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

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

Received: 18 June 2010
Revised: 9 May 2011

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.