Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
J Chem Phys. 2013 Aug 7;139(5):054104. doi: 10.1063/1.4816628.
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(N(6)) 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.
轨道优化耦合电子对理论[简称"优化 CEPA(0),"OCEPA(0)]及其解析能量梯度被提出。对于 OCEPA(0)方法的分子轨道的变分优化，使用了基于拉格朗日的方法，并结合轨道直接迭代子空间算法。该方法的成本与 CCSD[O(N(6))缩放]相当，用于能量计算。然而，对于解析梯度计算，OCEPA(0)方法的成本仅为 CCSD 的一半，因为不需要为 OCEPA(0)求解 λ2-振幅方程。将 OCEPA(0)方法的性能与规范 MP2、CEPA(0)、CCSD 和 CCSD(T)方法进行比较，用于平衡几何形状、谐波振动频率和自由基之间的氢转移反应。对于闭壳层和开壳层分子的键长，OCEPA(0)方法分别比 CEPA(0)和 CCSD 提高了 25%-43%和 38%-53%，采用 Dunning 的 cc-pCVQZ 基组。特别是对于开壳层测试集，OCEPA(0)的性能与 CCSD(T)相当(平均 ΔR 为 0.0003 Å)。对于闭壳层分子的谐波振动频率，OCEPA(0)方法再次分别比 CEPA(0)和 CCSD 提高了 33%-79%和 53%-79%。对于开壳层分子的谐波振动频率，OCEPA(0)方法的平均绝对误差(MAE)(39 cm(-1))幸运地甚至优于 CCSD(T)(50 cm(-1))，而 CEPA(0)(184 cm(-1))和 CCSD(84 cm(-1))的 MAE 则高得多。对于氢转移反应能的完全基组估计，OCEPA(0)方法再次表现出比 CEPA(0)更好的性能，提供了 0.7 kcal mol(-1)的平均绝对误差，比 CEPA(0)低 6 倍多(4.6 kcal mol(-1))，与 MP2(7.7 kcal mol(-1))相比，误差降低了 10 多倍。而 CCSD 方法的 MAE 仅比 OCEPA(0)低 0.1 kcal mol(-1)。总的来说，目前的应用结果表明，OCEPA(0)方法不仅对具有挑战性的开壳层系统，而且对闭壳层分子都非常有前途。
