Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
37/2011
QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations
Venera Khoromskaia, Boris N. Khoromskij and Reinhold Schneider
Abstract
In this paper, the tensor-structured numerical evaluation of the Coulomb and exchange operators in the Hartree-Fock equation is supplemented by the usage of recent quantics-TT (QTT) formats.
It leads to $O(\log n)$ complexity at computationally extensive stages in the rank-structured calculation of the respective 3D and 6D integral operators including the Newton convolving kernel, and discretized on the $n\times n\times n$ Cartesian grid. The numerical examples for some volumetric organic molecules show that the QTT ranks of the Coulomb and exchange operators are nearly independent on the one-dimension grid size $n$. Thus, paradoxically, the complexity of the grid-based evaluation of the 3D integral operators becomes almost independent on the grid size, being regulated only by the structure of a molecular system. Hence, the grid-based approximation of the Hartree-Fock equation allows to gain a guaranteed accuracy. In numerical illustrations we present the QTT approximation of the Hartree and exchange operators for some moderate size molecules.
