重新考虑分治自洽场方法中的解析梯度表达式：精确公式及其近似处理。

Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: exact formula and its approximate treatment.

机构信息

Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan.

出版信息

J Chem Phys. 2011 Jan 21;134(3):034105. doi: 10.1063/1.3524337.

DOI:10.1063/1.3524337

PMID:21261328

Abstract

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method.

摘要

在之前的一篇由杨和李（YL）发表的论文中，提出了一个基于密度矩阵的线性分割和征服（DC）自洽场（SCF）方法的解析能量梯度公式[J. Chem. Phys. 103, 5674 (1995)]。由于 YL 的公式并不对应于 DC-SCF 能量的精确梯度，我们通过直接微分推导了精确公式，这需要在包含子系统耦合项的同时求解耦合微扰方程。接下来，我们提出了一种用于近似评估 DC-SCF 能量梯度的替代公式，假设子系统密度矩阵的变分条件。数值评估证实，当采用可靠的缓冲区时，本公式得到的 DC-SCF 能量梯度值与传统 SCF 值具有合理的一致性。此外，还发现本方法的性能优于 YL 方法。