On the Use of Multipole Expansion of the Coulomb Potential in Quantum Chemistry

Int.J.Quant.Chem., v. 60, p. 843-852 (1996)

ABSTRACT. Some features of the multipole expansion of the Coulomb potential V for a system of point charges are studied. It is shown that multipole expansion is convergent both locally in L2(R3) and weakly on some classes of functions. One-particle Hamiltonians H(n) = H(0) + V(n) where H(0) is the kinetic energy operator and V(n) is the n-th partial sum of the multipole expansion of V, are discussed, and the convergence of their eigenvalues to those of H = H(0) + V with increasing n is proved. It is also shown that the discrete spectrum eigenfunctions of H(n) converge to those of H both in L2(R3) (together with their first and second derivatives) and uniformly on R3.

Laboratory of Molecular Structure and Quantum Mechanics