Collect. Czech. Chem. Commun. 2005, 70, 677-688

Infinite-Order Regular Approximation by the Metric Perturbation

Andrzej J. Sadlej

Department of Quantum Chemistry, Institute of Chemistry, Nicolaus Copernicus University, PL-87 100 Torun, Poland


The regular approximation methods for the reduction of the Dirac equation to a fully equivalent two-component form are considered in the framework of the perturbation theory. The usual Dirac hamiltonian is first transformed with the change of metric. Then, the change of metric is considered as a perturbation to the zeroth-order (ZORA) problem. General formulae for perturbation corrections to the ZORA wave function and energy are expressed solely in terms of the two-component solutions. The method presented in this paper gives the energy- independent scheme for the step-by-step generation of the infinite-order results which are equivalent to solutions of the Dirac equations. Several formal and computational aspects of the infinite-order regular approximation are discussed. It is concluded that, because of the use of well-behaved operators, the high-order regular approximation methods can be considered as competitive to high-order Douglas-Kroll approaches.

Keywords: Relativistic methods; Regular approximation; ZORA; FORA; IORA; NESC method; Metric perturbation theory; Quantum mechanics; Quantum chemistry.

References: 38 live references.