4-COMPONENT DIRAC-HARTREE-FOCK EQUATIONS FOR SOLIDS - GENERALIZATION OF THE RELATIVISTIC HARTREE-FOCK EQUATIONS

Relativistic Hartree-Fock equations will be presented for 1D-, 2D- and 3D-infinite systems. 4-Component spinors with Gaussian basis sets wil l be used and the so-called kinetic balance between the small and larg e components of the spinors is introduced. The resulting somewhat comp licated generalized matrix eigenvalue equation for solids is described . It is also shown for 1D- and 2D-systems how the MP2 and MP2-r(12) me thods could be applied in their relativistic form. With the help of th em, on the one hand, the total energy per unit cell (including correla tion effects) can be computed. On the other hand, applying the inverse Dyson equation, the relativistic band structure can also be corrected for correlation. Furthermore, it is argued that to obtain more reliab le one-electron functions and energies for the correlation calculation s, one has to include into the relativistic Hartree-Fock equations the frequency-dependent Breit operator, the first-order Lamb shift terms (the difference of the self energy and mass correction terms) and the vacuum polarization term in the Uehling potential approximation (all t he other quantum electrodynamical effects are order(s) of magnitude sm aller). Including all these terms into the expression of the relativis tic total energy, the corresponding generalized Dirac-Hartree-Fock equ ations obtained after performing the variational calculations are pres ented. Finally a scheme is proposed in which most of the electrons are treated in the standard way (Dirac-Hartree-Fock equations with only C oulomb interactions and calculation of all the other terms with the ai d of first-order perturbation theory), while for the core electrons of large Z atoms or ions, the generalized relativistic HF equations are used. Therefore, one applies the solutions of the generalized relativi stic HF equations for the construction of the relativistic Slater dete rminant in the case of core electrons, while for the rest of the elect rons the one-electron functions are obtained from the standard Dirac-H artree-Fock equations. (C) 1997 Elsevier Science B.V.