Model Order Reduction Algorithm for Estimating the Absorption Spectrum
Abstract
The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for mediumtolarge sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of Xray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrallymore »
 Authors:

 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of Washington, Seattle, WA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1465417
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Theory and Computation
 Additional Journal Information:
 Journal Volume: 13; Journal Issue: 10; Related Information: © 2017 American Chemical Society.; Journal ID: ISSN 15499618
 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
Van Beeumen, Roel, WilliamsYoung, David B., Kasper, Joseph M., Yang, Chao, Ng, Esmond G., and Li, Xiaosong. Model Order Reduction Algorithm for Estimating the Absorption Spectrum. United States: N. p., 2017.
Web. doi:10.1021/acs.jctc.7b00402.
Van Beeumen, Roel, WilliamsYoung, David B., Kasper, Joseph M., Yang, Chao, Ng, Esmond G., & Li, Xiaosong. Model Order Reduction Algorithm for Estimating the Absorption Spectrum. United States. doi:10.1021/acs.jctc.7b00402.
Van Beeumen, Roel, WilliamsYoung, David B., Kasper, Joseph M., Yang, Chao, Ng, Esmond G., and Li, Xiaosong. Fri .
"Model Order Reduction Algorithm for Estimating the Absorption Spectrum". United States. doi:10.1021/acs.jctc.7b00402. https://www.osti.gov/servlets/purl/1465417.
@article{osti_1465417,
title = {Model Order Reduction Algorithm for Estimating the Absorption Spectrum},
author = {Van Beeumen, Roel and WilliamsYoung, David B. and Kasper, Joseph M. and Yang, Chao and Ng, Esmond G. and Li, Xiaosong},
abstractNote = {The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for mediumtolarge sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of Xray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen Kedge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.},
doi = {10.1021/acs.jctc.7b00402},
journal = {Journal of Chemical Theory and Computation},
number = 10,
volume = 13,
place = {United States},
year = {2017},
month = {9}
}
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