NBO Analysis

Advance Natural Bond Orbital (NBO) Analysis
D Setiawan
Advance Computational Chemistry Laboratory
Southern Methodist University
dsetiawan@smu.edu
November 11, 2015
D Setiawan (Adv. Comp. Chem. Lab.) NBO Analysis November 11, 2015 1 / 36

NBO: Brief Overview
NBO is a calculated bonding orbital with maximum electron density.
Hierarchical Atomic/Molecular Orbitals in the NBO analysis:
AO → NAO → NHO → NBO → NLMO → MO
NAO: Natural Atomic Orbitals
NHO: Natural Hybrid Orbitals
NBO: Natural Bond Orbitals
NLMO: Natural (Semi-)Localized Molecular Orbitals

Natural Atomic Orbitals
”Natural” atomic orbitals are the optimal (maximum occupancy),
eﬀective AOs in the molecular environment, derived by:
diagonalizing the localized block of the full density matrix of a given
molecule,
which is associated with basis functions on that atom
Thus they meet simultaneous requirements of orthonormality and
maximum occupancy.
For isolated atoms: NAOs coincide with NOs.
For a polyatomic molecule: the NAOs mostly retain one-centre
character (in contrast to NOs that become delocalized over all
nuclear centers).

NBO Output: Natural AO Occupancies
Lists the atoms with their respective NAO types attached: angular momentum
type, orbital type, and orbital occupancy

NBO Output: NPA Summary
Population Inversion WARNING: occupancy ordering inconsistent with energy ordering;
May occurs for Rydberg-type orbitals of very low occupancy or near-degeneracy in
occupancy or energy, so that no signiﬁcant physical eﬀects are indicated.

NBO Output: NPA Summary
Gives natural atomic charges (or sometimes attributed as NBO charges) and total
core, valence, and Rydberg populations on each atom; Atomic charges are the
diﬀerences between the nuclear charge and the total (natural) electronic population.

NBO Output: Natural Electron Configuration
Given as “natural” electron configuration for each atom; Can be somewhat
related (idealized) to the Lewis’ electron configuration.

NBO Output: Wiberg Bond Index (NAO Basis)
Bond Order: Originally, a quantitative net measure of electronic population
occupying bonding (molecular) orbital.

Wiberg BI in NAO Basis
The original Wiberg’s BI was deﬁned for close-shell semi-empirical
wavefunctions with the orthonormal basis:
WAB =
µ∈A ν∈B
|Dµν|2
(1)
Dµν is the oﬀ-diagonal Density Matrix elements with NAO is an
orthonormal orbital.
For the “general” ab initio analysis, for which orthonormal basis sets
is not used: Mayer’s Bond Index

Historical Perspective: Mayer’s BI
Generalization of the original Wiberg’s BI for non-orthogonal basis
functions, by taking into account also the Overlap Matrix S
MAB =
µ∈A ν∈B
(DS)µν(DS)νµ (2)
Nowadays one may instead use some orthogonalization techniques
(e.g. Lowdin, OWSO analysis)
OWSO: Occupancy-weighted Symmetric Orthogonalization, is used in
the NBO analysis

Wiberg BI in NAO Basis: Spin Polarized Systems
For spin polarized systems NBO analysis is automatically performed
three times, yielding three diﬀerent part of the outputs
1 Total Spin Orbitals
2 Alpha Spin Orbitals
3 Beta Spin Orbitals
The spin-corrected bond order in the NAO basis will be:
WAB = 2W (α) + 2W (β) (3)

NBO Output: Bond Valencies

NBO Output: Search for An Optimum Lewis Structure
Check whether ”reasonable” Lewis structure is obtained, e.g. the occupancy of
Lewis orbitals should not be lower than 1.90 and non-Lewis orbitals (e.g.
anti-bonding, or Rydberg-types) should not higher than 0.10.

NBO Output: Natural Bond Orbitals
Gives: Occupancies, Bond-types, Atomic/Bonding-center, and their respective
Natural Hybrid Orbitals (NHOs) composition (i.e. “covalent” or “ionic”
character).

