Some properties of the coupling coefficients of real spherical harmonics and their relation to Gaunt coefficients

Spherical harmonics are of considerable importance for computations involving basis functions corresponding to large values of the angular momentum quantum number l. Their use allows efficient coding of programs involving such basis functions because the formulae of the coupling coefficients are simple. The choice of real spherical harmonics allows one to avoid the use of complex quantities in computer programs that increase storage and CPU time requirements. In this paper, certain properties of the coupling coefficients for real spherical harmonics are derived that are necessary for an efficient computation of coupling terms.