发表机构
College of Engineering, Shibaura Institute of Technology（芝浦工业大学工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出CIS(2)方法，一种基于CIS参考态的态特定二阶微扰理论，通过结合Canonical三激发与Block-diagonal双激发实现尺寸强度，并在QUEST#1基准上以更低成本获得优于CIS(D)的精度。
AI 中文摘要
我们提出了一种基于组态相互作用单激发（CIS）参考态及其广义Fock算子的态特定二阶微扰理论。从完全内收缩的构造出发，我们在第一阶波函数中保留了完整的双激发空间和内收缩的三激发。我们考虑了两种划分方式，即Canonical和Block-diagonal，其参考激发能分别由Fock激发能隙$\omega^{(0)}$和CIS激发能$\omega_{\rm CIS}$给出。我们的分析表明，当收缩三激发的分母使用裸Fock能隙，并且占据-虚Fock块被投影以去除残余的旁观者耦合时，严格的尺寸强度得以保持。基于这一观察，将Canonical三激发与Block-diagonal双激发相结合，产生了一个尺寸强度的Hybrid划分。这些性质通过水与非相互作用氦原子的体系得到了验证。我们的公式在半正则基中实现了每个矩阵-向量乘积$O(o^3v^2)$的成本。在QUEST\\#1基准上，Canonical和Block-diagonal表现出相反的系统偏差，而Hybrid在三种划分中给出了最佳的整体精度。其对单重态和三重态的平均绝对误差分别为0.24和0.15 eV，而CIS(D)的相应误差为0.28和0.22 eV。对于里德伯激发，改进最为显著，尽管CIS(D)在价层单重态上仍然更准确。
英文摘要
We present a state-specific second-order perturbation theory based on a configuration interaction singles (CIS) reference and its generalized Fock operator. Starting from a fully internally contracted construction, we retain the complete doubles space and internally contracted triples in the first-order wave function. We consider two partitions, Canonical and Block-diagonal, with reference excitation energies given by the Fock excitation gap $ω^{(0)}$ and the CIS excitation energy $ω_{\rm CIS}$, respectively. Our analysis establishes that strict size-intensivity is preserved when the contracted-triples denominators use bare Fock gaps and the occupied--virtual Fock block is projected to remove residual spectator coupling. Based on this observation, combining Canonical triples with Block-diagonal doubles yields a size-intensive Hybrid partition. These properties are verified for water with non-interacting helium atoms. Our formulation enables $O(o^3v^2)$ cost per matrix--vector product in a semicanonical basis. On the QUEST\#1 benchmark, Canonical and Block-diagonal show opposite systematic biases, whereas Hybrid gives the best overall accuracy among the three partitions. Its mean absolute errors for singlets and triplets are 0.24 and 0.15~eV, compared with 0.28 and 0.22~eV for CIS(D). The improvement is largest for Rydberg excitations, although CIS(D) remains more accurate for valence singlets.
