Programs in Physics & Physical Chemistry
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|Manuscript Title: DIRECTOR: a program for calculating representation matrices of the symmetric group in the Yamanouchi Kotani basis or in a direct product basis.|
|Authors: J.C. Manley, J. Gerratt|
|Program title: DIRECTOR|
|Catalogue identifier: ACFP_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 31(1984)75|
|Programming language: Fortran.|
|Computer: IBM 360/195.|
|Operating system: IBM/360 MVT.|
|RAM: 210K words|
|Word size: 8|
|Keywords: General purpose, Algebras, Symmetric group, Permutation group, Irreducible Representation, Direct product, Electronic structure, Spin function, Spin coupling, Branching diagram, Young tableau, Lattice permutation, Transposition, Single interchangematrix.|
Nature of problem:
The determination of wavefunctions for many-electron systems.
The wavefunctions are constructed as antisymmetrised products of spatial functions with coupled N-electron spin functions. The matrix elements of the Hamiltonian between such wavefunctions involve the matrices of irreducible representations of the symmetric group SN. These matrices are constructed in the Yamanouchi-Kotani basis for a given N and S, where S is the resultant spin of the system. If the system may be regarded as being formed from two groups A and B consisting of NA and NB electrons respectively (NA+NB=N), in addition to the intragroup matrices, the matrices corresponding to single interchanges between the groups are formed. The basis set for the single interchange matrices is constructed as a direct product of the basis functions for the individual groups.
Matrices in the Yamanouchi-Kotani basis: The number of electrons may not be greater than 10. Single Interchange Matrices in the Direct Product Basis: Neither group may contain more than 8 electrons. Both restrictions may be fairly easily relaxed if required.
Optional use of dynamic DEFINE FILE statements. See comments in 'Long Write-Up'.
Running times are strongly dependent upon the number of electrons, N. For N=6,S=1,NA=4,NB=2, fS**N=9 (as shown in the test output) the execution time was 3.1 s.
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