Abstract
The addition theorem of the spherical Laguerre Gaussian type function (LGTF) L n l+1/2(αr 2)r l e −αr 2 Y lm( r ̂ ) is derived by using a three-dimensional translational operator e R· ∇ , which upon expansion, generates spherical gradient operators. Due to the unique property of the spherical LGTF, the addition theorem obtained is in a closed and useful expression of spherical LGTFs. The addition theorem is then applied to evaluate analytically the molecular integrals of the spherical LGTFs. The basic two-center integrals evaluated are that of the overlap and that of the two-electron irregular solid spherical harmonics, Y lm( r ̂ 12)/r 12 l+1, which becomes the Coulomb repulsion when l=0, the spin–other-orbit interaction when l=1, and spin–spin interaction when l=2. The integral results, which agree with those previously derived by Fourier-transform and by gradient operator, are in terms of nuclear spherical LGTFs.
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