symmetry_gbl Module Reference

Data Types
module	geometry_obj
	Input data for the symmetry_objinit routine. More...
module	symmetry_obj
	This structure holds all necessary symmetry information on the symmetry of the molecule that can be used in the integral calculation. More...

Functions/Subroutines
integer function	check_geometry_obj (this)
integer function, public	determine_pg (no_sym_op, sym_op, print_to_stdout)
	Find point group by symmetry operations.
integer function, public	Xlm_mgvn (n, s, l, m)
	Get (zero-based) irreducible representation of a real spherical harmonic.
logical function, public	is_centre_symmetric (centre, no_sym_op, sym_op)
	Check if centre is symmetric w.r.t the symmetry operations.

Function/Subroutine Documentation

check_geometry_obj()

integer function symmetry_gbl::check_geometry_obj

(

class(geometry_obj)

this

)

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determine_pg()

integer function, public symmetry_gbl::determine_pg	(	integer	no_sym_op,
		character(len=sym_op_nam_len), dimension(3)	sym_op,
		logical, optional	print_to_stdout )

Find point group by symmetry operations.

Authors

Zdenek Masin

Date

2016

Returns the group identifier as defined in "const.f90", based on the set of symmetry operations passed as arguments (each one of 'X', 'Y', 'Z', 'XY', 'YZ', 'XZ', 'XYZ', indicating simple and combined plane reflections that produce no extra sign).

Parameters

no_sym_op	Number of symmetry operations set in sym_op.
sym_op	A triplet of strings, of which only no_sym_op need to be set.
print_to_stdout	Print the group name to stdout.

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is_centre_symmetric()

logical function, public symmetry_gbl::is_centre_symmetric	(	real(cfp), dimension(3), intent(in)	centre,
		integer, intent(in)	no_sym_op,
		character(len=sym_op_nam_len), dimension(:), intent(in)	sym_op )

Check if centre is symmetric w.r.t the symmetry operations.

Authors

J Benda

Date

2025

Given that all symmetry operations in UKRmol+ are composed of axis inversions, the check needs to verify simply that whenever a specific axis inversion is included in any composed symmetry operation, the corresponding component of centre position is zero.

Xlm_mgvn()

integer function, public symmetry_gbl::Xlm_mgvn	(	integer, intent(in)	n,
		character(len=sym_op_nam_len), dimension(:), intent(in)	s,
		integer, intent(in)	l,
		integer, intent(in)	m )

Get (zero-based) irreducible representation of a real spherical harmonic.

Authors

J Benda

Date

2025

We use the symmetry properties of the real spherical harmonics. Assuming that X, Y and Z are mirror operations by coordinate planes orthogonal to the given axes, i.e.,

• X: phi -> pi - phi
• Y: phi -> -phi
• Z: theta -> pi - theta

the symmetry properties of the real spherical harmonics are:

• X X_{l,-|m|} = -(-1)^m X_{l,-|m|}
• Y X_{l,-|m|} = -X_{l,+|m|}
• Z X_{l,-|m|} = (-1)^(l-m) X_{l,-|m|}
• X X_{l,0} = X_{l,0}
• Y X_{l,0} = X_{l,0}
• Z X_{l,0} = (-1)^(l-m) X_{l,0}
• X X_{l,+|m|} = (-1)^m X_{l,+|m|}
• Y X_{l,+|m|} = X_{l,+|m|}
• Z X_{l,+|m|} = (-1)^(l-m) * X_{l,+|m|}

Of these, only the specified symmetry elements are used. The relevant characters of the supported groups are the following (consistent with Molpro convention):

• C1: A
• Ci: Ag (XYZ+), Au (XYZ-)
• Cs: A' (X+), A'' (X-)
• C2: A (XY+), B (XY-)
• D2: A (XZ+,YZ+), B3 (XZ-,YZ+), B2 (XZ+,YZ-), B1 (XZ-,YZ-)
• C2h: Ag (Z+,XY+), Au (Z-,XY+), Bu (Z+,XY-), Bg (Z-,XY-)
• C2v: A (X+Y+), B1 (X-Y+), B2 (X+Y-), A2 (X-Y-)
• D2h: Ag (X+Y+Z+), B3u (X-Y+Z+), B2u (X+Y-Z+), B1g (X-Y-Z+), B1u (X+Y+Z-), B2g (X-Y+Z-), B3g (X+Y-Z-), Au (X-Y-Z-)

To maintain a predictable pattern in these tables, the symmetry operations have to be sorted by length (i.e. 'Z' first, then 'XY') and by alphabet ('X' first, then 'Y').