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Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistry

Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistry To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) basis set with a rectangular partitioning strategy was recently introduced [McClean et al, New J. Phys. 22, 093015, 2020]. We propose and numerically scrutinize a more general DG basis set construction based on a Voronoi decomposition with respect to the nuclear coordinates. This allows the construction of DG basis sets for arbitrary molecular and crystalline configurations. We here employ the planewave dual basis set as primitive basis set in the supercell model; as a set of grid-based nascent delta functions, the planewave dual functions provide sufficient flexibility for the Voronoi partitioning. The presented implementation of this DG-Voronoi approach is in Python and solely based on PySCF. We numerically investigate the performance, at the mean-field and correlated level of theory for quasi-1D, quasi-2D and fully 3D systems, and exemplify the application to crystalline systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistry

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Springer Journals
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Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
eISSN
2197-9847
DOI
10.1007/s40687-022-00365-9
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Abstract

To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the discontinuous Galerkin (DG) basis set with a rectangular partitioning strategy was recently introduced [McClean et al, New J. Phys. 22, 093015, 2020]. We propose and numerically scrutinize a more general DG basis set construction based on a Voronoi decomposition with respect to the nuclear coordinates. This allows the construction of DG basis sets for arbitrary molecular and crystalline configurations. We here employ the planewave dual basis set as primitive basis set in the supercell model; as a set of grid-based nascent delta functions, the planewave dual functions provide sufficient flexibility for the Voronoi partitioning. The presented implementation of this DG-Voronoi approach is in Python and solely based on PySCF. We numerically investigate the performance, at the mean-field and correlated level of theory for quasi-1D, quasi-2D and fully 3D systems, and exemplify the application to crystalline systems.

Journal

Research in the Mathematical Sciences – Springer Journals

Published: Dec 1, 2022

Keywords: Quantum chemistry; Electronic structure; Discontinuous Galerkin methods; Voronoi decomposition; Quantum computing

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