A Comparative Study of Atomic Variational Wave Functions

Rayleigh-Schrödinger perturbation theory and the variational principle combined furnish simple criteria for investigating and predicting the accuracy of arbitrary variational wave functions computed with a perturbed Hamiltonian operator. This permits the a priori classification of all perturbed variational wave functions into three broad categories which differ in their asymptotic behavior as the perturbation approaches zero. Wave functions belonging to one of these categories have the desirable characteristics of yielding variational energies correct at least through first order and other expectation values correct at least in zero order. These conditions are not fulfilled in the other two categories. The classification scheme is used to survey a wide variety of variational wave functions for atomic isoelectronic sequences. The construction of these wave functions determines their asymptotic category. A more systematic treatment of correlation energy is proposed and various methods of introducing correlation are discussed. Some recommendations are made for future progress in the calculation of accurate atomic wave functions.