Natural-bond orbital

Atomic charge, orbital energy, and population are important pieces of information for determining electronic configuration, net charge association, and the nature of the bond. Mulliken population analysis is a widely used method in most ab initio molecular orbital calculations. However, reports about Mulliken population analysis that fail to yield reliable characterization of molecular systems have appeared. A more accurate method for population analysis, NBO, was 

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Natural Atomic Orbital and Natural Bond Orbital Analysis... 

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

NATURAL ATOMIC ORBITAL AND NATURAL BOND ORBITAL ANALYSIS... 

Each pair of atoms (AB, AC, BC,...) is now considered, and the two-by-two subblocks of the density matrix (with the core and lone pair contributions removed) are diagonalized. Natural bond orbitals are identified as eigenvectors which have large eigenvalues (occupation numbers larger than say 1.90). 

Reed, A. E., Weinhold, F., Curtiss, L. A., Pochatko, D. J., 1986, Natural Bond Orbital Analysis of Molecular... 

Weinhold F (1997) Nature of H-bonding in clusters, liquids, and enzymes an ab initio, natural bond orbital perspective. J Mol Struct Theochem 398-399 181-197... 

The determination of atomic charges has been a controversial subject because there has been disagreement on how the atoms in a molecule should be defined or, in other words, how the electronic charge should be apportioned between the atoms. Proposed orbital methods for determining atomic charges include the natural bond orbital (NBO) method (Reed et al., 1985, 1988) and the Mulliken method (1985). However, these orbital methods have some unsatisfactory features. There is a certain arbitrary character associated with them because, as we saw in Chapter 3, the choice of orbitals to describe a given molecule is not unique and... 

In this section, we present a unified picture of the different electronic effects that combine to determine methyl rotor potentials in the S0, Sp and D0 electronic states of different substituted toluenes. Our approach is based on analysis of ab initio wavefunctions using the natural bond orbitals (NBOs)33 of Weinhold and cowork-ers. We will attempt to decompose the methyl torsional potential into two dominant contributions. The first is repulsive steric interactions, which are important only when an ortho substituent is present. The second is attractive donor-acceptor interactions between CH bond pairs and empty antibonding orbitals vicinal to the CH bonds. In the NBO basis, these attractive interactions dominate the barrier in ethane (1025 cm-1) and in 2-methylpropene (1010 cm-1) see Figure 3. By analogy, donor-acceptor attractions are important in toluenes whenever there is a substantial difference in bond order between the two ring CC bonds adjacent to the C-CH3 bond. Viewed the other way around, we can use the measured methyl rotor potential as a sensitive probe of local ring geometry. 

With accurate calculated barriers in hand, we return to the question of the underlying causes of methyl barriers in substituted toluenes. For simpler acyclic cases such as ethane and methanol, ab initio quantum mechanics yields the correct ground state conformer and remarkably accurate barrier heights as well.34-36 Analysis of the wavefunctions in terms of natural bond orbitals (NBOs)33 explains barriers to internal rotation in terms of attractive donor-acceptor (hyperconjuga-tive) interactions between doubly occupied aCH-bond orbitals or lone pairs and unoccupied vicinal antibonding orbitals. 

Paddon-Row MN, Shephard MJ (1997) Through-bond orbital coupling, the parity rule, and the design of superbridges which exhibit greatly enhanced electronic coupling a natural bond orbital analysis. J Am Chem Soc 119 5355-5365... 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

TABLE 3. Hybridizations of bonding orbitals for cr-bonds from NBO (Natural Bond Orbital) analyses based on MP2/6-31G(d,p) optimized structures... 

The program NBO 5.0 was developed by E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohmann, C. M. Morales, and F. Weinhold, Theoretical Chemistry Institute, University of Wisconsin, Madison (2001) F. Weinhold, NBO 5.0 Program Manual Natural Bond Orbital Analysis Programs (Madison, WI, Theoretical Chemistry Institute, 2001). 

A Natural Bond orbital Donor-Acceptor Perspective... 

Because we are both computational chemistry researchers, we have naturally directed the book also to specialists in this field, particularly those wishing to incorporate natural bond orbital (NBO) and natural resonance theory (NRT) analysis into their methodological and conceptual toolbox. Researchers will find here a... 

Recently, we analyzed the role of electron repulsion relative to bond breaking and antiaromaticity effects on a quantitative basis using Natural Bond Orbital (NBO) analysis.24 Two other destabilizing factors were considered at the initial stage of the cyclization in addition to four-electron repulsion between the filled in-plane acetylenic re-orbitals - distortion/breaking of the acetylenic bonds as a result of their bending, and the fact that, at a distance of ca. 3 A, the in-plane re-orbitals become parallel and reach a geometry that resembles the antiaromatic TS of the symmetry forbidden [2S + 2S] cycloaddition (vide infra). 

M. N. Paddon-Row, M. J. Shephard, Through-Bond Orbital Coupling, the Parity Rule, and the Design of Superbridges Which Exhibit Greatly Enhanced Electronic Coupling - a Natural Bond Orbital Analysis , J. Am. Chem. Soc 1997,119, 5355-5365. 

Weinhold, F. and Landis, C. R. 2005. Valency and Bonding A Natural Bond Orbital Donor-Acceptor Perspective. Cambridge University Press, Cambridge, UK. 

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