spherical_harmonics Module Reference

Calculate spherical harmonics. More...

Data Types
interface	y_lm
interface	dy_lm

Functions/Subroutines
real(kind=dp) function, public	legendre (x, l, m)
	...
real(kind=dp) function, public	dlegendre (x, l, m)
	...

Detailed Description

Calculate spherical harmonics.

Note

Spherical Harmonics Numerical Stability up to L=15 Accuracy > 1.E-12 up to L=15 tested Definition is consistent with orbital_transformation_matrices

History

JGH 28-Feb-2002 : Change of sign convention (-1^m) JGH 1-Mar-2002 : Clebsch-Gordon Coefficients

• Clebsch-Gordon coefficients and Wigner 3-j symbols added as generic routines using the standard normalization (19.09.2022, MK)
• Clebsch-Gordon coefficients (which were really Gaunt coefficients of the real spherical harmonics) moved to gaunt_coefficients, and the unused generic Clebsch-Gordon and Wigner 3-j routines dropped, in favour of the exact evaluation in libwignernj (09.2026, Susi Lehtola)

Author

JGH 6-Oct-2000, MK

Function/Subroutine Documentation

legendre()

real(kind=dp) function, public spherical_harmonics::legendre	(	real(kind=dp), intent(in)	x,
		integer, intent(in)	l,
		integer, intent(in)	m )

...

Parameters

x	...
l	...
m	...

Returns

...

Definition at line 845 of file spherical_harmonics.F.

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dlegendre()

real(kind=dp) function, public spherical_harmonics::dlegendre	(	real(kind=dp), intent(in)	x,
		integer, intent(in)	l,
		integer, intent(in)	m )

...

Parameters

x	...
l	...
m	...

Returns

...

Definition at line 989 of file spherical_harmonics.F.

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