Interactions between relativistic subsystems: consequences of the two-component approximation

Abstract

The operator for interactions between two relativistic subsystems is derived in the framework of the two-component ‘‘for electrons only’’ approximation to the Dirac–Coulomb (DC) theory. The consequences of the transition from the Dirac picture to the two-component scheme are analysed. It is shown that upon this transition the interaction operator undergoes the so-called change of picture transformation. This analysis shows that the two-component methods require that all terms of the DC hamiltonian are transformed in the same way. The same conclusion applies to all relativistic hamiltonians used in two-component many-electron theories. The long-range limit of the interaction operator in the two-component formalism is analysed and shown to convert into products of multipole operators in the changed picture. The presented formalism can be used in both perturbation and supermolecular (variational) approaches to the theory of intermolecular interactions. In comparison with non-relativistic theories, the only difference amounts to the evaluation of matrix elements with wave functions of the two-component formalism. Whenever the spin–orbit coupling effects are negligible, the present theory can be further reduced to the one-component (scalar, spin-averaged) form.