if the overlap matrix has been added to a Q Chem 2 x output file by running a special Q Chem output converter contact Professor C P Hsu at cherri sinica edu tw to request a copy of the converter Q available if the overlap matrix has been added to a Q Chem 2 x output file by running a special Q Chem output converter contact Professor C P Hsu at cherri sinica edu tw to r
6. 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 L 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 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 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 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 Page 55 of 89 Unoccupied MOs A B Occupied MOs ae Unoccupied MOs A B I rc MOs Dr S I Gorelsky
7. s energy decomposition analysis EDA this section of the AOMix manual will be added soon Evaluation of Electronic Coupling between Donor and Acceptor in Donor Bridge Acceptor Systems using AOMix CDA this section of the AOMix manual will be added soon Working with AOMix Execution environment of the AOMix software is controlled by the parameter file aomixpar txt This file will be created when you run AOMix exe for the first time You can modify the execution parameters to tune the program to your particular tasks See the AOMix keyword descriptions in this manual To start the AOMix program execute AOMix exe 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 AOMix exe reads the molecular orbital information directly from output files of the 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 printed in an output file You can select SCPA as an alternative method by adding the SCPA keyword to aomixpar txt Unless you want to treat all atomic orbitals o
8. 0 08764 0 00535 0O RRE 2PZ 0 02568 0 14132 0 03181 0O ts 3S 0 01522 0 08717 0 20222 O EKE 3PX 0 01543 0 04160 0 11174 0 KAR 3PY 0 04850 0 12485 0 01519 0O KER 3PZ 0 03569 0 22263 0 08798 O KRR 4D 0 0 00001 0 01147 0 00853 0 KER 4D 1 0 00125 0 00983 0 00432 0 KKK 4D 1 0 00000 0 00847 0 02461 0 KAK 4D 2 0 00135 0 00209 0 01908 0 EEK 4D 2 0 00344 0 00388 0 00551 0O x 118 H 15 0 01024 0 02248 0 06354 0 KAE 25 0 05947 0 15626 0 06432 O eee 119 H 15 0 00169 0 12149 0 08394 0 EAA 2S 0 02293 0 27698 0 06610 0 00048 00408 04061 12659 07398 11025 0 0 0 01109 0 05886 0 0 0 00101 07823 04233 0 17658 01036 0 00491 00508 0 00158 01637 0 00552 00488 0 00852 00235 0 01688 02228 0 06322 00795 0 00288 06407 0 02118 15275 0 27837 AOMix exe will process such output with no problem the AOMix program does not use orbital numbers printed in the first column by Gaussian EXAMPLE OF THE LCAO MO OUTPUT FROM HyperChem s c 1 0 36236 0 26975 0 39441 0 17211 0 Px C 1 0 13668 0 08866 0 06608 0 18388 0 Py C 1 0 07705 0 15871 0 10536 0 24226 0 Pz C 0 00000 0 00000 0 00000 0 00000 0 S C 2 0 36094 0 20123 0 43173 0 17441 0 Px C 2 0 13627 0 09761 0 04994 0 18252 0 Py C 2 0 07715 0 17237 0 07771 0 23894 0 Pz 2 0 00000 0 00000 0 00000 0 00000 0 Ss C 3 0 36904 0 48305 0 04042 0 35945 0 Px C 3 0 00029 0 01904 0 22765 0 0023
9. 4 5 18 59 Fragment 1 30 1 30 1 24 1 24 0 06 0 06 0 00 0 00 0 03 1 22 1 22 0 03 0 00 0 00 0 00 0 00 Fragment 98 70 98 70 98 62 98 62 0 08 0 08 0 00 0 00 0 00 0 00 98 61 0 01 0 01 98 61 0 00 0 00 0 00 0 08 0 08 0 00 0 00 0 00 Page 53 of 89 ooworoo0oO OWO0O0O0OrFRAOCO Oo Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 26 4 HOFO 2 BH 16 0 LUFO BHs 56 5 HOFO CO The LCFO MO coefficients Ca can be also printed to AOMix CDA output files by adding the LCFO keyword to the aomixpar txt file THE LCFO MO MATRIX 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 1 1 0 043 0 598 0 600 0 000 0 000 0 514 0 000 0 000 2 1 0 000 0 000 0 000 0 016 0 110 0 000 0 975 0 048 31 0 000 0 000 0 000 0 110 0 016 0 000 0 048 0 975 40 0 035 0 174 0 002 0 000 0 000 0 400 0 000 0 000 5 0 0 017 0 057 0 005 0 000 0 000 0 101 0 000 0 000 6 0 0 000 0 000 0 000 0 024 0 004 0 000 0 001 0 031 70 0 000 0 000 0 000 0 004 0 024 0 000 0 031 0 001 1 1 0 998 0 049 0 018 0 000 0 000 0 002 0 000 0 000 2 1 0 018 0 710 0 689 0 000 0 000 0 009 0 000 0 000 3 1 0 000 0 000 0 000 0 993 0 011 0 000 0 023 0 113 4 1 0 000 0 000 0 000 0 011 0 993 0 000 0 113 0 023 5 1 0 011 0 316 0 402 0 000 0 000 0 752 0 000 0 000 6 0 0 000 0 000 0 000 0 006 0 028 0 000 0 179 0 001 70 0 000 0 000 0 000 0 028 0 006 0
10. 47 51 Leks ATOM 2N 4 39 0 06 0 16 0 21 22 97 16 42 829 2 72 0 02 0 02 Net pop F669 0 05 053 0 14 23 49 2511 9 46 3 25 O01 O01 s s orbitals 22 0 00 0 01 0 00 0 00 4 27 0 00 0 00 0 00 0 00 p orbitals 3 15 0 06 016 012 22 89 12 13 8 20 2671 O02 D102 d orbitals 0 02 0 00 0 00 0 109 0 08 0 02 0 09 0 04 0 00 0 00 3N 42 0 06 0 30 8 49 6 47 Ois TT 12 21 0 04 0 01 001 In this table the gross and net populations are printed for each fragment it is followed by s p d orbital contributions In the above example the net and gross populations in the LUMO for the Cu atom fragment 1 are 48 6 and 54 7 respectively The net population of the Cu atom comes from the d and p orbitals their contributions to the LUMO are 47 5 and 1 1 respectively At the end of the AOMix S exe output for all non closed shell singlet calculations the contributions to the spin density are printed ATOM S SPIN DENSITY 1Cu Gross S9 sas p sandes f ete 0 471 0 006 0 025 0 503 Page 39 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 2N 0 000 0 000 0 000 0 000 3N 0 001 0 000 0 001 0 000 4N 0 071 0 019 0 052 0 000 5N 0 001 0 001 0 002 0 000 6N 0 071 0 019 0 052 0 000 7N 0 001 0 001 0 002 0 000 In the above example for the 1Cu atom fragment 1 the spin density 0 471 comes almost entirely from the difference 0 503 in the d orbital occupation and slightly
11. 7 66 a2 0 100 131 LUMO 1 7 79 e 8 92 130 LUMO 7 79 e 8 92 occupied unoccupied orbital gap 3 4leV 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 LUMO 0 1 70 8 62 HOMO gt LUMO 2 70 0 70 HOMO 1 2 gt LUMO 0 1 72 8 64 HOMO 1 2 gt 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 CT M C i M M 3 4 3 where C i gt are the appropriate coefficients of the th eigenvector of the Cl matrix So one can very effectively use the MO compositions in terms of fragment orbital contributions to probe the nature of electronic transitions Page 30 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Charge Decomposition Analysis CDA 1314 ig one of the two methods that are The CDA method of Frenking and co workers currently implemented in the AOMix CDA 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 2 Electron Donation and Back donation and Repulsion and Residue Terms Fragment 2 unoccupied FOs
12. A Solomon E Journal of the American Chemical Society 2006 128 16452 16453 42 Ponec R Yuzhakov G Cooper D L J Phys Chem A 2003 107 2100 2105 43 Johnston H S Adv Chem Phys 1960 85 131 44 Johnston H S Parr C J Am Chem Soc 1963 85 2544 45 Brookhart M Green M L H Parkin G Proceedings Of The National Academy Of Sciences Of The United States Of America 2007 104 6908 6914 46 Lafrance M Gorelsky S Fagnou K J Am Chem Soc 2007 129 14570 14571 47 Fukui K Yonezawa T Shingu H J Chem Phys 1952 20 722 725 48 Fukui K Yonezawa T Nagata C Shingu H J Chem Phys 1954 22 1433 1442 49 Fukui K Theory of Orientation and Stereoselection Springer Verlag Berlin 1975 50 Fukui K Science 1982 218 747 754 51 Chemical Reactivity and Reaction Paths Klopman G Ed John Wiley amp Sons New York 1974 52 Makedonas C Mitsopoulou C A European Journal of Inorganic Chemistry 2006 590 598 Page 88 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 53 Gorelsky S I In Comprehensive Coordination Chemistry II McCleverty J A Meyer T J Eds Elsevier Amsterdam 2004 Vol 2 p 651 660 54 Hughbanks T Hoffmann R Journal of the American Chemical Society 1983 105 3528 55 Ghosh S Gorelsky S I Chen P Cabrito I Moura J J G Moura l Solomon E
13. B8BLYP TZVP level Single bonds H2 1 00 Nas 1 00 K2 0 99 F2 0 90 Cl 0 97 Brz 1 00 Aromatic C C bonds CsHes 1 42 Double bonds H2C CH2 1 97 Oz spin triplet ground state 1 74 Triple bonds HC CH 3 12 N2 2 689 P2 2 90 Bond order indices can be used for describing and analyzing 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 15 41 42 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 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 on the bond order profile see Figure 1 occurs if there is a change in the ground state wave function Page 16 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Cu Cu Bond Order 2 4 2 6 2 8 3 0 3 2 Cu Cu Distance R Figure 1 adopted from Fig 3 in Ref A The ground state and the first excited state potential energy surfaces of the Cua cluster the Nuis Cu Scys 2Gu Nuis cluster and B Mayer bond order Bag between the two Cu atoms
14. J Am Chem Soc 2003 125 15708 15709 56 Lever A B P Gorelsky S Struct Bonding Berlin 2004 107 77 114 57 del Rio D Galindo A Resa Carmona E Angew Chem Intl Ed 2005 44 1244 1247 58 Platas Iglesias C Esteban Gomez D Enriquez Perez T Avecilla F de Blas A Rodriguez Blas T Inorg Chem 2005 44 2224 2233 59 Gorelsky S Lever A B P Can J Anal Sci Spectr 2003 48 93 105 60 Kitaura K Morokuma K nternational Journal Of Quantum Chemistry 1976 10 325 340 61 Pettersen E F Goddard T D Huang C C Couch G S Greenblatt D M Meng E C Ferrin T E Journal of Computational Chemistry 2004 25 1605 1612 62 Albright T A Burdett J K Whangbo M H Orbital Interactions in Chemistry John Willey amp Sons New York 1985 63 llango S Vidjayacoumar B Gambarotta S Gorelsky S Inorg Chem 2008 47 3265 3273 64 Ziegler T Rauk A Theoret Chim Acta 1977 46 1 10 65 Rusanova J Rusanov E Gorelsky S I Christendat D Popescu R Farah A A Beaulac R Reber C Lever A B P Inorganic Chemistry 2006 45 6246 6262 66 Schafer A Huber C Ahlrichs R Journal of Chemical Physics 1994 100 5829 5835 67 Godbout N Salahub D R Andzelm J Wimmer E Canadian Journal of Chemistry 1992 70 560 571 68 Boys S F Bernardi F Mol Phys 1970 19 553 69 Noodleman L Journal o
15. The Bold Italics font is used for file names The Bold Courier New font is used for program input and output examples The Elephant font is used for the AOMix keywords The Bold Verdana font is used for keywords of the other program packages such as Gaussian 03 etc Software Requirements MS Windows NT 2000 XP NO COMPLICATED INSTALLATION IS REQUIRED JUST DOWNLOAD THE SOFTWARE TO YOUR COMPUTER and operating systems RUN THE INITIALIZATION SCRIPT Supported Other CPU Pentium ll or higher an ethernet card Only necessary for a computer with requirements a single workstation license Page 2 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 AOMix processes output files from the following programs 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 CNDO INDO Dr J R Reimers U of Sydney Australia GAMESS GAMESS US Gordon group at lowa State University Gaussian 98 Gaussian 03 Gaussian Inc HyperChem HyperCube Inc Jaguar 3 x 6 x Schrodinger Inc MOPAC Dr J J P Stewart Fujitsu Limited Q Chem 2 x 3 x Q Chem Inc Spartan Wavefunction Inc Turbomole v 5 Quantum chemistry group University of Karlsruhe ZINDO M C Zerner Quantum Theory Project U of Florida USA ZINDO is available in Cerius
16. atom orbital list statements are not restricted to one line for a fragment You can use as many lines as necessary to list all relevant atoms orbitals 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 lt TAB gt 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 N4 No No etc N N2 N3 Na 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 The above formats can be used together For instance the following instructions tell AOMix exe 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 0 10 50 60 62 0 70 80 1 First fragment 234069 0 63 69 1 Second fragment Note that there should be no duplication in fragments two different fragments cannot contain the same basis functions AOMix exe automatically checks for duplications and will exit with an error message if it detects a duplication Don not worry if your
