Software for Quantum Chemistry, Electron Population Analysis (Mulliken, Lowdin, CDA)

Serge Gorelsky || AOMix user registration | Publications | FAQ | AOMix | AOMix-CDA | ALP-Vibro | RedS | SWizard | SIG-JK | U2WIN


	Developments and software modifications in the AOMix programs

Development of the AOMix suite of programs (see the AOMix manual for a complete description) is a continuous project. It started in 1997 at York University (Toronto, Canada). In 2002, it moved to Stanford / Mountain View (California) and, in 2006, to Ottawa (Ontario, Canada). I am glad that many people around the world found the software very useful and helpful for their research and data processing.

Development of additional software features (or features tuned for a specific user or a project) is possible on the contract basis. Please contact the author.

AOMix, Revision 6.47: AOMix (with Gaussian) can be used to evaluate contributions E_orb(a,b) to the fragment interaction energy E_int from individual donor-acceptor orbital pair a and b. This feature (the original idea came during the one-day trip to Caltech in August 2006) has been tested and will be documented soon.

AOMix, Revision 6.46: January 1, 2010. MS Windows 64-bit OS compatible version of AOMix for processing Gaussian and Turbomole output files. AOMix supports Turbomole 6 output files (aomix.in) that were generated by using the t2aomix script in Turbomole:

[AOMix Format] [Title] [SCF Energy / Hartree] -.13148671657790E+04 [Atoms] AU o 1 8 0.21549252131700E+00 0.59614303698830E+01 -.28174749460510E+01 o 2 8 0.22572784880900E+00 0.64422644598460E+01 0.19523633277080E+01 s 3 16 0.14931988896300E+00 0.47294490923450E+01 -.27550234799100E+00 c 4 6 -.25486991117690E+01 0.27494069690320E+01 -.99793941652000E-01 c 5 6 -.23143557694950E+01 0.16888497094600E+00 0.45155649775000E-01 n 6 7 -.22486500430000E-01 -.11016716519160E+01 0.84259037373000E-01 ...

Support for older versions of Turbomole has been removed from AOMix.

AOMix, Revision 6.45: AOMix allows a generation of initial guesses of the wave functions for GAMESS(US) calculations from GAMESS fragment wave functions. Please refer to APPENDIX II in the AOMix manual for details.

AOMix, Revision 6.44: AOMix supports Gaussian 09 and Spartan output files. The analysis of 5- and 6-center orbital interactions is added. This feature can be activated or de-activated by using the MULTI-CENTER keyword:

The analysis of the 3-center orbital interactions: A B C 3-center bond orders with B(ABC) > 0.01 ----- ----- ----- --------------------------------------- 1C 3C 9C B(ABC)= 0.017 1C 5C 7C B(ABC)= 0.017 1C 5C 9C B(ABC)= 0.017 3C 5C 7C B(ABC)= 0.017 3C 7C 9C B(ABC)= 0.017 Sum of (P*S)(P*S)(P*S)/4 : 35.9996 [OK] The analysis of the 4-center orbital interactions: A B C D 4-CENTER bond order index (value > 0.01) ----- ----- ----- ----- ---------------------------------------- 1C 3C 7C 9C B(ABCD)= 0.028 3C 5C 7C 9C B(ABCD)= 0.024 The analysis of the 5-center orbital interactions: A B C D E 5-CENTER bond order index (value > 0.01) ----- ----- ----- ----- ----- ---------------------------------------- 1C 3C 5C 7C 9C B(ABCDE)= 0.018 The analysis of the 6-center orbital interactions: A B C D E F 6-CENTER bond order index (value > 0.001) ----- ----- ----- ----- ----- ----- ----------------------------------------- all B(ABCDEF) < 0.001; no 6-center interactions.

AOMix, Revision 6.43: AOMix supports Q-Chem 3.2 output files. Support for older versions of Q-Chem has been removed from AOMix.

AOMix, Revision 6.42: AOMix processes NPA-derived populations (Gaussian calculations only) to calculate NPA-derived atomic spin density. The NPA-derived spin densities and charges are printed to UCSF Chimera attribute files for easy visualization.

