Subject: Re: CCL:charges

From: [email-masked] (Hinsen Konrad)
Date: Fri, 30 Sep 94 13:27:19 -0400

Wendy Cornell writes:

   I would be very interested to see a summary of this approach
   posted here.  It sounds like this is a molecule-based rather
   than an atom-based description.  How many parameters ("true
   unimolecular properties such as multipoles and polarizabilties")
   would describe a molecule such as alanine?  Can you even treat a 
   molecule that is that big?  Isn't this description also subject 
   to conformational dependence?  Has this model been tested for
   its ability to reproduce properties other than gas phase
   interaction energies, such as conformational energies or
   condensed phase properties?

Although I am rather new to the field of simulating big molecules,
I do have a lot of experience with multipole expansions, and
I would like to warn about a problem to watch out for:

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.

Even if you don't care about the convergence of the whole
series ("A dipole is good enough for me."), you can still
get some problems. For example, if you have a system of
induced dipoles (i.e. molecules with a dipole polarizability)
and place them too close to each other in some external field,
then the strength of the induced dipoles will diverge. The
reason is that such a system is unphysical: you can't have
arbitrarily polarizable materials, so to increase the
polarizability of a real object, you have to increase
its size. But that puts a lower limit on the distance
between two such objects. You can actually calculate the limit
in this way: take a sphere of radius r made out of the most
polarizable material (a perfect conductor) and calculate
its dipole polarizability (which is r^3 if I remember correctly).
That's the highest polarizability allowed for a distance
of 2r.

Finally, if you find that you can work with a multipole expansion,
don't assume that a dipole is sufficient. It might be, but
there is no way to know without trying with higher multipole
orders. So make sure your code can handle them. And take care
to pick a suitable representation. Most people use multipole
moments defined in terms of spherical harmonics, because that's
what you find in textbooks on electromagnetic theory. There
are however good reasons to choose other representations
for numerical work. If you can live with redundant elements,
the Cartesian multipole expansion (essentially a Taylor
series) is very simple to use. If you can't, have a look at
irreducible Cartesian tensors, which are equivalent to
spherical harmonics, but can be calculated without having
to deal with complex numbers and sines and cosines.

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Konrad Hinsen                     | E-Mail: [email-masked]
Departement de Chimie             | Tel.: +1-514-343-6111 ext. 3953
Universite de Montreal            | Fax:  +1-514-343-7586
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