17. column contains the overlap populations between the quinone ligand and the four ammonia ligands Positive OP g values represent a bonding interaction large negative OP s values correspond to an anti bonding interaction and OP 0 indicates no bonding between A and B As it can be seen from the table above the three highest occupied MOs HOMO 0 1 2 remain mostly non bonding with respect to metal ligand interactions tag Ru orbitals while LUMO 1 and LUMO 2 is anti bonding with respect to the Ru ligand interactions AO contributions 2 Cai Cbi Sab gt 0 01 to overlap populations can be printed to AOMix S output files by using the OP CONTRIBUTIONS keyword 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 4 23 Ca 0 4093 Cb 0 6021 Sab 0 1709 2 Ca Cb Sab 0 084 Page 13 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 the AOMix L program four types of bond order indices are available for the analysis of bonding between molecular fragments 1 generalized Wiberg indices calculated in the canonical MO basis 2 Wiberg indices calculated in the L wdin basis 21 24 3 Mayer indices calculated in the canonical MO basis and 4 3 and 4 center bond order indices calcula
18. e dat which will contain interaction diagrams for orbitals with a and e symmetry respectively see Figure below Page 64 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Orbital Interactions between BH and CO in BH CO AM1 calculation AOMix CDA ef oo 39 6 37 k S 8 8 L gt 10 10 gt c 12 12 Lu O 414 14 16 16 18 18 20 20 22 22 24 24 26 26 Bilg BH CO CO Orbital interaction diagram for the H 3B 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 CDA exe reads symmetry information from the aomix g file This information can read by AOMix exe from electronic structure 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 CDA exe will replace the symbol with the X symbol in the AOMix MO FO dat file names By default AOMix CDA exe connects MO FO pairs for which corresponding contributions are greater than 4 It is possible to change the value of this parameter You can use any graph Page 65 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 software of your choice SigmaPlot 2000 Excel etc to create orbital interaction diagrams from
19. matrix to an output file Page 47 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Q Chem 3 x use the keywords same as for a whole molecule calculations PRINT_ORBITALS 99999 calculation and IPRINT 200 ZINDO use the keyword MOS in the same as for a whole molecule ZDO calculations OUTPUT input section calculation a The NoSymm keyword is only necessary if the specified molecular geometry is not in the standard orientation defined in a particular QC package for example Gaussian 03 b Do not confuse the core functions and core orbitals please refer to the ADF user manual for details If you have never done AOMix CDA calculations before it can useful to run one or two sample AOMix CDA calculations first The AOMix CDA input and output examples are provided for the ADF GAMESS Gaussian and HyperChem packages and can be downloaded from http www sg chem net download FIVE STEPS FOR AOMIX CDA CALCULATIONS Sieps 1 and 2 are performed using a QC package see APPENDIX II if you want to use AOMix CDA exe to construct the wave function of a molecular systems from the wave functions of the fragments 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 calculations As a result the geometry specification of an entire molecule must follow this order fra
20. package with all executable exe files 114 The software license number is incorrect or the program could not read it 113 The program could not find registered MAC address or license file 114 aomixpar txt is missing from the AOMix directory Execute AOMix exe 200 The correct ASCII format of the output file is not detected Convert your input files to the MS DOS ASCII format using the U2WIN program or any other available method 201 The output file does not match the format of the quantum chemical package 202 AOMix exe could not determine the quantum chemical package 203 AOMix exe could not find the TITLE line in your output file 220 AOMix exe could not find the number of electrons in the output file 239 AOMix exe cannot process ADF calculations with core basis functions Please use the all electron basis sets without core functions 240 AOMix exe could not find the number of orbitals in the output file 242 Number of orbitals exceeds the program limit To proceed 1 Run AOMix exe with the LARGE keyword to generate AOMix x input files and 2 Run AOMix S exe to finish the calculation 243 Number of canonical orbitals is not valid 250 AOMix exe could not find the LCAO MO expansion in the output file you selected Make sure that it is in your output file 251 There was a problem while reading the LCAO MO data Inspect your output file 255 AOMix exe could not find the LCAO MO expansion for beta spin orbitals in the output file
21. shell has 7 a spin and 7 spin electrons however each CH radical in the quartet spin state has 5 a spin and 2 B spin electrons adding to a total of 10 a spin and 4 spin electrons in the default spin coupling scheme ferromagnetic CDA example 2 the input file for the whole molecule P B3LYP TZVP SCF Tight Pop Full I0p 3 33 1 The HC CH molecule 1 0 000000 0 000000 1 661837 0 000000 0 000000 0 599005 0 000000 0 000000 0 599005 0 000000 0 000000 1 661837 maaqwzo Page 59 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 the input file for Fragment 1 P UB3LYP TZVP SCF Tight Pop Full I0p 3 33 1 NoSymm Fragment 1 HC 0 4 H 0 000000 0 000000 1 661837 Cc 0 000000 0 000000 0 599005 the input file for Fragment 2 P UB3LYP TZVP SCF Tight Pop Full I0p 3 33 1 NoSymm Fragment 2 CH 4 0 000000 0 000000 0 599005 0 000000 0 000000 1 661837 mao the above example shows Gaussian 03 input files for the AOMix CDA calculation In this situation you want to couple the a spin FOs of the 1 fragment with the B spin FOs of the 2 fragment anti ferromagnetic spin coupling The anti ferromagnetic spin coupling scheme is added in AOMix CDA by the use of the FLIP x keyword in the aomixpar txt file This keyword instructs AOMix CDA to exchange swap a spin and f spin orbitals for fragment i Going back to the C2H2 example Afte
22. the script will include all molecular orbitals AOMix L exe Note 1 AOMix L will only run when molecular fragments are defined as e alist of atoms or orbitals or e each atom is a fragment AOMix L cannot be used for calculations when each atomic orbital is defined as a fragment NF the number of basis functions Note 2 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 gt Note 3 4 center bond order indices are printed if the 4 CENTER ON keyword is present in the aomixpar txt file Note 4 for spin unrestricted calculations the program projects B spin MOs on to a spin MOs and prints the overlap matrix g of the so called mutual overlap matrix for 8 highest occupied and 8 lowest unoccupied MOs the default settings 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 0FF Note 5 A user 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 Page 41 of 89 Dr S I Gorelsky AOMix
23. 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 Page 83 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Currently this AOMix CDA functionality to build wave functions of multi fragment molecular systems from fragment wave functions can be used for Gaussian calculations only In future releases similar functionality can be added for use with other quantum mechanical packages if they allow the same functionality as Gaussians Guess Cards keyword Page 84 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 By using AOMix and or its additional modules you fully agree with the following LICENSE AGREEMENT GRANT OF LICENSE The author S I Gorelsky grants you a nonexclusive nontransferable license to use the AOMix program and its additional modules if applicable the SOFTWARE according to the terms and conditions herein The workstation license permits a user to run the SOFTWARE on one computer unless addit
24. 0 370 0 001 HOMO 1 10 0 019 0 HOMO O 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 sss FO AO FO AQ S FO I 4 115 4 115 4 115 4 115 8 230 8 230 0 000 0 000 23 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 BH3 CO molecule CT 2 1 CT 1 2 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 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 Page 52 of 89 Dr S I Gorelsky AOMix manual www sg chem net 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 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 fo
25. 000 0 001 0 179 8 0 0 001 0 048 0 054 0 000 0 000 0 023 0 000 0 000 Note In order to produce concise output files AOMix CDA prints LCFO MO coefficients in the LONG FORM only if they are no less than the threshold value the default value is 0 1 a user can increase it to 1 by using the FORMAT P O keyword or decrease it to 0 01 by using the FORMAT P 2 keyword in the AOMix parameter file So if some LCFO MO coefficients went missing in the LONG FORM of your AOMix CDA output this is not a software bug After the LONG FORM AOMix CDA exe 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 Page 54 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 gt 1 CT 1 gt 2 11 5 net charge transfer 0 23 e If symmetry is present AOMix CDA exe prints a summary for each set of molecular orbitals of given irreducible representation AOMix CDA exe also prints contributions of each fragment molecular orbital to all occupied
26. 3 0 00000E 00 0 00000E 00 5 61000E 03 5 90000E 04 0 00000E 00 0 00000E 00 3 10000E 03 4 26000E 03 4 26000E 03 0 00000E 00 0 00000E 00 0 00000E 00 7 00000E 05 3 00000E 05 2 00000E 04 0 00000E 00 0 00000E 00 8 11000E 03 2 90000E 03 0 00000E 00 0 00000E 00 7 80000E 04 Page 79 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 APPENDIX Il AOMix CDA exe 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 63 69 71 open shell calculations of low spin anti ferromagnetically coupled systems such as for example a pentalene bridged V V complex where the two ions are separated by 2 54A and anti ferromagnetically coupled to yield a ground state wave function with Siota 0 V Cp 2CsHe a a D Ca e vit FF va Figure A ll Spin density of the broken symmetry state for V Cp o CgHg open shell singlet from the PBE TZVP calculation The initial guess wave function was generated from the fragment wave functions by AOMix CDA For this complex the closed shell singlet description with a triple vanadium vanadium bond proposed in Ref is incorrect see the gray line for the S 0 CS state in Figure A III and there is only a weak single V V bond in the true ground state
