Dirac-Fock models for atoms and molecules and related topics

Relativistic effects are important in the electrons’ dynamics and bound state energies in heavy atoms and molecules. When the nucleii involved are heavily charged, the velocities of the electrons of the inner layers are quite large, and so nonrelativistic modelling will lead to important errors. The usual strategies to address this issue are : either use nonrelativistic models together with relativistic corrections, or use relativistic models based on the Dirac operator. The free Dirac operator is the simplest first order (in time and space) constant coefficient operator which is invariant under the action of the Lorentz group, i.e. its is compatible with Relativity Theory. The free Dirac operator can be written as: i∂t +Hc , where Hc = −i c ~α · ∇+mcβ , with α1, α2, α3, β ∈ M4×4(CI )