Knowledge Bank

The spherical Laguerre Gaussian type function (LGTF) centered at nucleus $A$, $Lnl+1/2(aru2)Ym(ru)\exp (-aru2)$: can be generated by operating on the Gaussian exponential, exp ($-aru2$) with a generalized gradient operator, $Yn|m(\nabla A)$.$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ Through the vector coupling of the gradient operators, the Talmi coefficient of transforming the product of two LGTFs, one centered at $A$ and the other centered at $B$, into a linear combination of the products of two different LGTFs, one centered at $P$ (center of mass of $A$ and $B$) and the other made of the internuclear coordinates, has been obtained. Multicenter molecular integrals of the overlap, the Coulomb repulsion, the spin-spin interaction and the spin-other-orbit interaction can be evaluated analytically. The integral results are simpler than those obtained by Fourier transform convolution $theorem.2$