"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."
- Eugene Wigner
NBO Applications, 1980-1997 (1176)
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NBO Applications, 2012 (1287)
NBO Applications, 2013 (1673)
NBO Applications, 2014 (1865)
NBO Applications, 2015 (2008)
NBO Applications, 2016 (2008)
NBO Applications, 2017 (2019)
NBO Applications, 2018 (1969)
NBO Applications, 2019 (2249)
NBO Applications, 2020 (2531)
NBO Applications, 2021 (2443)
NBO Applications, 2022 (partial)

Marcel Patek
    (Jmol video 1)
    (Jmol video 2)
    (Gennbo Helper video)
    (NBO scripts and apps site)
    ( NBO tutorials)

Colby NBO Tutorial

Hendrik Zipse (LMU-Muenchen, Germany)

Patricia Hunt (Imperial College, London)

Angel Martin Pendas (Univ. Oviedo, Spain)

Alan Spivey (Imperial College, London)

J.P. Hagon (U. Newcastle)

Eric Clot (U. Montpellier)
    (Introduction to NBO)

Bernie Kirtman (UCSB)

Kit Cummins (MIT)

B. Rudshteyn/V.S. Batista (Yale)

Jay Shore (S. Dak. St.)

Piotr Wojciechowski (Warsaw)

John Keller (U. Alaska-Fairbanks)

Igor Alabugin (Florida St. Univ.)

LABFAMA Orca/NBO Tutorial (UAM Azcapotzalco, Mexico)

Alan Shusterman (Reed College) "Spartan tip"

Jmol NBO visualizations

Chemcraft NBO visualizations

Multiwfn NBO visualizations (in Chinese) "How to Visualize NBO on Gauss View?"

Molden output conversion to NBO .47 file

Toshi Nagata, Meijo Univ. (in Japanese)

Niko Prasetyo, Gadjah Mada Univ. (in Indonesian)

Chem 106, "Advanced Organic Chemistry" lectures (Harvard)

Chem 344, "Computational Molecular Modeling" video lectures (UW-Madison)


IUPAC Gold Book

Joaquin Barroso Blog

Ross McKenzie Blog

NNNNS Chemistry Blog

Jim Kress Blog

Michael Evans (Ga. Tech)
     Localized MOs and NBO Theory
     NBO Analysis of Methane
     Shapes of Natural Bond Orbitals
     Polarization and Relative Energies
     Orbital Theory Doesn't Have to Suck

Henry Rzepa "The Winnower"

Anna Krylov "Q-Chem Lab4-NBO"

Dani Setiawan (SMU), "Advance Natural Bond Orbital (NBO) Analysis""

Schrödinger's Kitten "How to install NBO on Mac OS X Yosemite"

     "NMR-NBO Tutorial"
     "NBO analysis: adfnbo, gennbo"

Lindqvist Blog: "N/EDA in GAMESS. Running NEDA"

El-Shafie A. Gad (Egyptian Petroleum Research Unit): "Natural bond orbitals (NBOs)" (in Arabic)

M. A. Hashmi (Wisdom Center)
     "Tutorial 12: Natural Bond Orbitals (NBOs) Calculation in Gaussian"
     "Tutorial 13: Natural Bond Orbitals NBOs Data Analysis"

Alexander Boldyrev
Alkaline earth octacarbonyl complex
Alkane stereochemistry
Anomeric effect
Aufbau principle
Aza-Cope rearrangement
Bent's rule
Bioorthogonal chemistry
Boranylium ions
Chalcogen bond
Chemical bond
Chemical structure
Coinage metal N-heterocyclic carbene complexes
Conformational isomerism
Covalent bond
Chalcogen bond
Dihydrogen cation
18-Electron rule
Estuarine acidification
Gallium monoiodide
Frank A. Weinhold
Germanium(II) dicationic complexes
Germanium(II) hydrides
Hugo Stintzing
Hydrogen bond
Inorganic chemistry/Chemical bonding/Hybridization
Jack D. Dunitz
Lewis acidic antimony compounds
Lewis structure
Ligand field theory
Lone pair
Metal aquo complex
Molecular orbital
Mulliken population analysis
Natural bond orbital
Natural resonance theory
N-heterocyclic silylene
Noble gas
Nontrigonal pnictogen compounds
Orbital hybridization
Octet rule
Organoactinide chemistry
Partial charge
Periodic table
Per-Olov Löwdin
Phosphirenium ion
Pi electron donor-acceptor
Selenate selenite
Sigma electron donor-acceptor
Sigma-pi and equivalent-orbital models
Steric effects
Sulfur dioxide
Three-center four-electron bond
Trivalent group 14 radicals
Tungsten hexafluoride
VSEPR theory
News Archive FAQ Featured apps NBO team contact us

