INTERFACING RELATIVISTIC AND NONRELATIVISTIC METHODS - II - INVESTIGATION OF A LOW-ORDER APPROXIMATION

The formalism presented in a previous paper for the introduction of re lativistic effects into nonrelativistic calculations is used to develo p an approximation which is correct to order alpha(2) and is similar t o the Breit-Pauli approximation. Although it corresponds to a projecti on of the Dirac Hamiltonian onto the nonrelativistic (Levy-Leblond) st ates which in principle should guarantee a lower bound, the bound depe nds on the form of the potential. The physical eigenstates correspond to a local minimum in the exponential parameter space which vanishes a t large Z. In an extended basis set an approximation to the hydrogenic ground state can always be identified, but the relativistic correctio n to the energy is grossly overestimated. In molecular calculations, t he restriction of the variational space involving the high-exponent fu nctions by general contraction did not yield improved numerical stabil ity in a variational scheme. The use of a low-order approximation in a quasivariational method is therefore not expected to yield reliable r esults. (C) 1998 American Institute of Physics.