A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels

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http://hdl.handle.net/10138/307920

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Parkkinen , P , Losilla , S A , Solala , E , Toivanen , E A , Xu , W-H & Sundholm , D 2017 , ' A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels ' , Journal of Chemical Theory and Computation , vol. 13 , no. 2 , pp. 654-665 . https://doi.org/10.1021/acs.jctc.6b01207

Title: A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels
Author: Parkkinen, Pauli; Losilla, Sergio A.; Solala, Eelis; Toivanen, Elias A.; Xu, Wen-Hua; Sundholm, Dage
Contributor: University of Helsinki, Department of Chemistry
University of Helsinki, Department of Chemistry
University of Helsinki, Department of Chemistry
University of Helsinki, Department of Chemistry
University of Helsinki, Department of Chemistry
University of Helsinki, Department of Chemistry
Date: 2017-02
Language: eng
Number of pages: 12
Belongs to series: Journal of Chemical Theory and Computation
ISSN: 1549-9618
URI: http://hdl.handle.net/10138/307920
Abstract: A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H-2, H2O, and CO. Our calculations show that an accuracy of 10(-4) to 10(-7) E-h can be reached in HF-SCF calculations on general molecules.
Subject: GRAPHICAL PROCESSING UNITS
DENSITY-FUNCTIONAL THEORY
MULTIRESOLUTION QUANTUM-CHEMISTRY
ELECTRONIC-STRUCTURE CALCULATIONS
HARTREE-FOCK PROGRAM
BASIS-SET
DIATOMIC-MOLECULES
CONFIGURATION-INTERACTION
MULTIWAVELET BASES
3 DIMENSIONS
116 Chemical sciences
114 Physical sciences
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