Optimization of numerical orbitals using the Helmholtz kernel

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Solala , E , Losilla , S A , Sundholm , D , Xu , W & Parkkinen , P 2017 , ' Optimization of numerical orbitals using the Helmholtz kernel ' , Journal of Chemical Physics , vol. 146 , no. 8 , 084102 . https://doi.org/10.1063/1.4976557

Title: Optimization of numerical orbitals using the Helmholtz kernel
Author: Solala, Eelis; Losilla, Sergio A.; Sundholm, Dage; Xu, Wenhua; Parkkinen, Pauli
Other 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
Date: 2017-02-28
Language: eng
Number of pages: 6
Belongs to series: Journal of Chemical Physics
ISSN: 0021-9606
DOI: https://doi.org/10.1063/1.4976557
URI: http://hdl.handle.net/10138/307281
Abstract: We present an integration scheme for optimizing the orbitals in numerical electronic structure calculations on general molecules. The orbital optimization is performed by integrating the Helmholtz kernel in the double bubble and cube basis, where bubbles represent the steep part of the functions in the vicinity of the nuclei, whereas the remaining cube part is expanded on an equidistant threedimensional grid. 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 kinds. The angular part of the bubble functions can be integrated analytically, whereas the radial part is integrated numerically. The cube part is integrated using a similar method as we previously implemented for numerically integrating two-electron potentials. The behavior of the integrand of the auxiliary dimension introduced by the integral transformation of the Helmholtz kernel has also been investigated. The correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations on H-2, H2O, and CO. The obtained energies are compared with reference values in the literature showing that an accuracy of 10(-4) to 10(-7) E-h can be obtained with our approach. Published by AIP Publishing.
Subject: MULTIRESOLUTION QUANTUM-CHEMISTRY
DENSITY-FUNCTIONAL THEORY
BASIS-SET CONVERGENCE
FAST MULTIPOLE METHOD
HARTREE-FOCK
MULTIWAVELET BASES
CORRELATED CALCULATIONS
EQUATION
SCHEME
POTENTIALS
116 Chemical sciences
114 Physical sciences
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