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Population

This properties keyword controls printing of molecular orbitals and several types of population analysis and atomic charge assignments. The default is to print just the total atomic charges and orbital energies, except for Guess=Only jobs, for which the default is Pop=Full (see Options). Populations are done once for single-point calculations and at the first and last points of geometry optimizations. Note that the Population keyword requires an option.

The density that is used for the population analysis is controlled by the Density keyword. Note that only one density and method of charge fitting can be used in a job step. If several combinations are of interest, additional jobs steps can be added by specifying Guess=Only Density=Check, to avoid repeating any costly calculations.

Population analysis results are given in the standard orientation.

Output controlled by the Population keyword includes:

  • Molecular orbitals and orbital energies. By default, all orbitals are included, but the output can be limited to a specific orbital range with the Orbital option.
  • Atomic charge distribution. The total charge per fragment is also reported if applicable.
  • Multipole moments: dipole through hexadecapole.

APT charges are also computed by default during vibrational frequency calculations [Cioslowski89].

Options Controlling Output File Contents

None

No orbitals are printed, and no population analysis is done. This is the default for all calculations using the ZIndo method.

Minimal

Total atomic charges and orbital energies are printed. This is the default for all job types and methods except Guess=Only and/or ZIndo.

Regular

The five highest occupied and five lowest virtual orbitals are printed, along with the density matrices and a full (orbital by orbital and atom by atom) Mulliken population analysis. Since the size of the output depends on the square of the size of the molecule, it can become quite substantial for larger molecules.

Full

Same as the Regular population analysis, except that all orbitals are printed. This is the default for Guess=Only jobs.

Always

Perform a population analysis at every optimization step rather than just the initial and final ones.

Orbitals[=N]

Perform a population analysis of the highest N occupied and lowest N virtual orbitals (see the examples below). N defaults to 10. AllOrbitals may also be specified instead of Orbitals=N to request analysis of all orbitals. For open shell calculations, both alpha and beta orbitals are included.

ThreshOrbitals=N

Set the minimum contribution percentage to include in individual orbital population analysis. The default is 10.

Population Analysis Options

Bonding

Do a bonding population analysis in addition to the standard analysis. This is a Mulliken population analysis in which only density terms involving pairs of basis functions on different centers are retained.

MBS

Perform minimum basis set Mulliken population analysis [Montgomery99, Montgomery00]. NoMBS tells the program not to perform MBS Mulliken population analysis.

Hirshfeld

Perform Hirshfeld population analysis [Hirshfeld77, Ritchie85, Ritchie87]. CM5 atomic charges [Marenich12] are computed along with Hirshfeld charges. CM5 is a synonym for Hirshfeld. The HirshfeldEE option requests interatomic electrostatic interactions as well.

Biorthogonalize

Biorthogonalize unrestricted molecular orbitals in order to maximally align electron pairs.

SaveBiorth

Save biorthogonalized orbitals in the checkpoint file over the canonical MOs.

DCT

Compute Adamo’s DCT charge transfer diagnostic [LeBahers11, Adamo15] for whichever unrelaxed excited-state density/densities are available and, if a relaxed density was requested, for that as well.

NaturalTransitionOrbitals

Requests Natural Transition Orbital analysis [Martin03] of a CI-Singles or TD-DFT excited state. Must be accompanied by Density=(Check,Transition=N) in order to specify which transition density is to be used to generate the orbitals. To print the orbitals from several states of interest, run successive Pop=NTO Density=(Check,Transition=N) Guess=Only jobs after the initial excited state calculation. NTO is a synonym for this option.

