Iterative solution of the one-electron Dirac equation based on the Bloch equation of the 'direct perturbation theory'

The one-electron Dirac equation is solved in an iterative manner starting w ith the solution of the Schrodinger equation. The method is based on 'direc t perturbation theory' for relativistic effects generalized to the case of a set of near-degenerate strongly interacting states. Relativistic energies are obtained by solving a Schrodinger-like equation within a non-relativis tic model space. The effective hermitian Hamiltonian and symmetric metric o perator are expressed with the help of a Moller waveoperator Ohm, which gen erates the complete four-component Dirac wavefunction from the non-relativi stic two-component one. The corresponding Bloch equation is solved to infin ite order by iteration in a basis of atom-centered Gaussian;type functions for the ground state of hydrogen-like ion Eka Pt109+ and for a few states o f the heavy quasi-molecule Th-2(179+). (C) 1999 Elsevier Science B.V. All r ights reserved.