We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
68/2011
Bridging the gap between quantum Monte Carlo and F12-methods
Sambasiva Rao Chinnamsetty, Hongjun Luo, Wolfgang Hackbusch, Heinz-Jürgen Flad and André Uschmajew
Abstract
Tensor product approximation of pair-correlation functions opens a new route from quantum Monte Carlo (QMC) to explicitly correlated F12 methods. Thereby one benefits from stochastic optimization techniques used in QMC to get optimal pair-correlation functions which typically recover more than 85% of the total correlation energy. Our approach incorporates, in particular, core and core-valence correlation which are poorly described by homogeneous and isotropic ansatz functions usually applied in F12 calculations. We demonstrate the performance of the tensor product approximation by applications to atoms and small molecules. It turns out that the canonical tensor format is especially suitable for the efficient computation of two- and three-electron integrals required by explicitly correlated methods. The algorithm uses a decomposition of three-electron integrals, originally introduced by Boys and Handy and further elaborated by Ten-no in his 3d numerical quadrature scheme, which enables efficient computations in the tensor format. Furthermore, our method includes the adaptive wavelet approximation of tensor components where convergence rates are given in the framework of best $N$-term approximation theory.
