Computational approaches of relativistic models in quantum chemistry

Jean-Paul Desclaux (1) , Jean Dolbeault (2) , Maria J. Esteban (2) , Paul Indelicato (3) , Eric Séré (2)

1 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LKB (Jussieu) - Laboratoire Kastler Brossel

This chapter is a review of some methods used for the computation of relativistic atomic and molecular models based on the Dirac equation. In the linear case, we briefly describe finite basis set approaches, including ones that are generated numerically, perturbation theory and effective Hamiltonians procedures, direct variational methods based on nonlinear transformations, min-max formulations and constrained minimizations. In the atomic case, we describe the MCDF method and some ways to solve numerically the homogeneous and inhomogeneous Dirac-Fock equations. Finally, we describe also some numerical methods relevant to the case of molecules.

Keywords: Rayleigh quotients; min-max; minimization; constraints; Dirac-Fock; MCDF method; quantum chemistry; relativistic models for atoms and molecules; computational methods; no-pair Hamiltonian; relativistic many-body perturbation theory; relativistic random phase approximation; Dirac equation; continuous spectrum; eigenvalues; variational collapse; spurious states; finite basis; numerical basis sets; spectral pollution

Domains: Numerical Analysis [math.NA]; Theoretical and/or physical chemistry

Jean-Paul Desclaux, Jean Dolbeault, Maria J. Esteban, Paul Indelicato, Eric Séré. Computational approaches of relativistic models in quantum chemistry. P.G. Ciarlet (series editor), C. Le Bris (guest editor). Handbook of numerical analysis, Vol. X. Special volume: computational chemistry., North-Holland, Amsterdam, pp.453-483, 2003, Handbook of numerical analysis. ⟨hal-00573854⟩