SPHERICALLY SYMMETRICAL PROPERTIES OF EXPANSION COEFFICIENTS FOR TRANSLATION OF SPHERICAL-HARMONICS

A theorem regarding the angular dependence has been established for th e expansion coefficients for translation of spherical harmonics (SH): If we add the products of all the translation coefficients with the sa me l values, but different m's, the result is independent of orientati on. The spherically symmetrical properties of the translation coeffici ents K-lm,K-l'm' for SH obtained in the present paper and, the rotatio n coefficients T-lm,l'm'(lambda), the two-center overlap integrals ove r arbitrary atomic orbitals S-nlm,S-n'l'm' and the translation coeffic ients V-nlm,n'l'm'(N) for Slater-type orbitals (STO's) given recently by the author [I.I. Guseinov, J. Mel. Struct. (Theochem), 343 (1995) 1 73] are the same. The analytical formulas also have been derived for t ranslation coefficients of SH in terms of binomial coefficients. The f inal results are especially useful for machine computations of arbitra ry multi-electron molecular integrals for which the series expansion f ormulas have recently been derived by the author.