Department of Chemistry, Atatürk University, Erzurum 25240, Turkey.
J Chem Phys. 2013 Sep 14;139(10):104116. doi: 10.1063/1.4820877.
Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory (OMP3) [U. Bozkaya, J. Chem. Phys. 135, 224103 (2011)] are presented. The OMP3 method is applied to problematic chemical systems with challenging electronic structures. The performance of the OMP3 method is compared with those of canonical second-order Møller-Plesset perturbation theory (MP2), third-order Møller-Plesset perturbation theory (MP3), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] for investigating equilibrium geometries, vibrational frequencies, and open-shell reaction energies. For bond lengths, the performance of OMP3 is in between those of MP3 and CCSD. For harmonic vibrational frequencies, the OMP3 method significantly eliminates the singularities arising from the abnormal response contributions observed for MP3 in case of symmetry-breaking problems, and provides noticeably improved vibrational frequencies for open-shell molecules. For open-shell reaction energies, OMP3 exhibits a better performance than MP3 and CCSD as in case of barrier heights and radical stabilization energies. As discussed in previous studies, the OMP3 method is several times faster than CCSD in energy computations. Further, in analytic gradient computations for the CCSD method one needs to solve λ-amplitude equations, however for OMP3 one does not since λ(ab)(ij(1))=t(ij)(ab(1)) and λ(ab)(ij(2))=t(ij)(ab(2)). Additionally, one needs to solve orbital Z-vector equations for CCSD, but for OMP3 orbital response contributions are zero owing to the stationary property of OMP3. Overall, for analytic gradient computations the OMP3 method is several times less expensive than CCSD (roughly ~4-6 times). Considering the balance of computational cost and accuracy we conclude that the OMP3 method emerges as a very useful tool for the study of electronically challenging chemical systems.
分析了轨道优化的三阶 Møller-Plesset 微扰理论（OMP3）[U. Bozkaya，J. Chem. Phys. 135, 224103（2011）]的能量梯度。OMP3 方法应用于具有挑战性电子结构的问题化学体系。将 OMP3 方法的性能与经典二阶 Møller-Plesset 微扰理论（MP2）、三阶 Møller-Plesset 微扰理论（MP3）、耦合簇单双（CCSD）和耦合簇单双加微扰三（CCSD(T)）进行比较，以研究平衡几何、振动频率和开壳反应能。对于键长，OMP3 的性能介于 MP3 和 CCSD 之间。对于简谐振动频率，OMP3 方法显著消除了由于对称破缺问题导致 MP3 中异常响应贡献引起的奇点，并为开壳分子提供了明显改进的振动频率。对于开壳反应能，OMP3 表现出比 MP3 和 CCSD 更好的性能，如在势垒高度和自由基稳定能方面。如前所述，OMP3 方法在能量计算方面比 CCSD 快几倍。此外，在 CCSD 方法的解析梯度计算中，需要求解 λ 幅度方程，但对于 OMP3 则不需要，因为 λ(ab)(ij(1))=t(ij)(ab(1))和 λ(ab)(ij(2))=t(ij)(ab(2))。此外，对于 CCSD，需要求解轨道 Z 向量方程，但对于 OMP3，由于 OMP3 的静止特性，轨道响应贡献为零。总的来说，对于解析梯度计算，OMP3 方法的成本比 CCSD 低几倍（大约~4-6 倍）。考虑到计算成本和准确性的平衡，我们得出结论，OMP3 方法是研究具有挑战性电子化学体系的非常有用的工具。
