A computer program for symmetry adaptation of electronic states in crystals

Abstract

A method of finding all the symmetry-adapted states for symmorphic as well as for nonsymmorphic crystallographic space groups has been programmed in FORTRAN 4. The program is called SYMPRJ and can be used for symmetry adaptation in lattice dynamics as well as in energy band theory for solids. A simple special case can be used also for symmetry adaptation of molecular orbitals. The most essential advantage of this program is the absence of a voluminous input. This is caused by the fact that all the crystallographic point groups and their multiplication tables have been stored in the computer once and for all. Furthermore all the irreducible matrix representatives are computed explicitly in a subprogram by means of which arbitrary finite groups can be treated according to a method reported at the Sanibel Symposium in 1970 [1]. This is very useful for crystallographic space groups, since the crystal factor group of a given k vector (the little group of the first kind) is defined as an abstract group by means of its multiplication table. Furthermore, no theoretical difficulties arise, when electron spin is also included, or when magnetic space groups are considered, although the high orders occurring for these groups will cause some problems because of the limited core memory space in the IBM 360/75 computer used in Stockholm.