TY - JOUR
T1 - Purification of the first-order density matrix using steepest descent and Newton-Raphson methods
AU - Pino, Ramiro
AU - Scuseria, Gustavo E.
N1 - Funding Information:
The authors would like thank P. Constans for useful comments, and V.N. Staroverov for reading the manuscript. This work was supported by the Department of Energy, SciDAC Computational Chemistry Program (Grant No. DE-FG02-01ER15232).
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2002/7/3
Y1 - 2002/7/3
N2 - We propose a powerful approach to purification of the first-order density matrix based on minimizing the trace of a fourth-order polynomial, representing a deviation from idempotency. Two variants of this strategy are discussed. The first, based on a steepest descent minimization is robust and efficient, especially when the trial density matrix is far from idempotency. The second, using a Newton-Raphson technique, is quadratically convergent if the trial matrix is nearly idempotent. A steepest descent method with a switch to McWeeny's purification method is found to have a lower computational cost and wider range of convergence than McWeeny's scheme alone.
AB - We propose a powerful approach to purification of the first-order density matrix based on minimizing the trace of a fourth-order polynomial, representing a deviation from idempotency. Two variants of this strategy are discussed. The first, based on a steepest descent minimization is robust and efficient, especially when the trial density matrix is far from idempotency. The second, using a Newton-Raphson technique, is quadratically convergent if the trial matrix is nearly idempotent. A steepest descent method with a switch to McWeeny's purification method is found to have a lower computational cost and wider range of convergence than McWeeny's scheme alone.
UR - http://www.scopus.com/inward/record.url?scp=0037014750&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037014750&partnerID=8YFLogxK
U2 - 10.1016/S0009-2614(02)00821-7
DO - 10.1016/S0009-2614(02)00821-7
M3 - Article
AN - SCOPUS:0037014750
VL - 360
SP - 117
EP - 122
JO - Chemical Physics Letters
JF - Chemical Physics Letters
SN - 0009-2614
IS - 1-2
ER -