Spin–Orbit Configuration Interaction Methods

Abstract

In this chapter, we address the following problem: Assume that we have derived a method that gives a good approximation to the treatment of relativistic effects in molecular systems, but that leaves out any explicit references to the spin—that is, a spin-free relativistic approximation. How can we go about getting a reliable estimate of the spin–orbit interaction in the system?There may be several reasons why we would want to take such an approach. One of them is that nonrelativistic calculations are much simpler to handle with respect to symmetry and logistics, and so if we could do the heavy computational work within the least demanding framework, it might entail considerable savings. Another reason might be that we are interested in light systems where the spin-free relativistic effects are small, but where the symmetry breaking induced by spin–orbit interaction may be of crucial importance for near-degenerate states and surface crossings. To solve this problem, we have to answer two questions, “What?” and “How?” The first one is concerned with finding an operator Ĥso that describes the spin–orbit interaction that has been left out of our zeroth-order Hamiltonian, Ĥ0, making the total Hamiltonian . . . Ĥ = Ĥ0 + Ĥso The form of this operator may be a matter of choice, but we would preferably like to restore the terms dropped in developing Ĥ0 from the fully relativistic Hamiltonian. This in turn leads to different Ĥso operators depending on the approach taken towards Ĥ0. The other question is concerned with how to treat these Ĥso operators in a computationally efficient manner in a configuration interaction calculation. Although the operators may differ, the problems inherent in their application are common for many of the choices of zeroth-order method. A further challenge is that spin–orbit energies are of comparable magnitude to the correlation energies for heavy elements. Thus, the two should be treated on a reasonably equal footing.