AOMix, Revision 6.40-6.42: AOMix-S, AOMix-L and AOMix-CDA are integrated into the AOMix program. This version allows a fully NON-INTERACTIVE execution of regular and CDA/EDA jobs. Bond orders and total overlap populations (TOPs) are printed in a more convinient format:

2-CENTER BOND ORDERS BETWEEN FRAGMENTS, B(AB) and its components, 2(PA*S)(PA*S) and 2(PB*S)(PB*S), and TOTAL OVERLAP POPULATIONS (TOPs) Wiberg Mayer bond orders(>0.01) Overlap populations A B (P*S)(P*S) B(AB) B(alpha) B(beta) TOP(alpha) TOP(beta) ----- ----- ---------- ------- -------- ------- --------- -------- 1Cu 2N 0.299 0.299 0.149 0.150 0.104 0.104 1Cu 3N 0.011 0.011 0.005 0.005 -0.004 -0.004 1Cu 4N 0.518 0.545 0.243 0.303 0.189 0.235 1Cu 6N 0.518 0.545 0.243 0.303 0.189 0.235 1Cu 8C 0.020 0.020 0.010 0.010 -0.009 -0.008 1Cu 10C 0.010 0.011 0.005 0.005 0.012 0.012 1Cu 11C 0.032 0.033 0.015 0.018 -0.017 -0.016 1Cu 13C 0.019 0.020 0.009 0.011 0.020 0.022 1Cu 14C 0.032 0.033 0.015 0.018 -0.017 -0.016 1Cu 16C 0.019 0.020 0.009 0.011 0.020 0.022 1Cu 28S 0.936 1.073 0.378 0.695 0.291 0.373 1Cu 29C 0.081 0.083 0.039 0.044 0.020 0.018 1Cu 30C 0.008 0.018 0.000 0.018 0.006 0.006 1Cu 32C 0.008 0.019 0.000 0.019 0.001 0.001 1Cu 39F 0.014 0.015 0.006 0.009 0.000 0.000 2N 3N 1.048 1.048 0.524 0.524 0.160 0.161 2N 5N 0.010 0.010 0.005 0.005 0.012 0.012 2N 7N 0.010 0.010 0.005 0.005 0.012 0.012 2N 8C 1.570 1.570 0.785 0.784 0.513 0.513 2N 10C 0.128 0.128 0.064 0.064 -0.065 -0.065 2N 27H 0.016 0.016 0.008 0.008 0.009 0.009 3N 4N 0.010 0.010 0.005 0.005 0.012 0.011 3N 6N 0.010 0.010 0.005 0.005 0.012 0.011 3N 8C 0.092 0.092 0.046 0.046 -0.044 -0.045 3N 10C 1.347 1.347 0.674 0.673 0.404 0.402 3N 17B 0.874 0.874 0.437 0.437 0.356 0.356 3N 23H 0.013 0.013 0.006 0.006 0.010 0.010 4N 5N 1.034 1.034 0.516 0.519 0.145 0.160 4N 7N 0.012 0.012 0.006 0.006 0.016 0.013 ...

The regular AOMix calculations in this new version with default fragment specification (atoms/orbitals) are executed by the following command:

AOMix.exe output-file-to-be-processed

See the picture below as an example.

The regular AOMix calculations with non-default fragment specification (user-defined list of atoms/orbitals) are executed by the following command:

AOMix.exe output-file-to-be-processed fragment-list-file

such as

AOMix.exe BH3CO.log fragments.dat

For CDA calculations, the command line is:

AOMix.exe output-file CDA

output-file is the name of the output file which contains results of MO calculation for the whole molecule. For example,

AOMix.exe BH3CO.log CDA

For CDA calculations, do not enter the names of fragment files (FRAGM1.LOG, FRAGM2.LOG, etc.) The possible number of fragments in the CDA calculations has been increased to 4000. The CDA calculations are followed by DOS calculations for the same fragments.

AOMix: the (automatic) analysis of bonding/antibonding character of the frontier orbitals (6 HOMOs and 6 LUMOs). This feature is to be documented in the AOMix manual.

AOMix: printing of the gross S-,P-,D-,(etc.) orbital populations of atoms/fragments is added to the AOMix output:

ATOM ====== ALPHA- and BETA-SPIN GROSS POPULATIONS ====== A: - s - - p - - d - B: - s - - p - - d - 1C 1.6193 1.5337 0.0202 1.5846 1.2321 0.0196 2C 1.6193 1.5337 0.0202 1.5846 1.2321 0.0196 3C 1.5781 1.3793 0.0197 1.6065 1.5036 0.0166 4C 1.6193 1.5337 0.0202 1.5846 1.2321 0.0196 5C 1.6193 1.5337 0.0202 1.5846 1.2321 0.0196 6C 1.5781 1.3793 0.0197 1.6065 1.5036 0.0166 7H 0.3758 0.0118 0.0000 0.3904 0.0109 0.0000 8H 0.3758 0.0118 0.0000 0.3904 0.0109 0.0000 9H 0.3899 0.0114 0.0000 0.3864 0.0116 0.0000 10H 0.3758 0.0118 0.0000 0.3904 0.0109 0.0000 11H 0.3758 0.0118 0.0000 0.3904 0.0109 0.0000 12H 0.3899 0.0114 0.0000 0.3864 0.0116 0.0000

AOMix: the analysis of four-center orbital interactions is added. This feature can be activated or de-activated by using the MULTI-CENTER keyword.

