Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method: Improving upon CCSD(T) and CCSD(T)_Λ: Preliminary application

Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OO-CCD or simply “OD” for short) method are investigated. The conventional symmetric and asymmetric perturbative triples corrections [(T) and (T)_Λ] are implemented, the latter one for the first time. Additionally, two new triples corrections, denoted as OD(Λ) and OD(Λ)_T, are introduced. We applied the new methods to potential energy surfaces of the BH, HF, C₂, N₂, and CH₄ molecules, and compare the errors in total energies, with respect to full configuration interaction, with those from the standard coupled-cluster singles and doubles (CCSD), with perturbative triples [CCSD(T)], and asymmetric triples correction (CCSD(T)_Λ) methods. The CCSD(T) method fails badly at stretched geometries, the corresponding nonparallelity error is 7–281 kcal mol⁻¹, although it gives reliable results near equilibrium geometries. The new symmetric triples correction, CCSD(Λ), noticeably improves upon CCSD(T) (by 4–14 kcal mol⁻¹) for BH, HF, and CH₄; however, its performance is worse than CCSD(T) (by 1.6–4.2 kcal mol⁻¹) for C₂ and N₂. The asymmetric triples corrections, CCSD(T)_Λ and CCSD(Λ)_T, perform remarkably better than CCSD(T) (by 5–18 kcal mol⁻¹) for the BH, HF, and CH₄ molecules, while for C₂ and N₂ their results are similar to those of CCSD(T). Although the performance of CCSD and OD is similar, the situation is significantly different in the case of triples corrections, especially at stretched geometries. The OD(T) method improves upon CCSD(T) by 1–279 kcal mol⁻¹. The new symmetric triples correction, OD(Λ), enhances the OD(T) results (by 0.01–2.0 kcal mol⁻¹) for BH, HF, and CH₄; however, its performance is worse than OD(T) (by 1.9–2.3 kcal mol⁻¹) for C₂ and N₂. The asymmetric triples corrections, OD(T)_Λ and OD(Λ)_T, perform better than OD(T) (by 2.0–6.2 kcal mol⁻¹). The latter method is slightly better for the BH, HF, and CH₄ molecules. However, for C₂ and N₂ the new results are similar to those of OD(T). For the BH, HF, and CH₄ molecules, OD(Λ)_T provides the best potential energy curves among the considered methods, while for C₂ and N₂ the OD(T) method prevails. Hence, for single-bond breaking the OD(Λ)_T method appears to be superior, whereas for multiple-bond breaking the OD(T) method is better.