27. 477 Sannigrahi A B Kar T Chemical Physics Letters 1990 173 569 572 Kar T Marcos E S Chemical Physics Letters 1992 192 14 20 deGiambiagi M S Giambiagi M Fortes M D Theochem Journal Of Molecular Structure 1997 391 141 150 28 Ponec R Mayer I J Phys Chem A 1997 101 1738 1741 29 Bochicchio R C Ponec R Lain L Torre A J Phys Chem A 1998 102 7176 7180 30 Ponec R Torre A Lain L Bochicchio R C International Journal Of Quantum Chemistry 2000 77 710 715 31 Mayer I Chemical Physics Letters 2004 393 209 212 Reed A E Weinhold F J Chem Phys 1983 78 4066 4073 Reed A E Weinstock R B Weinhold F J Chem Phys 1985 83 735 746 Reed A E Curtiss L A Weinhold F Chem Rev 1988 88 899 926 Haslingerova Czech J Phys 1977 B27 1389 1393 36 Hoffmann R Solids and Surfaces A Chemist s View of Bonding in Extended Structures VCH Publishers New York 1988 37 Glassey W V Hoffmann R Journal of Chemical Physics 2000 113 1698 NNNUNN MOOS ONS Cees 1704 38 Segal M D Phys Rev 1996 54 16317 16320 39 Gorelsky S Basumallick L Vura Weis J Sarangi R Hedman B Hodgson K O Fujisawa K Solomon E Inorganic Chemistry 2005 44 4947 4960 40 Solomon E Gorelsky S I Dey A Journal of Computational Chemistry 2006 27 1415 1428 41 Gorelsky S Xie X Chen Y Fee J
28. 5 0 Py Cc 3 0 15833 0 00765 0 00073 0 16561 0s Pz C 3 0 00000 0 00000 0 00000 0 00000 0 Atomic orbitals 1 4 are on atom 1 carbon atomic orbitals 5 8 are on 30592 0 08809 01395 0 29675 21133 0 13282 00000 0 00000 30181 0 09679 00357 0 29442 20795 0 13844 00000 0 00000 00208 0 04514 36219 0 00604 00344 0 31819 00000 0 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 list numbers in the LCAO MO output by counting orbitals manually Unless you want to treat all atomic orbitals or all atoms as individual fragments for AOMix S and AOMix L calculations you have to create an auxiliary ASCII file to specify molecular fragments AOMix exe 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 Page 34 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 2 fragment or a blank line etc The
29. 50 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 4 Start the AOMix exe program and run it using single point output files you prepared in Steps 1 and 2 for the current example calculation select the BH3CO og file as an output file for the whole molecule make sure that the output files for the molecular fragments fragm7 log and fragm2 log are present in the AOMix directory First you should see the message Preparing the AOMix CDA input files ON Then AOMix exe will create several files aomix c aomix e aomix g aomix ao and aomix o if it s an MPA calculation aomix c1 aomix e1 and aomix o7 if it s a non ZDO calculation aomix c2 aomix e2 and aomix o2 if it s a non ZDO calculation etc which will be used in the next step At the end of the AOMix exe run you should see the message Normal Termination 5 Start the AOMix CDA exe program in the same directory where the AOMix files from Step 4 are located The AOMix CDA program runs several checks before starting the main calculation 1 the program verifies the wave function of the whole molecule 2 the program verifies the wave functions of the fragments and 3 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 CDA exe runs a final check it compares and pri
30. A exhibit a rotational dependence can predict non equal populations for equivalent atoms and thus in this situation should not be used for the analysis Page 11 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 derived charges show very little variation Overlap Populations and Chemical Bonding The 2c_ S terms where ae atom A and be atom B are the overlap populations between the two atoms with atomic orbitals ya and 7 respectively of the i MO The total overlap population TOP between atoms A and Bin a molecule is calculated by adding together overlap populations for orbitals centered on these two atoms TOPas gt 7 gt gt 2C 04S05 3 2 1 i ac A beB where Cai is the LCAO MO coefficient of ya on atom A Cp is the coefficient of vy on atom B both in the MO and S is the overlap integral for these
31. AOMix CDA output files To create the orbital interaction plot 1 Import each of the AOMix MO FO alpha l dat files for 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 enter new parameters edit the line after the CDA keyword 4 0 0 0 0 0 If the above line is modified to be 3 0 1 55 1 41 AOMix CDA exe 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 CDA ou
32. AOMix L If the keyword is included in aomixpar txt AOMix L exe will generate the Gaussian input file Page 74 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 that contains the converged wave function as an initial guess see Appendix for details PSEUDOBONDS i AOMix L Assigns the print format threshold value and X color color to bond orders in UCSF Chimera PseudoBond attribute files Default is PSEUDOBONDS 3 0 1 blue AOMIX S TO FOLLOW AOMix L If the keyword is included in aomixpar txt AOMix S calculations will start automatically after AOMix L execution At the end of the run all temporary files will be deleted Several new program keywords have not been documented yet Watch for the updates of this manual a b In order to use these keywords a user must have an appropriate license Page 75 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 AOMix Error Codes AOMix exe and other programs in the AOMix package perform 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 100 One or more of the AOMix executable files aomix p exe are missing Make sure that you have downloaded the complete AOMix
33. AOMix manual www sg chem net A owe i Unoccupied MOs A B Occupied MOs Unoccupied MOs A B Occupied MOs Updated on August 14 2008 B OFO B OFO B g OFO B Scheme 4 Compositions of occupied and unoccupied molecular orbitals of A B in terms of occupied and unoccupied molecular orbitals of fragments A and B adopted 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 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 Page 56 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 A UFOs A Unoccupied MOs A A B
34. B Occupied MOs PL PL A a 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 5 Compositions of occupied and unoccupied molecular orbitals OMOs and 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 adopted from Ref 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 Page 57 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 gt 1 CT 1 gt 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 diff
35. Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 AO Mix Revision 6 36 AOMix and its additional modules AOMix CDA AOMix L and AOMix S is a user friendly comprehensive package for the molecular orbital analysis with additional useful utilities see Appendices and II in this manual 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 ADF GAMESS US Gaussian HyperChem Jaguar MOPAC Q Chem Spartan Turbomole ZINDO and CNDO INDO programs and produces data tables in the ASCII text format with relevant MO information condensed Fukui functions etc In addition AOMix S generates total partial and overlap population density of states DOS plots and can be used for MO composition analysis in systems with many fragments AOMix CDA 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 generates plot data for MO interaction diagrams and calculates Green function matrix elements for electronic coupling between donor and acceptor through the bridge In a
36. LLIKEN gt gt LOWDIN ATOM 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 Nog 3 512 Seale 7 023 0 00017 3 549 3 550 7 099 0 00041 3 N 3 592 2 993 7 205 0 00073 3 497 3 498 6 995 0 00045 4 N 3513 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 Beep 3 443 6 956 O 0 7057 3 563 3 505 7 068 0 05763 7 N 3 542 3 543 7085 0 000 8 gt 3 490 3 490 6 981 000010 S 3 107 3 107 6 214 0 00018 J0 T8 3018 6 037 0 00006 oi 3 001 3 001 6 002 0 00009 3 074 3 074 6 148 0 00007 GROSS ATOMIC ORBITAL POPULATIONS MULLIKEN gt LOWDIN AO FR ALPHA BETA TOTAL SPINDENS ALPHA BETA TOTAL SPINDENS 1 i 13000 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 l 0 613 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 0 639 0 00061 5 1 0 397 0 404 0 801 0 00659 0 159 OC LoL 0 320 0 00254 6 1 0 024 0 024 0 048 0 00040 0 062 0 063 0 126 0400105 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 dyx dyy dzz Oxy xz dyz or and 10 Cartesian f functions are used in calculations LP
37. OMix CDA analysis of the Fe CO 4 C2H 4 complex 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 Page 61 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 the input file for the Fe CO 4 C2H4 P B3LYP GEN 5D SCF Tight Pop Full I0p 3 33 1 The Fe CO 4 C2H4 complex the molecule is in standard orientation NOSYMM is not necessary Of Fe 0 000000 0 000000 0 018179 C 1 821462 0 000000 0 090291 C 1 821462 0 000000 0 090291 c 0 000000 1 503897 0 976361 C 0 000000 1 503897 0 976361 fe 0 000000 2 460510 1 620978 0 0 000000 2 460510 1 620978 0 2 968878 0 000000 0 160975 o 2 968878 0 000000 0 160975 Cc 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 kkkk ocCHO0 6 31G kkk the input file for Fragment 1 P B3LYP GEN 5D SCF Tight Pop Full I0p 3 33 1 NOSYMM Fragment 1 Fe CO 4 0 1 Fe 0 000000 0 000000 0 018179 1 821462 0 000000 0 090291 Cc 1 821462 0 000000 0 090291 C 0 000000 1 503897 0 976361 Cc 0 000000 1 503897 0 976361 o 0 000000 2 460510 1 620978 re 0 000000 2 460510 1 620978 o 2 968878 0 000000 0 160975 fe 2 968878 0 000000 0 160975 Fe 0 TZVP kkk oco 6 31G kkk th
38. OUTPUT FROM Gaussian 98 03 191 13 C 2S 0 00110 0 00000 0 01488 0 00262 0 01567 192 2S 0 00290 0 00000 0 03439 0 00783 0 03699 193 3S 0 00845 0 00000 0 06530 0 00508 0 08224 194 4PX 0 00000 0 03074 0 00000 0 00000 0 00000 195 4PY 0 01065 0 00000 0 01379 0 21671 0 01171 196 4PZ 0 01577 0 00000 0 13845 0 03374 0 28372 197 5PX 0 00000 0 00129 0 00000 0 00000 0 00000 198 5PY 0 00241 0 00000 0 03258 0 03023 0 04244 199 5PZ 0 00146 0 00000 0 00053 0 00159 0 01050 200 6D 0 0 00096 0 00000 0 00478 0 01128 0 00719 201 6D 1 0 00000 0 00295 0 00000 0 00000 0 00000 202 6D 1 0 00017 0 00000 0 01295 0 00131 0 02599 203 6D 2 0 00011 0 00000 0 00075 0 00406 0 00041 204 6D 2 0 00000 0 00284 0 00000 0 00000 0 00000 205 14 H 1S 0 05999 0 02475 0 00957 0 01148 0 00726 206 2S 0 00010 0 00412 0 00272 0 01142 0 00497 207 15 H 1S 0 05999 0 02475 0 00957 0 01148 0 00726 208 2S 0 00010 0 00412 0 00272 0 01142 0 00497 Atomic orbitals 191 204 are on atom 13 carbon atomic orbitals 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 997 117 0 15 0 00153 0 01285 0 00334 0 00332 0 01444 998 2S 0 00157 0 07079 0 05159 0 01941 0 06777 999 2PX 0 00900 0 00035 0 05751 0 00858 0 05029 Page 33 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 EER 2PY 0 03250
39. PEN_M2I0_FILES messages If they do just delete those lines MOPAC calculations use the keywords VECTORS EIGEN and ALLVEC Q Chem 2 x calculations use the keywords PRINT_ORBITALS 99999 and the converter utility to add the overlap matrix to an output file Q Chem 3 x calculations use the keywords PRINT_ORBITALS 99999 and IPRINT 200 Spartan calculations For processing use output files instead of spartan Page 37 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 files Turbomole calculations scfmo file mos last step dscf intsdebug cao scforbitalorder on 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 Working with AOMix L and AOMix S If the overlap matrix i
40. RAMO when going from the Koopmans state to the final state is presented by a red dashed arrow adopted from Ref 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 CDA will use CDA and ECDA The latter allows separate evaluation of charge transfer and polarization contributions see below In addition the AOMix CDA program version 2 2 and up allows the analysis of electronic coupling between donor and acceptor through the bridge AOMix CDA exe 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 you need to run regular AOMix calculations are not needed for AOMix CDA calculations because the fragments are defined by the fragmX log files see below The AOMix CDA program 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 Page 45 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 molecule is treate