SaveNaturalTransitionOrbitals

Save the generated orbitals in the checkpoint file, replacing the canonical ones if the density was read-in from there. SaveNTO is a synonym for this option. If you want to visualize the orbitals, you need to write them back to the checkpoint file. It is a good idea to do so with a copy of the checkpoint file for each state. After the initial excited state calculation (using %Chk=ex.chk), use a technique like the following to generate visualization data for each state:

$ g16 <<END Run a Guess=Only job just to generate orbitals.
%OldChk=excited.chk Work on copy of original checkpoint file.
%Chk=staten.chk Checkpoint file for this state.
# Geom=AllCheck ChkBas Guess=Only  
  Density=(Check,Transition=n) Pop=SaveNTO Repeat for each state.
END End of Gaussian input file.

Charge Save Options

NoOrthogonalize

Suppress orthogonalization of saved Pop=(SaveMixed,NoOrthogonalize) orbitals (primarily for visualizing raw NBO results).

SaveType

Computed atomic charges can be stored on the checkpoint file for use in a later MM calculation with Geom=Check. The options Pop=SaveMulliken, Pop=SaveESP, Pop=SaveNPA, Pop=SaveCM5, and so on can be used to save the corresponding charges. In the case of a multilayer ONIOM calculation, only explicitly computed charges are saved by default: i.e., charges for atoms in the QM layer(s). Any atomic charges present in the input file will not be used and they will be replaced by the newly fitted charges saved by these options.

The additional option Uncharged will keep the atomic charges present in the input file and only fit charges on uncharged atoms in the QM layers(s). The option combinations Pop=(Uncharged, SaveMulliken), Pop=(Uncharged, SaveCM5) and so on will save both the original atomic charges plus the newly fitted charges for the atoms that were originally uncharged.

Natural Orbital-Related Options

NaturalOrbitals

Do a natural orbital analysis of the total density. NO is a synonym for NaturalOrbitals.

NOAB

Do separate natural orbital analyses for the α and β densities. NaturalSpinOrbitals is a synonym for NOAB.

AlphaNatural

Do separate natural orbital analyses for the α and β densities, but store only the α densities for use in a .wfn file (see Output=WFN). NOA is a synonym for AlphaNatural.

BetaNatural

Do separate natural orbital analyses for the α and β densities, but store only the β densities for use in a .wfn file (see Output=WFN). NOB is a synonym for BetaNatural.

SpinNatural

Generate natural orbitals for the spin density (with α considered positive).

By default, natural orbitals are not included in the checkpoint file. Use a second job step of this form to place the natural orbitals into the checkpoint file:

--Link1--
%Chk=name
# Guess=(Save,Only,NaturalOrbitals) Geom=AllCheck ChkBasis

Run the formchk utility on the resulting checkpoint file to prepare the orbitals for visualization.

Options For Generating Electrostatic Potential-Derived Charges

MK

Produce charges fit to the electrostatic potential at points selected according to the Merz-Singh-Kollman scheme [Singh84, Besler90]. ESP and MerzKollman are synonyms for MK. The data file for Antechamber (the AMBER program for generating RESP charges) can be generated using Pop=MK IOp(6/50=1) and specifying the file name on a separate line at the end of the Gaussian input file.

MKUFF

Uses the MK fitting but using UFF radii, which are defined for the full periodic table.

CHelp

Produce charges fit to the electrostatic potential at points selected according to the CHelp scheme [Chirlian87].

CHelpG

Produce charges fit to the electrostatic potential at points selected according to the CHelpG scheme [Breneman90].

HLY

Specifies the Hu, Lu, and Yang charge fitting method [Hu07].

HLYGAt

Specifies the Hu, Lu, and Yang charge fitting method, but using Gaussian's standard atomic densities instead of those of HLY. The authors of HLY only parametrized the atomic densities required for the model for the first 18 elements. This is an alternative version that uses the HLY fitting scheme but with Gaussian’s standard atomic densities, which are available for the entire periodic table. For systems which can be done either way, the difference in atomic charges is usually between 1% and 5%.

Dipole

When fitting charges to the potential, constrain them to reproduce the dipole moment. ESPDipole is a synonym for Dipole.

AtomDipole

When fitting charges to the potential, also fit a point dipole at each atomic center.

