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
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.
UR - http://www.scopus.com/inward/record.url?scp=79551637999&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79551637999&partnerID=8YFLogxK
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 -