Explaining the derivation and functioning of the exact infinite-order two-component Dirac theory in terms of the Hückel model

Abstract

The transition from the four-component Dirac theory to the exact two-component formalism is considered by using a simple algebraic model of the Dirac hamiltonian. This model is found to correspond to the four-center Huckel matrix and permits to replace the complex operator algebra by very easy matrix operations. This mapping of operators onto number matrices shows how the exact two-component relativistic hamiltonians are derived. It also explains certain conceptual aspects of the relation between four-component and two-component hamiltonians and their eigenfunctions. The generalized Huckel model of a four-center heteroatomic π-electron system can be used to analytically analyze the essential features of a variety of different exact and approximate two-component methods of relativistic quantum chemistry.