I’m posting this white paper “as is” but I will keep on coming back to update it; the thing is that I haven’t had the time to post anything else lately and if I don’t do it like this then I will never get it out. Please be kind on your comments and ratings!

For a more thorough discussion of NBO analysis please check out the references.

Requesting an NBO population analysis on the route section of a Gaussian job (via the simplest option pop=nbo) generates a lot of information on the output file which sometimes is not too straightforward to read. Please refer to previous posts in this blog (all under the NBO category) for more info on NBO calculations. The first part of this post deals with the analysis of the default information obtained from an NBO calculation; the second part deals with some useful/popular options of the NBO analysis which are controlled through the pop=nboread keyword available in NBO3.1 which is the version incorporated in Gaussian.

pop=nbo

Perhaps the most common issue when reading NBO results is making sense of the hybridization shown. Take the example below as taken from the NBO manual for Methylamine:

(Occupancy)   Bond orbital/ Coefficients/ Hybrids

————————————————————-

1. (1.99858)  BD  (1)  C 1 – N 2

(40.07%)    0.6330*  C1 s(21.71%)p 3.61(78.29%)

-0.0003  -0.4653  -0.0238  -0.8808  -0.0291

-0.0786  -0.0110  -0.0000  -0.0000

(50.93%)     0.7742* N  2  s(30.88%)p 2.24(69.12%)

-0.0001  -0.5557  0.0011  0.8302  0.0004

0.0443  -0.0098  0.0000 0.0000

The first line shows the occupancy (between 0.00 and 2.00 electrons), then the label of the NBO (BD = Bonding (2 centers); CR = Core (1 center); LP = Lone pair; RY = Rydberg; BD* = Antibond), after that a ‘serial number‘ which corresponds to the connectivity (or idealized bond index between the atoms, i.e., single double triple bond), and finally the atom(s) to which the NBO belongs.

The next line describes the natural atomic hybrids of which the NBO is composed, giving the percentage (100|cA|^2) of the NBO on each hybrid (40% the C hybrid orbital and 60% the N hybrid orbital), the polarization coefficient cA (Nitrogen is more electronegative than Carbon, hence the polarization coefficients look like 0.633 for C and 0.7742 for N, i.e. this NBO is more polarized towards N), the atom label (self explanatory) , and a hybrid label showing the sp^x composition: for the C hybrid orbital it is sp^3.61 while for the one on N is sp^2.24. The number in parenthesis is just the percentage in composition of the hybrid (75%p and 25%s corresponds to an ideal sp^3 hybridization) Now, for the tricky part: Sometimes you’ll get numbers larger than 3 for an sp^x hybrid or even s^yp^x hybrids (for y>1 and x>3), this has to do with the basis set employed and the number of functions used to describe each atomic orbital. (EXAMPLE SOON, IM LAZY)

Below the hybridization we find the set of coefficients that specify how the NHO is written as a linear combination of Natural Atomic Orbitals. The previous NHO for C has the largest coefficients from the second (-0.4653) and fourth (-0.8808) natural atomic orbitals, corresponding to a rough description like: NHOc = -0.4653(2s)c -0.8808(2px)c

pop=nboread

To control the options in the Natural Bond Orbital population analysis the line $NBO keywords $END must be included at the end of the input file (after the infamous blank line located after the molecule specification)

Wiberg bond indexes

This is a feature I use a lot when dealing with adducts with closed shell molecules. It is achieved through the BNDIDX keyword. Two indexes are obtained: The Wiberg bond index which is presented as a matrix; and the Wiberg bond index total which is the summation of all Wiberg indexes for every atom. The latter index roughly resembles the number of covalent bonds each atom forms. When analyzing this total index on a given atom, it should be compared to a well defined one in another part of the molecule just to make sure that all numbers are reflecting the same trends. Wiberg’s is not the only bond index provided by NBO analysis: the BOAO keyword generates bond index on the basis of the natural atomic orbitals.

Some common errors and possible solutions

->> Concerning NBO Deletion analysis

***** WARNING ***** The variational principle has been violated and the above deletion energy is invalid!!

This usually caused by one of the following:

1) Wavefunction symmetry breaking: Use the Nosymm option on the route section of your input file.

2) The use of DFT methods: Strong deletions often lead to densities that derail the density functional.  Safest is to use HF, where the variational theorem can be counted on, and
DFT artifacts are averted.  The FIXDM keyword (available only in NBO 5.0) may also correct some numerical problems associated with large basis sets

3) Deletion of some degenerated orbitals which breaks the symmetry of the wavefunction. Sometimes it could be that although there are no formal degenerate states accidental degeneracies might occur, deletion of which will cause this error.

->> Also on NBO Deletion Analysis

************************************************
** ERROR IN INITNF. NUMBER OF VARIABLES ( 57) **
**  INCORRECT (SHOULD BE BETWEEN 1 AND 50)  **
************************************************

This is one weird error. I have solved it by changing the molecule specification from Z-Matrix to Cartesian coordinates. Also, if you are running a DFT calculation in an older revision of Gaussian 03, try using the IOp(5/48=10000). Later revisions of Gaussian 03 and the more recent Gaussian 09 claim to have fixed this problem.

