Subject: multipole expansion

From: [email-masked] (Bill Ross )
Date: Fri, 30 Sep 1994 12:53:06 -0700

From: [email-masked] (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.
	...

Another use of multipole expansions is for long-range forces 
exerted by collections of point charges (typically in a subcube
of the simulated volume) as a means to faster calculations in 
vacuum or solvated systems. There is an excellent brief summary 
of these methods by Leslie Greengard in a recent _Science_ issue 
featuring computers in science.

Bill Ross

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From: [email-masked] (Leboeuf Martin)
Date: Fri, 30 Sep 1994 18:28:33 -0400 (EDT)

>       approximately spherical molecules, or for molecules in a

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: [email-masked]