TY - JOUR
T1 - Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach
T2 - Exact formula and its approximate treatment
AU - Kobayashi, Masato
AU - Kunisada, Tomotaka
AU - Akama, Tomoko
AU - Sakura, Daisuke
AU - Nakai, Hiromi
N1 - Funding Information:
Some of the present calculations were performed at the Research Center for Computational Science (RCCS), Okazaki Research Facilities, National Institutes of Natural Sciences (NINS). This study was supported in part by Grants-in-Aid for Challenging Exploratory Research “KAKENHI 22655008” and for Young Scientists (B) “KAKENHI 22750016” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; by the Nanoscience Program in the Next Generation Super Computing Project from MEXT; by the Global Center of Excellence (COE) “Practical Chemical Wisdom” from MEXT; and by a project research grant for “Practical in-silico chemistry for material design” from the Research Institute for Science and Engineering (RISE), Waseda University.
PY - 2011/1/21
Y1 - 2011/1/21
N2 - 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.
AB - 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.
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U2 - 10.1063/1.3524337
DO - 10.1063/1.3524337
M3 - Article
C2 - 21261328
AN - SCOPUS:79551637999
VL - 134
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 3
M1 - 034105
ER -