The central-field model and Hartree’s self-consistent equations provide a first approximation of atomic orbitals and corresponding energies. In that context atomic wave functions are taken as products of one-electron wave functions. But this representation is not really adequate. The half-integral spin and the identity of all electrons bring important constraints on atomic wave functions: they must be completely antisymmetric with respect to permutation of the coordinates of any two electrons. This chapter is devoted mainly to the Hartree—Fock method, which determines atomic orbitals by enforcing the antisymmetry of the total wave function. The Hartree—Fock equations will be derived from the variational method, which itself has a large number of applications.1
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