NBO 7.0 Program Citation

NBO 7.0. E. D. Glendening, J, K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohmann, C. M. Morales, P. Karafiloglou, C. R. Landis, and F. Weinhold, Theoretical Chemistry Institute, University of Wisconsin, Madison (2018).

New features of the NBO 7.0 Program

E. D. Glendening, C. R. Landis, and F. Weinhold, "NBO 7.0: New Vistas in Localized and Delocalized Chemical Bonding Theory," J. Comput. Chem. 40, 2234-2241 (2019).

Didactic Introductions to NBO Concepts

L. Suidan, J. K. Badenhoop, E. D. Glendening, and F. Weinhold, "Common Textbook and Teaching Misrepresentations of Lewis Structures," J. Chem. Educ. 72, 583-586 (1995).

F. Weinhold, "Chemical Bonding as a Superposition Phenomenon," J. Chem. Educ. 76, 1141-1146 (1999).

F. Weinhold and C. R. Landis, "Natural Bond Orbitals and Extensions of Localized Bonding Concepts", Chem. Educ. Res. Pract. 2, 91-104 (2001).

F. Weinhold and R. A. Klein, "What is a Hydrogen Bond? Resonance Covalency in the Supramolecular Domain", Chem. Educ. Res. Pract. 15, 276-285 (2014).

A. D. Clauss, S. F. Nelsen, M. Ayoub, J. W. Moore, C. R. Landis, and F. Weinhold, "Rabbit Ears Hybrids, VSEPR Sterics, and Other Orbital Anachronisms", Chem. Educ. Res. Pract., 15, 417-434 (2014).

C. R. Landis and F. Weinhold, "The NBO View of Chemical Bonding", in, G. Frenking and S. Shaik (eds.), The Chemical Bond: Fundamental Aspects of Chemical Bonding (Wiley, 2014), pp. 91-120.

F. Weinhold, C. R. Landis, and E. D. Glendening, "What is NBO Analysis and How is it Useful?" Int. Rev. Phys. Chem. 35, 399-440 (2016).

E. D. Glendening, C. R. Landis, and F. Weinhold, "Natural Bond Orbital Theory: Discovering Chemistry with NBO7," in, S. Grabowsky (ed.), Complementary Bonding Analysis (de Gruyer, Amsterdam, 2021), pp. 129-156.

F. Weinhold, "The Path to Natural Bond Orbitals," Isr. J. Chem. 61 (2021). [DOI: 10.1002/ijch.202100026]

E. D. Glendening and F. Weinhold, "Pauling's Conceptions of Hybridization and Resonance in Modern Quantum Chemistry" Molecules 26, 4110 (2021) [Chemical Bonding: A Commemorative Special Issue Honoring Professor Linus Pauling].

Comparisons with Other Methods


F. Weinhold, "Natural Bond Orbital Analysis: A Critical Overview of its Relationship to Alternative Bonding Perspectives," J. Comp. Chem. 33, 2363-2379 (2012).


F. Weinhold, "Natural Bond Critical Point Analysis: Quantitative Relationships between NBO-based and QTAIM-based Topological Descriptors of Chemical Bonding," J. Comput. Chem. 33, 2440-2449 (2012).

F. Weinhold, P. v.R. Schleyer, and W. C. McKee, "Bay-Type H...H 'Bonding' in Cis-2-Butene and Related Species: QTAIM vs. NBO Description," J. Comput. Chem. 35, 1499-1508 (2014).


