Fighting the Curse of Dimensionality in First-Principles Semiclassical Calculations: Non-Local Reference States for Large Number of Dimensions

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Fighting the Curse of Dimensionality in First-Principles Semiclassical Calculations: Non-Local Reference States for Large Number of Dimensions

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Title: Fighting the Curse of Dimensionality in First-Principles Semiclassical Calculations: Non-Local Reference States for Large Number of Dimensions
Author: Ceotto, Michele; Tantardini, Gian Franco; Aspuru-Guzik, Alán

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Citation: Ceotto, Michele, Gian Franco Tantardini, and Alán Aspuru-Guzik. 2011. Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions. Journal of Chemical Physics 135(21): 214108.
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Abstract: Semiclassical methods face numerical challenges as the dimensionality of the system increases. In the general context of the theory of differential equations, this is known as the “curse of dimensionality.” In the present manuscript, we apply the recently-introduced multi-coherent states semiclassical initial value representation (MC-SC-IVR) approach to extend the applicability of first-principles semiclassical calculations. The proposed strategy involves the use of non-local coherent states with the goal of increasing accuracy in the Fourier transforms, and on the other hand, allows for the selection of peaks of different frequencies. The ability to filter desired peaks is important for analyzing the power spectra of complex systems. The MC-SC-IVR approach allows us to solve a 19-dimensional test system and to resolve on-the-fly the power spectra of the formaldehyde molecule with very few classical trajectories.
Published Version: doi:10.1063/1.3664731
Other Sources: http://www.ncbi.nlm.nih.gov/pubmed/22149780
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8438168

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  • FAS Scholarly Articles [6464]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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