The extended Koopmans' theorem (EKT), when combined with the second‐order Møller−Plesset (MP2) perturbation theory through the relaxed density matrix approach [J. Cioslowski, P. Piskorz, and G. Liu, J. Chem. Phys. 1997, 107, 6,804], provides a straightforward way to calculate the ionization potentials (IPs) as an one electron quantity. However, such an EKT‐MP2 method often suffers from the negative occupation problem, failing to provide the complete IP spectra for a system of interest. Here a small positive number scheme is proposed to cure this problem so as to remove the associated unphysical results. In order to obtain an in‐depth physical interpretation of the EKT‐MP2 method, we introduce a Koopmans‐type quantity, named KT‐MP2, based on which the respective contribution from the relaxation and the correlation parts in the EKT‐MP2 results are recognized. Furthermore, the close relationship between the EKT‐MP2 method and the derivative approach of the MP2 energy with respect to the orbital occupation numbers [N. Q. Su and X. Xu, J. Chem. Theory Comput. 2015, 11, 4,677] is revealed. When these MP2‐based methods are applied to a set of atoms and molecules, new insights are gained on the role played by the relaxation and the correlation effects in the electron ionization processes.

中文翻译：

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在二阶微扰理论中扩展 Koopmans 定理

通过松弛密度矩阵方法将扩展的 Koopmans 定理 (EKT) 与二阶 Møller-Plesset (MP2) 微扰理论相结合 [J. Cioslowski、P. Piskorz 和 G. Liu、J. Chem。物理。1997, 107, 6,804]，提供了一种将电离势 (IP) 计算为一个电子量的直接方法。然而，这种 EKT-MP2 方法经常存在负占用问题，无法为感兴趣的系统提供完整的 IP 光谱。这里提出了一个小的正数方案来解决这个问题，以消除相关的非物理结果。为了获得对 EKT-MP2 方法的深入物理解释，我们引入了一个名为 KT-MP2 的 Koopmans 型量，基于此，EKT-MP2 结果中松弛和相关部分的各自贡献被识别。此外，EKT-MP2 方法和 MP2 能量的导数方法与轨道占据数之间的密切关系 [NQ Su 和 X. Xu，J. Chem。理论计算。2015, 11, 4,677] 揭晓。当这些基于 MP2 的方法应用于一组原子和分子时，对电子电离过程中弛豫和相关效应所起的作用有了新的认识。