F. Weinhold and E. D. Glendening, "Comment on 'Natural Bond Orbitals and the Nature of the Hydrogen Bond'" J. Phys. Chem. A 122, 724-732 (2018).


F. Weinhold, "Rebuttal to the Bickelhaupt-Baerends Case for Steric Repulsion Causing the Staggered Conformation of Ethane", Angew. Chem. Intern. Ed. 35, 4188-4194 (2003).

C. R. Landis, R. P. Hughes, and F. Weinhold, "Bonding Analysis of TM(cAAC)2 (TM = Cu, Ag, Au) and the Importance of Reference State," Organometall. 34, 3442-3449 (2015).

Pseudo Jahn-Teller Theory

D. Nori-Shargh and F. Weinhold, "Natural Bond Orbital Theory of Pseudo Jahn-Teller Effects," J. Phys. Chem. A 122, 4490-4498 (2018).

Natural Hybrid and Bond Orbitals

J. P. Foster and F. Weinhold, "Natural Hybrid Orbitals," J. Am. Chem. Soc. 102, 7211-7218 (1980).

Natural Atomic Orbitals and Natural Population Analysis

A. E. Reed and F. Weinhold, "Natural Bond Orbital Analysis of Near-Hartree-Fock Water Dimer," J. Chem. Phys. 78, 4066-4073 (1983);

A. E. Reed, R. B. Weinstock, and F. Weinhold, "Natural Population Analysis," J. Chem. Phys. 83, 735-746 (1985).

Natural Localized Molecular Orbitals

A. E. Reed and F. Weinhold, "Natural Localized Molecular Orbitals," J. Chem. Phys. 83, 1736-1740 (1985).

Resonance Natural Bond Orbitals

E. D. Glendening and F. Weinhold, "Resonance Natural Bond Orbitals (RNBOs): Efficient Semi-Localized Orbitals for Computing and Visualizing Reactive Chemical Processes," J. Chem. Theory Comput. 15, 916-921 (2019)

Open-Shell NBO

J. E. Carpenter and F. Weinhold, "Analysis of the Geometry of the Hydroxymethyl Radical by the 'Different Hybrids for Different Spins' Natural Bond Orbital Procedure" J. Mol. Struct. (Theochem) 169, 41-62 (1988)

Natural Resonance Theory

E. D. Glendening and F. Weinhold, "Natural Resonance Theory. I. General Formulation," J. Comp. Chem. 19, 593-609 (1998)

E. D. Glendening and F. Weinhold, "Natural Resonance Theory. II. Natural Bond Order and Valency," J. Comp. Chem. 19, 610-627 (1998)

E. D. Glendening, J. K. Badenhoop, and F. Weinhold, "Natural Resonance Theory. III. Chemical Applications," J. Comp. Chem. 19, 628-646 (1998)

E. D. Glendening, S. J. Wright, and F. Weinhold, "Efficient Optimization of Natural Resonance Theory Weightings and Bond Orders by Gram-Based Convex Programming," J. Comput. Chem. 40, 2028-2035 (2019)

E. D. Glendening, C. R. Landis, and F. Weinhold, "Resonance Theory Reboot," J. Am. Chem. Soc. 141, 4156-4166 (2019)

Other NBO Keyword Options

Natural Bond-Bond Polarizability (NBBP):
H. E. Zimmerman and F. Weinhold, "Use of Hückel Methodology With Ab Initio Molecular Orbitals: Polarizabilities and Prediction of Organic Reactions," J. Am. Chem. Soc. 116, 1579-1580 (1994); H. E. Zimmerman and F. Weinhold, "Natural Bond-Bond Polarizability: A Versatile Hückel-Like Electronic Delocalization Index," J. Org. Chem. 78, 1844-1850 (2013)

Natural Energy Decomposition Analysis (NEDA):
E. D. Glendening and A. Streitwieser, "Natural Energy Decomposition Analysis - An Energy Partitioning Procedure for Molecular Interactions with Application to Weak Hydrogen-Bonding, Strong Ionic, and Moderate Donor-Acceptor Complexes," J. Chem. Phys. 100, 2900-2909 (1994);

