Interface to libwignernj for the angular momentum algebra. More...

Functions/Subroutines
real(kind=dp) function, public	real_gaunt (l1, m1, l2, m2, l3, m3)
	Gaunt coefficient of three real spherical harmonics, int S(l1,m1) S(l2,m2) S(l3,m3) dOmega.
real(kind=dp) function, public	complex_gaunt (l1, m1, l2, m2, l3, m3)
	Gaunt coefficient of three complex spherical harmonics, int Y(l1,m1) Y(l2,m2) Y(l3,m3) dOmega.

Detailed Description

Interface to libwignernj for the angular momentum algebra.

Note: libwignernj carries out all intermediate arithmetic exactly, in a prime factorization representation, and rounds only once at the end. The returned coefficients are therefore correct to the last bit, whereas the factorial-ratio expressions that CP2K used before lost roughly one digit per two units of l.

The library takes all angular momenta as twice their value so that half-integers stay exact; the wrappers here take the plain integer l and m of a spherical harmonic and do the doubling.

The real spherical harmonics S(l,m) follow the Condon-Shortley convention S(l, 0) = Y(l,0) S(l, m>0) = ( Y(l,-m) + (-1)^m Y(l,m) )/sqrt(2) S(l, m<0) = ( Y(l,m) - (-1)^|m| Y(l,-m) )*i/sqrt(2) which is the same convention as spherical_harmonics::y_lm, so no additional phase is needed on either side.

The interfaces below bind directly to the C API, so no compiler-specific Fortran module from libwignernj is required.

History: 09.2026 created [Susi Lehtola]

Author: Susi Lehtola

Function/Subroutine Documentation

◆ real_gaunt()

real(kind=dp) function, public wignernj_interface::real_gaunt	(	integer, intent(in)	l1,
		integer, intent(in)	m1,
		integer, intent(in)	l2,
		integer, intent(in)	m2,
		integer, intent(in)	l3,
		integer, intent(in)	m3 )

Gaunt coefficient of three real spherical harmonics, int S(l1,m1) S(l2,m2) S(l3,m3) dOmega.

Parameters

l1	angular momentum of the first harmonic
m1	magnetic quantum number of the first harmonic
l2	angular momentum of the second harmonic
m2	magnetic quantum number of the second harmonic
l3	angular momentum of the third harmonic
m3	magnetic quantum number of the third harmonic

Returns: the Gaunt coefficient, zero if the selection rules are violated

Definition at line 97 of file wignernj_interface.F.

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◆ complex_gaunt()

real(kind=dp) function, public wignernj_interface::complex_gaunt	(	integer, intent(in)	l1,
		integer, intent(in)	m1,
		integer, intent(in)	l2,
		integer, intent(in)	m2,
		integer, intent(in)	l3,
		integer, intent(in)	m3 )

Gaunt coefficient of three complex spherical harmonics, int Y(l1,m1) Y(l2,m2) Y(l3,m3) dOmega.