QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations
QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations
复制标题
Hartree 和交换算子在电子结构计算中的 QTT 表示
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Schneider
中科院分区：
文献类型：
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作者：
V. Khoromskaia;B. Khoromskij;R. Schneider
摘要本文利用最近的量子化-TT（QTT）格式，对Hartree-Fock方程中库仑和交换算子的张量结构数值计算进行了补充。在n×n×n大笛卡尔网格上分别离散三维Hartree势和交换势的秩结构计算中，在计算量很大的阶段导致O（log n）的复杂性。对有机分子体积的计算结果表明，这些势的QTT秩几乎与一维网格尺寸n无关。因此，矛盾的是，基于网格的库仑和交换矩阵的评估的复杂性变得几乎独立于网格的大小，仅由分子系统的结构来调节。因此，Hartree-Fock方程的网格近似允许在保证精度的情况下获得高分辨率。
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 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 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 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.