E. D. Glendening, "Natural Energy Decomposition Analysis: Explicit Evaluation of Electrostatic and Polarization Effects with Application to Aqueous Clusters of Alkali Metal Cations and Neutrals," J. Am. Chem. Soc. 118, 2473-2482 (1996);

G. K. Schenter and E. D. Glendening, "Natural Energy Decomposition Analysis: The Linear Response Electrical Self Energy," J. Phys. Chem. 100, 17152-17156 (1996)

Natural Steric Analysis (STERIC):
J. K. Badenhoop and F. Weinhold, "Natural Bond Orbital Analysis of Steric Interactions," J. Chem. Phys. 107, 5406-5421 (1997)

J. K. Badenhoop and F. Weinhold, "Natural Steric Analysis: Ab Initio Van der Waals Radii of Atoms and Ions," J. Chem. Phys. 107, 5422-5432 (1997)

Natural Chemical Shielding Analysis (NCS):
J. A. Bohmann, F. Weinhold, and T. C. Farrar, "Natural Chemical Shielding Analysis of Nuclear Magnetic Resonance Shielding Tensors from Gauge-Including Atomic Orbital Calculations," J. Chem. Phys. 107, 1173-1184 (1997)

Natural J-Coupling Analysis (NJC):
S. J. Wilkens, W. M. Westler, J. M. Markley, and F. Weinhold, "Natural J-Coupling Analysis: Interpretation of Scalar J-Couplings in Terms of Natural Bond Orbitals," J. Am. Chem. Soc. 123, 12026-12036 (2001)

Natural Bond Critical Point Analysis (NBCP):
F. Weinhold, "Natural Bond Critical Point Analysis: Quantitative Relationships between NBO-based and QTAIM-based Topological Descriptors of Chemical Bonding," J. Comp. Chem. 33, 2440-2449 (2012)

Natural Poly-Electron Population Analysis (NPEPA):

K. Kyriakidou, P. Karafiloglou, E. D. Glendening, and F. Weinhold, "To Be or Not to Be: Demystifying the 2nd-Quantized Picture of Complex Electronic Configuration Patterns in Chemistry with Natural Poly-Electron Population Analysis," J. Comput. Chem. 40, 1509-1520 (2019).

E. D. Glendening and F. Weinhold, "Efficient Evaluation of Poly-Electron Populations in Natural Bond Orbital Analysis," Chem. Phys. Lett. 711, 23-26 (2018).

Comprehensive Reviews of NBO Methods

F. Weinhold, "Natural Bond Orbital Methods," in, Encyclopedia of Computational Chemistry, P. v.R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer III, P. R. Schreiner (Eds.), (John Wiley & Sons, Chichester, UK, 1998), Vol. 3, pp. 1792-1811.

E. D. Glendening, C. R. Landis, and F. Weinhold, "Natural Bond Orbital Methods," WIREs Comput. Mol. Sci. 2, 1-42 (2012).

Other Review Articles

A. E. Reed, L. A. Curtiss, and F. Weinhold, "Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint," Chem. Rev. 88, 899-926 (1988);

F. Weinhold and J. E. Carpenter, "The Natural Bond Orbital Lewis Structure Concept for Molecules, Radicals, and Radical Ions," in, R. Naaman and Z. Vager (eds.), The Structure of Small Molecules and Ions (Plenum, New York, 1988), pp. 227-236;

F. Weinhold, "Natural Bond Orbital Analysis of Photochemical Excitation, with Illustrative Applications to Vinoxy Radical," in, A. G. Kutateladze (ed.), Computational Methods in Organic Photochemistry: Molecular and Supramolecular Photochemistry (Taylor & Francis/CRC Press, Boca Raton FL, 2005), pp. 393-476.

Comprehensive Treatise on NBO Theory and Applications

F. Weinhold and C. R. Landis, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective (Cambridge University Press, 2005), 760pp.

Practical Handbook of NBO Methods

F. Weinhold and C. R. Landis, Discovering Chemistry with Natural Bond Orbitals (Wiley-VCH, Hoboken NJ, 2012), 319pp.

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