Peng Degao, Yang Yang, Zhang Peng, Yang Weitao
Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA.
J Chem Phys. 2014 Dec 7;141(21):214102. doi: 10.1063/1.4901716.
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.
在本文中，我们系统地开发了用于计算分子激发能的粒子-空穴和粒子-粒子通道的二阶随机相位近似（RPA）和塔姆-丹科夫近似（TDA）。二阶粒子-空穴RPA/TDA能够捕捉到粒子-空穴RPA/TDA以及含时密度泛函理论（TDDFT）遗漏的双激发，而二阶粒子-粒子RPA/TDA则能找回粒子-粒子RPA/TDA遗漏的非最高占据分子轨道激发。通过适当的轨道限制，这些受限的二阶RPA和TDA在形式上的标度仅为O(N(4))。对二阶RPA和TDA的受限版本在各种小分子上进行了测试，并展示了一些积极的结果。数据表明，受限的二阶粒子-空穴TDA（r2ph-TDA）具有最佳的整体性能，其相关系数与TDDFT相似，但负偏差较大。r2ph-TDA的负偏差可能是由未考虑的基态相关能引起的，有待进一步研究。总体而言，推荐使用r2ph-TDA以中等精度研究同时包含单激发和一些低激发双激发的体系。还开发并测试了一些关于激发态性质评估的表达式，如⟨Ŝ(2)⟩ 。
