Spin contamination for Hartree-Fock, optimized effective potential, and density functional approximations.

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 |[uppercase_phi_synonym]_M> in terms of eigenstates of S². 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 |<φ_i|φ_i^′>| 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 |<φ_i|φ_i^′>| 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. [ABSTRACT FROM AUTHOR]