Home
This Title All WIREs
WIREs RSS Feed
How to cite this WIREs title:
WIREs Comput Mol Sci
Impact Factor: 8.836

Natural bond orbital methods

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

Abstract Natural bond orbital (NBO) methods encompass a suite of algorithms that enable fundamental bonding concepts to be extracted from Hartree‐Fock (HF), Density Functional Theory (DFT), and post‐HF computations. NBO terminology and general mathematical formulations for atoms and polyatomic species are presented. NBO analyses of selected molecules that span the periodic table illustrate the deciphering of the molecular wavefunction in terms commonly understood by chemists: Lewis structures, charge, bond order, bond type, hybridization, resonance, donor–acceptor interactions, etc. Upcoming features in the NBO program address ongoing advances in ab initio computing technology and burgeoning demands of its user community by introducing major new methods, keywords, and electronic structure system/NBO communication enhancements. © 2011 John Wiley & Sons, Ltd. This article is categorized under: Structure and Mechanism > Molecular Structures

Overview of orthogonal and nonorthogonal basis sets underlying natural bond orbital (NBO) methods.

[ Normal View | Magnified View ]

Potential curves for Lewis‐type (EL: steric, electrostatic), non‐Lewis‐type (ENL: resonance‐type charge transfer), and total interaction energy of (HF)2 dimer, showing competition between exponentially varying EL, ENL components that leads to the characteristic short bond length and anharmonic vibrational potential for the equilibrium H‐bonded species.

[ Normal View | Magnified View ]

$DEL‐reoptimization of (HF)2 with intermolecular resonance‐type nH → σHF* charge‐transfer interaction deleted, showing reversion to a feeble, long‐range ‘dipole–dipole complex’ having no resemblance to the actual H‐bonded species.

[ Normal View | Magnified View ]

Mnemonic arrow‐pushing and resonance structure diagrams for intermolecular donor–acceptor interactions (cf. Figure 26), with sample input and output for H‐bonded (HF)2 dimer.

[ Normal View | Magnified View ]

‘Natural bond orbital (NBO) Aufbau diagram’ for multicenter delocalizations, showing leading steps of 2c/2e, 3c/2e (hypovalent), and 3c/4e (hypervalent) bond formation from starting 1c/1e hybrids.

[ Normal View | Magnified View ]

Natural resonance theory (NRT) description of 3c/4e hyperbonding in F3, with associated nF → σFF* donor–acceptor diagram.

[ Normal View | Magnified View ]

Sample $NRTSTR input for specifying 3c/4e hyperbonded resonance structures (ω‐bonded I, II; η‐bonded III) for trifluoride ion (F3), all within the framework of the octet rule.

[ Normal View | Magnified View ]

Successive carbonyl additions to tungsten, W(CO)n, n = 1–6, showing Lewis‐like coordination from hypovalent precursors (n = 1,2) to normal‐valent W(CO)3 (12e, C3v‐symmetric), and thereafter to W(CO)6 (18e, Oh‐symmetric) by hypervalent 3c/4e aggregation.

[ Normal View | Magnified View ]

Duodectet diagrams and graphical forms of natural hybrid orbital (NHOs) and natural bond orbitals (NBOs) for high‐order metal–metal multiple bonds in HWWH, H2WWH2, and H3WWH3.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) descriptors of group 6–11 MHn metal hydrides of the third transition series, showing percentage accuracy of Lewis‐like description (%ρL), metal hybrid (hM), percentage polarization toward M (100cM2), and occupancy of σMH NBOs.

[ Normal View | Magnified View ]

Further details of idealized sdμ hybrids and bond angles for Lewis‐like bonding of transition metals.

[ Normal View | Magnified View ]

Bonding sdμ hybrids for WH6, illustrating centrosymmetric character of natural hybrid orbital (NHOs) and directional alignments with respect to nodal planes to achieve mutual orthogonality.

[ Normal View | Magnified View ]

Sample natural population analysis (NPA)/natural bond orbital (NBO) output for WH6, illustrating the near‐ideal Lewis‐like hybridization and bonding motifs for the strange‐looking (non‐VSEPR!) optimized ground‐state geometry.

[ Normal View | Magnified View ]

Further natural resonance theory (NRT) output for formamide (cf. Figure 34), showing weightings and structural bonding patterns for leading resonance structures.

[ Normal View | Magnified View ]

Lewis‐like structures for transition metals, illustrating the ‘Rule of 12’ for idealized sdμ‐type hybridized bonding.

[ Normal View | Magnified View ]

Similar to Figure 7, for transition metal bonding, showing Lewis‐like ‘duodectet rule’ and hybrid formulations for D‐block (sdμ‐type) valence‐shell bonding.

[ Normal View | Magnified View ]

Further natural resonance theory (NRT) output for formamide (cf. Figures 34 and 35), showing covalent, electrovalent (ionic), and total contributions to NRT bond order and valency.

[ Normal View | Magnified View ]

Outline of natural resonance theory (NRT) algorithm and sample output for formamide.

[ Normal View | Magnified View ]

Illustrative $DEL input and resulting geometry for a ‘nostar’ (‘delete all non‐Lewis natural bond orbital (NBOs)’ and associated resonance delocalizations) geometry optimization of formamide, showing reversion to pyramidalized amine group and near‐ideal NC, CO bond lengths in the absence of amide resonance.

[ Normal View | Magnified View ]

Table and graphs illustrating overall correlation between E($DEL) and E(2) estimates of donor–acceptor interaction strength.

