Spin contamination in MP2 and CC2, a surprising issue

When calculating the spin multiplicity at either the second-order Møller-Plesset (MP2) or the iterative second-order approximate coupled-cluster singles and doubles (CC2) levels of theory using the same strategy for the calculation of the expectation value as in regular CC theory together with the usual definitions of the MP2 and CC2 density matrices, artificial spin contamination occurs in closed-shell molecules. Non-intuitively, for open-shell systems, results at the MP2 or CC2 levels of theory based on this procedure even suggest stronger contamination at the correlated level than for the Hartree-Fock reference, although treatment of electron correlation should lower spin contamination. In this Communication, the reasons behind this inconsistency are investigated and a solution is proposed, which removes spin contamination for closed-shell molecules and leads to physically meaningful results for open-shell cases. Additionally, we show that CC2 significantly outperforms MP2 in describing systems with a strongly spin-contaminated reference with a performance similar to that of full coupled-cluster with singles and doubles substitutions (CCSD).