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Article: Linear-scaling quantum mechanical methods for excited states

TitleLinear-scaling quantum mechanical methods for excited states
Authors
Issue Date2012
PublisherRoyal Society of Chemistry. The Journal's web site is located at http://www.rsc.org/Publishing/Journals/cs/index.asp
Citation
Chemical Society Reviews, 2012, v. 41 n. 10, p. 3821-3838 How to Cite?
AbstractThe poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems. © 2012 The Royal Society of Chemistry.
Persistent Identifierhttp://hdl.handle.net/10722/159313
ISSN
2015 Impact Factor: 34.09
2015 SCImago Journal Rankings: 15.228
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorYam, Cen_HK
dc.contributor.authorZhang, Qen_HK
dc.contributor.authorWang, Fen_HK
dc.contributor.authorChen, Gen_HK
dc.date.accessioned2012-08-16T05:48:35Z-
dc.date.available2012-08-16T05:48:35Z-
dc.date.issued2012en_HK
dc.identifier.citationChemical Society Reviews, 2012, v. 41 n. 10, p. 3821-3838en_HK
dc.identifier.issn0306-0012en_HK
dc.identifier.urihttp://hdl.handle.net/10722/159313-
dc.description.abstractThe poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems. © 2012 The Royal Society of Chemistry.en_HK
dc.languageengen_US
dc.publisherRoyal Society of Chemistry. The Journal's web site is located at http://www.rsc.org/Publishing/Journals/cs/index.aspen_HK
dc.relation.ispartofChemical Society Reviewsen_HK
dc.titleLinear-scaling quantum mechanical methods for excited statesen_HK
dc.typeArticleen_HK
dc.identifier.emailYam, C:yamcy@graduate.hku.hken_HK
dc.identifier.emailChen, G:ghc@yangtze.hku.hken_HK
dc.identifier.authorityYam, C=rp01399en_HK
dc.identifier.authorityChen, G=rp00671en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1039/c2cs15259ben_HK
dc.identifier.pmid22419073-
dc.identifier.scopuseid_2-s2.0-84860451619en_HK
dc.identifier.hkuros203766en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84860451619&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume41en_HK
dc.identifier.issue10en_HK
dc.identifier.spage3821en_HK
dc.identifier.epage3838en_HK
dc.identifier.eissn1460-4744-
dc.identifier.isiWOS:000303320400010-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridYam, C=7004032400en_HK
dc.identifier.scopusauthoridZhang, Q=55203461500en_HK
dc.identifier.scopusauthoridWang, F=34976037400en_HK
dc.identifier.scopusauthoridChen, G=35253368600en_HK

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