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Error Estimates of Some Numerical Atomic Orbitals in Molecular Simulations

Part of: Partial differential equations, boundary value problems General mathematical topics and methods in quantum theory Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  03 July 2015

Huajie Chen  and
Reinhold Schneider
Huajie Chen*
Affiliation:
Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3,85747 Garching, Germany
Reinhold Schneider
Affiliation:
Institut fur Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
*
*Corresponding author. Email addresses: chenh@ma.tum.de (H. Chen), schneidr@math.tu-berlin.de (R. Schneider)
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Abstract

Numerical atomic orbitals have been successfully used in molecular simulations as a basis set, which provides a nature, physical description of the electronic states and is suitable for 𝒪(N) calculations based on the strictly localized property. This paper presents a numerical analysis for some simplified atomic orbitals, with polynomial-type and confined Hydrogen-like radial basis functions respectively. We give some a priori error estimates to understand why numerical atomic orbitals are computationally efficient in electronic structure calculations.

Keywords

Kohn-Sham density functional theorynumerical atomic orbitalsSlater-type orbitalsa priori error estimate

MSC classification

Secondary: 65N15: Error bounds 65N25: Eigenvalue problems 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 81Q05: Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 125 - 146
Copyright
Copyright © Global-Science Press 2015 

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