MiS Preprint Repository

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 ( 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

Mesh-Free Canonical Tensor Products for Six-Dimensional Density Matrix: Computation of Kinetic Energy

Sambasiva Rao Chinnamsetty, Mike Espig and Wolfgang Hackbusch


The computation of a six-dimensional density matrix is the crucial step for the evaluation of kinetic energy in electronic structure calculations. For molecules with heavy nuclei, one has to consider a very refined mesh in order to deal with the nuclear cusps. This leads to high computational time and needs huge memory for the computation of the density matrix. To reduce the computational complexity and avoid discretization errors in the approximation, we use mesh-free canonical tensor products in electronic structure calculations. In this paper, we approximate the six-dimensional density matrix in an efficient way and then compute the kinetic energy. Accuracy is examined by comparing our computed kinetic energy with the exact computation of the kinetic energy.

Density matrix, Laplacian, Kinetic energy, Electronic structure calculations, Nuclear cusps, Mesh-free, Canonical tensor products

Related publications

2015 Repository Open Access
Sambasiva Rao Chinnamsetty, Mike Espig and Wolfgang Hackbusch

Mesh-free canonical tensor products for six-dimensional density matrix : computation of kinetic energy

In: Computing and visualization in science, 17 (2015) 6, pp. 267-275