Subject: Coulombic Potential Summary

From: Patricia Lozano-Casal <P.Lozano-Casal.-at-.ed.ac.uk>
Date: Wed, 12 May 2004 13:05:56 +0100

Dear all,
this are the answers that I got to my problem with the Coulombic Potential.
Thank you very much for your help.
Patricia

SUBJECT: QUESTION ABOUT COULOMBIC POTENTIAL

Dear all,

I am trying to write a program to calculate the electrostatic contribution of
the lattice energy for molecular crystals. I have run plane-wave DFT
calculations (using the CASTEP package) to calculate the total lattice energy
and using Mulliken charges I hoped to estimate the electrostatic contribution
by coding a simple Coulombic potential. But, I get really weird results!! I am
overestimating my lattice energy by many orders of magnitude.

I know that Mulliken charges are not the ideal point charge to use for this but
I had not expected my numbers to be that wrong. Could anybody help or if not,
could anybody recommend and existing program to use instead (preferably free)?

Many thanks,

Patricia Lozano-Casal (p.lozano-casal.-at-.ed.ac.uk)

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Calculating electrostatic potentials of crystals can be a very daunting
task considering that the sum of Coulombic interactions in an infinite
crystal is only conditionally convergent.  That is it only converges
(when it actually does converge) to a finite number because of the
alternating signs of the terms in the series.  As a result the summation
can have serious problems with numerical error.  So, I hope you are
using an Ewald method to calculate the electrostatic contribution and
that your Muliken charges in your unit cell sum to exactly zero.  To the
first point, the Ewald sum is THE way to calculate the electrostatic
energy of an infinite lattice, but even with it care must be taken to
reduce round-off error in the numerical calculation.  To the second
point, if your unit cell is not neutral, then the strict sum includes
the summation of an infinite number of positive interactions, which of
course is an infinite value.  In a truncated (i.e. any real numerical)
Ewald summation, this could just lead to a large finite value such as
you are getting.  Just a thought.

Malcolm

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Dear Patricia,

 GULP (General Utility Lattice Code), written by Julian Gale, can
calculate very easily the electrostatic contribution to the lattice
energy of a crystal. You should specify the charges in  the input file,
although some methods to estimate them (e.g. by electronegativity
equalisation) are also implemented. The code is free for academic users.
Best regards,

Ricardo.

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