Evaluation of S2 for correlated wave functions and spin projection of unrestricted Mo/ller–Plesset perturbation theory

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Abstract
The value of S2 can be an important diagnostic tool for judging the quality of correlated wave functions. A production code has been developed to evaluate S2 for unrestricted Mo/ller–Plesset perturbation theory (UMPn), coupled clusters (UCCSD), quadratic configuration interaction (UQCISD), and Brueckner doubles (UBD) methods, and to evaluate UMP3 and UMP4 energies with spin projection. The code has been used to examine the bond dissociation potentials for HF→H+F and CH4→CH3+H. For both systems, the onset of the RBD-UBD instabitity occurs near S2≊0.35 for UCCSD or UQCISD calculations. Maximum errors in the UMP4, UCCSD(T), UQCISD(T), and UBD(T) single bond dissociation curves are near S2≊0.5. The behavior of S2 for UCCSD and UQCISD is closer to BD than MP4. Projected MP4 energies are in good agreement with full CI calculations, but between the onset of the RHF-UHF instability and the RBD-UBD instability, CCSD(T), QCISD(T), and BD(T) are significantly better. If ANorm≳1.2 for restricted calculations on single bond dissociations, it is better to use a spin-unrestricted method.