Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA.
J Chem Phys. 2010 Jan 7;132(1):014109. doi: 10.1063/1.3276630.
The frozen natural orbital (FNO) approach, which has been successfully used in ground-state coupled-cluster calculations, is extended to open-shell ionized electronic states within equation-of-motion coupled-cluster (EOM-IP-CC) formalism. FNOs enable truncation of the virtual orbital space significantly reducing the computational cost with a negligible decline in accuracy. Implementation of the MP2-based FNO truncation scheme within EOM-IP-CC is presented and benchmarked using ionized states of beryllium, dihydrogen dimer, water, water dimer, nitrogen, and uracil dimer. The results show that the natural occupation threshold, i.e., percentage of the total natural occupation recovered in the truncated virtual orbital space, provides a more robust truncation criterion as compared to the fixed percentage of virtual orbitals retained. Employing 99%-99.5% natural occupation threshold, which results in the virtual space reduction by 70%-30%, yields errors below 1 kcal/mol. Moreover, the total energies exhibit linear dependence as a function of the percentage of the natural occupation retained allowing for extrapolation to the full virtual space values. The capabilities of the new method are demonstrated by the calculation of the 12 lowest vertical ionization energies (IEs) and the lowest adiabatic IE of guanine. In addition to IE calculations, we present the scans of potential energy surfaces (PESs) for ionized (H(2)O)(2) and (H(2))(2). The scans demonstrate that the FNO truncation does not introduce significant nonparallelity errors and accurately describes the PESs shapes and the corresponding energy differences, e.g., dissociation energies.
冻结自然轨道（FNO）方法已成功应用于基态耦合簇计算中，现被扩展到含时耦合簇（EOM-IP-CC）理论的开壳层离子化电子态。FNO 可显著截断虚拟轨道空间，从而大幅降低计算成本，同时精度几乎不受影响。本文介绍了在 EOM-IP-CC 中基于 MP2 的 FNO 截断方案的实现，并使用铍、氢二聚体、水、水二聚体、氮和尿嘧啶二聚体的离子化态对其进行了基准测试。结果表明，与保留的固定数量的虚拟轨道相比，自然占据阈值（即在截断的虚拟轨道空间中恢复的总自然占据的百分比）提供了更稳健的截断标准。采用 99%-99.5%的自然占据阈值，可将虚拟空间减少 70%-30%，得到的误差低于 1 kcal/mol。此外，总能量表现出与保留的自然占据百分比呈线性关系，允许外推至完整的虚拟空间值。通过计算鸟嘌呤的 12 个最低垂直电离能（IE）和最低绝热 IE，展示了新方法的能力。除了 IE 计算，我们还展示了离子化（H2O）2 和（H2）2 的势能面（PES）扫描。扫描表明，FNO 截断不会引入显著的非平行误差，并能准确描述 PES 的形状和相应的能量差，例如离解能。
