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We propose a possible generalization of Gaussian-type orbital (GTO) bases by means of canonical tensor products. The presentwork focus on the application of tensor products as an alternative to conventional GTO based density fitting schemes. Tensorproduct approximation leads to highly nonlinear optimization problems which require sophisticated algorithms. We give a briefdescription of the optimization problem and algorithm. The present work extends our previous paper [S. R. Chinnamsetty, M.Espig, B. N. Khoromskij, W. Hackbusch and H.-J. Flad, J. Chem. Phys.  127  (2007), 084110], where we discussed tensor product approximations of the electron density and the Hartree potential, to orbitalproducts which are required for the exchange part of Hartree-Fock and in post Hartree-Fock methods. We provide a detailederror analysis for the Coulomb and exchange terms in Hartree-Fock calculations. Furthermore, a comparison is given betweenall-electron and pseudopotential calculations.

Canonical Tensor Products as a Generalization of Gaussian-type Orbitals