Reduced Density Matrix-Driven Complete Active Apace Self-Consistent Field Corrected for Dynamic Correlation from the Adiabatic Connection

Maradzike, Elvis; Hapka, Michał; Pernal, Katarzyna; DePrince, A. Eugene

doi:10.1021/acs.jctc.0c00324

Cited by 17 publications

(13 citation statements)

References 88 publications

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“…In order to treat both the static and dynamical correlations simultaneously, several hybrid schemes, where wave function theory is combined with the aforementioned reduced quantity theories [37][38][39][40][41][42][43][44][45][46][47], have been proposed. Quite recently, Pernal [48] also suggested to use the adiabatic connection (AC) formalism to recover the electron correlation that is missing in multiconfigurational wave functions [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Senjean¹,

Yalouz²,

Nakatani³

et al. 2022

Preprint

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Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC is a better strategy. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.

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Section: Introductionmentioning

confidence: 99%

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Senjean¹,

Yalouz²,

Nakatani³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…However, the complexity of the solution generally limits such methods to quite moderate active spaces, for example, the exact complete active space self-consistent field (CASSCF) method suffers from the exponential growth of the active space that restricts the maximum size approximately up to 20 orbitals. The density matrix renormalization group (DMRG) − is one of the methods which can operate on larger active spaces and has been used in conjunction with many multireference methods as an active space solver to reduce their cost and accurately reproduce both static and dynamic correlations. − …”

Section: Introductionmentioning

confidence: 99%

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Golub

Antalík

Veis

et al. 2021

J. Chem. Theory Comput.

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Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)–porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

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“…34,35 This approach can be used in connection with CASSCF-type wave functions 35 and has the advantage of requiring only the one and two-body active space RDMs. It therefore seems to be an ideal dynamical electron correlation method suitable for large-scale DMRG (or similar methods, where only loworder density matrices are available 36 ).…”

Section: Introductionmentioning

confidence: 99%

Density matrix renormalization group with dynamical correlation via adiabatic connection

Beran¹,

Matoušek²,

Hapka³

et al. 2021

Preprint

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The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique, which requires only up to two-body active space reduced density matrices. We report encouraging results of this approach on typical candidates for DMRG computations, namely the n-acenes (n = 2 → 7), Fe(II)-porphyrin, and Fe 3 S 4 cluster.

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Reduced Density Matrix-Driven Complete Active Apace Self-Consistent Field Corrected for Dynamic Correlation from the Adiabatic Connection

Cited by 17 publications

References 88 publications

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Density matrix renormalization group with dynamical correlation via adiabatic connection

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