Basis-set expansion of the Dirac equation without variational collapse: Numerical test of the forth-back free-particle Foldy-Wouthuysen transformation
Journal Article
·
· Phys. Rev. A; (United States)
Expansion of the Dirac operator in a finite basis set in analogy to the current matrix eigenvalue approach in nonrelativistic molecular quantum mechanics leads to unpleasant results known as ''variational collapse.'' This is avoided if one first performs a Foldy-Wouthuysen transformation to the free-particle part of the Dirac operator, then constructs the matrix representation, and transforms back ''on matrix level.'' The matrix representation so obtained has the correct ''Schroedinger limit'' for c..-->..infinity and furnishes very accurate relativistic corrections, even for moderate basis sets. This is illustrated by numerical calculations for the one-electron atom O/sup 7 +/, the H/sub 2/ /sup +/ ion, and by relativistic Hartree-Fock calculations for He and Be.
- Research Organization:
- Lehrstuhl fuer Theoretische Chemie, Abteilung fuer Chemie, Ruhr-Universitat Bochum, D-4630 Bochum, Federal Republic of Germany
- OSTI ID:
- 5375904
- Journal Information:
- Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 28:5; ISSN PLRAA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ALKALINE EARTH METALS
BERYLLIUM
CANONICAL TRANSFORMATIONS
CATIONS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DIRAC OPERATORS
EIGENVALUES
ELEMENTS
EQUATIONS
FLUIDS
FOLDY-WOUTHUYSEN TRANSFORM
GASES
HELIUM
HYDROGEN IONS
HYDROGEN IONS 2 PLUS
IONS
MATHEMATICAL OPERATORS
METALS
MOLECULAR IONS
MULTICHARGED IONS
NONMETALS
OXYGEN IONS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
RARE GASES
SCHROEDINGER EQUATION
TRANSFORMATIONS
VARIATIONAL METHODS
WAVE EQUATIONS
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ALKALINE EARTH METALS
BERYLLIUM
CANONICAL TRANSFORMATIONS
CATIONS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DIRAC OPERATORS
EIGENVALUES
ELEMENTS
EQUATIONS
FLUIDS
FOLDY-WOUTHUYSEN TRANSFORM
GASES
HELIUM
HYDROGEN IONS
HYDROGEN IONS 2 PLUS
IONS
MATHEMATICAL OPERATORS
METALS
MOLECULAR IONS
MULTICHARGED IONS
NONMETALS
OXYGEN IONS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
RARE GASES
SCHROEDINGER EQUATION
TRANSFORMATIONS
VARIATIONAL METHODS
WAVE EQUATIONS