Wavelet approximation of correlated wave functions. I. Basics

Heinz-Jürgen Flad, Wolfgang Hackbusch, Dietmar Kolb, Reinhold Schneider
2002 Journal of Chemical Physics  
We suggest an alternative a p p r o a c h 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 energy-scales inherently connected with di erent t ypes of electron correlations. Taking a product ansatz for the wavefunction = F , where corresponds to a given mean-eld solution like Hartree-Fock or a linear combination of Slater determinants, we a p p r o ximate the symmetric
more » ... ion factor F in terms of hyperbolic wavelets. Such k i n d o f w avelets are especially adapted to high dimensional problems and allow for local re nement in the region of the electron-electron cusp. The variational treatment o f the ansatz leads to a generalized eigenvalue problem for the coe cients 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 two-electron integrals, involving the nonstandard representation of Coulomb matrix elements, is discussed in detail. No use has been made of speci c analytic expressions for the wavelets, instead we employ exclusively the wavelet lter coe cients, which makes our method applicable to a wide class of di erent w avelet schemes. In order to illustrate the various features of the method, we present some preliminary results for the helium atom.
doi:10.1063/1.1476008 fatcat:axyo766blbacjb5dg7wzqv3kiy