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Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group

Chan, Garnet Kin-Lic and Head-Gordon, Martin (2002) Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group. Journal of Chemical Physics, 116 (11). pp. 4462-4476. ISSN 0021-9606. doi:10.1063/1.1449459. https://resolver.caltech.edu/CaltechAUTHORS:20161220-095020446

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Abstract

We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yield arbitrarily high accuracy in the energy with only polynomial computational effort. We describe in some detail how this is achieved. We begin by introducing the principles of the renormalization procedure, and how one formulates an algorithm for use in quantum chemistry. The renormalization group algorithm is then interpreted in terms of familiar quantum chemical concepts, and its numerical behavior, including its convergence and computational cost, are studied using both model and real systems. The asymptotic convergence of the algorithm is derived. Finally, we examine the performance of the DMRG on widely studied chemical problems, such as the water molecule, the twisting barrier of ethene, and the dissociation of nitrogen. In all cases, the results compare favorably with the best existing quantum chemical methods, and particularly so when the nondynamical correlation is strong. Some perspectives for future development are given.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1449459DOIArticle
http://aip.scitation.org/doi/abs/10.1063/1.1449459PublisherArticle
ORCID:
AuthorORCID
Chan, Garnet Kin-Lic0000-0001-8009-6038
Head-Gordon, Martin0000-0002-4309-6669
Additional Information:© 2002 American Institute of Physics. Received 16 October 2001; accepted 18 December 2001. G.K.-L.C. acknowledges S. R. White for many interesting discussions, and the Miller Institute for Basic Research in Science for funding.
Funders:
Funding AgencyGrant Number
Miller Institute for Basic Research in ScienceUNSPECIFIED
Issue or Number:11
DOI:10.1063/1.1449459
Record Number:CaltechAUTHORS:20161220-095020446
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161220-095020446
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72971
Collection:CaltechAUTHORS
Deposited By: Donna Wrublewski
Deposited On:20 Dec 2016 18:54
Last Modified:11 Nov 2021 05:09

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