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Model Order Reduction Algorithm for Estimating the Absorption Spectrum
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DOI：10.1021/acs.jctc.7b00402.png)
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Abstract
En 中文
The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modem electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large 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 X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. 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.
Keywords:
DENSITY-FUNCTIONAL THEORY
COUPLED-CLUSTER METHOD
DIAGRAMMATIC CONSTRUCTION SCHEME
TRANSITION-METAL-COMPLEXES
SELF-CONSISTENT-FIELD
HARTREE-FOCK THEORY
POLARIZATION PROPAGATOR
EXCITATION-ENERGIES
RESPONSE THEORY
COMPUTING EIGENVALUES
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