Subroutine tabgen

The subroutine tabgen reads in the table form for generating the b_(lm)s.

Input data records for tabgen

  1. pgroup, ngroup, nabop, lmod, mmod
  2. For irep = 1 to ngroup
    1. symtyp(irep), nrdim(irep)
    2. For icomp = 1 to nrdim(irep)
      1. ifrmtp(ntype), (iabel(j, ntype), j = 1, nabop)
      2. (lmodv(k, ntype), mmodv(k, ntype), isgnm(k, ntype), phase(k, ntype), k = 1, ifrmtp(ntype))

Definition of the input variables:

pgroup
a character string (LEN=5) with the point group name
ngroup
number of irreducible representations (IR)
nabop
number of operations in the abelian subgroup not counting the E operation
lmod
used to determine which l values are included in a given symmetry type
mmod
used to determine which m values are included in a given symmetry type
sumtyp(irep)
a character string (LEN=5) with the name of the IR
nrdim(irep)
dimensionality of the IR
ifrmtp(j)
number of formulas for function type j
iabel(m, j)
eigenvalue of the m'th operation of the abelian subgroup (either 1 or -1) for the j'th type
lmodv(i, j)
required mod(l, lmod) for type j from the i'th formula
mmodv(i, j)
required mod(m, mmod) for type j function from the i'th formula
isgnm(i, j)
sign of m (+1 for cos like terms, -1 for sin like terms) for the type j function from the i'th formula
phase(i, j)
overall phase which all the b_(lm) are multiplied by

The number of "types" is the sum of the dimensionalities of all of the IRs of the group.

A particular real spherical harmonic Y_(l, m, s or c) is included in a given type j if mod(l, lmod) = lmodv(i, j), mod(m, mmod) = mmodv(i, j), and isgnm(i, j) = 1 for the cosine like function or isgnm(i, j) = -1 for the sine like function for one value of i = 1, ..., ifrmtp(j) if this condition is satisfied then the b_(lm) will be given the value phase(i, j) (i. e. 1 or -1)

These factors can be determined from the paper: S. L. Altmann, "On the symmetries of spherical harmonics," Proceedings of the Cambridge Philosophical Society, Vol. 53, Part 2, pp. 343-367, 1957.