A full coupled-cluster singles and doubles model: The inclusion of disconnected triples

TLDR

CCSD is derived algebraically and its full equations are presented in spin–orbital form. The authors implemented CCSD, including cubic and quartic terms, and compared its results with full CI for H2O and BeH2, while also estimating the impact of higher‑order terms T1T2, T21T2, T31, and T41 via comparisons with low‑order models. CCSD reproduces 98 % of the full CI correlation energy for BeH2 near its transition state and, with a fourth‑order triple correction, matches the full CI energy for H2O within 0.5 kcal/mol, demonstrating efficient summation of higher‑order correlation effects.

Abstract

The coupled-cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher-order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth-order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low-order models provide estimates of the effect of the higher-order terms T1T2, T21T2, T31, and T41 on the correlation energy.