Natural Bond Orbitals
The NHOs part lists the orbital-hybridization (given in percentage,
and also in a relative-scale, with lowest percentage orbital set as 1);
For bonding and anti-bonding type orbitals, contribution of the NHOs
(i.e. the polarization coefficient) are also given.
Below each NHO label is the set of NAOs coefficients, ordered
according to NAOs listed at the top part of the output (e.g. Carbon
atom thus will have set of 9 coefficients if calculated using a double
zeta basis sets).

NBO Output: NHO Directionality
Summary of the angular properties of the NHOs; The ”direction” of a hybrid is speciﬁed
in terms of the polar (θ) and azimuthal (φ) angles (in a polar coordinate system: θ =
90.0, means orbitals are on the XY plane; φ = 0.0, means orbitals are on the X axis).

NBO: 2nd
Order Perturbation Analysis of Fock Matrix
Summary of the 2nd
-order perturbative estimates of donor-acceptor
(bonding-antibonding) interactions in the NBO basis.

NBO: 2nd
The purpose of this analysis is to give estimates of a “delocalization”
corrections w.r.t the zeroth-order natural Lewis structure (i.e. charge
transfer characteristic).
These perturbations lead to donation of electron (occupancy) from
the localized NBOs of the idealized Lewis structure into the (empty)
non-Lewis orbitals (and thus, to departures from the idealized Lewis
structure description):

NBO: 2nd
E(2) = ∆Eij = qi
F(i, j)2
j − i
(4)
E(2) refers to the“(2-electron) stabilization energy” (see also the
related Perturbational MO (PMO) Theory Models & Concepts Class)
qi is the donor orbital occupancy; i , i are NBO orbital energies; and
F(i, j) is the oﬀ-diagonal elements of the NBO Fock matrix.
All possible interactions are considered.
Default threshold for printing is 0.50 kcal/mol.

NBO Output: NBO Summary
The qualitative delocalization to non-Lewis orbitals: (i.e. the acceptor NBOs):
corresponds to the “principal delocalization tails” of the natural localized molecular
orbital (NLMO) associated with the parent donor NBO.

Natural (Semi-)Localized Molecular Orbitals (NLMO)
Notes: NLMO summary table or plotting will require “NLMO” keyword in the NBO
input ﬁle.
Image Source: http://nbo6.chem.wisc.edu/

MO vs. NLMO: H-Bond in HSSH Dimer
Image Source: http://nbo6.chem.wisc.edu/

NBO Orbitals: Sorting & Reordering
NBO orbitals are sorted by type: BD, CR, RY*, and BD* (NBO3)
NBO orbitals are sorted by type: CR, BD, BD*, and RY (NBO6)
NBO programs will resorting these orbitals based on their
occupancies, from lower to higher, which will go in this order: CR,
BD, BD*, RY* (RY, NBO6)
The numbering in the molecular viewer (e.g. GaussView, Avogadro)
are thus not referring to the numbering used by the NBO program!

NBO Orbitals: Sorting & Reordering (NBO3)

Running NBO in Gaussian09
G09 Input File
# METHOD/BasisSet Pop(NBO)
G09 Input File: Read from Chk Files
#P METHOD/BasisSet Geom(AllCheck) Guess=(Read,Only)
Pop(NBO6read,SaveNBOs)
NBO Keywords: At the end of ﬁle
$nbo reson bndidx [other-keywords] $end

Running NBO in the cluster
Maneframe
module load gaussian
module load nbo
SMUHPC
export PATH=/data/share/software/NBO6/nbo6/bin:$PATH

Some Important NBO Keywords
NBOSUM, requests printing of the NBO summary table.
RESON, requests search for highly delocalized structures.
NOBOND, requests that no bonds (2-center NBOs) are to be
formed in the NBO procedure; This is useful for highly ionic species.
3CBOND, requests search for 3-center bonds; This is useful for
diborane and other electron-deﬁcient ’bridged’ species.
NLMO computes and prints out the summary table of Natural
Localized Molecular Orbitals (NLMOs).
BNDIDX, calculates and prints Wiberg bond indices.
NRT, calculates and prints Natural Resonance Theory analysis and
bond indices.
E2PERT=N, increase/decrease the printing threshold for the 2nd
Order Perturbation stabilization energies (in kcal/mol).

Questions?