ReadRadii

Read in alternative radii (in Angstroms) for each element for use in fitting potentials. These are read as pairs of atomic symbol and radius, terminated by a blank line.

ReadAtRadii

Read in alternative radii (in Angstroms) for each atom for use in fitting potentials. These are read as pairs of atom number and radius, terminated by a blank line.

NBO-Related Options (Version 3)

NBO

Requests a full Natural Bond Orbital analysis, using NBO version 3 [Foster80, Reed83a, Reed85, Reed85a, Carpenter87, Carpenter88, Reed88, Weinhold88].

NCS

Requests a partitioning of the NMR shielding tensors (computed using GIAOs) into magnetic contributions from bonds and lone pairs using the Natural Chemical Shielding analysis of Bohmann et al. [Bohmann97], which is based upon the NBO analysis method. By default, an analysis of the isotropic shielding is performed. NoNCS skips this analysis.

NCSDiag

Requests an NCS analysis of the diagonal tensor elements.

NCSAll

Requests an NCS analysis of all tensor components.

NPA

Requests just the Natural Population Analysis phase of NBO.

NBORead

Requests a full NBO analysis, with input controlling the analysis read from the input stream. Use this option to specify keywords for NBO. Refer to the NBO documentation for details on this input.

NBODel

Requests NBO analysis of the effects of deletion of some interactions. Only possible with SCF methods. Implies that NBO input will be read; refer to the NBO documentation for details. Note that NBO input starts in column 2 so that the UNIX shell does not interpret the initial $.

SaveNBOs

Save natural bond orbitals in the checkpoint file (for later visualization).

SaveNLMOs

Save natural localized molecular orbitals in the checkpoint file (for later visualization).

SaveMixed

Save the NBOs for the occupied orbitals and the NLMOs for the unoccupied orbitals in the checkpoint file (for later visualization).

NBO-Related Options (Version 6)

An interface to NBO version 6 is provided. Pop=NPA6, Pop=NBO6, Pop=NBO6Read and Pop=NBO6Delete request use of the separate NBO6 program via the external interface. The script required to run NBO6 and the program itself must be obtained from Frank Weinhold (nbo6.chem.wisc.edu).

Orbital-by-Orbital Population Analysis. The following route section requests population analysis of the lowest 3 virtual orbitals and the highest 3 occupied orbitals:

# UHF/6-311+G(d) Pop=Orbitals=3

Here is the resulting output from a calculation on FeO+ quartet:

 Atomic contributions to Alpha molecular orbitals:
 Alpha occ 16 OE=-0.923 is Fe1-d=1.00
 Alpha occ 17 OE=-0.699 is O2-p=0.88
 Alpha occ 18 OE=-0.690 is O2-p=0.68 Fe1-s=0.21
 Alpha vir 19 OE=-0.253 is Fe1-s=0.70 Fe1-p=0.27
 Alpha vir 20 OE=-0.188 is Fe1-p=0.71 O2-p=0.29
 Alpha vir 21 OE=-0.133 is Fe1-p=1.04
 
 Atomic contributions to Beta  molecular orbitals:
 Beta  occ 13 OE=-0.801 is O2-p=0.79
 Beta  occ 14 OE=-0.783 is Fe1-d=1.00
 Beta  occ 15 OE=-0.758 is O2-p=0.89
 Beta  vir 16 OE=-0.241 is Fe1-s=0.81 Fe1-p=0.17
 Beta  vir 17 OE=-0.139 is Fe1-p=0.91 Fe1-d=0.14

Note that both alpha and beta orbital information is included. For each orbital, the output reports the orbital energy (labeled OE and given in atomic units), followed by the fractional contribution of all basis functions of a given angular momentum for each relevant atom.

