In quantum chemistry, a natural bond orbital or NBO is a calculated bonding orbital with maximum electron density. The NBOs are one of a sequence of natural localized orbital sets that include "natural atomic orbitals" (NAO), "natural hybrid orbitals" (NHO), "natural bonding orbitals" (NBO) and "natural (semi-)localized molecular orbitals" (NLMO). These natural localized sets are intermediate between basis atomic orbitals (AO) and molecular orbitals (MO):
Natural (localized) orbitals are used in computational chemistry to calculate the distribution of electron density in atoms and in bonds between atoms. They have the "maximum-occupancy character" in localized 1-center and 2-center regions of the molecule. Natural bond orbitals (NBOs) include the highest possible percentage of the electron density, ideally close to 2.000, providing the most accurate possible “natural Lewis structure” of ψ. A high percentage of electron density (denoted %-ρL), often found to be >99% for common organic molecules, correspond with an accurate natural Lewis structure.
The concept of natural orbitals was first introduced by Per-Olov Löwdin in 1955, to describe the unique set of orthonormal 1-electron functions that are intrinsic to the N-electron wavefunction.[1]
Each bonding NBO σAB (the donor) can be written in terms of two directed valence hybrids (NHOs) hA, hB on atoms A and B, with corresponding polarization coefficients cA, cB:
σAB = cAhΑ + cBhB
The bonds vary smoothly from covalent (cA = cB) to ionic (cA >> cB) limit.
Each valence bonding NBO σ must be paired with a corresponding valence antibonding NBO σ* (the acceptor) to complete the span of the valence space:
σAB* = cAhΑ − cBhB
The bonding NBOs are of the "Lewis orbital"-type (occupation numbers near 2); antibonding NBOs are of the "non-Lewis orbital"-type (occupation numbers near 0). In an idealized Lewis structure, full Lewis orbitals (two electrons) are complemented by formally empty non-Lewis orbitals. Weak occupancies of the valence antibonds signal irreducible departures from an idealized localized Lewis structure, which means true "delocalization effects".[1]
With a computer program that can calculate NBOs, optimal Lewis structures can be found. An optimal Lewis structure can be defined as that one with the maximum amount of electronic charge in Lewis orbitals (Lewis charge). A low amount of electronic charge in Lewis orbitals indicates strong effects of electron delocalization.
In resonance structures, major and minor contributing structures may exist. For amides, for example, NBO calculations show that the structure with a carbonyl double bond is the dominant Lewis structure. However, in NBO calculations, "covalent-ionic resonance" is not needed due to the inclusion of bond-polarity effects in the resonance structures.[2] This is similar to other modern valence bond theory methods.
^ abWeinhold, Frank; Landis, Clark R. (2001). "Natural Bond Orbitals and Extensions of Localized Bonding Concepts" (PDF). Chemistry Education Research and Practice. 2 (2): 91–104. doi:10.1039/B1RP90011K.
^Weinhold, Frank; Landis, Clark R. (2012). Discovering Chemistry With Natural Bond Orbitals. New Jersey: John Wiley & Sons. pp. 132–133. ISBN978-1-118-22916-3.
Free, open-source implementation for Atomic orbital → NAO transformation and Natural Population Analysis methods: JANPA package
April 13, 2024
natural, bond, orbital, quantum, chemistry, natural, bond, orbital, calculated, bonding, orbital, with, maximum, electron, density, nbos, sequence, natural, localized, orbital, sets, that, include, natural, atomic, orbitals, natural, hybrid, orbitals, natural,. In quantum chemistry a natural bond orbital or NBO is a calculated bonding orbital with maximum electron density The NBOs are one of a sequence of natural localized orbital sets that include natural atomic orbitals NAO natural hybrid orbitals NHO natural bonding orbitals NBO and natural semi localized molecular orbitals NLMO These natural localized sets are intermediate between basis atomic orbitals AO and molecular orbitals MO Atomic orbital NAO NHO NBO NLMO Molecular orbitalNatural localized orbitals are used in computational chemistry to calculate the distribution of electron density in atoms and in bonds between atoms They have the maximum occupancy character in localized 1 center and 2 center regions of the molecule Natural bond orbitals NBOs include the highest possible percentage of the electron density ideally close to 2 000 providing the most accurate possible natural Lewis structure of ps A high percentage of electron density denoted rL often found to be gt 99 for common organic molecules correspond with an accurate natural Lewis structure The concept of natural orbitals was first introduced by Per Olov Lowdin in 1955 to describe the unique set of orthonormal 1 electron functions that are intrinsic to the N electron wavefunction 1 Contents 1 Theory 2 Lewis structures 3 See also 4 References 5 External linksTheory editEach bonding NBO sAB the donor can be written in terms of two directed valence hybrids NHOs hA hB on atoms A and B with corresponding polarization coefficients cA cB sAB cA hA cB hBThe bonds vary smoothly from covalent cA cB to ionic cA gt gt cB limit Each valence bonding NBO s must be paired with a corresponding valence antibonding NBO s the acceptor to complete the span of the valence space sAB cA hA cB hBThe bonding NBOs are of the Lewis orbital type occupation numbers near 2 antibonding NBOs are of the non Lewis orbital type occupation numbers near 0 In an idealized Lewis structure full Lewis orbitals two electrons are complemented by formally empty non Lewis orbitals Weak occupancies of the valence antibonds signal irreducible departures from an idealized localized Lewis structure which means true delocalization effects 1 Lewis structures edit nbsp Resonance structures of an amideWith a computer program that can calculate NBOs optimal Lewis structures can be found An optimal Lewis structure can be defined as that one with the maximum amount of electronic charge in Lewis orbitals Lewis charge A low amount of electronic charge in Lewis orbitals indicates strong effects of electron delocalization In resonance structures major and minor contributing structures may exist For amides for example NBO calculations show that the structure with a carbonyl double bond is the dominant Lewis structure However in NBO calculations covalent ionic resonance is not needed due to the inclusion of bond polarity effects in the resonance structures 2 This is similar to other modern valence bond theory methods See also editMolecular orbital theory Basis set chemistry References edit a b Weinhold Frank Landis Clark R 2001 Natural Bond Orbitals and Extensions of Localized Bonding Concepts PDF Chemistry Education Research and Practice 2 2 91 104 doi 10 1039 B1RP90011K Weinhold Frank Landis Clark R 2012 Discovering Chemistry With Natural Bond Orbitals New Jersey John Wiley amp Sons pp 132 133 ISBN 978 1 118 22916 3 External links editHomepage for the NBO computer program http nbo6 chem wisc edu IUPAC Gold Book definition natural bond orbital NBO Free open source implementation for Atomic orbital NAO transformation and Natural Population Analysis methods JANPA package Retrieved from https en wikipedia org w index php title Natural bond orbital amp oldid 1116491350, wikipedia, wiki, book, books, library,
