Aufsatz in einer Fachzeitschrift
Wavelet approximation of correlated wave functions. I. Basics
Details zur Publikation
Autor(inn)en:  Flad, H.; Hackbusch, W.; Kolb, D.; Schneider, R.

Zeitschrift:  Journal of Chemical Physics 
Zusammenfassung, Abstract
We suggest an alternative approach to electronic structure calculations based on numerical methods from multiscale analysis. By this we are aiming to achieve a better description of the various length and energyscales inherently connected with different types of electron correlations. Taking a product ansatz for the wave function Psi=FPhi, where Phi corresponds to a given meanfield solution like HartreeFock or a linear combination of Slater determinants, we approximate the symmetric correlation factor F in terms of hyperbolic wavelets. Such kinds of wavelets are especially adapted to high dimensional problems and allow for local refinement in the region of the electronelectron cusp. The variational treatment of the ansatz leads to a generalized eigenvalue problem for the coefficients of the wavelet expansion of F. Several new numerical features arise from the calculation of the matrix elements. This includes the appearance of products of wavelets, which are not closed under multiplication. We present an approximation scheme for the accurate numerical treatment of these products. Furthermore the calculation of one and twoelectron integrals, involving the nonstandard representation of Coulomb matrix elements, is discussed in detail. No use has been made of specific analytic expressions for the wavelets, instead we employ exclusively the wavelet filter coefficients, which makes our method applicable to a wide class of different wavelet schemes. In order to illustrate the various features of the method, we present some preliminary results for the helium atom. (C) 2002 American Institute of Physics.Autor(inn)en / Herausgeber(innen)