Computational approaches of relativistic models in quantum chemistry
Résumé
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.
Mots clés
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