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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.

Restrictions:
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.

References:
[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).