Nonsingular Two / One-Component Relativistic Hamiltonians Accurate Through Arbitrary High Order in a2

ABSTRACT: A series of nonsingular two-component relativistic Hamiltonians is derived from the Dirac Hamiltonian by first performing the free-particle Foldy]Wouthuysen transformation and then a block-diagonalizing transformation. The latter is defined in terms of operators which can be determined iteratively through arbitrary order in a, leading to transformed Hamiltonians with the two-component block accurate through a2k, k s 1, 2, 3,.... These Hamiltonians give relativistic energies which differ from Dirac’s energies only in terms higher than a2k. Their relation to other nonsingular methods of relativistic quantum chemistry the Douglas]Kroll method, the.regular Hamiltonian schemes is discussed. By removing the spin-dependent operators, the derived Hamiltonians can be written in spin-free one-component form. The computational effort involved is essentially the same as in the case of the Douglas]Kroll scheme and amounts to relatively easy modification of the core Hamiltonian. Q 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 225]239, 1997 Key words: relativistic Hamiltonians; two-component methods in relativity; perturbation methods in relativity; Douglas]Kroll approximation; regular approximations in relativit