Population Analysis MPA

An improvement on Mulliken population analysis (MPA) is natural population analysis (NPA) [A. E. Reed, R. B. Weinstock, and F. Weinhold, /. Chem. Phys., 83,735 (1985)], which uses ideas related to natural orbitals (Section 13.21). Here, one first cal-... 

A coarse-grained atom by atom representation of the Fukui function, called condensed-to-atom Fukui function, was proposed by Yang and Mortier [262] and based on a fimte-difference approach in terms of the Mulliken population analysis (MPA) scheme, they may be represented as... 

The most popular and widely used procedure is the Mulliken population analysis (MPA). ... 

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 plane wave basis set with an orbital cutoff distance of 3.9 A was used. All-electron calculations and a double numerical basis set with polarization functions (DNP) were employed. Wave function integration in reciprocal space was performed via fine grid sampling of k points with a separation of 0.02 A . For the calculation of the density of states (DOS), a 5 X 8 X 3 Monkhorst-Pack grid was used. Charge transfer was calculated based on the Mulliken Population Analysis (MPA) (Mulliken 1955). 

Virtually all current molecular orbital programs produce as the standard output the Mulliken population analysis. Even though this analysis is readily available and computationally inexpensive, the MPA results are fraught with dangers. The method is inordinately basis set dependent. The complete lack of any spatial component leads to serious superposition errors. The use of a... 

Based on model population analysis, here we propose to perform model comparison by deriving an empirical distribution of the difference of RMSEP or RMSECV between two models (variable sets), followed by testing the null hypothesis that the difference of RMSEP or RMSECV between two models is zero. Without loss of generality, we describe the proposed method by taking the distribution of difference of RMSEP as an example. We assume that the data X consists of m samples in row and p variables in column and the target value Y is an m-dimensional column vector. Two variable sets, say Vi and V2, selected from the p variables, then can be compared using the MPA-based method described below. 

The reason for these problems is the imbalance of overlap populations and the net atomic populations, and this imbalance is due primarily to the arbitrary equal distribution of the overlap population between atoms involved. In spite of these two problems, which have to be remembered when analyzing populations of orbitals and atoms, MPA is still frequently used for electron population analysis. 

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