41. _ c 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 y to the i MO is equal to Secs 3 1 A b and the gross atomic population of atom A is GP F n 9 CuS o 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 Page 6 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 4 100 gt e S 4 3 1 6 acA k The above expression can be re written in the following form 44 od X F eS a Bg reas 3 1 7 acA atA acA b 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 AOMix exe and AOMix S exe can be used to calculated the MO compositions gross fragment populations and the overlap populations between fragments in addition AOMix S exe will also print the net populations the first sum in E
42. ake seconds or minutes on a modern workstation For large molecule calculations with more than 1000 orbitals you may lose hours or days of CPU time to recover your converged wave functions Keeping the checkpoint files is not necessary anymore AOMix L exe can recover the converged wave function from an output To activate this option include the GUESS CARDS keyword in the aomixpar txt file Then run AOMix L exe as you would run it for regular AOMix L calculations For Gaussian calculations AOMix L exe 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 0 1 B 0 905721 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 017251 0 0 38420 0 20138 0 91730 5E16 5 1 1 00000E 05 2 00000E 04 1 50000E 04 0 00000E 00 0 00000E 00 4 10000E 04 6 00000E 05 0 00000E 00 0 00000E 00 3 80000E 04 4 00000E 05 4 00000E 05 0 00000E 00 0 00000E 00 0 00000E 00 1 00000E 05 7 00000E 05 1 00000E 05 7 00000E 05 1 00000E 05 7 00000E 05 4 00000E 05 0 00000E 00 6 30000E 04 0 00000E 00 0 00000E 00 9 80000E 04 8 40000E 04 0 00000E 00 0 00000E 00 1 31000E 03 6 00000E 05 6 00000E 05 0 00000E 00 0 00000E 00 0 00000E 00 9 94670E 01 2 11400E 02 2 03000E 0
43. altered by spin polarization of the s and p orbitals their contributions to the atom spin density are 0 006 and 0 025 respectively AOMix S exe 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 and HyperChem and Gaussian 03 output files If you basis set has 6 Cartesian d functions and 10 Cartesian f functions AOMix S exe will skip the spdf analysis Note 2 Overlap populations and DOS plot data are generated only if NF lt 13 this is done to limit the size of AOMix S output files Note 3 Atomic orbital contributions to overlap populations can be printed to AOMix S output files by using the OP CONTRIBUTIONS keyword Note 4 For Gaussian calculations AOMix S exe will generate two scripts AOMix S cube win bat for MS Windows and AOMix S cube bat for Linux UNIX for cube file generation These AOMix scripts will be very helpful to Gaussian users to generate cube files for visual analysis of molecular orbitals spin density and electrostatic potential The example of the UNIX script AOMix S cube bat is shown below touch temp fchk rm temp fchk formchk temp chk cubegen 0 potential temp fchk C9H1L7CuN4S2 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
44. ames are pre defined as described below For correct AOMix and AOMix CDA execution output files from your electronic structure package ADF Gaussian GAMESS etc must be named as follows Output for 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 BH3CO 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 EXAMPLE 1 Building the wave function of the BH3CO molecule from the wave functions of BH and co 1 fragment BH3 the Gaussian 03 input file P HF 6 31G d NoSymm Pop Full I0p 3 33 1 SCF Tight Fragment 1 BH3 O 1 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 oF fragment CO the Gaussian 03 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 ono Page 82 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 3 Uncomment remove the CDA keyword in the AOMix parameter file aomixpar txt If you are using non Latin MS Windows version execute the US command in the Windows command prompt 4 Start the AOMix exe program and run it with single point output files you prepared in Step 2 First you should see the mes
45. ap populations are not considered and the contribution of yato the i MO is assumed to be equal to 2 C i Dcu 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 W C O 3 1 12 In a general case of many electron many orbital systems where the majority of overlap integrals Sa 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 st
46. centered MC metal to 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 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 Page 29 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 CTM 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 gt LUMO y excitation the metal CT character is CT M M Homo x M Lumosy 3 4 2 For example here are the frontier MOs of the Ru terpy 2 complex from B3LYP LanL2DZ calculations MO Number Eigenvalue eV Contribution Symmetry Fragment Ru terpy 132 LUMO 2
47. d at the spin unrestricted level while one or all of molecular fragments are treated at the spin restricted level The requirements for AOMix CDA calculations are Number of basis functions in the molecule number of basis functions of all molecular fragments Number of a spin electrons in the molecule number of a spin electrons of all molecular fragments Number of B spin electrons in the molecule number of spin electrons of all molecular fragments Number of canonical orbitals number of basis functions These requirements does not apply for calculations 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 CDA CALCULATIONS section below If this is not the case then your QC package has removed nearly linearly dependent functions from the basis set which generally stabilizes the SCF and post SCF calculations AOMix CDA requires that Number of canonical orbitals NBF and will use the full NBFxNBF array You can force Gaussian 98 03 to turn off the projection of basis functions to obey the Number of canonical orbitals NBF condition by adding the LOp 3 32 2 keyword to the route A similar option is present in the other QC packages Page 46 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 The necessary and highly recommended keywords for preparing output files of QC sof
48. ddition AOMix CDA 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 AOMix L calculates total and free valence indices of fragments 2 center Wiberg L wdin and Mayer and 3 and 4 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 For Mayer bond orders AOMix L prints and spin orbital and symmetry contributions AOMix L 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 spin B yr The AOMix package helps to analyze the nature of the chemical bonding in molecular molecular orbitals on to a spin molecular orbitals and prints the overlap matrix we 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 densit
49. e input file for Fragment 2 P B3LYP 6 31G d 5D SCF Tight Pop Full I0p 3 33 1 NOSYMM Fragment 2 C2H4 0 1 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 Page 62 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 CDA example 4 The following example shows how to setup Gaussian 03 calculations for the AOMix CDA 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 the input file for the Fe CO 4 C2H4 P B3LYP GEN SCF Tight Pop Full I0p 3 33 1 Pseudo Read 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 Cc 1 821462 0 000000 0 090291 Cc 1 821462 0 000000 0 090291 Cc 0 000000 1 503897 0 976361 Cc 0 000000 1 503897 0 976361 0 0 000000 2 460510 1 620978 o 0 000000 2 460510 1 620978 fo 2 968878 0 000000 0 160975 0 2 968878 0 000000 0 160975 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 Fe 0 LANL2DZ kkkk oc HH 6 31G kkk Fe 0 LANL2DZ the input file for Fragment 1 P B3LYP GEN SCF T
50. ed on August 14 2008 In addition to the LONG FORM you can use the SHORT FORM section of AOMix CDA 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 1 For 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 7 11 072 eV 95 1 H 1 1 3 2 L 0 2 1 3 H 1 2 HOMO 2 6 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 CDA outputs is H 3 1 HOFO 3 of Fragment 1 L 0 1 LUFO of Fragment 1 H O 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 CDA exe settings you will not be able to complete calculations because of non conservation of the number of a and B spin electrons NF NF molecule ragment i molecule ragment i peee g N nie nie gN pe a B B i i a l For instance if you want to study orbital interactions between two CH radicals forming the CH2 molecule you have the following situation the CH2 molecule closed
51. ell MO output alpha and beta for the open shell MO output and run it with your output file from Gaussian 03 or from the other AOMix supported package You should see the message Preparing the AOMix L S input files ON Then AOMix will create several files AOMix c AOMix ind AOMix e etc which will be used in Step 3 The fragment list file is not required if you ant to treat all basis functions or all atoms as individual fragments Otherwise the same format rules are in place see the format description of AOMix fragment list files in this manual Run AOMix L exe and or AOMix S exe in the same directory where the AOMix files from Step 2 are located If you include the AOMIX S TO FOLLOW keyword in the AOMix parameter file aomixpar txt AOMix S exe calculations will run automatically after the AOMix L exe execution and at the end of the program run AOMix temporary files will be deleted Here is an example of the AOMix S MO composition output Beta MO 111 112 113 114 115 116 LT 118 119 120 HOMO 7 HOMO 6 HOMO 5 HOMO 4 HOMO 3 HOMO 2 HOMO 1 HOMO LUMO LUMO 1 Energy eV 1eD3 7 47 Te32 7230 7 19 7 14 p87 6 63 4 24 1 01 ATOM 1Cu 17 42 0 07 18 59 282 3325 3508 037 24 14 48 57 1 47 Net pop 18 05 0 06 17 21 2 94 307 SMe 10 0 31 22 40 54 73 1 71 orpitalsi 015 0 00 2 56 0 00 0 00 190 0 00 0 00 0 00 0 00 p orbitals A FAL 001 4 20 0 25 0 49 2 95 0 09 3 46 1 06 0 29 d orbitals 15 55 0 05 11 82 2 56 Zela Sis LS 0 27 20 68
52. equest a copy of the converter Page 4 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Procedures for population analysis in AOMix Mulliken population analysis MPA modified Mulliken population analysis MMPA gt in AOMix S exe c population analysis SCPA PO ost L wdin population analysis LPA and other types based on the S P S formula in AOMix L exe User can set his her own value of the parameter a a 0 5 corresponds to L wdin population analysis a 1 corresponds to MPA 5 the MO analysis in terms of the contributions from fragment molecular orbitals and charge decomposition analysis CDA using AOMix CDA exe 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 Duncanson model For ab initio and DFT wave functions AOMix CDA uses the CDA method of Frenking and co workers and the extended CDA ECDA which includes evaluation of charge transfer and polarization contributions 18 19 20 24 6 Calculation of the two center Wiberg L wdin AOMix L exe 7 Calculation of the three and four center bond order indices Bagc and Basco in AOMix L exe and Mayer bond orders Baz in Methods to Derive Atomic Orbital Cont
