The spin purity of states described by the coupled-cluster singles and doubles (CCSD) approximation based on unrestricted and restricted open-shell Hartree–Fock (UHF and ROHF) determinants is investigated. By contracting matrix elements of the S2 operator with reduced one- and two-particle density matrices, the extent of spin contamination in ROHF-CCSD and UHF-CCSD solutions is quantitatively characterized. Results are presented for a representative set of molecules in doublet electronic states with UHF values of S2 that range from 0.76 to 1.18. In these examples, ROHF-CCSD and UHF-CCSD expectation values of S2 are similar, with both less than 0.015 above the nominally exact value of 3/4. This finding illustrates the characteristic insensitivity of CC methods with respect to the choice of orbitals. Finally, the negligible differences between UHF-CCSD values of S2 and those corresponding to a spin eigenfunction suggests that modest reference state spin contamination does not represent a serious problem when this method is applied to chemical problems.
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John F. Stanton (1994) studied this question.