AOMix: printing of three-center bond order indices (for example, see [Ref.]) is expanded for molecular systems with more than 100 fragments.

AOMix: printing of two-center attribute files (PseudoBond attributes) for visualization in UCSF Chimera is enabled:

The Mayer bond orders for the C-C and C-H bonds in the anthracene molecule (C₁₄H₁₀)

AOMix-CDA: the program has been modified to simplify the preparation of (Initial wave function = a sum of fragment wave functions) input files for Gaussian 98 / 03 calculations.

AOMix-CDA: the new keyword (CORE) is added to simplify the construction of orbital interaction diagrams.

AOMix: the CUBE keyword is extended. This keyword instructs the AOMix program to create two scripts (one for UNIX, one for MS Windows) for cube file generation for the cubegen utility in the Gaussian package. Please refer to the AOMix manual for details.

AOMix-CDA: energy decomposition analysis (Morokuma's EDA, for Gaussian calculations only)
. AOMix allows to evaluate the following two terms of EDA: E_steric and E_orb:

E_int = E_steric + E_orb

E_steric is the sum of two components, the electrostatic interaction energy between the fragments with the frozen electronic distributions and Pauli repulsion.

Electronic energy (a.u.) ===================== E(SCF) =========================== Whole molecule -82.611817 -82.535557 from CARDS, E(orb)= -47.9 kcal mol-1 Sum of fragments -82.552583 Fragment 1 -56.184287 Fragment 2 -26.368297 Interaction energy between the fragments (without the BSSE correction) ---------------------------------------------------------------------- Delta E(SCF)= -1.612 eV, -37.17 kcal mol-1

AOMix: Turbomole output files can be processed for AOMix calculations.

AOMix-CDA: with the FO OVERLAP keyword, the LCFO-MO output for non-ZDO calculations is expanded to include overlap integrals and overlap populations between the contributing FO pairs of the two fragments for each MO in the output:

--- ALPHA-SPIN ORBITALS --- Mol. Orbital Compositions in terms of dominant FO contributions Overlap integrals S and overlap populations,OP=2c*c*S ========================================================================= ... LUMO+1[#13, 3.161 eV]= Fr 1: 7.1%L+2 3.0%H-1 1.9%L+1 Fr 2: 46.7%L+0 S(-0.32 0.24 0.09 ) OP(0.07 -0.10 -0.01 ) 40.0%L+1 S(0.09 -0.06 0.32 ) OP(0.02 -0.02 0.04 ) 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-0[#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 )

In the above example, the HOMO of the complex (orbital #12 with the energy of -12.718 eV) is a mixture of 94.9% HOMO of Fragment 1 and 3.6% LUMO+1 and 1.4% HOMO-1 of Fragment 2. The overlap integral between the HOMO of Fragment 1 and LUMO+1 of Fragment 2 is 0.24 and the overlap population for this fragment orbital pair is 0.05 for this molecular orbital of the complex. The overlap integral between the HOMO of Fragment 1 and HOMO-1 of Fragment 2 is 0.06 and the overlap population for this fragment orbital pair is -0.02.

AOMix: the LOWDIN population analysis keyword has been modified. The new default is to apply LPA to all AOMix calculations in which the number of orbitals is 500 or less and to skip it for larger (>500 orbitals) MO calculations.

AOMix: the OP-CONTRIBUTIONS keyword is added. This keyword instructs AOMix to print AO contributions (2*C_a*C_b*S_ab absolute values that are greater than 0.01) to the overlap populations between two fragments. For example:

Alpha MO 7, OP contributions > 0.01: 5 17 Ca= 0.2832 Cb= 0.2742 Sab=-0.2372 2*Ca*Cb*Sab= -0.037 5 20 Ca= 0.2832 Cb= -0.4442 Sab=-0.3048 2*Ca*Cb*Sab= 0.077 5 21 Ca= 0.2832 Cb= 0.6196 Sab=-0.1509 2*Ca*Cb*Sab= -0.053 9 17 Ca= 0.1484 Cb= 0.2742 Sab=-0.6042 2*Ca*Cb*Sab= -0.049 9 20 Ca= 0.1484 Cb= -0.4442 Sab=-0.2327 2*Ca*Cb*Sab= 0.031 9 21 Ca= 0.1484 Cb= 0.6196 Sab=-0.5103 2*Ca*Cb*Sab= -0.094

These data can be helpful in the analysis of molecular orbital calculations.

