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Program synthesis of sparse algorithms for wave function and energy prediction in grid-based quantum simulations
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Habershon, Scott (2022) Program synthesis of sparse algorithms for wave function and energy prediction in grid-based quantum simulations. Journal of Chemical Theory and Computation, 18 (4). pp. 2462-2478. doi:10.1021/acs.jctc.2c00035 ISSN 1549-9618.
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Official URL: http://dx.doi.org/10.1021/acs.jctc.2c00035
Abstract
We have recently shown how program synthesis (PS), or the concept of “self-writing code”, can generate novel algorithms that solve the vibrational Schrödinger equation, providing approximations to the allowed wave functions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wave function ψ(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this Article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wave functions and energy eigenvalues of representative model PESs (both 1-D and multidimensional). We show that PS can generate algorithms that offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods that exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multidimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order of magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wave function propagation and evaluation of molecular electronic structure.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QD Chemistry |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Chemistry Faculty of Science, Engineering and Medicine > Science > Chemistry > Computational and Theoretical Chemistry Centre |
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Library of Congress Subject Headings (LCSH): | Wave functions , Potential energy surfaces , Quantum chemistry, Hamiltonian systems , Automatic programming (Computer science), Neural networks (Computer science) | ||||||||
Journal or Publication Title: | Journal of Chemical Theory and Computation | ||||||||
Publisher: | American Chemical Society | ||||||||
ISSN: | 1549-9618 | ||||||||
Official Date: | 12 April 2022 | ||||||||
Dates: |
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Volume: | 18 | ||||||||
Number: | 4 | ||||||||
Page Range: | pp. 2462-2478 | ||||||||
DOI: | 10.1021/acs.jctc.2c00035 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 5 May 2022 | ||||||||
Date of first compliant Open Access: | 5 May 2022 | ||||||||
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