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Hyperbolic wavelet discretization of the two-electronSchrödinger equation in an explicitly correlated formulation

Published online by Cambridge University Press:  30 March 2012

Markus Bachmayr
Markus Bachmayr*
Affiliation:
RWTH Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, 52056 Aachen, Germany. e-mail: bachmayr@igpm.rwth-aachen.de
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Abstract

In the framework of an explicitly correlated formulation of the electronic Schrödingerequation known as the transcorrelated method, this work addresses some fundamental issuesconcerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases.Focusing on the two-electron case, the integrability of mixed weak derivatives ofeigenfunctions of the modified problem and the improvement compared to the standardformulation are discussed. Elements of a discretization of the eigenvalue problem based onorthogonal wavelets are described, and possible choices of tensor product bases arecompared especially from an algorithmic point of view. The use of separable approximationsof potential terms for applying operators efficiently is studied in detail, and estimatesfor the error due to this further approximation are given.

Keywords

Schrödinger equationmixed regularitytranscorrelated methodwaveletsseparable approximation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1337 - 1362
Copyright
© EDP Sciences, SMAI, 2012

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