Extended Hartree–Fock self-consistent field with some results for berylliumlike atomic systems

The general methods of deriving the extended Hartree–Fock equations are described. The rules for going over from the energy expression in the ordinary method of calculation to that in an extended one are reformulated and illustrated. The extended Hartree—Fock equations for berylliumlike atomic systems based on the use of nonorthogonal radial orbitals are given and solved. The numerical values of overlap integrals and total energies are given and discussed.