[ Normal View | Magnified View ]

Further details of $DEL output (cf. Figures 29 and 30), comparing quasivariational deletion energy (61.81 kcal/mol) with corresponding perturbative E(2) estimate (59.58 kcal/mol).

[ Normal View | Magnified View ]

Output for $DEL deletion of Figure 29, showing restoration of occupancy in natural bond orbitals (NBOs) 10, 85 to near‐idealized NCO Lewis structural form.

[ Normal View | Magnified View ]

Mnemonic table relating natural bond orbital (NBO) donor–acceptor interactions to associated ‘arrow pushing’ and resonance diagrams, with details of leading interactions and resonance structures for formamide.

[ Normal View | Magnified View ]

Illustrative $DEL keylist input to delete the leading nN → πCO* (NBO 10 → 85) donor–acceptor interaction of formamide.

[ Normal View | Magnified View ]

Illustrative input and output for $CHOOSE option to test alternative N(+) = C−O(−) resonance structure of formamide.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) compositions of σCN, σNH ‘natural localized molecular orbitals’ (NLMOs) of formamide, showing dominant Lewis‐type ‘parent’ and leading non‐Lewis‐type ‘delocalization tails’ of each NLMO.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) second‐order perturbation theory output for ‘E(2)’ donor–acceptor interactions of formamide, showing dominant stabilization (∼60 kcal/mol) due to nN → πCO* delocalization, as pictured in PNBO overlap diagrams [cf. Figure 21 for mathematical details of tabulated ‘E(j) − E(i)’ orbital energy differences and ‘F(i, j)’ Fock matrix elements].

[ Normal View | Magnified View ]

Natural hybrid orbital (NHO) directionality output for formamide, showing ‘bond bending’ descriptors for sigma and pi bonds.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) summary output for formamide, showing the evident ‘charge transfer’ from nN lone pair (NBO 10) to πCO* antibond (NBO 88) that underlies amide resonance.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) search summary for formamide (NH2CHO), showing unusually large non‐Lewis ‘errors’ associated with quantum mechanical resonance.

[ Normal View | Magnified View ]

Natural population analysis (NPA) summary output for hydrogen fluoride (HF), showing effective condensation of electron occupancy (99.9%) in the (natural minimal basis' set of natural atomic orbitals (NAOs).

[ Normal View | Magnified View ]

Mathematical and graphical summary of natural bond orbital (NBO) donor–acceptor perturbation theory.

[ Normal View | Magnified View ]

Hybrid composition versus hybrid directionality relationship as summarized in Coulson's theorem.

[ Normal View | Magnified View ]

Comparison of alpha and beta spin natural bond orbitals (NBOs) for O2, showing ‘different Lewis structures for different spins’ open‐shell character.

[ Normal View | Magnified View ]

Natural hybrid orbital (NHO) Fock matrix for hydrogen fluoride (HF), showing strong off‐diagonal interaction element between NHOs despite their mutual orthogonality.

[ Normal View | Magnified View ]

Natural hybrid orbital (NHO) (orthogonal) versus PNHO (nonorthogonal) comparisons for hydrogen fluoride (HF) molecule.

[ Normal View | Magnified View ]

Comparison of orthogonal natural atomic orbitals (NAOs) and overlapping PNAOs (‘visualization orbitals’) for hydrogen fluoride (HF) molecule.

[ Normal View | Magnified View ]

Table of natural electronegativity values for elements 1–120, as calculated from natural bond orbital (NBO) polarities of ground‐state AHn Lewis‐like hydrides.

[ Normal View | Magnified View ]

Summary of Bent's rule and natural bond orbital (NBO) based relationship of electronegativity and bond polarity.

[ Normal View | Magnified View ]

Details of hydrogen fluoride (HF) bond hybrid composition and ionicity.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) search summary for hydrogen fluoride (HF) molecule, showing high accuracy (>99.95%) of Lewis‐type ‘natural Lewis structure’ description.

[ Normal View | Magnified View ]

Comparison of valence‐shell bond (NBO 1) and antibond (NBO 29) for hydrogen fluoride (HF) molecule.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) listing with natural hybrid orbital (NHO) compositions and natural atomic orbital (NAO) coefficients, for hydrogen fluoride (HF) molecule.

[ Normal View | Magnified View ]

Density matrix in natural atomic orbital (NAO) (upper) and natural bond orbital (NBO) (lower) basis, showing high condensation of ‘electron‐pair’ occupancy in diagonal DMNBO elements.

[ Normal View | Magnified View ]

Overview of main‐group valency, hybridization, and bonding principles, showing Lewis‐like ‘octet rule’ and electron‐pair functions as formulated by Pauling (Heitler–London valence bond) or Lennard–Jones (bond orbital).

[ Normal View | Magnified View ]

Natural atomic orbital (NAO) Fock (F), kinetic (K), 1e‐potential (V), and e–e repulsions (R) matrices for lowest singlet and triplet states of O atom (UHF level), showing electronic origin of Hund's rule in V (not R) differences in the two states.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) Summary output for alpha‐spin NBOs of F atom.

[ Normal View | Magnified View ]

Natural bond orbital (NBO) listing with natural hybrid orbital (NHO) compositions and natural atomic orbital (NAO) coefficients, for alpha (majority spin) NBOs of F atom.

[ Normal View | Magnified View ]

Natural population analysis (NPA) summary output for F atom.

[ Normal View | Magnified View ]

NAO output for F atom (all calculations at B3LYP/6–311++G** theory level unless otherwise noted.)

[ Normal View | Magnified View ]

Browse by Topic

Structure and Mechanism > Molecular Structures

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts