Multipole moment expansion solvent

THE MULTIPOLE MOMENT EXPANSION SOLVENT CONTINUUM MODEL A BRIEF REVIEW... 

Abstract The multipole moment expansion solvent continuum model is being developed by our... 

The Multipole Moment Expansion Solvent Continuum Model... 

Ruiz-Lopez MF (2008) The multipole moment expansion solvent continuum model a brief review. In Canuto S (ed) Solvation effects on molecules and biomolecules, vol 6. Challenges and advances in computational chemistry and physics. Springer, Netherlands, pp 23-38. doi 10.1007/978-l-4020-8270-2 2... 

The charge distribution of the molecule can be represented either as atom-centred partial charges or as a multipole expansion. For a neutral molecule, the lowest order approximation considers only the dipole moment. This may be a quite poor approximation, and fails completely for symmetric molecules that do not have a dipole moment. For obtaining converged results, it is often necessarily to extend the expansion up to order six or more, i.e. including dipole, quadrupole, octupole, etc., moments. Furthermore, only for small and symmetric molecules can the approximation of a spherical or ellipsoidal cavity be considered realistic. The use of the Bom/ Onsager/Kirkwood models should therefore only be considered as a rough estimate of the solvent effects, and quantitative results can rarely be obtained. 

Abstract - The temperature dependence of the proton nmr spectra of dithiocarbamato iron(III) complexes is markedly solvent dependent. A study is made of the temperature dependence of the nmr shifts for the N-CH2 protons in tris(N,N-dibutyldithiocar-bamato) iron(III) in acetone, benzene, carbon disulfide, chloroform, dimethyIformamide, pyridine and some mixed solvents. This contribution shall outline first how the nmr shifts may be interpreted in terms of the Fermi contact interaction and the dipolar term in the multipole expansion of the interaction of the electron orbital angular momentum and the electron spin dipol-nuclear spin angular momentum. This analysis yields a direct measure of the effect of the solvent system on the environment of the transition metal ion. The results are analysed in terms of the crystal field environment of the transition metal ion with contributions from (a) the dithiocarbamate ligand (b) the solvent molecules and (c) the interaction of the effective dipole moment of the polar solvent molecule with the transition metal ion complex. The model yields not only an explanation for the unusual nmr results but gives an insight into the solvent-solute interactions in such systems. 

Methods based on multipole expansion The simplest versions of these methods rely on the use of spherical cavities and in the truncation of the multipole expansion at the monopole or dipole level. These methods correspond to the well known models of Born [35] and Bell-Onsager [36,37], whose expressions are given in equations 11 and 12, where q is the charge representing the solute charge distribution, p. is the dipole moment, e is the permittivity and R is the radius of the cavity defining the solute/solvent interface. 

The earlier attempt to approach the electrostatic contribution to the free energy of solvation is due to Kirkwood (1934). This model is based on a multipole expansion of the charge distribution of the solute at the center of a spherical cavity surroimded by a continuum represented by the dielectric permittivity of the solvent. When this expansion is limited to rank 1 which corresponds to a pure dipole fi, one finds the Onsager model (Onsager 1936) in which the electrostatic contribution to the free energy of solvation by a solvent of dielectric constant e of a molecule having a dipole moment in a cavity of radius a takes the expression ... 

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