Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory.

Unrestricted coupled cluster spin contamination corrected [UCCSD(T)] and unrestricted Brueckner doubles [UBD(T)] variations of the Weizmann-1 theory (W1), denoted as W1U, W1Usc, and W1BD, respectively, are compared with the restricted open-shell W1 theory [W1(RO)]. The performances of the four W1 variants are assessed with 220 total atomization energies, electron affinities, ionization potentials, and proton affinities in the G2/97 test set, for consistency with the error analysis of the original W1(RO) study. The root-mean-square deviations from the experiment of W1U (0.65 ± 0.48 kcal/mol), W1Usc (0.57 ± 0.48 kcal/mol), W1BD (0.62 ± 0.48 kcal/mol), and W1(RO) (0.57 ± 0.48 kcal/mol) show that the four methods are virtually indistinguishable. This error analysis excludes the "singlet biradicals," C2 and O3, since single determinantal methods are not really adequate for these strongly multireference systems. The unrestricted W1 variants perform poorly for such highly spin-contaminated and multireference species (the largest deviation from experiment for W1Usc is -4.2 ± 0.1 kcal/mol for the O3 EA). W1(RO) performs much better than its unrestricted counterparts for these pathological cases (the deviation from experiment is reduced to -1.5 ± 0.1 kcal/mol for the O3 EA), though the errors are significantly larger than those for the overall test set. The examples of C2, O3, and the F2 potential energy curve indicate that an advantage to using W1BD is that the error in ⟨S(2)⟩ correlates with the magnitude of the error in energy, whereas W1(RO) loses accuracy without such a warning.