Gaussian: How to Compute Bond Energy and Bond Order using NBO

With the Gaussian program, we can determine the structural properties of molecules, such as bond energy, bond strain, and bond order using Natural Bond Orbital (NBO) analysis. NBO is used for population analysis for characterizing "bond" and "electron density" in computed molecules.

A) Add a keyword that related to the type of NBO analysis

1. NBO analysis - Gaussian Keyword
- Ex: #p B3LYP/6-31G(d) POP=NBO
2. Bond-Order analysis - Gaussian keyword
- Ex: #p B3LYP/6-31G(d) POP=NBOREAD

B) Add the keyword at the last line of the input file

$NBO BNDIDX $END

C) Compute NBO analysis (very quick)

D) After the calculation is done, open the output file and the search with keyword

"Wiberg bond index matrix in the NAO basis:"

Consider NBO analysis for only the last optimized structure at the final step

For a system with spin unpolarized: the spin-corrected =
For system with spin-polarized: THE spin-corrected = 2*W(alpha) + 2*W(beta),
- where W(alpha) is the Wiberg bond index in NAO basis for alpha spin-orbital
- where W(beta) is the Wiberg bond index in NAO basis for beta spin-orbital

The part of an output of NBO Analysis of oxygen gas

******* Alpha spin orbitals *****

*********************************

(deleted lines)

Wiberg bond index matrix in the NAO basis:

Atom 1 2 ---- ------ ------

1. O 0.0000 0.2560

2. O 0.2560 0.0000 (more deleted lines)

**********************************

******* Beta spin orbitals *******

********************************** (deleted lines)

Wiberg bond index matrix in the NAO basis:

Atom 1 2 ---- ------ ------

1. O 0.0000 0.7505

2. O 0.7505 0.0000

(more delete lines)

The bond order of O2 is = (2x0.2560) + (2x0.7505) = 2.013

P.S. No matter whether we select the Wiberg bond index whether, from 1,2 or 2,1, the computed values are symmetric. So the bond order for atom1 and atom2 are the same.

Rangsiman Ketkaew