Subject: Summary: Geometry optimization of periodic systems

From: News user <[email-masked]>
Date: Fri, 22 Sep 2000 14:56:42 -0500 (CDT)

A few days ago I asked the following question:

>  Dear collegues
> 
>  I am looking for references that describe geometry optimization methods
> for periodic systems, and their applications. Specifically, I would like
> to know about any algorithm that employs something more complicated than
> the usual Cartesian coordinates for atomic positions and lattice vectors.
> An example of such more elaborate method would be a variable-cell-shape
> (VCS) algorithm which optimizes the dot products between the lattice
> vectors instead of the Cartesian components of these vectors.
> {I. Souza and J.L. Martins, Phys. Rev. B, 55, 8733 (1997).}
> 
>  Regards,
>  Konstantin Kudin

 Quite amazingly, the number of requests for a summary exceeded the number
of informative replies. So here it is.

 The following algorithms currently seem to be available for optimization
of periodic systems and are documented at least in some details in the
literature:

- a variable-cell-shape (VCS) algorithm, uses fractional coordinates for
atoms within the cell and optimizes lattice vectors via their dot
products. Originally developed for molecular dynamics, recently used for
periodic system optimizations. The details about which Hessian is used
seem to be unavailable.
{I. Souza and J.L. Martins, Phys. Rev. B, 55, 8733 (1997).}

   Dr. Keith Refson provided some other references for earlier VCS
dynamics algorithms.

- the GULP computer program for periodic molecular mechanics, also uses
fractional coordinates. The lattice vectors are optimized via the strain
matrix with the 6 independent components. The GULP uses the exact Hessian
computed once every few cycles.
{http://www.ch.ic.ac.uk/gale/Research/gulp.html
 GULP - a computer program for the symmetry adapted simulation of solids,
J.D. Gale, JCS Faraday Trans., 93, 629 (1997) }

 The info was provided by:
 Ricardo Grau-Crespo <[email-masked]>
 Centro de Investigaciones del Petroleo
 Unidad de Catalisis
 Washington 169 Esq. Churruca. Habana 12000
 CUBA

- a redundant internal coordinate algorithm for optimization of periodic
systems. Both atomic positions and lattice vectors are optimized via a
bunch of redundant internal coordinates. The method employs relatively
expensive tranformations redundant internals <--> Cartesians,
but permits high optimization efficiency with a simple diagonal guess for
the Hessian. Therefore the method goes very well with expensive electronic
structure calculations.
{K.N. Kudin, G.E.Scuseria, H.B. Schlegel, J. Chem. Phys., submitted}

  Regards,
 Konstantin Kudin