Theoretical Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
J Chem Phys. 2014 Feb 28;140(8):084113. doi: 10.1063/1.4866365.
A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O-H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λpq = ∑s|ps - qs|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and coupled-cluster with singles, doubles, and perturbative triples level of electronic structure theory, is generated and employed in the oc-VQDPT2 calculation to obtain the fundamental tones as well as selected overtones/combination tones coupled to the fundamentals through the Fermi resonance. The calculated frequencies of ethylene and trans-1,3-butadiene are found to be in excellent agreement with the experimental values with a mean absolute error of 8 and 9 cm(-1), respectively.
提出了一种基于准简并微扰理论（QDPT）的优化坐标振子自洽场（oc-VSCF）的微扰扩展。开发了一种构建简并空间（P 空间）的方案，该方案包含简并构型，并缓解了 oc-VSCF 中局部坐标引起的微扰展开的发散（例如水的局部 O-H 伸缩模式）。还实现了一种有效的构型选择方案，该方案基于它们量子数的差异（λpq = ∑s|ps - qs|），根据 P 空间构型（p）和互补 Q 空间构型（q）之间的哈密顿矩阵元素来筛选。结果表明，基于优化坐标的二阶振动 QDPT（oc-VQDPT2）相对于模式耦合的阶数平稳收敛，并且优于基于正则坐标的传统方法。此外，还开发了一种改进的快速坐标优化算法。首先，在受限参数空间中进行 VSCF 能量的最小化，在此空间中仅选择性地转换部分坐标对。为此目的设计了一个合理的指标，该指标根据转换引起的谐耦合的大小，从其他可能保持不变的坐标对中识别要混合的重要坐标对。其次，采用立方力场（CFF）代替四次力场，从而避免了由于存在四阶力常数而引起的密集程序。结果发现，基于 CFF 的 oc-VSCF 与对选择方案相结合，可得到与传统方法相似的特征的坐标，从而在获得数量级加速的同时，对最终振动能量的影响很小。该方法应用于乙烯和反式-1,3-丁二烯。生成并在 oc-VQDPT2 计算中使用结合了 MP2 和耦合簇与单、双和微扰三重电子结构理论的多分辨率势，以获得基频以及通过费米共振与基频耦合的选定泛音/组合音。计算出的乙烯和反式-1,3-丁二烯的频率与实验值非常吻合，平均绝对误差分别为 8 和 9 cm-1。
