topology_symmetry Module Reference

Native character decomposition and metric-aware inversion representations. More...

Functions/Subroutines
subroutine, public	character_multiplicities (character, table, multiplicities, tolerance, status)
	Decompose a character against a complete unitary character table.
subroutine, public	inversion_representation (metric, coeff, mapping, phase, energies, check_tr, tolerance, energy_tolerance, counts, error, energy_error, status, diagnostics)
	Inversion irreps of an isolated scalar or spinor eigenspace in an AO metric.

Detailed Description

Native character decomposition and metric-aware inversion representations.

Function/Subroutine Documentation

character_multiplicities()

subroutine, public topology_symmetry::character_multiplicities	(	complex(kind=dp), dimension(:), intent(in)	character,
		complex(kind=dp), dimension(:, :), intent(in)	table,
		integer, dimension(:), intent(out)	multiplicities,
		real(kind=dp), intent(in)	tolerance,
		integer, intent(out)	status )

Decompose a character against a complete unitary character table.

Parameters

CHARACTER	One character per group element (not per conjugacy class)
table	Characters, group element first and irrep second; identity first
multiplicities	Nonnegative integer multiplicities, invalid unless status=0
tolerance	Absolute numerical tolerance
status	Zero on success, negative for invalid/incomplete/nonintegral data

Note

All projective irreps must use the same factor system. This kernel does not infer a space group or certify the supplied character table's provenance.

Definition at line 30 of file topology_symmetry.F.

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inversion_representation()

subroutine, public topology_symmetry::inversion_representation	(	complex(kind=dp), dimension(:, :), intent(in)	metric,
		complex(kind=dp), dimension(:, :), intent(in)	coeff,
		integer, dimension(:), intent(in)	mapping,
		complex(kind=dp), dimension(:), intent(in)	phase,
		real(kind=dp), dimension(:), intent(in)	energies,
		logical, intent(in)	check_tr,
		real(kind=dp), intent(in)	tolerance,
		real(kind=dp), intent(in)	energy_tolerance,
		integer, dimension(2), intent(out)	counts,
		real(kind=dp), intent(out)	error,
		real(kind=dp), intent(out)	energy_error,
		integer, intent(out)	status,
		real(kind=dp), dimension(4), intent(out), optional	diagnostics )

Inversion irreps of an isolated scalar or spinor eigenspace in an AO metric.

Parameters

metric	Scalar AO overlap at a TRIM
coeff	Selected coefficients, spinor components stacked by AO
mapping	Target AO index under inversion
phase	Source-AO multiplier, including orbital parity and lattice phase
energies	Selected eigenvalues in Hartree
check_tr	Check physical spinful time reversal as well as inversion
tolerance	Dimensionless metric/subspace/character tolerance
energy_tolerance	Eigenvalue-commutator tolerance in Hartree
counts	Multiplicities of even/odd inversion irreps, counting states not pairs
error	Largest dimensionless residual
energy_error	Largest projected symmetry/eigenvalue commutator
status	Zero on success; invalid output for nonzero status
diagnostics	Optional metric, normalization, inversion and time-reversal residuals

Definition at line 93 of file topology_symmetry.F.

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