Atomic charge dipole-fitting

The Hirshfeld functions give an excellent fit to the density, as illustrated for tetrafluoroterephthalonitrile in chapter 5 (see Fig. 5.12). But, because they are less localized than the spherical harmonic functions, net atomic charges are less well defined. A comparison of the two formalisms has been made in the refinement of pyridinium dicyanomethylide (Baert et al. 1982). While both models fit the data equally well, the Hirshfeld model leads to a much larger value of the molecular dipole moment obtained by summation over the atomic functions using the equations described in chapter 7. The multipole results appear in better agreement with other experimental and theoretical values, which suggests that the latter are preferable when electrostatic properties are to be evaluated directly from the least-squares results. When the evaluation is based on the density predicted by the model, both formalisms should perform well. 

Atomic charges on the guest molecules were obtained from first principles Hartree-Fock calculations, fitting the electrostatic potential surface (EPS), then scaled up or down in order to reproduce the experimental dipole moments. Table 2 gives partial charges of typical molecules considered in our work. 

When the potential is calculated from Eq. 22 (i.e., includes aspherical terms of electron density) the potential is reasonably well reproduced at the van der Waals surface by point charges, as shown in Figure 22 which gives the comparison between the total potential in a peptide plane of tbuCOprohisNHme and the point charges fitted potential. The rms deviation is = 0.03 elk, and it could be important to include dipolar terms on hydrogen atoms [43b,53]. At the present time, it then seems possible to build a data bank of experimental atomic charges and dipole moments which could be used to parametrize the force fields in the molecular modeling codes. 

The effect of induced dipoles in the medium adds an extra term to the molecular Hamilton operator. = -r R (16.49) where r is the dipole moment operator (i.e. the position vector). R is proportional to the molecular dipole moment, with the proportional constant depending on the radius of the originally implemented for semi-empirical methods, but has recently also been used in connection with ab initio methods." Two other widely available method, the AMl-SMx and PM3-SMX models have atomic parameters for fitting the cavity/dispersion energy (eq. (16.43)), and are specifically parameterized in connection with AMI and PM3 (Section 3.10.2). The generalized Bom model has also been used in connection with force field methods in the Generalized Bom/Surface Area (GB/SA) model. In this case the Coulomb interactions between the partial charges (eq. (2.19)) are combined... 

However, charges, dipoles, etc. do not correspond to real physical phenomena when assigned to atomic centers. Similarly, point-charge representations of lone pairs do not represent real physically observable quantities. With this understood, one can appreciate that atomic charges and so on can be looked upon not as physical quantities, but rather as adjustable parameters. These parameters can be fit to best reproduce certain desired quantities, either experimental or theoretical [14,19-21]. Of most relevance are those which are geared toward the electrostatic interactions of the molecule in question. 

Both rms and rrms are sensitive to the choice of grid point locations where the QM potential is evaluated. Typical values of rms and rrms are 1 to 3 kJ/mol and 3 to 9% with 6-3IG" wavefunctions. The fit generally worsens as grid points are placed closer to the molecule. In certain cases (e.g., strong lone pair effect) worse fits may be obtained with net atomic charge models. Models utilizing additional nonatomic sites, site dipoles, and/or quadrupoles usually give a much better fit. 

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