AOMix-CDA: printing of a table of changes in atomic orbital populations in the whole molecule relative to non-interacting fragments is added. See this example.

AOMix with AOMix-CDA: setting up wave function calculations for molecular systems using converged wave functions of molecular fragments as an initial guess (any spin states). This option is very useful for generation of the correct guess wave function for broken symmetry calculations and open-shell low-spin states in which unpaired electrons are antiferromagnetically coupled. Please refer to APPENDIX II of the AOMix manual for details.

AOMix: the ENERGYRANGE keyword is added. This keyword instructs the AOMix program to use a user-defined energy range for DOS calculations (instead of the default program values). Please refer to the AOMix manual for details.

AOMix: AOMix can be used to recover the initial guess from the converged wave function. See Appendix I of the AOMix manual for details. This option is very useful for large molecule calculations if the corresponding checkpoint file was lost.

AOMix-CDA: the program output is extended to include (if needed) the full LCFO-MO matrix.

AOMix-CDA: the program can be used for orbital relaxation analysis for molecular systems. The new functionality derives from the ability of the program to analyze MO compositions of molecule/ion X in terms of MOs of the other, reference state of X. So, for example, you can obtain MO compositions of cation X⁺ and/or anion X^- in terms of MOs of the neutral molecule X to identify the redox active orbitals. For more details, check the following publication:

Extended Charge Decomposition Analysis and Its Application for the Investigation of Electronic Relaxation
S. I. Gorelsky, E. I. Solomon
Theoret. Chem. Acc., 2008, 119, 57-65 [PDF]

AOMix: the CUBE keyword is added. This keyword instructs the AOMix program to create a script for cube file generation for the cubegen utility in the Gaussian package. Please refer to the AOMix manual for details.

AOMix: the SPDF keyword is expanded to include more print options for the orbital composition analysis in terms of s-, p-, d-, and f-atomic orbitals. Please refer to the AOMix manual for details.

AOMix:

The wave function verification procedure is extended.

AOMix writes two UCSF Chimera attribute files. The first file (with atomic attributes) allows easy visualization of atom-based properties:

atomic MPA-, NPA- and LPA-derived charges of atoms/fragments,
MPA-, NPA- and LPA-derived spin densities of atoms/fragments,

total and free valence indices of atoms/fragments.

Atomic valence indices in the anthracene molecule (C₁₄H₁₀)

The second file (with the two-atom attributes) allows easy visualization of pseudo-bond-based properties:

Lowdin and Wiberg bond orders,
Mayer bond orders and its components.

If each atom is a fragment, AOMix generates a UCSF Chimera attribute file. This file allows easy visualization of atomic contributions to the frontier orbitals (10 HOMOs and 10 LUMOs).

AOMix and AOMix-CDA: the additional information is recorded in AOMix output files to help a user in identifying a molecule and details of an original calculation, such as:
Molecule: C6H12Cl2N4Ru(1+,2) Details: #P B3LYP/LANL2DZ 5D Test SCF=Tight Guess=Check Geom=Check Pop=Full IOp(3/33=1)

AOMix: an extra option has been added for presenting density-of-states plot data: line DOS plots.

AOMix: automatic printing of MO compositions in terms of s,p,d,f,(etc) orbital contributions for each atom/fragment (in addition to the MO gross compositions).

AOMix: printing of net MO compositions (in addition to the MO gross compositions) in AOMix-S output files is available.

AOMix: evaluation of atomic (or fragment) total and free valence indices is added; bond-order contributions from orbitals of a given symmetry type (irreducible representation) is printed in a more convinient format.

AOMix: a user can define non-default weighting coefficients in DOS calculations using the pseudo-Voigt function; MMPA calculations are made easier to run in AOMix.

AOMix: the AOMix output has been extented to include the calculation of symmetry components of Mayer bond orders.

AOMix-CDA: charge decomposition analysis scheme has been extended to extract polarization and pure charge transfer contributions, the MO-FO output has been extended.

AOMix: Support for Q-Chem output files is added.

AOMix-CDA: Support for molecular orbital symmetry is added. A user can now easily sort molecular orbital interactions between orbitals of different symmetry.

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All contents copyright � 1997-2010 S. I. Gorelsky
Last updated: January 2010