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Title: Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction

Abstract

The Green's function coupled cluster (GFCC) method is a powerful many-body tool for computing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, for the GFCC to be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its high computational overhead. In our recent studies, we demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly, for a frequency regime which requires high resolution spectral function, instead of solving GFCC linear equation of full dimension for every single frequency point, an efficiently-solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Furthermore, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linearmore » equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace and the linear system model can be systematically improved. The method is tested in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct, the obtained reduced order model may provide a high quality initial guess which improves the convergence rate for the existing iterative linear solver.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [2]; ORCiD logo [1];  [2]
+ Show Author Affiliations
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1498694
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 15; Journal Issue: 5; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Peng, Bo, Van Beeumen, Roel, Williams-Young, David B., Kowalski, Karol, and Yang, Chao. Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b00172.
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Peng, Bo, Van Beeumen, Roel, Williams-Young, David B., Kowalski, Karol, & Yang, Chao. Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction. United States. https://doi.org/10.1021/acs.jctc.9b00172
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Peng, Bo, Van Beeumen, Roel, Williams-Young, David B., Kowalski, Karol, and Yang, Chao. Fri . "Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction". United States. https://doi.org/10.1021/acs.jctc.9b00172. https://www.osti.gov/servlets/purl/1498694.
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@article{osti_1498694,
title = {Approximate Green’s Function Coupled Cluster Method Employing Effective Dimension Reduction},
author = {Peng, Bo and Van Beeumen, Roel and Williams-Young, David B. and Kowalski, Karol and Yang, Chao},
abstractNote = {The Green's function coupled cluster (GFCC) method is a powerful many-body tool for computing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, for the GFCC to be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its high computational overhead. In our recent studies, we demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly, for a frequency regime which requires high resolution spectral function, instead of solving GFCC linear equation of full dimension for every single frequency point, an efficiently-solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Furthermore, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace and the linear system model can be systematically improved. The method is tested in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct, the obtained reduced order model may provide a high quality initial guess which improves the convergence rate for the existing iterative linear solver.},
doi = {10.1021/acs.jctc.9b00172},
journal = {Journal of Chemical Theory and Computation},
number = 5,
volume = 15,
place = {United States},
year = {Fri Apr 05 00:00:00 EDT 2019},
month = {Fri Apr 05 00:00:00 EDT 2019}
}
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