Natural Population Analysis scheme

Spin density calculations analyze the difference between each atom s population of a- and [3-electrons using various techniques. Mulliken population analysis140 is still often used for determining spin densities despite its deficiencies experienced sometimes when large basis sets are used. The Lowdin population analysis Scheme141 tries to circumvent some of the unreasonable orbital populations predicted by the Mulliken scheme however it is somewhat still basis set dependent. The natural bond orbital (NBO) methodology142 is a whole set of analysis techniques, including natural population analysis (NPA), which is less basis set dependent than the Mulliken scheme and often considered one of the most reliable methods for population analysis. 

All calculations in Ref. [22] were performed utilizing the Gaussian-98 code [30]. The potential energy scan was performed by means of the Mqller-Plesset perturbation theory up to the fourth order (MP4) in the frozen core approximation. The electronic density distribution was studied within the population analysis scheme based on the natural bond orbitals [31,32], A population analysis was performed for the SCF density and MP4(SDQ) generalized density determined applying the Z-vector concept [33]. 

Bond and Valence Indices. - Atomic charges, bond indices (two-centre and three-centre) and valences have been calculated for a number of closed-shell molecules using HF and KS orbitals. It was observed that, compared to the HF orbitals, the KS orbitals predicted a slightly enhanced covalency. Beside AIM the authors employed MuUiken, Lowdin and Natural Population Analysis and noted that the AIM scheme led to a more polar charge distribution than NPA. 

Table 1.29 Distribution of charge in the transition state structures shown in Scheme 1.24. Natural population analysis on structures optimized at the MP2/6-311++G(d,p) level... 

Copper-metal bonds have been synthesized by the condensation of (NHC)CuOFt with the acidic metal hydride CpMo(H)(CO)3 [171], or by halide displacement from (NHC)copper(l) using anions such as CpFe(CO)2 and CpMo(CO)3" (Cp = ri -CjHj Scheme 11.6) [172]. The net metal-metal interaction in these complexes is a a-bond In (lDipp)Cu-Fe(CO)2Cp, with a Cu-Fe distance of only 2.3462(5) A, the HOMO—1 and HOMO are Fe- Cu ic orbitals, and the LUMO is the a orbital. Natural population analysis indicates significant ionic character, consistent with unequal sharing of an... 

At the same time, the formally independent particle nature of DFT allows the application of standard interpretative tools developed for the HF approach. This is true not only for the standard MuUiken population analysis, but also for more sophisticated schemes, like the Natural Bond Orbital (NBO) analysis [9], the Atomic Polarizable Tensor population [10], or the Atom in Molecule (AIM) approach [11]. These tools allow the use of familiar and well known models to analyze the molecular wave function and to rationalize it in terms of classical chemical concepts. In short, DFT is providing very effective quantum... 

The results of chemical-bonding analysis for crystal MgO, performed via the conventional and WF schemes of population analysis, were compared in [608]. The MgO crystal is a good testing system for studying the accuracy of such methods, since on the one hand, the nature of chemical bonding in it is well known to be ionic, and on the other hand, some of the methods give contradictory results of chemical-bonding analysis in this crystal (see below and [601,609]). 

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