Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany.
J Chem Phys. 2019 Sep 21;151(11):111101. doi: 10.1063/1.5119695.
A resolution-of-the-identity (RI) approximation for two-electron integrals over Gaussian basis functions with a complex-scaled exponent is presented. Such functions are used in non-Hermitian quantum mechanics to represent electronic resonances by L integrable wave functions with complex energies. We have implemented this new RI approximation for second-order Møller-Plesset perturbation (MP2) theory as well as for the Coulomb and exchange contributions in Hartree-Fock (HF) theory. We discuss the differences to the standard RI approximation of Hermitian quantum mechanics and demonstrate the utility of the non-Hermitian RI-MP2 and RI-HF methods by computations of the orientation-dependent ionization rates of CO, CH, and CH in static electric fields. Our results illustrate that RI-MP2 correctly describes correlation effects in molecular electronic resonances while the computational cost is low enough to allow for investigations of medium-sized molecules.
提出了一种用于复标度指数下的高斯基函数双电子积分的解析近似方法。在非厄米量子力学中，此类函数用于通过具有复能的 L 可积波函数来表示电子共振。我们已经将这种新的解析近似方法应用于二阶 Møller-Plesset 微扰（MP2）理论以及 Hartree-Fock（HF）理论中的库仑和交换贡献。我们讨论了与标准厄米量子力学的解析近似方法的区别，并通过计算静态电场中 CO、CH 和 CH 的取向相关的电离率，展示了非厄米 RI-MP2 和 RI-HF 方法的实用性。我们的结果表明，RI-MP2 正确描述了分子电子共振中的相关效应，而计算成本足够低，足以允许对中等大小的分子进行研究。
