Extension of Nonrelativistic Computational Techniques

The relativistic Schrodinger equation is very difficult to solve because it requires that electrons be described by four component vectors, called spinnors. When this equation is used, numerical solution methods must be chosen. 

The most common description of relativistic quantum mechanics for Fermion systems, such as molecules, is the Dirac equation. The Dirac equation is a one-electron equation. In formulating this equation, the terms that arise are intrinsic electron spin, mass defect, spin couplings, and the Darwin term. The Darwin term can be viewed as the effect of an electron making a high-frequency oscillation around its mean position. 

The Dirac equation can be readily adapted to the description of one electron in the held of the other electrons (Hartree-Fock theory). This is called a Dirac-Fock or Dirac-Hartree-Fock (DHF) calculation. 

---