Orbital-optimized coupled-electron pair theory and its analytic gradients: Accurate equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions

Orbital-optimized coupled-electron pair theory [or simply “optimized CEPA(0),” OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N⁶) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ₂-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%–43% and 38%–53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%–79% and 53%–79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm⁻¹) is fortuitously even better than that of CCSD(T) (50 cm⁻¹), while the MAEs of CEPA(0) (184 cm⁻¹) and CCSD (84 cm⁻¹) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol⁻¹, which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol⁻¹), and comparing to MP2 (7.7 kcal mol⁻¹) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is only 0.1 kcal mol⁻¹ lower than that of OCEPA(0). Overall, the present application results indicate that the OCEPA(0) method is very promising not only for challenging open-shell systems but also for closed-shell molecules.