Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory

Abstract

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 ⟨S²⟩ correlates with the magnitude of the error in energy, whereas W1(RO) loses accuracy without such a warning.