gaunt_coefficients Module Reference

Expansion of the product of two real spherical harmonics in real spherical harmonics. More...

Functions/Subroutines
subroutine, public	real_gaunt_coefficients (my_cg, maxl1, maxl2, llmax, cg_none0_list, ncg_none0)
	Calculate the expansion of the product of two real spherical harmonics in real spherical harmonics, S(l1,m1) S(l2,m2) = sum_lm my_cg(iso1,iso2,iso) S(l,m).

Detailed Description

Expansion of the product of two real spherical harmonics in real spherical harmonics.

Note

The expansion coefficients are the Gaunt coefficients of the real spherical harmonics; they are obtained from libwignernj, which evaluates them in exact integer arithmetic. Historically CP2K called these "Clebsch-Gordon coefficients", which they are not, and built them from a table of factorial ratios that lost about one digit per two units of l.

History

09.2026 created out of the five copies of this loop that lived in qs_rho_atom_methods, qs_tddfpt2_soc, qs_cneo_utils, xas_tdp_atom and generic_shg_integrals_init [Susi Lehtola]

Author

Susi Lehtola

Function/Subroutine Documentation

real_gaunt_coefficients()

subroutine, public gaunt_coefficients::real_gaunt_coefficients	(	real(kind=dp), dimension(:, :, :), intent(out), pointer	my_cg,
		integer, intent(in)	maxl1,
		integer, intent(in)	maxl2,
		integer, intent(in)	llmax,
		integer, dimension(:, :, :), intent(out), optional, pointer	cg_none0_list,
		integer, dimension(:, :), intent(out), optional, pointer	ncg_none0 )

Calculate the expansion of the product of two real spherical harmonics in real spherical harmonics, S(l1,m1) S(l2,m2) = sum_lm my_cg(iso1,iso2,iso) S(l,m).

Parameters

my_cg	the expansion coefficients, allocated here; the pointer is INTENT(OUT), so the caller must not rely on its previous contents
maxl1	maximal angular momentum of the first harmonic
maxl2	maximal angular momentum of the second harmonic
llmax	maximal angular momentum retained in the expansion
cg_none0_list	list of the harmonics with a non-zero coefficient, allocated here if present
ncg_none0	number of harmonics with a non-zero coefficient, allocated here if present

Definition at line 59 of file gaunt_coefficients.F.

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