An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry

Chan, Garnet Kin‐Lic; Dorando, Jonathan J.; Ghosh, Debashree; Hachmann, Johannes; Neuscamman, Eric; Wang, Haitao; Yanai, Takeshi

doi:10.1007/978-1-4020-8707-3_4

Cited by 92 publications

(122 citation statements)

References 52 publications

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“…For a more detailed discussion of the tensor structure of the manyelectron wavefunction, see for example, Refs. [19][20][21] and chapter 8.4 in Ref. [57].…”

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

“…However, the factorial scaling with the size of the active space puts rather severe limits on the size of the active space, which prevents most applications to polynuclear transition metal complexes and clusters. Novel approaches, such as the density matrix renormalization group algorithm [19,20] and its generalizations [21] might make it possible to overcome this limitation, although the molecular sizes that can be studied are clearly much smaller compared to those accessible to DFT methods. Therefore, DFT is usually the method of choice in theoretical studies of transition-metal catalysis as well as molecular and spectroscopic properties of open-shell molecular systems.…”

Section: Introductionmentioning

confidence: 99%

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Spin in density‐functional theory

Jacob¹,

Reiher²

2012

Int J of Quantum Chemistry

225

224

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The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. Although density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchangecorrelation energy functional and lead to different exact conditions on this functional. Finally, we suggest possible directions for future developments.

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“…For a more detailed discussion of the tensor structure of the manyelectron wavefunction, see for example, Refs. [19][20][21] and chapter 8.4 in Ref. [57].…”

Section: Spin Structure Of the Many-electron Wavefunctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spin in density‐functional theory

Jacob¹,

Reiher²

2012

Int J of Quantum Chemistry

225

224

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“…Since the computational cost of traditional CASSCF scales exponentially with the number of active orbitals and electrons, tractable active orbital spaces are presently limited to about 18 electrons in 18 orbitals 29 . These limitations can be overcome by resorting to the density matrix renormalization group (DMRG) approach [30][31][32][33] in quantum chemistry [34][35][36][37][38][39][40][41][42][43][44] which, in combination with a self-consistent-field orbital optimization ansatz (DMRG-SCF) 45,46 , is capable of approximating CASSCF wave functions to chemical accuracy with merely a polynomial scaling.…”

Section: Introductionmentioning

confidence: 99%

A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

Knecht

Keller

Autschbach

et al. 2016

J. Chem. Theory Comput.

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We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between arbitrary electronic states provided that they share the same one-electron basis functions and active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non-unitary transformations following a proposal by Malmqvist (Int. J. Quantum Chem. 30, 479 (1986)). This is well-known for traditional wave-function parametrizations but has not yet been exploited for MPS wave functions.

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“…For more detailed information we refer to a number of reviews about the application of MPS's and DMRG in quantum chemistry. 12,25,[47][48][49] In molecular ab initio DMRG calculations, the DMRG algorithm is used to approximate the full-CI solution within the active orbital space. For this purpose, the k (usually localized) active orbitals are projected on a onedimensional lattice as depicted in Figure 1.…”

Section: A Matrix Product States and The Dmrg Algorithmmentioning

confidence: 99%

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

Roemelt

Guo

Chan

2016

The Journal of Chemical Physics

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A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space.

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An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry

Cited by 92 publications

References 52 publications

Spin in density‐functional theory

Spin in density‐functional theory

A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

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