QTT representation of the Hartree and exchange operators in electronic structure calculations

In this paper, the tensor-structured numerical evaluation of the Coulomb and ex-change 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 ex-tensive 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 potentials 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 be-comes 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. Key words: Tensor-structured methods, QTT format, electronic structure calculations, Hartree-Fock equation, Coloumb and exchange operators