1. Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: Exact formula and its approximate treatment.
- Author
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Kobayashi, Masato, Kunisada, Tomotaka, Akama, Tomoko, Sakura, Daisuke, and Nakai, Hiromi
- Subjects
SELF-consistent field theory ,APPROXIMATION theory ,DENSITY matrices ,PERTURBATION theory ,NUMERICAL analysis ,PHYSICS periodicals ,SCIENCE publishing - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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