Truflandier Lionel A, Dianzinga Rivo M, Bowler David R
Institut des Sciences Moléculaires (ISM), Université Bordeaux, CNRS UMR 5255, 351 cours de la Libération, 33405 Talence Cedex, France.
London Centre for Nanotechnology, UCL, 17-19 Gordon St., London WC1H 0AH, United Kingdom and Department of Physics and Astronomy, UCL, Gower St., London WC1E 6BT, United Kingdom.
J Chem Phys. 2020 Oct 28;153(16):164105. doi: 10.1063/5.0022244.
Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrödinger perturbation theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method.
密度矩阵微扰理论（DMPT）被认为是瑞利 - 薛定谔微扰理论的一种有前景的替代方法，其中态叠加（SOS）被以微扰密度矩阵作为输入变量的算法所取代。在本文中，我们阐述并讨论了三种类型的DMPT，其中两种仅基于密度矩阵：库斯曼和奥克森费尔德的方法[《化学物理杂志》127, 054103 (2007)]通过西尔维斯特方程重新表述，尼克拉斯森和查拉科姆的递归DMPT[《物理评论快报》92, 193001 (2004)]从特鲁夫兰迪耶等人[《化学物理杂志》144, 091102 (2016)]的空穴 - 粒子正则纯化（HPCP）扩展而来。计算性能的比较表明，上述方法优于标准的SOS。与原始递归多项式方法相比，HPCP - DMPT表现出稳定的收敛曲线，但计算成本更高。
