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The Hartree–Fock (HF) method, widely used for the calculation of ground state properties, in recent years has been extended for calculating excited states. In this article, we develop an approach, which does not require time consuming calculations and can give a good approximation for the excitation energies. The method is based on the fact that the subspaces of the occupied and virtual orbitals are mutually orthogonal. We test the accuracy of our method by evaluating the excited state wavefunctions and the corresponding energies for the Li, N, F, Ne, and Na atoms and for the BeH and CH molecules, and we found good agreement with configuration interaction and experimental results. © 2012 Wiley Periodicals, Inc.

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In an earlier paper [S. Thanos and A. K. Theophilou J. Chem. Phys. 124, 204109 (2006)], we found an explicit formula for the expansion of a Slater determinant |Phi(M)> in terms of eigenstates of S(2). In this paper, we use the same formula to determine the spin contamination S(con) of the unrestricted single determinant approximations, i.e., Hartree-Fock, optimized effective potential, and density functional theory. We derived an expression which gives S(con) in terms of the overlap of the spatial parts of the spin up and spin down "corresponding" orbitals. It was found that S(con) does not depend on M, the eigenvalue of S(z), at least for the lower order approximations, i.e., when || is large. In this case, the predominant coefficient of the expansion assumes its maximum value when S=M. However, for the class of solutions that || is small, the spin L of the largest coefficient increases with the number of unpaired electrons. We also derived the explicit form of the expansion states.