17 - The Electronic States of Atoms. II. Higher-Order Approximations for Multielectron Atoms

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There are three principal approximation schemes that go beyond the zero-order orbital approximation. This chapter introduced three approximation schemes and discussed their application to atoms with two or more electrons. The first scheme is the variational method, which is based on the variation theorem. The variation theorem allows calculation of upper bounds to ground-state energies. The second approximation method, the perturbation method allows approximate calculations of energies and wave functions for any states. The third approximation scheme, the self-consistent field method allows generation of the best possible orbital wave function, leaving only the error due to neglect of electron correlation. In the orbital approximation, the energies of the orbitals in multielectron atoms depend on the angular momentum quantum number as well as on the principal quantum number, increasing as l increases. The ground state is identified by the Aufbau principle, choosing orbitals that give the lowest sum of the orbital energies consistent with the Pauli exclusion principle. For those elements with partially filled subshells, the detailed configuration and the values of the quantum numbers L and S of the ground level can be predicted, using rules due to Hund.