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Title: Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method

Abstract

A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method. A local cluster in which electrons are fully correlated is defined, and the frozen orbital method is used on the remainder of the system to construct an effective Hamiltonian, which operates within the local cluster. Local embedding, which involves only the occupied sector, has previously been employed in the context of Co/graphene. Here, the methodology is extended in order to allow for effective downfolding of the virtual sector, thus allowing for significant reduction in the computational effort required for AFQMC calculations. The system size, which can be feasibly treated with AFQMC, is therefore greatly extended as only a single local cluster is explicitly correlated at the AFQMC level of theory. The approximation is controlled by the separate choice of the spatial size of the active occupied region (Ro) and of the active virtual region (Rv). In conclusion, the systematic dependence of the AFQMC energy on Ro and Rv is investigated, and it is found that relative AFQMC energies of physical and chemical interest converge rapidly to the full AFQMC treatment (i.e., using no embedding or downfolding).

Authors:
ORCiD logo [1];  [1];  [2]
  1. College of William and Mary, Williamsburg, VA (United States)
  2. College of William and Mary, Williamsburg, VA (United States); The Flatiron Institute, New York, NY (United States)
Publication Date:
Research Org.:
College of William and Mary, Williamsburg, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
OSTI Identifier:
1544771
Grant/Contract Number:  
SC0001303
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 15; Journal Issue: 7; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Eskridge, Brandon, Krakauer, Henry, and Zhang, Shiwei. Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.8b01244.
Eskridge, Brandon, Krakauer, Henry, & Zhang, Shiwei. Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method. United States. https://doi.org/10.1021/acs.jctc.8b01244
Eskridge, Brandon, Krakauer, Henry, and Zhang, Shiwei. Tue . "Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method". United States. https://doi.org/10.1021/acs.jctc.8b01244. https://www.osti.gov/servlets/purl/1544771.
@article{osti_1544771,
title = {Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method},
author = {Eskridge, Brandon and Krakauer, Henry and Zhang, Shiwei},
abstractNote = {A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method. A local cluster in which electrons are fully correlated is defined, and the frozen orbital method is used on the remainder of the system to construct an effective Hamiltonian, which operates within the local cluster. Local embedding, which involves only the occupied sector, has previously been employed in the context of Co/graphene. Here, the methodology is extended in order to allow for effective downfolding of the virtual sector, thus allowing for significant reduction in the computational effort required for AFQMC calculations. The system size, which can be feasibly treated with AFQMC, is therefore greatly extended as only a single local cluster is explicitly correlated at the AFQMC level of theory. The approximation is controlled by the separate choice of the spatial size of the active occupied region (Ro) and of the active virtual region (Rv). In conclusion, the systematic dependence of the AFQMC energy on Ro and Rv is investigated, and it is found that relative AFQMC energies of physical and chemical interest converge rapidly to the full AFQMC treatment (i.e., using no embedding or downfolding).},
doi = {10.1021/acs.jctc.8b01244},
journal = {Journal of Chemical Theory and Computation},
number = 7,
volume = 15,
place = {United States},
year = {Tue Jun 25 00:00:00 EDT 2019},
month = {Tue Jun 25 00:00:00 EDT 2019}
}

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Cited by: 7 works
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Figures / Tables:

Figure 1 Figure 1: Schematic representation of the local embedding and downfolding procedure. The leftmost column represents energetically ordered orthonormal core, occupied valence, and unoccupied virtual eigenstates, obtained from a lower level of theory such as HF or DFT. The occupied $ψ_o(ε)$ and virtual $ψ_v(ε)$ orbitals undergo separate unitary transformations to localizedmore » orbitals $ψ_o(R)$ and $ψ_v(R)$ as indicated in the center column of the figure; R indicates the spatial distance of the orbital from the localized cluster. Localized orbitals have been arranged so R increases downward for $ψ_o(R)$ and upward for $ψ_v(R)$. The rightmost column shows the partitioning of the Hilbert space into active $\mathbb{A}$ and inactive $\mathbb{I}$ sectors (see text). The cutoffs RRo and RRv define, respectively, the occupied and virtual orbitals that are assigned to the active sector $\mathbb{A}$. The remaining $ψ_o(R ≥ R_o)$ and core orbitals are assigned to $\mathbb{I}$ (blue box); they contribute one-body embedding contributions to the effective Hamiltonian $\hat{H}_A$. The $ψ_v(R ≥ R_o)$ are discarded.« less

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