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

Sambasiva Rao Chinnamsetty, Mike Espig, and Wolfgang Hackbusch

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Submission date: 05. Aug. 2013
Pages: 17
published in: Computing and visualization in science, 17 (2015) 6, p. 267-275 
DOI number (of the published article): 10.1007/s00791-016-0263-5
Bibtex
Keywords and phrases: Density matrix, Laplacian, Kinetic energy, Electronic structure calculations, Nuclear cusps, Mesh-free, Canonical tensor products
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Abstract:
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.