# Re: multipole expansion

> From: hinsenk |-at-| ERE.UMontreal.CA (Hinsen Konrad)
>
> ...
> A multipole expansion is an expansion of the potential generated
> by a spatially localized charge distribution for long distances.
> Its convergence is guaranteed only outside a sphere containing
> all the charges. To see if you can use multipole expansions
> for molecular systems, draw a sphere around every molecule.
> If any two spheres overlap, you are in trouble. In practice
> this means that multipole expansions are useful only for
> approximately spherical molecules, or for molecules in a
> gas phase.
> ...
In other words, the multipole expansion (ME) is the solution of Laplace
equation, which is why you have to be outside of the sphere containing
the charge distribution. But recently, Koester et al. (JCP, 99 p1224 (1993))
developped a model for the solution of the Poisson equation. Since you
are now solving Poisson's equation, there is no longer the restriction
of being outside of your charge distribution. And in fact, we have implemented
this scheme in our DFT code (deMon) and the molecular electrostatic
potential calculated with this model has the right behavior both at
long AND short distances from the molecules. And the computational
effort is very similar to a ME calculation.
Martin Leboeuf
Departement de Chimie
Universite de Montreal
Montreal, Canada
email: leboeuf |-at-| cerca.umontreal.ca