Chinnamsetty Sambasiva Rao, Espig Mike, Khoromskij Boris N, Hackbusch Wolfgang, Flad Heinz-Jürgen
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany.
J Chem Phys. 2007 Aug 28;127(8):084110. doi: 10.1063/1.2761871.
Tensor product decompositions with optimal separation rank provide an interesting alternative to traditional Gaussian-type basis functions in electronic structure calculations. We discuss various applications for a new compression algorithm, based on the Newton method, which provides for a given tensor the optimal tensor product or so-called best separable approximation for fixed Kronecker rank. In combination with a stable quadrature scheme for the Coulomb interaction, tensor product formats enable an efficient evaluation of Coulomb integrals. This is demonstrated by means of best separable approximations for the electron density and Hartree potential of small molecules, where individual components of the tensor product can be efficiently represented in a wavelet basis. We present a fairly detailed numerical analysis, which provides the basis for further improvements of this novel approach. Our results suggest a broad range of applications within density fitting schemes, which have been recently successfully applied in quantum chemistry.
具有最优分离秩的张量积分解为电子结构计算中传统的高斯型基函数提供了一种有趣的替代方法。我们讨论了一种基于牛顿法的新压缩算法的各种应用，该算法为给定张量提供了固定克罗内克秩下的最优张量积或所谓的最佳可分离近似。结合用于库仑相互作用的稳定求积方案，张量积格式能够高效地计算库仑积分。通过对小分子的电子密度和哈特里势的最佳可分离近似来证明这一点，其中张量积的各个分量可以在小波基中得到有效表示。我们进行了相当详细的数值分析，为进一步改进这种新方法提供了基础。我们的结果表明，在最近已成功应用于量子化学的密度拟合方案中有广泛的应用。