This is an example of a system where it is hard to tell the spin state of the system, because the canonical α and β orbitals are quite different. If you subsequently run a Guess=(Read,Only,BiOrthogonalize) Pop=Orbital calculation to analyze the results, then the program transforms the α and β orbitals to match up as much as possible (occupied and virtual separately). In this case, orbital energies for the transformed orbitals are nor given. Rather, the Pop=Orbital analysis reports the overlaps between the pairs of corresponding orbitals (i.e., α 19 with β 19), with a value of 1 indicating 100% correspondence. Instead of labeling the orbitals as occupied or virtual, they are labeled:

Docc    Doubly occupied: alpha and beta are occupied, with a match of 90% or better.
Asing, Bsing   Singly occupied: alpha without matching beta occupied, or lower occupieds which do not match up with any orbital of the opposite spin.
Dvir    Virtual orbital with nearly the same alpha and beta orbitals.
AVir, BVir    Virtual orbital which does not match up with any of the other opposite-spin virtuals.

The program lists the orbitals which match another orbital only once within the output. Also, for each unpaired excess alpha spin occupied orbital, there is always some beta virtual orbital which matches it, and the latter are also omitted.

Here is the output for FeO+ quartet, which has 3 more alpha electrons than beta but which turns out to really have 4 unpaired alpha occupieds and one unpaired beta occupied (the lowest doubly occupied and highest unoccupied orbitals have been cut from the output):

 Atomic contributions to molecular orbitals:
 Docc. orb 13 abOv=0.999 is Fe1-d=1.00
 Docc. orb 14 abOv=0.990 is O2-p=0.72 Fe1-s=0.14 Fe1-d=0.14
 Asing orb 15 abOv=0.316 is Fe1-d=0.99
 Asing orb 16 abOv=1.000 is Fe1-d=0.94
 Asing orb 17 abOv=1.000 is Fe1-d=0.91
 Asing orb 18 abOv=1.000 is Fe1-d=0.91
 Dvirt orb 19 abOv=1.000 is O2-s=1.92 Fe1-s=-0.67 O2-p=-0.43 Fe1-p=0.14
 Dvirt orb 20 abOv=1.000 is Fe1-s=0.52 Fe1-p=0.37
 Bsing orb 15 abOv=0.316 is O2-p=0.92

Orbitals 1-14 are doubly occupied. Alpha orbital 15 and beta orbital 15 are different singly occupied orbitals; all 4 unpaired alpha spins are on the Fe, and the one unpaired beta spin is on the oxygen. There are no unmatched alpha and beta virtuals within the default range of orbitals analyzed.

Fragment Level Decomposition. If fragment information is present, the output also reports populations over fragments. For Pop=Orbital jobs, the decomposition of each orbital by fragment is reported.

 Default output including fragment populations:
 Mulliken charges with hydrogens summed into heavy atoms:
              1
     1  Pd  -0.265855
     2  P    0.346314
     3  P    0.346314
     4  Cl  -0.168156
     5  Cl  -0.168156
     6  C    0.060982
     7  C    0.060982
     8  C   -0.106213
     9  C   -0.106213
 Sum of Mulliken charges with hydrogens summed into heavy atoms =   0.00000
          Condensed to fragments (all electrons):
     1      -0.265855
     2      -0.168156
     3      -0.168156
     4       0.060982
     5       0.060982
     6       0.480203
 
 Pop=Orbital output:
 Alpha occ 60 OE=-0.247 is Cl4-p=0.22 Cl5-p=0.22 P3-p=0.12 P2-p=0.12
                           Fr6=0.36 Fr2=0.22 Fr3=0.22

Sample NBO 3 Input. The following input file requests a bond order analysis using NBO 3:

# B3LYP/6-31G(d,p) Pop=NBORead 

Example of NBO bond orders

 0  1
C     0.000000    0.665676    0.000000
H     0.919278    1.237739    0.000000
H    -0.919239    1.237787    0.000000
C     0.000000   -0.665676    0.000000
H    -0.919278   -1.237739    0.000000
H     0.919239   -1.237787    0.000000

$nbo bndidx $end

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