Spherical tensor distributed multipoles

Let us consider a molecule placed in a cavity surrounded by a dielectric continuum (fig. 1). The relative dielectric permittivity of the continuum is assumed to be e and in the cavity it is taken as equal to the permittivity of a vacuum. In the following we shall assume that the charge distribution of the solute is represented by a single center multipole expansion. An equivalent distributed multipole 2,3] representation may be used without further difficulty. We shall use the spherical tensors formalism [4,5] for the multipoles in which the 2/4 1 components of the multipole of rank / at the origin are defined from unnormalized spherical harmonics [6] by the equation ... 

It has recently become clear that classical electrostatics is much more useful in the description of intermolecular interactions than was previously thought. The key is the use of distributed multipoles, which provide a compact and accurate picture of the charge distribution but do not suffer from the convergence problems associated with the conventional one-centre multipole expansion. The article describes how the electrostatic interaction can be formulated efficiently and simply, by using the best features of both the Cartesian tensor and the spherical tensor formalisms, without the need for inconvenient transformations between molecular and space-fixed coordinate systems, and how related phenomena such as induction and dispersion interactions can be incorporated within the same framework. The formalism also provides a very simple route for the evaluation of electric fields and field gradients. The article shows how the forces and torques needed for molecular dynamics calculations can be evaluated efficiently. The formulae needed for these applications are tabulated. 

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