Mutual conversion of three flavors of gaussian type orbitals

摘要

Mutual expansion formulas are developed for three types of Gaussian orbitals:Hermite Gaussians,Cartesian Gaussians,and spherical Gaussians.Overlap,kinetic energy,and Coulomb energy matrix elements are presented for generalized spherical basis functions proporitional to r~(n+s) exp(-alphar~2) (gamma_n~m(r) where gamma_n~m represents spherical harmonics,where -n<=m<=n,and where s=0,2,4,...Hartree-Fock benchmark calcualtions on isolated,neutral _He,_6C,and _(12)Mg atoms indicate that inclusion of the s>=2 generalized functions is slightly unfavorable if the electronic ground state energy is to be minimized.