tabgen
The subroutine tabgen
reads in the
table form for generating the b_(lm)s.
tabgen
pgroup, ngroup, nabop, lmod, mmod
irep = 1
to ngroup
symtyp(irep), nrdim(irep)
icomp = 1
to nrdim(irep)
ifrmtp(ntype), (iabel(j, ntype), j = 1, nabop)
(lmodv(k, ntype), mmodv(k, ntype), isgnm(k, ntype),
phase(k, ntype), k = 1, ifrmtp(ntype))
pgroup
(LEN=5)
with the point group name
ngroup
nabop
lmod
mmod
sumtyp(irep)
(LEN=5)
with the name of the IR
nrdim(irep)
ifrmtp(j)
j
iabel(m, j)
lmodv(i, j)
mmodv(i, j)
isgnm(i, j)
phase(i, j)
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.