2005
DOI: 10.1063/1.1899124
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Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes

Abstract: We describe the theory and implementation of two extensions to the density-matrix renormalization-group ͑DMRG͒ algorithm in quantum chemistry: ͑i͒ to work with an underlying nonorthogonal one-particle basis ͑using a biorthogonal formulation͒ and ͑ii͒ to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. T… Show more

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Cited by 70 publications
(61 citation statements)
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“…16 very recently. The studies of Chan and co-workers comprise benchmark calculations on the dinitrogen ground state potential energy curve, 10 an extension of the DMRG algorithm for nonorthogonal orbitals, 17 a quadratic scaling algorithm, 18 and a harmonic Davidson algorithm. 19 Our group provided a feasibility study on the curve crossing of the two lowest lying electronic states of cesium hydride using relativistically contracted orbitals, 20 systematic studies on the convergence properties of DMRG, 21,22 and recently, a way to decompose DMRG states into a Slater determinant basis, 16 which allows one to understand DMRG convergence in terms of the uptake or rejection of certain electronic configurations for the representation of the DMRG state during the iterations.…”
Section: Introductionmentioning
confidence: 99%
“…16 very recently. The studies of Chan and co-workers comprise benchmark calculations on the dinitrogen ground state potential energy curve, 10 an extension of the DMRG algorithm for nonorthogonal orbitals, 17 a quadratic scaling algorithm, 18 and a harmonic Davidson algorithm. 19 Our group provided a feasibility study on the curve crossing of the two lowest lying electronic states of cesium hydride using relativistically contracted orbitals, 20 systematic studies on the convergence properties of DMRG, 21,22 and recently, a way to decompose DMRG states into a Slater determinant basis, 16 which allows one to understand DMRG convergence in terms of the uptake or rejection of certain electronic configurations for the representation of the DMRG state during the iterations.…”
Section: Introductionmentioning
confidence: 99%
“…Over the past decades, the applicability of quantum chemical DMRG has been studied for various molecular systems, ranging from basic molecules, such as water molecule, 3,6,7 to polymeric organic systems, such as polyenes, 10,11,14,23 acenes, 12,13 polycarbenes, 17,45 graphene nanoribbons, 47 etc. Inorganic chemical systems are also included in the application domain, such as chromium dimer, 5,27,44,46,51,53 dicopper-dioxygen isomers, 35,44,55 tetranuclear manganese cluster, 49 2Fe-2S/ 4Fe-4S clusters, 21,22 etc; their full single-shell (or even double-shell) valence d-block configurations can be highly correlated using the DMRG method with such a great accuracy to account for the full quantum degrees of freedom and with an affordable computational cost.…”
Section: Introductionmentioning
confidence: 99%
“…10 In each of these cases, we obtained DMRG energies within 0.001-0.1 mE h of the ͑estimated͒ exact full configuration interaction energies in the active space, but for active spaces that, in some problems, have been as large as 100 active electrons in 100 orbitals. 10 The development of the DMRG in quantum chemistry has proceeded through the efforts of several groups, and we mention here the work of White and co-workers, 3,13,14 Mitrushenkov et al, 4,15,16 our contributions, 5,[8][9][10][11][12]17,18 the work of Legeza, Hess, and co-workers, 6,[19][20][21] the work of Reiher and co-workers, 7,[22][23][24] and most recently the work of Zgid and Nooijen. 25 Also related, but too numerous to cite in full here, are earlier developments of the method for semiempirical Hamiltonians; some representative contributions are those in Refs.…”
Section: Introductionmentioning
confidence: 99%