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Data for Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression
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Habershon, Scott, Alborzpour, Jonathan and Tew, David P. (2016) Data for Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression. [Dataset]
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Official URL: http://wrap.warwick.ac.uk/82278
Abstract
Solution of the time-dependent Schro ̈dinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approx- imate the PES with a second order Taylor expansion, for example centred at each GWP. In this Article, we propose an alternative method for approximating PES ma- trix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited num- ber of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5- and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of- magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the op- portunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.
Item Type: | Dataset | ||||||
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Subjects: | Q Science > QC Physics Q Science > QD Chemistry |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Chemistry | ||||||
Type of Data: | Simulation results | ||||||
Library of Congress Subject Headings (LCSH): | Schrödinger equation, Potential energy surfaces, Gaussian processes | ||||||
Publisher: | University of Warwick, Department of Chemistry | ||||||
Official Date: | 4 October 2016 | ||||||
Dates: |
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Status: | Not Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Media of Output (format): | .pdf .txt | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
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