PD Atomic Multipole Models

When considering goodness-of-fits in Table 12 one should remember the number of variables in the model. In the absence of symmetry, there is one parameter per atom for the M model, three per atom for the D model, and five per atom for the Q model. Thus the M + D + Q model can have nine adjustable parameters per atom. The restricted bond dipole has one parameter per bond the other two parameters of a dipole model are eliminated by requiring the dipole to be parallel to the bond. 

The table shows that the M + D + Q atomic multipole expansion is sufficient for most purposes. The largest rms value is just 0.03 kj/mol. So the curve fitting exercise is successful when carried to atomic quadrupole level, satisfying mathematical requirements of accuracy and convergence. But what about chemical reasonableness and transferability. Judged by these criteria, the M a- D -I- Q model is poor. As a practical matter, it may be necessary to always evaluate M + D -I- Q parameters for the specific molecule being considered and not expect the parameter values to have any obvious intuitive chemical meaning. 

Surprisingly, the atomic dipole model (D) is nearly as good as the atomic charge (M) model. If only dipoles are used, it may be better to locate them in the bonds. The table shows that the bond dipole model (BD) gives a better representation of the electric potential for most of the molecules considered. Of course, at least one monopole is needed if the molecule is an ion and therefore has a net charge. 

The M + D model looks interesting as a good compromise that could represent the molecular electric potential of neutral or charged molecules. Table 12 shows that the electric potential can be fitted fairly well (within about 0.6 kJ/mol) with this model, which is considerably better than the M or the D model. However, the dipole directions and monopole values are erratic and not very transferable. It is possible that the M -H D model could become more useful by allowing only certain atoms (e.g., those with lone pairs) to have a dipole. If additionally the dipole direction can be restricted to a lone pair direction, the number of parameters is greatly reduced compared to a completely general M-l-D model. The reduction in parameters could be accompanied by better chemical reasonableness and transferability properties. 

Dinur and Hagler propose a novel method to determine atomic point charges and point dipoles from derivatives of the molecular dipole moment and second moments. The method is limited to planar molecules and has been applied to hydrogen fluoride, water, formaldehyde, formamide, ethylene, benzene, and pyridine. As was also noted by Williams, they found that atomic dipoles do not necessarily point along the bond directions. Price proposed a distributed multipole model for several aromatic hydrocarbons using carbon sites only. 

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