QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations

Venera Khoromskaia, Boris Khoromskij, Reinhold Schneider
2011 Computational Methods in Applied Mathematics  
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 quantized-TT (QTT) formats. It leads to O(log n) complexity at computationally extensive stages in the rank-structured calculation with the respective 3D Hartree and exchange potentials discretized on large n × n × n Cartesian grids. The numerical examples for some volumetric organic molecules confirm that the QTT ranks of these
more » ... tials are nearly independent of the one-dimension grid size n. Thus, paradoxically, the complexity of the grid-based evaluation of the Coulumb and exchange matrices becomes almost independent of the grid size, being regulated only by the structure of a molecular system. As a result, the grid approximation of the Hartree-Fock equation allows to gain the high resolution with a guaranteed accuracy. 2010 Mathematical subject classification: 65F30; 65F50; 65N35; 65F10.
doi:10.2478/cmam-2011-0018 fatcat:hc6iy7knobhhvapz4nrhrrdqkm