Relativistic self-consistent-field (RSCF) theory for closed-shell molecules

The relativistic Hartree–Fock–Roothaan (RHFR) formalism for closed-shell molecules is given. The wavefunction for such systems is taken as a single Slater determinant of 4-component molecular spinors (MS), where each MS is written as a linear combination of atomic spinors (LCAS/MS). The radial part of the atomic spinor (AS) is expanded in terms of Slater-type basis functions (STBF). The relativistic electronic Hamiltonian for the molecular system (in Born–Oppenheimer approximation) is the sum of Dirac Hamiltonians plus the interelectronic Coulomb repulsion and the magnetic part of the Breit interaction, but the retardation term is neglected at present. The reduction of the matrix elements of the relativistic Hamiltonian in terms of the nonrelativistic-type matrix elements is shown for any molecular system. Expressions for the matrix elements of the above-mentioned relativistic Hamiltonian are given for diatomics.