Subject: Damped Coulomb Potential Summary

From: Fernando Vila <[email-masked]>
Date: Wed, 10 Mar 1999 16:30:57 -0500 (EST)

Dear Fellows;

   I would like to thank all the people that replied to me request. Right
after I sent my e-mail to the list I decided to give it a new try. At the
very beginning of my equations I found an error that was complicating
everything. After I fixed that the integrals turned out to be
embarrassingly easy, easier than those including only the Coulomb
potential. The references you sent will be useful to double check my
results.

My original question was:

Dear Fellows,

   For the past weeks I have been trying to calculate the matrix elements
for a damped Coulomb potential to no avail. The potential has the form:

         erf(a|r-R|)
V(r) =  -------------
            |r-R|

where r and R are position vectors and erf(t) is the error function:

             2       t
erf(t) = -------- int  exp(-x^2) dx.
         PI^(1/2)    0

The matrix elements then are of the form:

                                     erf(a|r-R|) gij
<gi|V|gj> = int gi V(r) gj dr = int ----------------- dr
                                        |r-R|

Here gi are spherical Gaussians and gij is the resulting Gaussian from the
Gaussian Product Theorem.

I have tried using techniques similar to those used for the calculation of
the pure Coulomb potential (based on Fourier or Laplace transforms) but
the usual cancellation is not complete.

Any pointers to papers, books or web pages are welcome.. The complete
solution is also very much welcome.. :-)

Thanks to all in advance, Fer.

Here is a summary of the replies I received:

==========================================================================
From: koelmel <[email-masked]>

Hi,

Lecture Notes in Chemistry, vol. 48, authored by C. Pisani, R. Dovesi
and C. Roetti, titled
"Hartree-Fock Ab Initio Treatment of Crystalline Systems"
(1988, springer)

may be a useful reference. What you're looking for is mentioned
on page 60.

One way is to convert 1/r into an integral using the Laplace transform
trick, then change the order of integration, I think.

Hope this helps somewhat

Cheers,
Christoph

==========================================================================
From: Frank Jensen <[email-masked]>

	Try looking up some of Peter Gill's work in
recent years. They have played with screened
Coulomb potentials.
	Frank

==========================================================================
From: Norge Cruz Hernandez <[email-masked]>

Hi ,

Try to see :

S. Obara and A. Saika.
J. Chem. Phys. 84(7), 3963 

best regard 
Norge

==========================================================================
From: "Jeremy P. Dombroski" <[email-masked]>

Dear Fernando:

This is work that myself, Professor Peter Gill and Dr Ross Adamson have
spent considerable time on (in particular, the latter). We have recently
published an article in J. Comp. Chem. and if you contact Ross at
[email-masked] he may provide you with a preprint should the
article not yet be in print.

Q-Chem 1.2 performs O(N) damped Coulomb SCF calculations, including
energies, optimizations and frequencies using what we have called the
CASE approximation where we replace all occurrences of the Coulomb
operator with the so-called Damped Coulomb potential.

May I ask where your research interest lies in this damped Coulomb
potential?

Regards,
Jeremy Dombroski

==========================================================================
From: "Jan H. Jensen" <[email-masked]>

Hello,
	I believe Peter Gill at Cambridge has worked on something quite
similar.  I don't have any references on hand.

	Best regards,

			Jan Jensen

*******************************************************************************
Fernando D. Vila       
Department of Chemistry              Voice    (412)624-8691
University of Pittsburgh             Fax      (412)624-8552             
Box 90 Chevron Science Center        E-mail   [email-masked]
Pittsburgh, PA 15260, USA            WWW      http://www.pitt.edu/~fer
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