Subject: Summary: Convergent Lattice Sum for Lennard-Jones terms

From: bruno <[email-masked]>
Date: Sat, 02 May 1998 20:48:27 +0200

A few days ago I mailed the following message:

>I've heard about the use of convergent lattice sum for Lennard Jones
>terms in MD computations. This should have been done by Willians some
>decade ago. As far as I know, I don't remember MD simulations involving
>the use of such technique, as well as I do not know of any largely used
>MD software which implements it. Probably this is due to the peculiar
>short range nature of the LJ interactions which make this correction
>less important than the use of ewald sums for coulombic forces. Am I
>wrong?
>Do anyone has some considerations at this regard or can suggest some
>readings on this subject?

I thank all people who answered and report here a summary of their
mails:

------------------------------------------------------------------------
Darden and co-workers have published on using the particle mesh Ewald
technique to perform the 1/r**6 part of the LJ terms in Essman et al.,
J.
Chem. Phys. 103, 8577 (1995), "A smooth particle mesh Ewald method".
While this method works well for potentials applying geometric combining
rules (such as GROMOS) and only involves a single reciprocal space
calculation, with Lorentz-Bertholet combining rules (rij = (ri + rj)/2,
such as in CHARMM or AMBER) this requires 7 reciprocal space
calculations
and is therefore prohibitively expensive.   Moreover, as you mention,
the
correction is likely small, although it may be necessary in crystal
simulation.

Good luck with your search,

Thomas Cheatham, III
CBS, NHLBI, 12A/2041
National Institute of Health
Bethesda, MD  20892-5626
[email-masked]
(301) 402-0617
FAX: (301) 496-2172
------------------------------------------------------------------------
From: 
        Andrew Rohl <[email-masked]>

The MSI product discover has had the ability to do this as long as
I have used it!  If you want something a little less expensive, I
can recommend GULP from julian gale at Imperial College, London which
is I believe free to academic institutions

   Andrew
------------------------------------------------------------------------
I suggest you look at the book of Hockney and Easwtwood:
@Book{Hockney81,
  author =       "R. W. Hockney and J. W. Eastwood",
  title =        "Computer simulation using particles",
  publisher =    "McGraw-Hill",
  year =         "1981",
  address =      "New York",

We are currently busy implementing the dispersion term in the GROMACS
package:
http://rugmd0.chem.rug.nl/~gmx
Groeten, David.
________________________________________________________________________
Dr. David van der Spoel         Biomedical center, Dept. of Biochemistry
s-mail: Husargatan 3, Box 576,  75123 Uppsala, Sweden
e-mail: [email-masked]    www: http://zorn.bmc.uu.se/~spoel
phone:  46 18 471 4205          fax: 46 18 511 755
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
------------------------------------------------------------------------
bruno manunza writes:
 > I've heard about the use of convergent lattice sum for Lennard Jones
 > terms in MD computations. This should have been done by Willians some
 > decade ago. 

D. E. Williams, Acta Cryst A27 (1971) 4680-4684.  There's also a
discussion in M.T. Dove, "Introduction to Lattice Dynamics" (1993)
Cambridge University Press in Appendix A.

 > As far as I know, I don't remember MD simulations involving
 > the use of such technique, as well as I do not know of any largely
used
 > MD software which implements it. 

I have a vague recollection that Martin Dove might have done this, but
in general it isn't worth the effort.  You really need it for r**(-1)
and r**(-3) porentials where the sum is long-ranged and conditionally
convergent, but in the case of a r**(-6) potential there is
rapid convergence in real space. 

Keith Refson
------------------------------------------------------------------------
Within Cerius2 Open Force Field ( used in Cerius2 MD, mechanics, ... )
the 
vdW r^{-6} is treated by an Ewald summation, based on:

@article{
        Author = "Karaswa N. and Goddard III W.A.",
        Title ="",
        Journal =  "J. Phys. Chem.",
        Volume = 93,
        Pages = "7320--",
        Year = 1989}

Simon
Dr Simon Miller ([email-masked])  : Web  : http://www.msi.com
Molecular Simulations.            :
------------------------------------------------------------------------

From: 
        Konrad Hinsen <[email-masked]>

> MD software which implements it. Probably this is due to the peculiar
> short range nature of the LJ interactions which make this correction
> less important than the use of ewald sums for coulombic forces. Am I
> wrong?

Right. Electrostatic sums are conditionally convergent, which presents
some major problems. LJ sums are well-behaved, and sufficiently
short-ranged
that a finite cutoff can usually be compensated with a correction
term (see the book by Allen & Tildesley for this).

Nevertheless, LJ terms can be treated better, either by explicit
summation, or by techniques known from electrostatics, i.e. Ewald-like
formulas or fast multipole techniques. The only problem with the
latter techniques is that they require purely multiplicative
combination rules for the LJ parameters of different atom species,
whereas many force fields are designed with a combination rule that
uses the average of the vdW-radii.
 
-------------------------------------------------------------------------------
Konrad Hinsen                          | E-Mail: [email-masked]
Laboratoire de Dynamique Moleculaire   | Tel.: +33-4.76.88.99.28
Institut de Biologie Structurale       | Fax:  +33-4.76.88.54.94
41, av. des Martyrs                    | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France         | Nederlands/Francais
-------------------------------------------------------------------------------
------------------------------------------------------------------------
There is a summary of this technique in the International Tables for
Crystallography, Volume B, p. 374.
-Donald Williams

-- 
Dr. Donald E. Williams          email:[email-masked]
Department of Chemistry
University of Louisville        phone:502-852-5975
Louisville, KY 40292            fax:  502-852-8149
-----------------------------------------------------------------------
Dear Dr. Manunza,
    In response to your recent query on the CCL about use of convergent
lattice sum expressions for the Lennard Jones potential, we have
recently been working with convergent lattice sum expressions for the
Lennard Jones potential.  Our initial interest was in developing an
extended potential accurately calculated for solid phase problems, but
then realized that it also has application for MC and MD.  We
generalized the forms derived by Van Der Hoff and Benson to the
triclinic case for our solids applications.  For MC or MD use, that is
unnecessary.  We developed some functional code for MC calculations and
have compared its performance with the conventional algorithm with a
cutoff radius.  For conventional fluid simulations, the convergent sum
expressions in our hands yield longer compute times than the
conventional algorithm.
For problems involving solid phases, the use of the convergent sum
algorithm should mean that the simulation can obtain suitable
reliability with many fewer atoms in the simulation.  This gives a
distinct computational advantage.  We are pursuing this point.  I would
appreciate hearing of any work you pursue or of others in this
area.        Bill Fink, Professor of Chemistry, University of
California, Davis,CA, USA
            [email-masked]
----------------------------------------------------------------------
--
Dr Bruno Manunza
DISAABA - Environmental Sciences Dept.
V.le ITALIA 39
07100 SASSARI, ITALY
phone 39 79 229215
fax   39 79 229276
e-mail: [email-masked]
e-mail: [email-masked]
e-mail: [email-masked]

http://antas.agraria.uniss.it