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Manuscript Title: Program packages for point groups and space groups with subgroup chain symmetry adaptation.
Authors: J.-L. Ping, J.-Q. Chen
Program title: PGSG
Catalogue identifier: ABHE_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 120(1999)71
Programming language: Fortran.
Computer: PC 486.
Operating system: MS-DOS.
RAM: 4M words
Word size: 16
Keywords: Point groups, Space groups, Complete set of commuting operators, Single-valued and Double-valued irreps, Clebsch-gordan coefficients.
Classification: 4.2.

Nature of problem:
The program computes the characters, subgroup chain symmetry adapted irreducible representations (irreps) and Clebsch-Gordan (CG) coefficients of 32 point groups and the little-cogroups, as well as the grounded representations, the wave-vector selection rules in 230 space groups, for both single-valued and double-valued representations. The components of irreps of point groups are labeled by the Koster irrep labels [2] of the subgroups contained in the subgroup chain, and the subgroup chain can be chosen according to a menu.

Solution method:
The program is based on the complete-set-of-computing-operator (CSCO) approach to group representation developed in [3]. The characters, CG coefficients and irreducible matrix elements are obtained by solving the eigenvalue equations of the CSCO-I, -II, and -III in the class space, Kronecker product space and group space, respectively.

The program is designed for any crystallographic point group and any space group for any value of the wave vector k in the first Brillouin zone.

Unusual features:
The program is written in a menu form and everything can be computed ab initio without input of any complicated results. The irreducible matrices and CG coefficients are symmetry adapted to any user-chosen subgroup chain. The tables of the characters, irreducible matrices and CG coefficients are printed out in an easily recognizable form and with exact values in the form of sqrt(p/q exp(i pi sqrt(m/n))) or sqrt(p/q exp (i cos**-1 sqrt(m/n))).

Running time:
A few minutes.

[1] J.L. Ping, Q.R. Zheng, B.Q. Chen and J.Q. Chen, Computer Phys. Commun., 52, 355 (1989).
[2] G.F. Koster, J.O. Dimmock, R.G. Wheeler and H. Statz, Properties of the Thirty Two Point Groups, (M.I.T. Press, Cambridge, 1963).
[3] J.Q. Chen, Group Representation Theory for Physicists, (World Scientific, Singapore, 1989), J.Q. Chen, M.J. Gao and G.Q. Ma, Rev. Mod. Phys. 57, 211 (1985).