->> NBO Analysis

WARNING: Population inversion found on atom X#

This is not a problem! NBO lists orbitals within each atom according to their energy and their population afterwards. This warning only states that some low energy lying orbitals are less populated than others with higher energy. It cannot be “fixed” since this is a natural consequence of the orthonormalization process of the NBO generation.

References

NBO5.0 Home. Site of the creator of NBO and NBOView (Dr. Frank Weinhold)

FAQ‘s on NBO Home. I can’t recommend it enough!!!

Population Analysis Keyword in Gaussian

This is the second post on a series which will try to address common technical questions in computational chemistry that recursively appear on the CCL.

The Natural Bond Orbitals analysis is a powerful tool in population analysis calculations which is more robust than the traditional Mulliken approach, if for no better reason because its almost insensitive to the change of basis set while Mulliken’s P.A. is highly sensitive to basis set effects. Another advantage of the NBO analysis is that it provides a localized depiction of the electron density over a molecule, making it more related to chemists intuition. So far I have only worked with Gaussian 98, Gaussian 03 and only recently with Gaussian 09 in calculating NBO’s although it is possible also to perform them with GAMESS and the standalone NBO5.0 program created by Frank Weinhold. Visualizing them, however is never a straightforward process, and quite often we see more questions on the CCL than answers trying to address the matter. Most of the answers are concerned with what visualization programs to use but they seldom provide step by step instructions, furthermore most manuals are a bit cryptic about the procedure to plot this orbitals.

In Molekel 4.3

http://molekel.cscs.ch/wiki/pmwiki.php

Make sure that the route section in your input file includes the following options: pop=nboread; gfoldprint (in case you are using G03 or even G09) or gfprint (in case you are still running G98), e.g.:

#P opt rhf/6-31G(d,p) pop=(full,nboread) gfoldprint geom=connectivity

This calculation requests a geometry optimization followed by a Natural Bond Orbital population analysis (with keywords to be read) using the Restricted Hartree-Fock method with the split valence basis set 6-31G(d,p)

NOTE: I have my own issues and concerns about the use of DFT along with NBO but maybe that will be treated in another post.

At the end of the input file, after the infamous blank line type the following:

$NBO PLOT $END

You may include other keywords such as BNDIDX which generates a Wiberg bond index (order) matrix; or BOAO which generates the same matrix but in the Natural Atomic Orbitals basis. The PLOT option will generate a series of files with numerical extensions. The one you want to pay attention to is filename.47

If you are using Gaussian 03 or Gaussian 09 and STILL want to use Molekel 4.3 then you probably already know you have to change 03 for 98 on the header of the output file:

****************…              ****************
Gaussian 03:  x86…  –>       Gaussian 98:  x86-
2-Feb-2009                               2-Feb-2009
***************…                ****************

That aside, load your output file (filename.out or filename.log) on Molekel 4.3 as usual. Then go to Load -> nbo orb and load filename.47. Now, go to Compute -> Orbital and now select the Natural Bond Orbital you are interested in. This should do it! As an interesting exercise try computing the same orbitals (lets say HOMO and HOMO-1) with and without loading filename.47 in order to observe the difference between the shape of the MO’s and NBO’s. Molekel 4.3, though, is filled with bugs that will make it close unexpectedly, specially when running under Windows Vista. Sometimes the window closes because some sort of resolution problem, specially when taking snapshots (interestingly enough this happened to me when the background color was set to white) decrease the resolution of your monitor before taking the snapshot to prevent this problem. Some people complain about the look and feel of the latest molekel version so they stick to this old bugged one, so that is why I’m posting this method.

In Gasusview 3.0

This is the gaussview version I currently work with. When performing the NBO analysis on Gaussian (by the way, Gaussian 09 cannot be visualized with gaussview 3.x) use the savenbo option in the rout section, for example:

#P opt HF/6-31G(d) freq=noraman pop=(ful,nboread,savenbo) geom=connectivity

This will save the NBO coefficients into the checkpoint file. Load the output file with gaussview normally and then click on the Molecular Orbital icon (or go to Edit -> MO’s). This will open a new window with four tabs at the bottom of the molecule image. Click on the ‘New’ tab and load your checkpoint file. Gaussview will automatically format the chk file (this can cause some troubles when crossing architectures or platforms, so be careful to generate the proper formatted chk file!) Once load select the orbital you need to visualize and go to the ‘Visualize’ tab and click update; the orbital displayed is the Natural Bond Orbital. In this tab you can also adjust certain parameters like the isovalue (which is set to 0.02 by default) or the cube grid which controls how smooth the surface looks. UPDATE: According to John Keller from Alaska you can use this methodology when calculating with G09 and using Gview3.x, this also allows to visualize vibrations when this same software combination is used.

As usual, this post will be updated whenever I find some more useful information about the matter. Rate this post or leave a comment, just to know if you found it useful. Thanks!