Natural bond orbital
Encyclopedia
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.
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:
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".
In resonance structures
, major and minor contributing structures may exist. For carbon monoxide, for example, NBO calculations show that the structure with a triple bond
is the optimal Lewis structure.
Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...
, 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 orbitalAtomic orbitalAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...
→ NAO → NHO → NBO → NLMO → Molecular orbitalMolecular orbitalIn chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...
Natural (localized) orbitals are used in computational chemistry
Computational chemistry
Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids...
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
Per-Olov Löwdin
Per-Olov Löwdin was a Swedish physicist, professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993....
in 1955, to describe the unique set of orthonormal 1-electron functions that are intrinsic to the N-electron wavefunction.
Theory
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 = cA hΑ + cB hB
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
Antibonding
Antibonding is a type of chemical bonding. An antibonding orbital is a form of molecular orbital that is located outside the region of two distinct nuclei...
NBO σ* (the acceptor) to complete the span of the valence space:
- σAB* = cA hΑ − cB hB
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
Lewis structure
Lewis structures are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds...
, full Lewis orbitals
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....
(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".
Lewis structures
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
Resonance (chemistry)
In chemistry, resonance or mesomerism is a way of describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis formula...
, major and minor contributing structures may exist. For carbon monoxide, for example, NBO calculations show that the structure with a triple bond
Triple bond
A triple bond in chemistry is a chemical bond between two chemical elements involving six bonding electrons instead of the usual two in a covalent single bond. The most common triple bond, that between two carbon atoms, can be found in alkynes. Other functional groups containing a triple bond are...
is the optimal Lewis structure.
Weblinks
- Homepage for the NBO computer program: http://www.chem.wisc.edu/~nbo5/
- IUPAC Gold Book definition: natural bond orbital (NBO)