53. erence 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 0 115 0 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 molecular 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 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 Page 58 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updat
54. f Chemical Physics 1981 74 5737 70 Noodleman L Lovell T Han W G Liu T Torres R A Himo F In Comprehensive Coordination Chemistry II McCleverty J A Meyer T J Eds Elsevier Amsterdam 2004 Vol 2 p 491 510 71 Noodleman L Lovell T Han W G Li J Himo F Chem Rev 2004 104 459 508 72 Jones C J O Hare D Chemical Communications 2003 2208 Page 89 of 89
55. fchk C9H17CuN4S2 A 80 HOMO O 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 375 temp fchk C9H17CuN4S2 B 78 HOMO 1 cub 0 h cubegen 0 MO 376 temp fchk C9H17CuN4S2 B 79 HOMO 0O 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 Page 40 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 In the above script AOMix S exe 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
56. fference approximation they can be expressed by the following equations f pP N p N condensed Fukui function for a nucleophilic attack fi P N p N D condensed Fukui function for an electrophilic attack fi P N p N D 2 condensed Fukui function for a radical attack where k are sites atoms molecular fragments for nucleophilic electrophilic and radical agents and px are their gross electron populations A high value of fk 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 resorting to additional calculations involving the systems with N 1 and N 1 electrons as an example see Ref 2 fi y Cy gt Cy Sap where i LUMO ack b a 2 f Ca gt Cy Sas where i HOMO aek L b a Because the above two expressions represent the fragment contributions in the MPA framework to the LUMO and the HOMO 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 n
57. gment 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 In this example atoms 1 3 belong to Fragment 1 atoms 4 5 form to Fragment 2 and all remaining atoms form Fragment 3 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 Page 48 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 and Gaussian 03 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 in HyperChem Fragment file names are pre defined as described below For correct AOMix and AOMix CDA execution output files from your electronic structure package ADF Gaussian GAMESS etc except Turbomole must be named as follows Ou
58. gments as necessary For example FLIP 2x 4x applies the orbital swap to Fragments 2 and 4 FO OVERLAP ON OFF AOMix CDA The keyword controls printing of the FO overlap matrix LCFO ON OFF AOMix CDA The keyword controls printing of the LCFO MO matrix CORE X X must be a real number 50 0 100 0 200 0 etc AOMix CDA Include MOs within the X eV range in the MO interaction plot CLEANUP AOMix CDA If the keyword is included in aomixpar txt at the end of the AOMix CDA exe run all AOMix temporary files will be deleted 3 CENTER ON OFF AOMix L 3 CENTER ON turns on printing of the 3 center bond order indices 4 CENTER ON OFF AOMix L 4 CENTER ON turns on printing of the 4 center bond order indices Note that if 3 CENTER OFF is selected then 4 CENTER OFF is set S EIGV ON OFF AOMix L 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 ALWAYS AOMix L LOWDIN ON Instructs the program to perform LDA if the number of orbitals is 500 or less LOWDIN ALWAYS Instructs the program to perform LPA for all calculations PROJECTION FULL OCCUPIED 8 OFF AOMix L The keyword controls printing of the overlap matrix between a and B spin MOs GUESS CARDS
59. he gng fragment d orbitals of Ru atom atoms 2 3 8 13 and 26 29 into the 3 fragment quinone and atoms 4 7 and 14 25 into the 4 fragment the NH ligands Page 36 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 functions use the symmetry nosym keyword your ADF output file should contain energies and coefficients of all molecular orbitals the TITLE field must be present in your output file because it is used as an identifier for the results section HyperChem calculations use QuantumPrintLevel 1 GAMESS US calculations use RUNTYP ENERGY and NPRINT 3 in the SCONTRL input section Gaussian 98 Gaussian 03 e for ab initio DFT calculations e for ZINDO calculations use a single point job with the keywords POP FULL SCF TIGHT and I0p 3 33 1 use a single point job with IOp 5 33 2 Jaguar 3 x 6 x calculations use the keywords ipvirt 1 ip102 8 ip18 2 and numd 6 in the amp gen input section If you are using more than 1 CPU to run your Jaguar calculations make sure that the output files do not contain any lines with the WARNING O
60. hem net Updated on August 14 2008 2 2 1 1 76 sp 0 d 2 C 79 sp 2 d 2 56 sp 24 d 18 Cl 0 0 1 A LUFOHP 36 sp 47 d 8 Cl a 2 L a 2 gt 7 Sp 77 d 8 CI b D 1 D c 3 b 3 LU g LUFO G 4 4 O Ru HOFO 1 sp 62 d 37 Cl 5 60 d 40 Cl 5 HOFO 1 ack donation 1 sp 92 d 5 Cl 6 HOFO 2 6 88 93 CI HOFO a y J HOFO 1 X amp N QS A L SS OS HOFO 2 AN Ru NH Cl NIT ZTR 9 BQDI 9 Ru NH Cl BQDI The orbital interaction diagram illustrating the coupling of the Ru NH3 Cl and BQDI fragments in the Ru NH3 CI BQDI complex with Czy symmetry the AOMix CDA calculation based on B8LYP LanL2DZ results molecular orbitals of the Ru NH3 2Clo and BQDI fragments are shifted by 0 7 eV and 0 7 eV respectively Page 69 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 NHs3 2Clo is mixing with the LUFO of the BQDI ligand green lines As a result the AOMix CDA results for this complex are Electron donation between fragments Ru gt BQDI BODI gt Ru b2 orbitals 0 000 0 140 al orbital
61. hem net Updated on August 14 2008 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 Fukui functions and AOMix Overlap Matrix between a and 8 Spin Molecular Orbitals In a spin unrestricted wave function the a and 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 If AOMix L exe is instructed using the PROJECTION keyword to print the full or partial MO overlap matrix yelet for a spin unrestricted wave function Y the expectation value of S is computed by the AOMix L program occupied EATA 1 Ng ng han OP LSE gt Parlen where n is the number of a spin electrons and ngis the number of B spin electrons Total Partial and Overlap Population Density of States Plots If the number of fragments in a calculation is less than 14 AOMix S exe 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 O
62. ight Pop Full I0p 3 33 1 Pseudo Read NOSYMM Fragment 1 Fe CO 4 0 1 Fe 0 000000 0 000000 0 018179 Cc 1 821462 0 000000 0 090291 c 1 821462 0 000000 0 090291 Cc 0 000000 1 503897 0 976361 Cc 0 000000 1 503897 0 976361 o 0 000000 2 460510 1 620978 o 0 000000 2 460510 1 620978 fe 2 968878 0 000000 0 160975 0 2 968878 0 000000 0 160975 Fe 0 LANL2DZ kkkk oco 6 31G kkk Fe 0 Page 63 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 LANL2DZ the input file for Fragment 2 P B3LYP 6 31G d SCF Tight Pop Full I0p 3 33 1 NOSYMM Fragment 2 C2H4 0 1 C 0 000000 0 704147 2 039071 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 Construction of Orbital Interaction Diagrams NF 2 Orbital interaction diagrams are constructed easily from AOMix CDA output files For molecular systems with no symmetry AOMix CDA exe will create files AOMix MO FO alpha dat and AOMix MO FO beta dat which contain orbital interaction plot data for a and spin orbitals respectively For molecular systems with symmetry AOMix CDA exe will create files AOMix MO FO alpha l dat and AOMix MO FO beta l dat for orbitals of each irreducible representation For example for H3B CO complex which has C3 symmetry AOMix CDA exe will create files AOMix MO FO alpha a1 dat and AOMix MO FO alpha
63. ignored by the program Keyword and its possible Program Keyword description and default values affected by keyword SCPA AOMix Specifies SCPA as a method for population AOMix S analysis instead of MPA for ab initio DFT calculations MMPA AOMix S Specifies MMPA as an additional method to MPA for population analysis for ab initio DFT calculations SPDF ALL OFF AOMix S SPDF ALL instructs AOMix S to print NOSINGLE or a list of S P D F etc orbital contributions for all atoms or fragments up to 20 integer fragments numbers in a list SPDF NOSINGLE instructs AOMix S 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 S to print S P D F orbital contributions for atoms fragments 1 15 31 and 45 NETPOP ON OFF AOMix S The keyword controls printing of net orbital populations OP ON OFF AOMix S The keyword controls printing of overlap populations OP CONTRIBUTIONS AOMix S The keyword instructs AOMix S to print ON OFF contributions to overlap populations Currently it only works if NF 2 CUBE OFF 5 10 20 AOMix S The keyword instructs the program to create a ALL ESP script for the Gaussian cubegen utility Xis a number of frontier occupied and unoccupied orbitals to be included in the script the ESP sub keyword indicates that the script will include the command to genera
64. iken R S J Chem Phys 1955 23 2343 2346 5 Stout E W Politzer P Theoret Chim Acta 1968 12 379 386 6 Christoffersen R E Baker K A Chem Phys Lett 1971 8 4 9 7 Grabenstetter J E Whitehead M A Theoret Chim Acta 1972 26 390 8 Gorelsky S Lever A B P Journal of Organometallic Chemistry 2001 635 187 196 Ros P Schuit G C A Theoret Chim Acta Berl 1966 4 1 12 Lowdin P O Adv Quantum Phys 1970 5 185 199 Dewar M J S Bull Soc Chim Fr 1951 C79 Chatt J Duncanson L A J Chem Soc 1953 2929 Dapprich S Frenking G Journal of Physical Chemistry 1995 99 9352 9362 Frenking G Frohlich N Chem Rev 2000 100 717 774 a i l i l O OS RON O Perera Page 87 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 15 Gorelsky S 1 Ghosh S Solomon E Journal of the American Chemical Society 2006 128 278 290 16 Gorelsky S I Solomon E Theoretical Chemistry Accounts 2008 129 57 65 Wiberg K B Tetrahedron 1968 24 1083 Borisova N P Semenov S G Vestn Leningrad Univ 1976 98 Natiello M A Medrano J A Chem Phys Lett 1984 105 180 Mayer Chemical Physics Letters 1983 97 270 274 Mayer Chem Phys Lett 1984 110 440 Mayer Theor Chim Acta 1985 67 315 322 Mayer Int J Quantum Chem 1986 29 73 Mayer Int J Quantum Chem 1986 29
65. ional workstation licenses have been obtained The academic research group license permits users from the same research group to run the SOFTWARE on their computers at one academic institution department only The 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 You 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 You shall include a proper reference in any publications and conference presentations where you utilized or reported the data which you obtained using the SOFTWARE Percentage compositions of molecular orbitals the overlap populations and bond orders between molecular fragments and density of states spectra were calculated using the AOMix program 1 2 Or Molecular orbitals were analyzed using the AOMix program 1 2 1 S I Gorelsky AOMix Program for Molecular Orbital Analysis University of Ottawa 2008 hitp www sg chem net 2 S I 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