Tasks: Fluoroamines
H
N
H
H
F
N
H
F
F
N
F
F
H
N
F
H
C N
F
H
H
N N
F
H
N N
F
F
Input Files can be found in SMUHPC:/users/chem/Temp/NBOLab

Tasks: Fluoroamines
How does different fluorination affect the charge distributions and NF
bond order?
How does different substituents affect the charge delocalizations?
Which orbitals might be involved in this?
What are the characteristics of the bonds? Can there be more than
one possible (resonance) structures?
Bonus:
Sum up the total 2pz (oop, ⊥ w.r.t. the molecular plane) orbital
occupancies.
How do these electron population might affect NF bond order upon
planarization?

NBO Analysis: Fluoroamines
H
N
H
H
F
N
H
F
F
N
F
F
H
N
F
H
-1022 -358 +169 +571
-190-265 -232+341 +312 +296
C N
F
H
H
+14
-258
+187
-106
+192
N N
F
H
N N
F
F
+215 +192
-193-258
+336
-294

# Molecule Central PYR PLA ∆Pop Substituent PYR PLA ∆Pop ∆Pop PYR-∆E PLA-∆E
Atom (E) Pop[LP(E)] Pop[LP(E)] [LP(E)] Atom (X) Pop[LP(X)] Pop[LP(X)] [LP(X)] TOTAL (lpE−lpX) (lpE−lpX)
4 H2N-H(1A1), C3v N 1996.60 1994.97 -1.63 H -1.63
5 H2N-F(1A ), Cs N 1995.13 1989.10 -6.03 F 1995.79 1996.81 1.02 -5.01 3.18 128.82
6 H(F)N-F(1A ), Cs N 1996.46 1987.39 -9.07 F 1994.08 1996.70 2.62 -6.45 41.15 126.33
7 F2N-F(1A1), C3v N 1996.19 1994.40 -1.79 F 1980.43 1997.78 17.35 15.56 61.91 125.36
31 H2N-Cl(1A ), Cs N 1994.59 1986.82 -7.77 Cl 1995.60 1997.18 1.58 -6.19 85.23 17.38
32 H(Cl)N-Cl(1A ), Cs N 1993.53 1981.33 -12.20 Cl 1994.24 1997.79 3.55 -8.65 113.50 4.27
33 Cl2N-Cl(1A1), C3v N 1992.60 1978.22 -14.38 Cl 1982.25 1998.25 16.00 1.62 61.81 9.60
34 H2P-H(1A1), C3v P 1998.48 1993.37 -5.11 H -5.11
35 H2P-F(1A ), Cs P 1996.75 1979.41 -17.34 F 1984.21 1991.55 7.34 -10.00 42.85 225.13
36 H(F)P-F(1A ), Cs P 1996.46 1964.46 -32.00 F 1981.29 1990.22 8.93 -23.07 42.95 241.25
37 F2P-F(1A1), C3v P 1997.11 1994.61 -2.50 F 1971.21 1921.90 -49.31 -51.81 40.64 22.00
38 H2As-H(1A1), C3v As 1998.22 1993.15 -5.07 H -5.07
39 H2As-F(1A ), Cs As 1996.60 1976.73 -19.87 F 1989.36 1995.09 5.73 -14.14 2.03 216.84
40 H(F)As-F(1A ), Cs As 1996.58 1967.08 -29.50 F 1987.55 1993.80 6.25 -23.25 3.07 234.70
41 F2As-F(1A1), C3v As 1997.14 1998.03 0.89 F 1978.60 1938.76 -39.84 -38.95 0.73 53.83
Table 1: Lone pair orbital population based on Natural Bond Orbital Analysis on the central E = N, P, or As atoms and on substituent atoms
X = F or Cl of molecule 4-7 and 31-41. The electron occupancies and diﬀerences are given in me. It is shown that the lone pair occupancies
at central atoms are decreasing at the planar form, with exception of atom As of molecule 41, while for substituent atoms, lone pair densities
gaining electrons, except for molecule 37 and 41. ∆Pop TOTAL shows how many (partial) electrons gain/loss by the lone pair orbitals of E and
X as results of planarization. The ∆E(lpE-lpX) shows the energy diﬀerences between the lone pair orbitals in kcal/mol. All values are based on
CCSD(T)/aug-cc-pVTZ calculations.
1

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