Two-component methods of relativistic quantum chemistry: from the Douglas-Kroll approximation to the exact two-component formalism

The two-component methods of relativistic quantum chemistry based on the Fo ldy-Wouthuysen (FW) transformations of the Dirac hamiltonian are reviewed. Following the strategy designed by Douglas and Kroll, the FW transformation is carried out in two steps. The first amounts to performing the exact fre e-particle FW transformation. At variance with other approaches, the second step is written in the form, which results in a nonlinear operator equatio n. This equation can be solved iteratively, leading to two-component hamilt onians of arbitrarily high accuracy in even powers of the fine structure co nstant. All these hamiltonians can be classified according to their complet eness with respect to the leading order in the fine structure constant. On passing to the basis set representation one obtains the usual Douglas-Kroll hamiltonian and all possible higher-order approximations. By a simple modi fication of the operator equation which determines the block-diagonalizing transformation one can obtain numerical infinite-order solutions, i.e. one can obtain the exact numerical solution for the separation of the pure elec tronic part of the Dirac spectrum. This gives the exact two-component metho d for the use in relativistic quantum chemistry. The computational aspects of this approach are discussed as well. The transition from the Dirac formalism to any two-component approximation is accompanied by the change of all operators, including those which corres pond to external perturbations and lead to properties of different orders. This so-called change of picture problem is given particular attention and its importance for certain operators is identified. (C) 2001 Elsevier Scien ce BN. All rights reserved.