A variational method for relativistic computations in atomic and molecular physics

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2003), A variational method for relativistic computations in atomic and molecular physics, International Journal of Quantum Chemistry, 93, 3, p. 149-155. http://dx.doi.org/10.1002/qua.10549

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2002-8.ps.gz (439.1Kb)

Type

Article accepté pour publication ou publié

Date

2003

Nom de la revue

International Journal of Quantum Chemistry

Volume

Numéro

Éditeur

Wiley

Pages

149-155

Résumé (EN)

This article is devoted to a two-spinor characterization of energy levels of Dirac operators based at a theoretical level on a rigorous variational method, with applications in atomic and molecular physics. This provides a numerical method that is free of the numerical drawbacks often present in discretized relativistic approaches. It is moreover independent of the geometry and monotone: Eigenvalues are approximated from above. We illustrate our numerical approach by the computation of the ground state in atomic and diatomic configurations using B-splines.

Mots-clés

quantum chemistry; relativistic quantum mechanics; relativistic models for atoms and molecules; computational methods; ab initio methods; basis sets; B-splines; Dirac operators; effective Hamiltonians; Variational methods; min–max; minimization; continuous spectrum; eigenvalues; Rayleigh–Ritz technique; minimization; variational collapse; spurious states; two components spinors