Natural atomic orbitals , Weinhold

The Natural Bond Orbital analysis of Weinhold [Foster and Weinhold, 1980 Reed, Weinstock etal., 1985 Reed, Curtiss etal., 1988] generates, departing from canonical MOs, a set of localized one center (core, lone pairs) and two center (jt and a bonds) strongly occupied orbitals, and a set of one center (Rydberg) and two center (a, Jt ) weakly occupied orbitals the NBOs. The Natural Bond Orbitals (NBOs) are obtained by a sequence of transformations from the input basis to give, first, the Natural Atomic Orbitals (NAOs), then the Natural Hybrid Orbitals (NHOs), and finally the Natural Bond Orbitals (NBOs). For NAOs, atomic charges can be calculated as a summation of contributions given by orbitals localized on each atom moreover, from NBOs, bond order can be also calculated. 

G and 6-31G basis sets [Ig], pp. 337-339). Other approaches to partitioning elecuons among orbitals and thus calculating charges and bond orders are the Lowdin method [167] and the natural atomic orbitals (NAO) population analysis of Weinhold [168]. 

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

An improvement on Mulliken population analysis (MPA) is natural population analysis (NPA) [A. E. Reed, R. B. Weinstcx k, and F. Weinhold, J. Chem. Phys., 83, 735 (1985)], which uses ideas related to natural orbitals (Pilar, Section 10-7). Here, one first calculates a set of orthonormal natural atomic orbitals (NAOs) from the AO basis set Xr The NAOs are then used to compute a set of orthonormal natural bond orbitals (NBOs), where each occupied NBO is classifiable as a core, lone pair, or bond orbital. Using these NBOs, one carries out a population analysis. NPA net atomic charges show less basis-set dependence than those from Mulliken population analysis. Other methods of assigning net atomic charges are discussed in the next section. Still another method of population analysis that yields net atomic charges is Lowdin population analysis (Cramer, Section 9.1.3.2). 

A more elaborate formalism, called natural population analysis (NPA), has been advanced by Weinhold and coworkers. In this formalism, atomic charges are computed as differences between nuclear charges and the respective sums of populations of natural atomic orbitals (NAOs). The NAOs, which form orthonormal sets, ate obtained from the... 

Traditionally, the exact same basis set will be used to define atoms in varying chemical environments. The 6-310 carbon basis set is the same regardless of the nature of the carbon (alkane, olefin, alcohol, carbanion, ketone, carboxylic acid, etc.). The three-dimensional space of the carbon atom must be different in these molecules, yet the Mulliken procedure sums up the occupancy of identically defined orbitals in all these different chemical environments. The natural population analysis (NPA), developed by Reed, Weinstock, and Weinhold,i0 > 8 attempts to define atomic orbitals based on the molecular wavefunction, thereby obtaining different atomic orbitals depending on the chemical environment. 

Taking this idea one step further, Weinhold and co-workers define natural bond orbitals (NBO) by diagonalizing the two-center subblocks of the density matrix.23 These NBOs are the maximum occupancy two-atom orbitals and are constructed from hybrids that are formed from the NAOs. The procedure begins with the NAOs and removes all orbitals that have high occupancy (> 1.999e) as unhybridized core orbitals. Next, all NAOs having an occupancy... 

Bohmaim JA, Weinhold F, Farrar TC (1997) Natural chemical shielding analysis or nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations. J Chem Phys 107 1173-1184... 

The central teaching of the Lewis model is that the electrons are localized in the comers of a tetrahedron, where they are shared by two atoms. The Lewis model is, to a large extent, inconsistent with physical principles, since charged particles cannot be fixed in space, according to classical mechanics. However, the Lewis model may be justified on the basis of quantum mechanics. This is expressed in the natural bond orbital (NBO) model of Frank Weinhold. The MOs are also expressed in terms of hybridized AOs. The hybridized electron clouds replace the Lewis dots. In most cases, the NBO model shows that the time-independent wave function is in agreement with the Lewis model. 

An alternative description of the chemical bonding between a transition metal atom and its surrounding atoms is provided by the natural bond orbital analysis (NBO). This method developed by Weinhold et al. [23] uses the one-electron matrix as starting point to find the... 

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