Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method
Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method
复制标题
使用鲁棒伪谱方法与高斯基集快速交换
DOI：
10.1021/acs.jctc.2c00720
复制
发表时间：
2022
影响因子：
5.5
通讯作者：
Beylkin, Gregory
中科院分区：
文献类型：
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作者：
Sharma, Sandeep;White, Alec F.;Beylkin, Gregory
在这篇文章中，我们提出了一个算法，以有效地评估交换矩阵的周期系统时，使用的高斯基集与赝势。通常计算交换矩阵的算法是与系统规模成三次方的，因为必须进行O（N2）次快速傅立叶变换（FFT）。在这里，我们介绍了一种算法，该算法保留了立方缩放，但通过消除在每次交换构建期间进行FFT的需要来显着减少前因子。这是通过使用辅助基的线性组合来表示高斯基函数的乘积来实现的，辅助基的数量与系统的大小成线性比例。我们将由于这些辅助函数而产生的势存储在存储器中，这允许我们在不需要进行FFT的情况下获得交换矩阵，尽管以额外的存储器需求为代价。虽然使用辅助函数的基本思想并不新颖，但我们的算法由于三个成分的组合而更便宜：（a）我们使用鲁棒的伪谱方法，允许我们使用相对少量的辅助基来获得高精度：（B）我们使用occ-RI交换，这消除了构造完整交换矩阵的需要;（c）利用插值可分离密度拟合算法构造了用于稳健伪谱方法的辅助基组。由此产生的算法是准确的，我们注意到，在最终的能量的误差呈指数迅速减少的辅助功能的数量。
In this article, we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when a Gaussian basis set with pseudopotentials is used. The usual algorithm for evaluating exchange matrix scales cubically with the system size because one has to performO(N2) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matrix without the need to do FFT, albeit at the cost of additional memory requirement. Although the basic idea of using auxiliary functions is not new, our algorithm is cheaper due to a combination of three ingredients: (a) we use a robust pseudospectral method that allows us to use a relatively small number of auxiliary basis to obtain high accuracy; (b) we use occ-RI exchange, which eliminates the need to construct the full exchange matrix; and (c) we use the (interpolative separable density fitting) ISDF algorithm to construct these auxiliary basis sets that are used in the robust pseudospectral method. The resulting algorithm is accurate, and we note that the error in the final energy decreases exponentially rapidly with the number of auxiliary functions.