Orbital-optimized MP2.5 and its analytic gradients: Approaching CCSD(T) quality for noncovalent interactions

Abstract

Orbital-optimized MP2.5 [or simply "optimized MP2.5," OMP2.5, for short] and its analytic energy gradients are presented. The cost of the presented method is as much as that of coupled-cluster singles and doubles (CCSD) [O(N(6)) scaling] for energy computations. However, for analytic gradient computations the OMP2.5 method is only half as expensive as CCSD because there is no need to solve λ2-amplitude equations for OMP2.5. The performance of the OMP2.5 method is compared with that of the standard second-order Møller-Plesset perturbation theory (MP2), MP2.5, CCSD, and coupled-cluster singles and doubles with perturbative triples (CCSD(T)) methods for equilibrium geometries, hydrogen transfer reactions between radicals, and noncovalent interactions. For bond lengths of both closed and open-shell molecules, the OMP2.5 method improves upon MP2.5 and CCSD by 38%-43% and 31%-28%, respectively, with Dunning's cc-pCVQZ basis set. For complete basis set (CBS) predictions of hydrogen transfer reaction energies, the OMP2.5 method exhibits a substantially better performance than MP2.5, providing a mean absolute error of 1.1 kcal mol(-1), which is more than 10 times lower than that of MP2.5 (11.8 kcal mol(-1)), and comparing to MP2 (14.6 kcal mol(-1)) there is a more than 12-fold reduction in errors. For noncovalent interaction energies (at CBS limits), the OMP2.5 method maintains the very good performance of MP2.5 for closed-shell systems, and for open-shell systems it significantly outperforms MP2.5 and CCSD, and approaches CCSD(T) quality. The MP2.5 errors decrease by a factor of 5 when the optimized orbitals are used for open-shell noncovalent interactions, and comparing to CCSD there is a more than 3-fold reduction in errors. Overall, the present application results indicate that the OMP2.5 method is very promising for open-shell noncovalent interactions and other chemical systems with difficult electronic structures.

Orbital-optimized linearized coupled-cluster doubles with density-fitting and Cholesky decomposition approximations: an efficient implementation

“…Orbital-optimized electron correlation methods have been reported for the coupled-cluster doubles (CCD), 1,2,13 the linearized coupled-cluster doubles (LCCD), 18 coupled pair functional theories, 25,26 active space and excited state CC methods, 3,5 the second-order perturbation theory (MP2), 13,17,22,23 the third-order perturbation theory (MP3), 14,19 MP2.5, 24 and the density-cumulant functional theory (DCFT). Orbital-optimized electron correlation methods have been reported for the coupled-cluster doubles (CCD), 1,2,13 the linearized coupled-cluster doubles (LCCD), 18 coupled pair functional theories, 25,26 active space and excited state CC methods, 3,5 the second-order perturbation theory (MP2), 13,17,22,23 the third-order perturbation theory (MP3), 14,19 MP2.5, 24 and the density-cumulant functional theory (DCFT).…”

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability

“…This method has been found [134][135][136] to give rather accurate results for non-covalent interaction energies at a substantially reduced cost compared to CCSD(T).…”

The extended Koopmans' theorem for orbital-optimized methods: Accurate computation of ionization potentials

“…For a more detailed discussion of these methods one can refer to our previous studies. [35][36][37][38][39][40][41][42] For the parametrization of the wave functions, we will follow our previous studies. [35][36][37][38][39][40][41] The orbital variations may be carried out with an exponential unitary operator, [69][70][71][72] …”

“…In this research, the EKT for the orbital-optimized methods, such as orbital-optimized second-and thirdorder Møller-Plesset perturbation theories (OMP2 35,39 and OMP3, 36,41 as well as OMP2.5 42 ) and the orbital-optimized coupled-electron pair theory [OCEPA(0)], 40 are presented. The EKT approaches for the orbital-optimized methods are applied to IPs of the second-and third-row atoms, and closed-and open-shell molecules.…”