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

Markus Bachmayr

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1337-1362
  • ISSN: 0764-583X

Abstract

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

How to cite

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Bachmayr, Markus. "Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1337-1362. <http://eudml.org/doc/277843>.

@article{Bachmayr2012,
abstract = {In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue problem based on orthogonal wavelets are described, and possible choices of tensor product bases are compared especially from an algorithmic point of view. The use of separable approximations of potential terms for applying operators efficiently is studied in detail, and estimates for the error due to this further approximation are given.},
author = {Bachmayr, Markus},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Schrödinger equation; mixed regularity; transcorrelated method; wavelets; separable approximation; error estimate; molecular system; Galerkin method; eigenvalue problem},
language = {eng},
month = {3},
number = {6},
pages = {1337-1362},
publisher = {EDP Sciences},
title = {Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation},
url = {http://eudml.org/doc/277843},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Bachmayr, Markus
TI - Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/3//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1337
EP - 1362
AB - In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue problem based on orthogonal wavelets are described, and possible choices of tensor product bases are compared especially from an algorithmic point of view. The use of separable approximations of potential terms for applying operators efficiently is studied in detail, and estimates for the error due to this further approximation are given.
LA - eng
KW - Schrödinger equation; mixed regularity; transcorrelated method; wavelets; separable approximation; error estimate; molecular system; Galerkin method; eigenvalue problem
UR - http://eudml.org/doc/277843
ER -

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