66. is 0 24 at the HF 6 31G level In the C2H4 H30 complex with the Tlethylene On interaction the Benc index is 0 224 at the B3LYP TZVP level For systems with no 3 center bonds the 3 center Basc indices have values near zero The 3 center bond order index can be used to identify agostic interactions Page 18 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 33 4d 11 5s Pd Figure 2 adopted from Fig 1 in Ref Calculated TS for concerted palladation deprotonation Select H atoms have been removed for clarity Relevant two and three center bond orders red distances A black and NPA derived atomic charges 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 In addition to 3 center bond indices the 4 center bond orders Bascp gt Biscp mE 5 gt gt PS PS PS PS printed for closed shell species acA beB ceC deD and a and B spin components of lasco printed for open shell species Bosco gt gt gt 2 P S as P S P S og P S a and acA beB ceC deD Bho a Sa P S8 q P S P S 4 P S ac A beB ceC deD can be evaluated by using AOMix L exe to identify the 4 center interactions in molecules Page 19 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Total and free valence indices of atom
67. lar 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 OP Overlap population OPDOS Overlap population density of states PB Pseudobond PDOS Partial density of states PUHF Projected unrestricted Hartree Fock method RHF Spin restricted Hartree Fock method QC Quantum chemistry SCPA c population analysis TDOS Total density of states TOP Total overlap population UFO Unoccupied vacant fragment molecular orbital UHF Spin unrestricted Hartree Fock method ZDO Zero differential overlap Page 78 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 lose these files or you have switched from one operating system to other and forgot to keep formatted checkpoint files you have to re run your calculations from scratch to obtain converged wave functions For small molecule calculations it is not a big problem new single point calculations will t
68. manual www sg chem net Updated on August 14 2008 Visualization of AOMix L S 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 If AOMix L exe and AOMix S exe are executed with each atom defined as a fragment the programs will generate Chimera readable atomic attribute files AOMix L atom chimera txt and AOMix S MPA atom chimera txt and pseudobond attribute files AOMix L atom chimera2 txt Those contain the following data AOMix L output AOMix L atom chimera txt 1 center attributes such as MPA and LPA derived spin densities total and free valences of atoms AOMix L atom chimera2 txt 2 center pSeudobond attributes such as Mayer bond orders AOMix S output AOMix S MPA atom chimera txt atomic contributions to the frontier orbitals 10 HOMOs and 10 LUMOs which also represent the condensed Fukui functions If AOMix L exe and AOMix S exe are executed with user defined fragments and NF is the number of fragments the two programs will generate attribute files AOMix L frNF chimera txt AOMix L frNF chimera2 txt and AOMix S MPA frNF chimera txt These files contain the same data as AOMix L atom chimera AOMix L atom chimera2 and AOMix S atom chimera However one can only use AOMix L frNF chimera txt AOMix L frNF chimera2 txt and AOMix S MPA f
69. meter 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 applies if the peak shape parameter is 2 pseudo Voigt Se SE OSE HE HE HEHEHE DOS 0 10 0 0 5 0 05 0 50 lst parameter must be an integer parameters 2 5 must be real numbers ENERGY RANGE 20 0 10 0 Page 28 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 AOMix S exe writes the OPDOS data to the following files AOMix S MPA OPDOS ixt continuous plot and AOMix S MPA OPDOS line ixt line plot and The data structure of these files is the same as the order of overlap populations in AOMix S output files NF Order of columns in OPDOS data files AOMix S MPA OPDOS txt and AOMIix S MPA OPDOS line txt 2 Energy eV OPDOS 2 a and OPDOS 2 f if this is a spin unrestricted calculation 3 Energy eV OPDOS a OPDOS 3 a OPDOS23 a and OPDOS 2 8 OPDOS 8 OPDOS B if this is a spin unrestricted calculation 4 Energy eV OPDOS 2 a OPDOS 3 a OPDOS 4 a OPDOS23 a OPDOS2 a OPDOS 3 a and OPDOS 2 8 OPDOS 3 6 OPDOS 8 OPDOS23 6 OPDOS gt 2 6 OPDOS 8 if this is a spin unrestricted calculation 3 4 Charge Transfer Character of Electronic Transitions Typically one interprets features in electronic spectra of transition metal complexes as metal
70. 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 CDA 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 Page 67 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 2 2 1 1 0 0 A al S 2 1 Lumo 2 O 82 4s C 18 4p Cu 5 3 D E b a 4 4 5 Oo 5 Lumo HOMO 49 3d C NN oll 7 HOMO 1 z Q 6 HOMO Lj f 7 7 8 a 8 T Nee CuL CuL SC F SCF B Spin orbital interaction diagram illustrating the coupling of the metal and thiolate fragments in the CuL SC F complex the AOMix CDA calculation based on BBLYP TZVP results MOs with a and a symmetries are shown in red and blue respectively molecular orbitals of the ML and SC F fragments are shifted by 4 0 eV and 4 5 eV respectively Page 68 of 89 Dr S I Gorelsky AOMix manual www sg c
71. nergy regions where A B anti bonding level are located Thus the OPDOS functions enable one to ascertain the bonding characteristics of electronic levels in a given energy range with respect to any pair of molecular fragments Since Page 24 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 calculations of the OPDOS functions require the overlap populations OP4g the OPDOS plots are only calculated for non ZDO calculations with MPA as a method for 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 Page 25 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 In the above example two DOS plots are shown The PDOS plot on the left indicates the sulfur atom character in the molecular 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
72. nts 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 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 If fragment populations calculated in the AO and FO basis sets are different AOMix CDA exe will print a warning message At the end of the AOMix CDA exe run you should see the message Normal Termination of AOMix CDA Page 51 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 AOMix CDA Output Donation back donation repulsion and residue terms that are printed in the AOMix CDA txt file are computed using the CDA scheme 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 10 0 044 0 001 HOMO O 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 2 0 000 0 000 HOMO 7 4 0 003 0 000 HOMO 6 5 0 116 0 001 HOMO 5 6 0 107 0 000 HOMO 2 9
73. of Cua 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 There are systems in which three center two electron bonds are proposed The 3 center bond orders Bagcfor closed shell species are Bic gt gt gt _ PS PS PS acA beB ceC For open shell species RX B ABC T Busc Bisc B where Page 17 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Bose gt gt gt P S P S P S and ac A beB ceC Bire gt gt PS a PS PS acA beB ceC These indices can be used to identify the 3 center orbital interactions in molecules The bond order indices of 3 center bonds are positive with the maximum theoretically possible value of 0 296 AOMix L exe will print a and B spin components of Basc for open shell species An example of a 3 center 2 electron bond is the cyclic H3 ion H 0844 A H H where the 3 center bond order index l123is 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 CzHy H30 complexes are also systems with two electron 3 center chemical bonds also known in the literature as In BoHe the Bgng index
74. omplex 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 03 input file P HF 6 31G d NoSymm Pop Full I0p 3 33 1 SCF Tight BH3 CO O 1 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 0 0 38420 0 20138 0 91730 The results of the calculation are written to the output file BH3CO log 1 fragment BH3 the Gaussian 03 input file P HF 6 31G d NoSymm Pop Full I0p 3 33 1 SCF Tight Fragment 1 BH3 O 1 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 2nd fragment CO the Gaussian 03 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 3 Uncomment remove the CDA keyword in the AOMix parameter file aomixpar txt If you are using non Latin MS Windows version execute the US command in the Windows command prompt Page
75. ot suitable for systems with high density of states near the HOMO LUMO gap such as transition metal systems Page 21 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 lhe fp 1 2 As an example let s consider naphthalene Cj 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 B3LYP 6 31G level The HOMO 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 ite 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 B positions are 17 0 and 7 8 respectively These contributions indicate that electrophilic nucleophilic and radical since f f f 2 attacks at the a carbon atom of naphthalene should be more effective than those at the B carbon atom Page 22 of 89 Dr S I Gorelsky AOMix manual www sg c
76. partitioning is not complete If you do not include all atoms or orbitals in fragments AOMix exe will find omitted orbitals atoms and will include them as an additional fragment named Leftovers Page 35 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 HOW TO DEFINE FRAGMENTS the format of fragment list files EXAMPLE 1 A list of atomic orbitals 3 fragments 3 0 1 22 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 exe 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 NH ligands EXAMPLE 2 A list of atoms 3 fragments 3 1 2 Ru atom 2 3 0 8 13 0 26 29 2 Quinine 0470 14 25 2 NH3 ligands These instructions tell AOMix exe 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 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 2 3 0 8 13 0 26 29 2 Quinine 0470 14 25 2 NH3 ligands These instructions tell AOMix exe to group atomic orbitals 1 12 into the 1 fragment s p orbitals of Ru atom atomic orbitals 13 22 into t
77. qn 3 1 7 if the NETPOP ON keyword is present in aomixpar txt 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 c 8 is greater than 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 Sa and the coefficient Cp are large This is a typical situation for high energy unoccupied MOs from calculations that use an extended or unbalanced basis set In this case it is not reasonable to split the overlap populations equally rather it would be better to assign a smaller portion of 2c_ S to Zand the greater portion to Page 7 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Modified Mulliken Population Analysis One approach to address some of the MPA deficiencies is to divide the overlap populations in a way tha
78. r 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 HsB CO complex Updated on August 14 2008 BH3 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 HOMO 7 HOMO 6 HOMO 5 HOMO 4 HOMO 3 E eV 44 37 26 31 21 04 18 59 Total 0 34 39 18 36 03 SumOFO 0 19 35 82 36 03 SumUFO 0 15 3 36 0 00 6 HOMO 2 14 11 7 HOMO 1 11 07 8 HOMO 11 307 FO OC 11 0 19 35 82 36 03 21 0 00 0 00 0 00 3 1 0 00 0 00 0 00 40 0 13 3 04 0 00 5 0 0 03 0 33 0 00 Total 99 66 60 82 63 97 SumOFO 99 66 60 58 63 68 SumUFO 0 00 0 23 0 29 FO OC 11 99 62 0 24 0 03 21 0 03 50 34 47 52 3 1 0 00 0 00 0 00 4 1 0 00 0 00 0 00 5 1 0 01 10 00 16 13 6 0 0 00 0 00 0 00 70 0 00 0 00 0 00 8 0 0 00 0 23 0 29 The signs after the FO contributions in the above Table indicate the signs wave function phase factors of the LCFO MO coefficients Ca NF vray Lew k a From the above table for example it can be seen that the HOMO of BH3CO is composed of 95 1 HOFO BHs 3 2 LUFO 1 CO 1 3 HOFO 2 CO and HOMO 2 of BH3CO is composed of
