Natural atomic orbitals , Weinhold population analysis

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]. 

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. 

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