The Fourier transform Coulomb method:: Efficient and accurate calculation of the Coulomb operator in a Gaussian basis
The Fourier transform Coulomb method:: Efficient and accurate calculation of the Coulomb operator in a Gaussian basis
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DOI：
10.1063/1.1510121
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发表时间：
2002-11-01
影响因子：
4.4
通讯作者：
Pulay, P
中科院分区：
文献类型：
--
作者：
Füsti-Molnár, L;Pulay, P
我们描述了一种方法，用于计算高斯基组的库仑算子的矩阵元素，使用中间离散傅立叶变换的密度。我们的目标是相同的高斯和增广平面波方法的Parrinello和同事[M。Krack和M. Parrinello，Phys.Chem.Chem.Phys.2，2105（2000）]，但是我们的技术完全不同。特别是，我们的目标是更高的数值精度比典型的程序使用平面波展开。我们的方法是免费的周期性图像的影响，并产生充分的精度。其他低尺度的库仑算子的方法相比，傅立叶变换方法的数值精度，渐近缩放与分子大小，渐近缩放与基组大小，起始点（计算的大小，该方法优于传统的高斯积分技术的一个因素2），并能够计算哈特里-福克交换算子。傅立叶变换法上级大多数标准的替代品。特别是，对于典型的分子应用，它具有比快速多极方法更早的起始点。(C)2002年美国物理学会。
We describe a method for calculating the matrix elements of the Coulomb operator for Gaussian basis sets using an intermediate discrete Fourier transform of the density. Our goals are the same as those of the Gaussian and augmented-plane-wave method of Parrinello and co-workers [M. Krack and M. Parrinello, Phys. Chem. Chem. Phys. 2, 2105 (2000)], but our techniques are quite different. In particular, we aim at much higher numerical accuracy than typical programs using plane wave expansions. Our method is free of the effects of periodic images and yields full precision. Other low-scaling methods for the Coulomb operator are compared to the Fourier transform method with regard to numerical precision, asymptotic scaling with molecular size, asymptotic scaling with basis set size, onset point (the size of the calculation where the method outperforms traditional Gaussian integral techniques by a factor of 2), and the ability to calculate the Hartree-Fock exchange operator. The Fourier transform method is superior to alternatives by most criteria. In particular, for typical molecular applications it has an earlier onset point than fast multipole methods. (C) 2002 American Institute of Physics.