Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

Waldrop, Jonathan M.; Windus, Theresa L.; Govind, Niranjan

doi:10.1021/acs.jpca.1c03821

Cited by 15 publications

(21 citation statements)

References 55 publications

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“…( 8). Single-orbital entropy and/or the mutual information are usually employed as a diagnostic measure of the correlation for the active space selection in the complete active space calculations or system partitioning in the quantum embedding calculations [31][32][33] . In this work we propose a way to utilize the single-orbital entropy values to conduct orbital selection for correlation energy calculation.…”

Section: Single Orbital Entropymentioning

confidence: 99%

Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing

Mehendale¹,

Peng²,

Govind³

et al. 2023

Preprint

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One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupledcluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. We also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

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Section: Single Orbital Entropymentioning

confidence: 99%

Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing

Mehendale¹,

Peng²,

Govind³

et al. 2023

Preprint

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“…One possible solution to the problems caused by point charges and link atoms is the projector-based embedding (PbE) technique of Manby and Miller, which allows for the combination of high-level DFT or wave function theory (WFT) methods with cost-effective DFT methods. The algorithm, which has also been greatly improved in the past decade, − follows a top-down strategy: after solving the low-level KS equations of the whole system, the KS molecular orbitals (MOs) are localized, and the system is split up at the MO level. Subsequently, a high-level calculation is performed in the constant potential of the environment, while the MOs of the environmental subsystem are kept fixed through projection.…”

Section: Introductionmentioning

confidence: 99%

Performance of Multilevel Methods for Excited States

et al. 2022

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The performance of multilevel quantum chemical approaches, which utilize an atom-based system partitioning scheme to model various electronic excited states, is studied. The considered techniques include the mechanical-embedding (ME) of “our own N-layered integrated molecular orbital and molecular mechanics” (ONIOM) method, the point charge embedding (PCE), the electronic-embedding (EE) of ONIOM, the frozen density-embedding (FDE), the projector-based embedding (PbE), and our local domain-based correlation method. For the investigated multilevel approaches, the second-order algebraic-diagrammatic construction [ADC(2)] approach was utilized as the high-level method, which was embedded in either Hartree–Fock or a density functional environment. The XH-27 test set of Zech et al. [ 29906111 J. Chem. Theory Comput. 2018 14 4028 ] was used for the assessment, where organic dyes interact with several solvent molecules. With the selection of the chromophores as active subsystems, we conclude that the most reliable approach is local domain-based ADC(2) [L-ADC(2)], and the least robust schemes are ONIOM-ME and ONIOM-EE. The PbE, FDE, and PCE techniques often approach the accuracy of the L-ADC(2) scheme, but their precision is far behind. The results suggest that a more conservative subsystem selection algorithm or the inclusion of subsystem charge-transfers is required for the atom-based cost-efficient methods to produce high-accuracy excitation energies.

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“…Based on some criteria for associating the molecular orbitals to the active and environment subsystems, the corresponding density matrix γ is partitioned into the active subsystem A and the environment subsystem B, γ A and γ B , respectively. Originally, this was achieved by means of the occupied orbital localization and Mulliken population analysis, though alternative more robust approaches have also been developed. , In the case of the DFT-in-DFT embedded calculation, the total energy can be expressed as E DFT‐in‐DFT false[ bold-italicγ normale normalm normalb normalA ; bold-italicγ normalA , bold-italicγ normalB false] = E D F T false[ bold-italicγ normale normalm normalb normalA false] + E D F T false[ bold-italicγ normalA + bold-italicγ normalB false] − E D F T false[ bold-italicγ normalA false] + normalt normalr [ false( bold-italicγ normale normalm normalb normalA − bold-italicγ normalA false) v e m b false[ bold-italicγ normalA , bold-italicγ <...…”

mentioning

confidence: 99%

“…Originally, this was achieved by means of the occupied orbital localization and Mulliken population analysis, 19 though alternative more robust approaches have also been developed. 29,30 In the case of the DFT-in-DFT embedded calculation, the total energy can be expressed as 25 ) where E DFT denotes the DFT energy evaluated using the bracketed density matrix, emb A is the embedded subsystem A density matrix, and P B is a projection operator enforcing mutual orthogonalization, P B = Sγ B S. S denotes the atomic orbital overlap matrix. In the limit where the level shift parameter μ → ∞, the A and B orbitals are exactly orthogonal, but μ is for practical purposes taken to be 10 6 , causing negligible error.…”

mentioning

confidence: 99%

Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding

Beran

Pernal

Pavošević

et al. 2023

J. Phys. Chem. Lett.

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The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.

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Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

Cited by 15 publications

References 55 publications

Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing

Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing

Performance of Multilevel Methods for Excited States

Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding

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