Stavros C. Farantos
Institute of Electronic Structure and Laser,
Foundation for Research and Technology - Hellas,
and
Department of Chemistry
University of Crete,
Iraklion, Crete 711 10, Greece.
Published in "Computer Physics Communications Vol. 108, p. 240, 1998."
Title of the program: POMULT (Periodic Orbit MULTishooting)
Catalogue number: POMT
Program obtainable form: CPC Program Library, Queen's University
of Belfast, N. Ireland
Licensing provisions: Numerical Recipes
Computer: Tested on workstations HP-9000/735, IBM-7030/3CT,
PC-Linux
Installation: IESL-FORTH, Iraklion, Crete, Greece
Operating system: UNIX
Programming language used: FORTRAN 77 with extensions, lower
case, implicit, include
Memory required to execute with typical data: 5 Mbytes
No. of bits in a word: 32
No. of bytes in distributed program, included test data etc:
2211840
Distribution format: gzip compressed tar file
Keywords: molecular dynamics and spectra, periodic orbits, multiple
shooting algorithm, damped Newton-Raphson method
Nature of the physical problem:
Given a multidimensional highly coupled molecular potential energy
surface we want to compute families of periodic solutions of Hamilton equations.
These families of periodic orbits reveal the structure of the classical
phase space by detecting the regions of phase space with regular and chaotic
motions. Furthermore, periodic orbits point out possible localization of
the quantum wavefunctions, and explain/predict spectroscopic features.
Method of solution:
The location of periodic orbits is based on damped Newton-Raphson methods
or secant-Quasi Newton methods. Simple or Multiple shooting algorithms
are employed which are robust in cases of long period or highly unstable
periodic orbits.
Restrictions on the complexity of the problem:
The program has been tested with 2-, 3-, 5-, and 6-dimensional molecular
potential functions. Limitations are observed in cases of high instability
or in regions of phase space densely occupied by periodic orbits. The above
difficulties cause also limitations in the continuation of a family of
periodic orbits with a parameter.
Typical running time:
This depends on the complexity of the potential function, the period
and the number of periodic orbits which are computed, and whether the equations
of motion are stiff or not.
Remarks:
Standard numerical actions like integration of ordinary differential
equations and solution of linear algebraic equations are carried out with
routines from the package ``Numerical Recipes''. The program can be interfaced
with ODESSA or other available programs which carry out sensitivity analysis
of differential or algebraic equations. Generally, the program has been
written in such a way that the user can incorporate his/her own favorable
subroutines. A Makefile, a README file as well as a help file are provided
for the installation of the program and the explanation of the input data.
Graphical User Interface for the input data has been written in a tcl-tk
script language. The user should ensure that the libraries versions tcl7.0
and tk4.0 or higher are installed in her/his system.