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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
29/2009

Canonical tensor products as a generalization of Gaussian-type orbitals

Sambasiva Rao Chinnamsetty, Mike Espig, Heinz-Jürgen Flad and Wolfgang Hackbusch

Abstract

We propose a possible generalization of Gaussian-type orbital (GTO) bases by means of canonical tensor products. The present work focus on the application of tensor product as an alternative to conventional GTO based density fitting schemes. Tensor product approximation leads to highly nonlinear optimization problems which require sophisticated algorithms. We give a brief description 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 orbital products which are required for the exchange part of Hartree-Fock and in post Hartree-Fock methods. We provide a detailed error analysis for the Coulomb and exchange terms in Hartree-Fock calculations. Furthermore, a comparison is given between all-electron and pseudopotential calculations.

Received:
Jul 8, 2009
Published:
Jul 13, 2009
Keywords:
Tensor product approximation, Density-fitting method, Orbital products, Two-electron integrals, Pseudopotentials, Hartree-Fock energy

Related publications

inBook
2010 Repository Open Access
Sambasiva Rao Chinnamsetty, Mike Espig, Heinz-Jürgen Flad and Wolfgang Hackbusch

Canonical tensor products as a generalization of Gaussian-type orbitals

In: Progress in physical chemistry 3 : modern and universal first-principles methods for many-electron systems in chemistry and physics / Michael Dolg (ed.)
München : Oldenbourg-Verlag, 2010. - pp. 391-404
inJournal
2010 Repository Open Access
Sambasiva Rao Chinnamsetty, Mike Espig, Heinz-Jürgen Flad and Wolfgang Hackbusch

Canonical tensor products as a generalization of Gaussian-type orbitals

In: Zeitschrift für physikalische Chemie, 224 (2010) 3/4, pp. 681-694