symgen
Symgen computes the b_(lm) values for the symmetry adapted angular functions. There are two forms of input. The first is the table input which can be used for point groups where all of the real harmonics are part of a particular irreducible representation without the need for linear combinations. The second format for the input is where the character table of the point group is specified and all of the symmtery operations. In this case the program directly computes the matrix representations for the various irreducible representations and then constucts the appropriate symmetry adapted angular functions using the standard projection operator technique.
The following input records are required for symgen:
lmax
iuout, iumatrep
iprnfg
lmax < 0
then read: (luse(i), i = 1, ABS(lmax))
calctp, rtype
nthd, nphid
calctp
= 'table' calctp
= 'compute'
calctp = 'compute'
then read: nabop, (iabop(j), j = 1, nabop)
lmax
l
of b_(lm) to compute
iuout
iumatrep
iprnfg
luse(i)
l
to compute the b_(lm)s for,
if lmax
> 0 then comput b_(lm)s for all values of l
up to lmax
calctp
rtype
nthd
nphid
nabop
iabop(i)
The possible values of nthd
and
nphid
for the abelian point groups are
as follows:
Symmetry | nthd | nphid |
Comments |
---|---|---|---|
C1 | 1 | 1 | |
Cs | 1 | 2 | |
Ci | 2 | 1 | |
C2 | 1 | 2 | |
D2 | 1 | 4 | |
C2v | 1 | 4 | |
C2h | 2 | 2 | |
C2h(x) | 2 | 1 | (C2 axis along the x axis) |
D2h | 2 | 4 |
For non-abelian point groups, the values from the largest abelian subgroup should be used.
The controlling creiterion is that the real spherical harmmonics belonging to the same representation in the abelian subgroup must be orhtonormal when integrated over the points left in the grid.
nphid
= 2 is OK when sin(m phi) and cos(n phi) do not belong
to the same representation, or sin(m phi) and cos(m phi)
belong to the same representation only when both n
and m are the same parity (i.e. either both even or
both odd.
nphid
= 4 is OK when
The program also assumes that the first coulmn of the character table is for the identity element.