Programs in Physics & Physical Chemistry
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|Manuscript Title: Programs for the coupling of spherical harmonics.|
|Authors: E.J. Weniger, E.O. Steinborn|
|Program title: YLM-COUPLING|
|Catalogue identifier: AARL_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 25(1982)149|
|Programming language: Fortran.|
|Computer: TR 440.|
|Operating system: BS3 MV 19.|
|RAM: 12K words|
|Word size: 48|
|Keywords: General purpose, Function, Spherical harmonics, Gaunt coefficient, Condon-shortley Coefficient, Coupling of two orbital Angular momenta.|
Nature of problem:
The subroutines GAUNT and RECYLM allow the linearization of the product of two spherical harmonics. The summation limits are determined by certain selection rules for the GAUNT coefficients.
The subroutine GAUNT computes a whole string of Gaunt coefficients <l3m3|l2m2|l1m3-m2> for all allowed l1 values (l2,m2,l3 and m3 are mixed input quantities) using their representation in terms of 3jm-symbols. The 3jm-symbols are computed using a homogeneous 3-term recurrence relation derived by Schulten and Gordon. The computational algorithm used is apart from certain modifications the same as that developed by Schulten and Gordon. The subroutine RECYLM computes a string of spherical harmonics Ylm for all l with lmin = |m| <= l <= lmax (m and lmax are input quantities) recursively using their homogeneous 3-term recurrence relation in l. Both programs use DOUBLE PRECISION arithmetic for floating point numbers.
In order to avoid complex arithmetic the azimuth angle theta is set to equal to zero, i.e. RECYLM calculates a string of spherical harmonics Ylm(theta,0). In order to prevent overflow or underflow two DOUBLE PRECISION variables HUGE and TINY have to be defined.
Approximately 1 ms per Gaunt coefficient for the string < 15 0|15 0| l 0>, approx. 3 ms for the string <15 15|15 15|l 0> and approx. 4.5 ms for the string <8 -5|10 7|l-12>. Approximately 1.3 ms per spherical harmonic for the string Ylo, 0<= l<= 15, and approx. 1.5 ms for the string Yl**-2,2<= l<= 5. To make these absolute numbers comparable: On the TR 440 one evaluation of DSQRT requires approx. 0.43 ms.
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