Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in ?2

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 α, leading to transformed Hamiltonians with the two-component block accurate through α2k, k=1, 2, 3,… . These Hamiltonians give relativistic energies which differ from Dirac's energies only in terms higher than α2k. 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.