79. r all atoms as individual fragments for AOMix S and AOMix L calculations 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 Page 32 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 Option to specify molecular fragments as a list of ORBITALS ATOMS Both ORBITALS and ATOMS ADF available GAMESS US available available available Gaussian 98 03 ab initio available available available Gaussian 98 03 ZINDO available HyperChem available available available Jaguar 3 x available Jaguar 4 x 6 x available available available MOPAC available available available Reimers CNDO INDO available Q Chem 2 x available Q Chem 3 x available Spartan available Turbomole available ZINDO available available available a available by using AOMix prep exe to prepare AOMix L S input files EXAMPLE OF THE LCAO MO
80. r application of the FLIP 2x keyword the second CH fragment has 2 a spin and 5 f spin electrons Thus NF NF molecule __ fragment i molecule __ fragment i ngs Ying ng Ying i i and the number of a and B spin electrons in the whole molecule is correct Page 60 of 89 Dr S I Gorelsky AOMix manual www sg chem net Orbital energy eV 10 15 HC fragment Mi z E mw eT UY BRASS HTS Wi Updated on August 14 2008 CH fragment SIKH INSEE ERE py TH A a e TORR WNIT VAN TN B3LYP TZVP Vy fp Aol CBA HC CH i y j M N NANTI T A WY NY NYH In 30 KY WY 30 g N P Wp g In Hi SK ix 30 M N gt 30 Orbital interaction diagram for the HC CH molecule which is formed by two CH radicals B3LYP TZVP calculation a spin orbitals are shown in blue B spin orbitals are shown in red AOMix CDA calculations with mixed basis sets AOMix CDA 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 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 CDA example 3 The following example shows how to setup Gaussian 03 calculations for the A
81. rNF chimera txt with UCSF Chimera if user defined fragments are individual atoms Importing 1 center attribute data Define Render by poe mone 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 L atom chimera txt or AOMix S MPA atom chimera txt then you should employ the Actions Label other command to show a desired attribute such as the HOMO composition Figure 2 or MPA derived 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 Page 42 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Importing 2 center attribute data PB LSS In UCSF Chimera 2 center interactions 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 L atom chimera2 txt Bond order depiction e g line style and color can be controlled with PseudoBond Panel under the Tools General controls See the FAQ page ht
82. rbital Overlap Population COOP diagrams The total density of states TDOS at energy Eis written as TDOS E gt 5 E Page 23 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 where the summation index i goes over all one electron energy levels Thus the integral of TDOS E over an energy interval E41 to E2 gives the number of one electron states in that energy interval In DOS calculations with AOMix S exe the function can be substituted by Lorentzians Gaussians or pseudo Voigt functions F TDOS E gt F 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 C These fragment characters are determined by means of MPA or SCPA Thus for the partial density of states one gets PDOS E gt C F E A sum of PDOS E for all fragments gives TDOS E TDOS E PDOS E A The overlap population density of states for fragments A and B is OPDOS 4 E gt OP x F E The integration of the OPDOS s E function over all populated levels gives the total overlap population TOP4s between fragments A and B Ep TOP OPDOS EME Positive OPDOS 4g E regions represent energy regions where A B bonding levels are located and negative OPDOS E regions represent e
83. ributions 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 UX 3 1 1 a 1 Page 5 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 Sab lt Xa gt 3 1 2 is neglected and the contribution of the atomic orbital AO ya to the i MO is equal to the square of the corresponding LCAO coefficient Ca and the electron population of atom A equals to Ste 3 1 3 acA where the index a runs over all AOs localized on atom A n are MO occupation numbers 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
84. rongly bonding or antibonding MOs with large overlap populations Page 9 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 LIGAND X Net Population Net Population Metal X Oveslap Population 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 Using AOMix L exe a user can employ L wdin population analysis LPA and other related methods based on the S P S formula In the L wdin approach nonorthogonal AOs are transformed to an orthogonal set The transformed orbitals 4 are given by x SOIE In LPA the a and gross electron populations associated with fragment A are GP gt a SP P S acA aa GPP S PPS and acA aa GP GP GP The spin density is given by Page 10 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 SP GP GP The AOMix L 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 GROSS POPULATIONS OF ATOMS MU
85. s 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 a2 symmetry these orbitals play no role in covalent bonding between the metal fragment and the BQDI ligand Page 70 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 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 MO contributions from fragments that are greater than 100 in the MO composition analy
86. s or fragments In addition to bond orders and fragment and orbital populations AOMix L calculates the total and free valences of fragments The total valence of atom A fragment A is defined as Va 2 gt PS gt PS PS 5 acA 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 gt Baz gt P S P S q5 B B A a beA From the above equation it is clear that the free valence index F vanishes for all closed shell systems PS 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 H 0 942 0 000 4 H 0 942 0 000 5 B 3 527 0 000 6 F 0 904 0 000 7 EF 0 904 0 000 8 FEF 0 904 0 000 Condensed Fukui Functions in Molecules 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 dp r f aN v r Page 20 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 di
87. s included in an output file of a QC package ADF GAMESS Gaussian Jaguar Q Chem the default scheme for population analysis of HF DFT calculations is MPA in AOMix S exe and both MPA and LPA in AOMix L exe In AOMix S exe you can select SCPA or MMPA as alternative methods for the population analysis by adding the SCPA MMPA keywords to the AOMix execution parameter file aomixpar txt You can utilize several keywords see the AOMix keyword table in this manual to control the printing level for AOMix L exe AOMix S exe output files For example if you do not need to perform LPA in AOMix L calculations you can use the LPA OFF keyword or LOWDIN OFF This will reduce the CPU time required for the calculation 1 Uncomment remove the LARGE keyword in the AOMix parameter file aomixpar txt Note that the LARGE keyword will be ignored by AOMix exe if the CDA keyword is uncommented in the parameter file If you prepare input files for AOMix L S calculations make sure that the CDA keyword is absent or commented CDA 2 If you are using non Latin MS Windows version execute the US command in the Windows command prompt before you start AOMix exe Page 38 of 89 Dr S I 3 Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Start the AOMix exe program or AOMix prep exe for Turbomole files for Turbomoles files with the default names will be required DSCF for the overlap matrix mos for the closed sh
88. sage Preparing the AOMix CDA input files ON Then AOMix exe will create several files aomix c1 aomix e1 aomix o7 if it s a non ZDO calculation aomix c2 aomix e2 aomix o2 if it s a non ZDO calculation etc which will be used in the next step 5 Run the AOMix CDA exe program in the same directory where the AOMix files from Step 4 are located AOMix CDA exe will generate the AOMix fragment wave gjf file that contains the wave function the AO coefficients after the 5E16 8 Fortran format line that is constructed from the converged wave functions of the fragments As in regular AOMix CDA calculations the anti ferromagnetic spin coupling scheme can be added if necessary by the use of the FLIP x keyword in the aomixpar txt file This keyword instructs AOMix CDA to exchange swap a spin and f spin orbitals for fragment i After AOMix CDA execution modify the keywords of the AOMix fragment wave gjf file to suit your needs The following example shows the input file for the BH3CO molecule P HF 6 31G d SCF Tight Guess Cards The spin restricted wave function from the molecular fragments Frag 1 AE 4 BE 4 BH3 Frag 2 AE 7 BE 7 CO O 1 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 c 0 13818 0 16800 0 01251 0 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
89. sis 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 CDA 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 Page 71 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 accurate description and lack the necessary flexibility Thus recommend the use of basis sets such as TZVP to run AOMix CDA calculations and to build MO interaction diagrams The large flexible triple zeta basis sets minimize the BSSE to a small negligible value In future releases AOMix CDA exe will include the capabili
90. sult 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 provided AS IS and is subject to change without notice You may copy distribute this manual in any medium provided that this document is presented distributed in its complete form Page 86 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 I Gorelsky Centre for Catalysis Research and Innovation Department of Chemistry the University of Ottawa D lorio Hall 10 Marie Curie Pvt Ottawa Ontario CANADA K1N 6N5 E mail software sg chem net Fax 613 562 5170 S Gorelsky 1997 2008 References 1 Mulliken R S J Chem Phys 1955 23 1833 1840 2 Mulliken R S J Chem Phys 1955 23 1841 1846 3 Mulliken R S J Chem Phys 1955 23 2338 2342 4 Mull
91. t 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 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 Page 77 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Abbreviations AO Atomic orbital BSSE Basis set superposition error CDA Charge decomposition analysis CMO Canonical molecular orbital COOP Crystal orbital overlap population identical to OPDOS 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 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 molecu
92. t 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 Ca and Cpi c z for atom A 3 1 8 Cai Cz c A 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 S exe In MMPA the contribution of ya to the i MO is equal to 2 c 2 5 Ci gt 206 D5 hee 3 1 1 0 b a ai Ci 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 it is available in AOMix S exe and can be applied by using the MMPA keyword in the AOMix parameter file aomixpar txt Page 8 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 SCPA An alternative way to partition electron density in molecules was proposed by Ros and Schuit SCPA In this method the overl
