Program packages for point groups and space groups with subgroup chain symmetry adaptation. J.-L. Ping, J.-Q. Chen.

PROGRAM SUMMARY
Title of program: PGSG
Catalogue identifier: ADKG
Ref. in CPC: 120(1999)71
Distribution format: uuencoded compressed tar file
Operating system: MS-DOS
High speed store required: 4MK words
Number of bits in a word: 16
Number of lines in distributed program, including test data, etc: 16209
Programming language used: Fortran
Computer: PC 486

Other versions of this program:

 Cat. Id.  Title                             Ref. in CPC
 ABHE      IR, CGC                            52(1989)355                    
 

Nature of physical 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.

Method of solution
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 on the complexity of the problem
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.

Typical running time
A few minutes.

Unusual features of the program
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))).

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).