Multipole representations, molecular

Sokalski WA, Poirier RA (1983) Cumulative atomic multipole representation of the molecular charge distribution and its basis set dependence. Chem Phys Lett 98 86-92... 

W. A. Sokalski, C/zem, Phys. Lerf., 98, 86 (1983). Cumulative Atomic Multipole Representation of the Molecular Charge Distribution and Its Basis Set Dependence. 

W. A. Sokalski and R. A, Poirer, Chem. Phys, Lett., 98, 86 (1983). Cumulative Atomic Multipole Representation of the Molecular Charge Distribution and Its Basis Set Dependence. D. E. Williams and D. J. Craycroft, J. Phys, Chem., 89, 1461 (1985). Estimation of Dimer Coulombic Intermolecular Energy and Site Charge Polarization by the Potential-derived Method. 

Williams, D. E. 1988. Representation of the Molecular Electrostatic Potential by Atomic Multipole and Bond Dipole Models. J. Comp. Chem. 9, 745. 

The electrostatic interaction, which is defined as the classical Coulombic interaction between the undistorted charge distributions of the isolated molecules, is the easiest to derive from wavefunctions. When there is no overlap of the charge distributions of the molecules, all that is required is a representation of the molecular charge density. The traditional, and simplest, representation of the molecular charge distribution is in terms of the total multipole moments. The first nonvanishing multipole moment could often be derived from experi-... 

F. Vigne-Maeder and P. Claverie /. Ghent. Phys., 88, 4934 (1988). The Exact Multicenter Multipolar Part of a Molecular Charge-Distribution and Its Simplified Representations. R. J. Wheatley, Ghent. Phys. Lett., 208,159 (1993). A New Distributed Multipole Procedure for Linear Molecules. 

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

Over the years various approximate formulas for interactions between large molecules have been derived from perturbation theory (91) The better of such perturbation theory expansions customarily include a short-range first order "exchange" term and long range terms (electrostatic, polarization and dispersion). Various approximations (such as the multi-centered multipole expansion, representation of transition densities by bond dipole and the decomposition of molecular polarizability into bond polarizabilities, the use of atomic polarizabilities, bond-bond interaction terms, etc.) have been introduced for the calculation of certain of the terms. 

The radial deformation of the valence density is accounted for by the expansion-contraction variables (k and k ). The ED parameters P, Pim , k, and k are optimized, along with conventional crystallographic variables (Ra and Ua for each atom), in an LS refinement against a set of measured structure factor amplitudes. The use of individual atomic coordinate systems provides a convenient way to constrain multipole populations according to chemical and local symmetries. Superposition of pseudoatoms (15) yields an efficient and relatively simple analytic representation of the molecular and crystalline ED. Density-related properties, such as electric moments electrostatic potential and energy, can readily be obtained from the pseudoatomic properties [53]. 

Indeed, this idea lies at the heart of the venerable notion of assigning partial charges to the atoms in a molecule [17]. One may think of this practice as a representation of the true charge distribution of the molecule by a series of distributed multipoles (in this case, limited to monopoles) at various sites, namely, atomic centers. Even if limited to monopoles, the act of spreading them out over the entire molecule is equivalent in some sense to simulation of high orders of molecular center-based multipoles. 

The principal reason for the latter failings lies in the absence of any representation of the lone electron pairs on the O atom. It is the presence of these lone pairs, above and below the molecular plane, that result in the correct signs of all the multipole elements and that contribute heavily to the interaction of water with an approaching molecule. There are a number of ways in which the atomic charge model can be expanded to address this problem. One possibility is to add more centers to the representation, e.g., partial negative charges above and below the molecular plane, in the approximate centers of the two lone pairs. This concept is illustrated in Fig. 2f, where overall molecular neutrality requires that 2qu + qo + 2[Pg.245]

The distributed multipole analysis method of Stone and co-workers is similar in concept but is based on nonredundant spherical harmonic representation of the multipoles (recall that whereas there are six second moments, only five are independent). He initially places numerous site multipoles at centers of orbital overlap. The individual monopoles are spread out along the molecular axis, and are thought to represent the distribution of charge the site dipoles are also spread out along the bond axis. This very detailed description is simplified into a three-site model, which includes a site in the F—H bond. However, the multipole expansion does not converge well, especially for the bond center site. 

D. E. Williams, /. Comput. Chem., 9, 745 (1988). Representation of the Molecular Electrostatic Potential by Atomic Multipole and Bond Dipole Models. See also, D. E. Williams, in Reviews in Computational Chemistry, Vol. 2, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, pp. 219-271. Net Atomic Charge and Multipole Models for the Ab Initio Molecular Electric Potential. 

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