93. te the CUBE file for the electrostatic potential ENERGYRANGE AOMix S The keyword instructs the program to use user E1 E2 defined energy range from E7 to E2 eV for DOS calculations FORMAT P 0 1 2 AOMix Specifies the number of digits after the decimal AOMix CDA point in MO compositions of AOMix output files It also defines the cutoff limit for the LONG FORM of AOMix CDA output files POP FULL or positive AOMix POP FULL instructs the program to include integer number all MOs in output If POP 20 printing will be limited to 20 HOMOs and 20 LUMOs only if POP 50 printing will be limited to 50 HOMOs and 50 LUMOs etc Page 73 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 FILEFORMAT CHECK NOCHECK AOMix FILEFORMAT CHECK instructs the program to verify the MS DOS ASCII format of user s output files FILEFORMAT NOCHECK disables this feature LARGE AOMix Turns on the input preparation for AOMix L P S CDA AOMix Turns on the input preparation for AOMix CDA exe NOSYMM AOMix CDA AOMix L If the keyword is included in aomixpar txt the use of symmetry is turned off FLIP x AOMix CDA Exchanges swaps a and B spin molecular orbitals for a selected molecular fragment FLIP Ix applies the orbital swap to Fragment 1 FLIP 2x applies the orbital swap to Fragment 2 etc A user can apply this keyword to as many fra
94. ted in the canonical MO basis AOMix 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 PS ac A beB and the Mayer bond orders Bag are Bas gt X PS PS P S _ PS ac A beB 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 B spin orbitals Bap 2 gt P S P S and ae A beB Bap 2 gt 2 P S P S ae X beY Thus the total Mayer bond orders are Page 14 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Bas Bro Bas 2 gt P S P S P S PPS ae A beB For the closed shell spin singlet state calculations P P and as a result Bap Bas and Bag Bas In a general case with P P the generalized Wiberg and Mayer bond orders are not equal It is also possible to define components of bond orders by performing the summation only for orbitals of the given symmetry type In this manner the bond order may be broken down into the contributions from the different symmetry orbital charac
95. ter contributions Bas iD Bap I T If molecular symmetry is present AOMix L attempts to resolve the bond order contributions B4s and Bas By for each irreducible presentation For example for a molecule with Ca symmetry AOMix L prints e Bag for a spin orbitals with a symmetry Bag a1 e Bag for a spin orbitals with a2 symmetry Bag a2 e Bas for a spin orbitals with b symmetry Bag b e Bas for a spin orbitals with b symmetry Bag b2 e and Bag Bag a Bas a2 Bas b Bas b2 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 Cs 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 Resolved contributions to 2 PB S PB S that are larger than 0 01 FRI FR2 a a 1Cu 28S 0 36 0 33 Page 15 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Thus the results from the AOMix L exe calculations can deliver local information on the chemical bonding between molecular fragments and the symmetry decomposition with respect to T makes it possible to resolve the o T and contributions Table 2 Mayer bond orders for selected small molecules at the
96. tp Awww sg chem net NP fag php for more details 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 L atom chimera2 txt You can change the default values by using the PPEUDOBONDS keyword in the aomixpar txt file PSEUDOBONDS 2 0 3 red The above line will instruct AOMix L exe to assign red color to bond orders and print them to AOMix L atom chimera2 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 default keyword values correspond to PSEUDOBONDS 3 0 1 blue Thus AOMix L exe will assign blue color to bond orders and print them to AOMix L atom chimera2 txt using the X X output format with the 0 1 threshold value all bond order indices with values less than 0 1 will be omitted The figure below shows the Mayer bond orders in anthracene at the BSLYP TZVP level of theory Page 43 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 You can edit AOMix created atom bond attribute files using any text editor Such as Notepad before importing them to UCSF Chimera to fit your needs Working with AOMix CDA exe AOMix CDA can be most helpful for the analysis for chemical bonding in molecules However a user must understand how to select appropriate fragments to describe the chemical bonding in a given system There are man
97. tput 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 fragm1 log fragm9999 log names are reserved for fragment output files This name scheme is implemented to make it easier to run AOMix CDA 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 Output files from Turbomole must be named as follows this is the proposed name scheme If you think you can suggest a better more convenient scheme please contact the author Output File Names Whole molecule DSCF mos Fragment 1 DSCF1 mos1 Fragment 2 if present DSCF2 mos2 Fragment 3 if present DSCF3 mos3 In the case of spin unrestricted Turbomole calculations the alpha and beta files are required instead of mos files Page 49 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Let s take the BH3CO c
98. tput will print the recommended 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 keyword is included in the aomixpar txt file the SHOFT FORM of the AOMix CDA output will include the overlap integrals Si wr i and overlap populations 2c e S7 where the are the LCFO MO coefficients c from ai ai ab ai NF the yr L AA expansions k Page 66 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 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
99. tware packages for AOMix CDA calculations QC package Type of calculation Calculation keywords in Step 1 a whole molecule Calculation keywords in Step 2 molecular fragments ADF with no core use the symmetry nosym same as for a whole molecule functions keyword and basis sets with no calculation core functions the TITLE field must be present in your output file GAMESS US Use RUNTYP ENERGY and same as for a whole molecule ab initio DFT NPRINTS 3 in the CONTRL input calculation section Gaussian 98 03 POP FULL IOp 3 33 1 POP FULL IO0p 3 33 1 ab initio DFT NoSymm SCF Tight NoSymm SCF Tight Gaussian 98 03 IOp 5 33 2 NoSymm I0p 5 33 2 NoSymm ZINDO keyword Jaguar 3 x 6 x isymm 0 ipvirt 1 same as for a whole molecule ab initio DFT ip102 8 ip18 2 numd 6 calculation iacc 2 in the amp gen input section If you are using more than 1 CPU to run your Jaguar calculations make sure that the output files do not contain any lines with the WARNING OPEN_M2I0 FILES messages If they do just delete those lines HyperChem QuantumPrintLevel 1 same as for a whole molecule ZDO calculations calculation MOPAC use the keywords VECTORS same as for a whole molecule ZDO calculations EIGEN and ALLVEC calculation Q Chem 2 x use the keywords same as for a whole molecule calculations PRINT_ORBITALS 99999 calculation and the converter utility to add the overlap
100. 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 exe and AOMix S exe 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 gt Cai iS as 3 2 2 ac A beB Page 12 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 TOP gt n OP x5 gt gt gt 2CaiC5 S ab 3 2 3 i ae A beB The TOP g and OPag values are printed in the AOMix output file AOMix MP txt For example in the Ru NH3 4 quinone complex one gets OVERLAP POPULATIONS 2 c c i S where a belongs to fragment A and b belongs to fragment B Overlap Populations between Fragments MO OP 1 amp 2 OP 1 amp 3 OP 2 amp 3 TOP 0 404 0 472 0 044 58 LUMO 2 0 465 0 542 0 059 57 LUMO 1 0 144 1 0 0 09 56 LUMO 0 045 0 041 0 007 occupied virtual orbital gap 55 HOMO 0 112 0 053 0 001 54 HOMO 1 0 067 0 053 0 007 53 HOMO 2 0 026 0 062 0 004 Fragment 1 is the central atom Ru fragment 2 is the quinone ligand and fragment 3 is the four NH ligands In this example the second column contains the overlap populations between the central atom and the quinone ligand The 3 column contains the overlap populations between Ru and the ammonia ligands The 4
101. ty to deal with the BSSE explicitly Program Max number of Max number of orbitals fragments basis functions AOMix 7 2000 AOMix with the LARGE keyword 4000 4000 AOMix prep of basis functions No program limit AOMix with the CDA keyword 99 4000 AOMix S of basis functions No program limit AOMix L of basis functions No program limit AOMix CDA 99 No program limit a If there is a need to obtain information for a larger number of fragments or orbitals execute the AOMix exe program with the LARGE keyword and then run the AOMix S exe program see the instructions related to the AOMix S exe program in this manual b The 2000 orbital limit does not apply if you prepare AOMix x input files using the CDA and LARGE keywords c The programs use dynamic memory allocation techniques for storage and transformation of integrals and matrices The only real limitation is the amount of virtual memory RAM in your computer Typically a PC with 512 MB RAM can handle AOMix calculations with up to 2500 basis functions If you plan to run larger calculations you may need a computer with 1 2 GB RAM d This number will be expanded to 9999 in the future release Page 72 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 Keywords in the AOMix parameter file aomixpar txt All lines with a hash symbol in this file are treated as comments and will be
102. w sg chem net Updated on August 14 2008 Column NF 2 TDOS a spin orbitals Column NF 3 PDOS contribution of Fragment 1 to TDOS f spin orbitals Column 2 NF 2 PDOSye contribution of Fragment N to TDOS f spin orbitals Column 2 NF 3 TDOS f spin orbitals By default AOMix S exe calculates continuous DOS data in a omo 10 eV gt ELumo 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 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 HEE HH HH FE FE E FE FE E FE FE HE HE FE FE HE FE FE HE FE FE aE aE aE E aE aE EEE EE EE HEE HE EE HE EE HHH Density of States DOS convolution parameters HHH EH for the AOMix S program Ha HE TE FE HE HE FE FE HE FE FE HE HH HE HE FE FE HE FE FE aE HE FE E aE EE EEE EEE EE EE FE aE HE FE aE EE EE EE HEHE HE H 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 para
103. y books for example Ref describing this topic in considerable detail You can find additional information in the papers quoted in this manual AOMix CDA 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 The MOs of a molecular system can be expanded as linear combinations of the MOs of fragments gi the LCFO MO expansion NF eo D Deeaan k a where NF is a number of fragments In AOMix CDA a possible number of fragments varies from 1 to 99 For calculations with NF 1 AOMix CDA calculates the MO compositions of a molecule in terms of the MOs of the same molecule in some other reference 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 At A YW Ve d a or the Koopmans state Page 44 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 RAMO a MO Relaxation B MO Relaxation Koopmans State Final State Koopmans State Final State Scheme 3 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
104. y of states DOS plots Page 1 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 The main use of DOS plots is to provide a pictorial representation of MO populations The orbital character is determined by means of the Mulliken population analysis MPA or another available population analysis procedure such as SCPA per molecular orbital The DOS plots 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 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 Italics font is used for program names and variables
105. you selected 260 AOMix exe could not find the overlap matrix Make sure that it is 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 exe limit Use AOMix S exe for this calculation 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 Page 76 of 89 Dr S I Gorelsky AOMix manual www sg chem net Updated on August 14 2008 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 ne

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