Relativistic regular approximations revisited: An infinite-order relativistic approximation

Journal Article · Thu Jul 01 04:00:00 EDT 1999 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.479395· OSTI ID:351845

Dyall, K G ^[1]; van Lenthe, E ^[2]

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1. Thermosciences Institute, NASA Ames Research Center, Mail Stop 230-3, Moffett Field, California 94035-1000 (United States)
2. Afdeling Theoretisch Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam (The Netherlands)

The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy{endash}Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy{endash}Wouthuysen transformation, which results in the ZORA Hamiltonian and a nonunit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E{sup 3}/c{sup 4} for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the nonvariational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 351845
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 111; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ATOMIC IONS
DIRAC EQUATION
EIGENVALUES
ELECTRONIC STRUCTURE
HAMILTONIAN FUNCTION
MULTICHARGED IONS
RADIATIVE CORRECTIONS
RELATIVITY THEORY
URANIUM
WAVE FUNCTIONS