Efficient implementations of the orbital-optimized coupled-cluster doubles [or simply "optimized CCD", OCCD, for short] method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of Psi4) is compared with that of the conventional OCCD (from the Q-Chem package). The OCCD computations were performed with the Q-chem package, in which it is denoted by OD. In the conventional OCCD, one needs to perform four-index integrals transformations at each CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, there are almost 8-fold reductions in the computational time for the C 6 H 14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Further, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD there is no need for orbital relaxation contributions in analytic gradient computations (2) active spaces can readily be incorporated into DF-OCCD (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory (5) Symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] has a significantly better performance in near degeneracy regions.

MacroQC is a quantum chemistry software for high-accuracy computations and large-scale chemical applications. MacroQC package features energy and analytic gradients for a broad range of many-body perturbation theory and coupled-cluster (CC) methods. Even when compared to commercial quantum chemistry software, analytical gradients of second-order perturbation theory, CC singles and doubles (CCSD), and CCSD with perturbative triples approaches are particularly efficient. MacroQC has a number of peculiar features, such as analytic gradients with the density-fitting approach, orbital-optimized methods, extended Koopman’s theorem, and molecular fragmentation approaches. MacroQC provides a limited level of interoperability with some other software. The plugin system of MacroQC allows external interfaces in a developer-friendly way. The linear-scaling systematic molecular fragmentation (LSSMF) method is another distinctive feature of the MacroQC software. The LSSMF method enables one to apply high-level post-Hartree–Fock methods to large-sized molecular systems. Overall, we feel that the MacroQC program will be a valuable tool for wide scientific applications.

Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-index integral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8–14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.

Efficient implementations of the orbital-optimized coupled-cluster doubles [or simply ``optimized CCD'', OCCD, for short] method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method is compared with that of the conventional OCCD. In the conventional OCCD, one needs to perform four-index integrals transformations at each CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides significantly lower computational costs compared to OCCD, there are almost 7-fold reductions in the computational time for the \ce{C5H12} molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Further, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD there is no need for orbital relaxation contributions in analytic gradient computations (2) active spaces can readily be incorporated into DF-OCCD (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory (5) Symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] has a significantly better performance in near degeneracy regions.

Efficient implementations of the orbital-optimized coupled-cluster doubles [or simply ``optimized CCD'', OCCD, for short] method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method {(available in a plugin version of the {\sc DFOCC} module of {\sc Psi4})} is compared with that of the conventional OCCD {(from the {\sc Q-Chem} package)}. The OCCD computations were performed with the {\sc Q-chem} package, in which it is denoted by OD. In the conventional OCCD, one needs to perform four-index integrals transformations at each CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, there are almost 8-fold reductions in the computational time for the \ce{C6H14} molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. {Further, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry breaking problems. Moreover,} several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD there is no need for orbital relaxation contributions in analytic gradient computations (2) active spaces can readily be incorporated into DF-OCCD (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory (5) Symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] has a significantly better performance in near degeneracy regions.