Gu Yonghao, Xu Xin
Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, China.
J Comput Chem. 2020 May 5;41(12):1165-1174. doi: 10.1002/jcc.26163. Epub 2020 Jan 31.
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.
扩展的库普曼斯定理（EKT），通过松弛密度矩阵方法与二阶莫勒-普列斯特定理（MP2）微扰理论相结合时[J. 乔斯洛斯基、P. 皮斯科尔兹和G. 刘，《化学物理杂志》，1997年，第107卷，第6期，6804页]，提供了一种将电离势（IPs）作为单电子量进行计算的直接方法。然而，这种EKT-MP2方法常常受到负占据问题的困扰，无法为感兴趣的体系提供完整的IP光谱。本文提出了一种小正数方案来解决这个问题，以消除相关的非物理结果。为了深入理解EKT-MP2方法的物理意义，我们引入了一个库普曼斯型量，命名为KT-MP2，基于此可以识别EKT-MP2结果中弛豫部分和相关部分各自的贡献。此外，还揭示了EKT-MP2方法与MP2能量相对于轨道占据数的导数方法之间的紧密关系[N. Q. 苏和X. 徐，《化学理论与计算杂志》，2015年，第11卷，第4期，4677页]。当将这些基于MP2的方法应用于一组原子和分子时，我们对弛豫和相关效应在电子电离过程中所起的作用有了新的认识。
