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Manuscript Title: Fast computation of close-coupling exchange integrals using polynomials in a tree representation
Authors: Markus Wallerberger, Katharina Igenbergs, Josef Schweinzer, Friedrich Aumayr
Program title: TXINT
Catalogue identifier: AEHS_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)775
Programming language: Fortran 95.
Computer: All with a Fortran 95 compiler.
Operating system: All with a Fortran 95 compiler.
RAM: Depends heavily on input, usually less than 100 MiB
Keywords: Exchange integrals, Symbolic manipulations, Polynomials.
Classification: 16.10.

Nature of problem:
Analytical calculation of one- and two-center exchange matrix elements for the close coupling method in the impact parameter model.

Solution method:
Similar to the code of Hansen and Dubois [1], we use the Fourier transform method suggested by Shakeshaft [2] to compute the integrals. However, we heavily speed up the calculation using a library for symbolic manipulation of polynomaials.

We restrict ourselves to a defined collision system in the impact parameter model.

Unusual features:
A library for symbolic manipulation of polynomials, where polynomials are stored in a space-saving left-child right-sibling binary tree. This provides stable numerical evaluation and fast mutation while maintaining full compatibility with the original code.

Additional comments:
This program makes heavy use of the new features provided by the Fortran 90 standard, most prominently pointers, derived types and allocatable structures and a small portion of Fortran 95. Only newer compilers support these features.
Following compilers support all features needed by the program.
  • - GNU Fortran Compiler "gfortran" from version 4.3.0
  • - GNU Fortran 95 Compiler "g95" from version 4.2.0
  • - Intel Fortran Compiler "ifort" from version 11.0

Running time:
Heavily dependent on input, usually less than one CPU second.

[1] Hansen, J.-P. and Dubois, A., Comput. Phys. Commun. 67 (1992) 456 .
[2] Shakeshaft, R., J. Phys. B: At. Mol. Opt. Phys. 8 (1975) L134.