Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids

Journal Article · Tue Mar 01 00:00:00 EST 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.12.012· OSTI ID:21499778

Son, Sang-Kil ^[1]

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1. Department of Chemistry, University of Kansas, Lawrence, KS 66045 (United States)

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schroedinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.

• OSTI ID: 21499778
• Journal Information: Journal of Computational Physics, Vol. 230, Issue 5; Other Information: DOI: 10.1016/j.jcp.2010.12.012; PII: S0021-9991(10)00676-5; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
COULOMB FIELD
DENSITY FUNCTIONAL METHOD
ELECTRONIC STRUCTURE
FINITE DIFFERENCE METHOD
LAPLACIAN
MATHEMATICAL MODELS
POISSON EQUATION
SCHROEDINGER EQUATION
SINGULARITY
SPHERICAL CONFIGURATION
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
CONFIGURATION
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
ITERATIVE METHODS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
VARIATIONAL METHODS
WAVE EQUATIONS