Approximate charge distributions

Charge Distributions. Mulliken population analyses have been used to calculate approximate charge distributions in a number of carbene complexes (see, for example, Refs. 10 and 12) and several conclusions can be drawn ... 

Fig. 7.10. Approximate charge distribution in methyl acetate and S-methyl thioacetate, as calculated by the INDO quantum-mechanical method [144]...

Fig. 19.3 The complex cation [Co(NH3)g] (a) a conventional diagram showing the donation of lone pairs of electrons from ligands to metal ion (b) the charge distribution that results from a 100% covalent model of the bonding (c) the charge distribution that results from a 100% ionic model of the bonding and (d) the approximate charge distribution that results from applying the electroneutrality principle.

Another, even more drastic approximation was proposed by Wilhite and Euwema. In this method, the entire charge distribution function (which is the product of two contracted Gaussians) is replaced by a few s-type Gaussian functions. To minimize the error, coefficients and exponents of the replacement functions are calculated by equating the magnitudes of several multipole moments of the original and approximate charge distributions. 

A more in-depth study of similarity indices will, however, be presented in the section on Quantum Molecular Similarity Indices. Modeling the potential of a charge distribution by an approximate charge distribution was previously... 

Function e provides a critical test for the approximate charge distribution model related to real applications. As the first example, we used imidazole, which frequently models histidine residue. In the Table 3 we compare results obtained for four different molecular charge density models Mulliken [27], CHELP [28] and ESP [29] charges and CAMM (up to quadruples). In general, electrostatic potentials on solvent accessible surfaces described by CAMM series truncated at quadrupole term tend to perform slightly better s = 2-10% than those calculated using potential-derived atomic charges. 

Despite th ese reservation s. Mu Ilikeri population -derived atomic charges arc easy to compute. Empirical investigation shows that they have various uses, they provide approximate representation of the 3D charge distribution within a molecule. 

The charge distribution of the molecule can be represented either as atom centred charges or as a multipole expansion. For a neutral molecule, the lowest-order approximation considers only the dipole moment. This may be quite a poor approximation, and fails completely for symmetric molecules which do not have a dipole moment. For obtaining converged results it is often necessarily to extend the expansion up to order 6 or more, i.e. including dipole, quadrupole, octupole, etc. moments. 

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