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Manuscript Title: POMULT: a program for computing periodic orbits in Hamiltonian systems based on multiple shooting algorithms.
Authors: S.C. Farantos
Program title: POMULT
Catalogue identifier: ADHG_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 108(1998)240
Programming language: Fortran, tcl, tk.
Computer: HP-9000/735.
Operating system: UNIX.
RAM: 5M K words
Word size: 32
Keywords: Molecular physics, Molecular dynamics and, Spectra, Periodic orbits, Multiple shooting, Algorithm, Damped newton-raphson, Method.
Classification: 16.2.

Nature of 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.

Solution method:
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.

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.

Unusual features:
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" [1]. The program can be interfaced with ODESSA [2] 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 favourable 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 [3,4]. The user should ensure that the libraries versions tcl7.0 and tk4.0 or higher are installed in her/his system.

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.

[1] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling. Numerical Recipes. Cambridge Univ. Press, (1986).
[2] J.R. Leis and M.A. Kramer, ACM Trans. Math. Software (1985).
[3] J.K. Ousterhout. Tcl and TK Toolkit. Addison-Wesley, (1994).
[4] B.B. Welch. Practical Programming in Tcl and Tk. Prentice Hall PTR, (1995).