Using Wavelets to Make an Adapted Basis Set

A wavelet transformation is a special type of filter usually reserved for image processing and other applications. We show that wavelets can be used to coarse grain a low-level calculation, such as density functional theory or Hartree-Fock, for use as a basis set in a high-level method, such as density matrix renormalization group or quantum Monte Carlo, in one dimension. The goal is to adapt a basis set to a given quantum chemical system using 2-3 basis functions per electron. We compare a variety of orthogonal wavelets such as coiflets, symlets, and daubechies wavelets as well as a new type of orthogonal wavelet with dilation factor three. Extending the method to three dimensions is also considered.