论文标题
低阶缩放$ g_0w_0 $ by poiy atomic密度拟合
Low-order Scaling $G_0W_0$ by Pair Atomic Density Fitting
论文作者
论文摘要
我们使用配对原子密度拟合（PADF）和绿色功能的假想时间表示，我们得出了一个低缩放的$ G_0W_0 $算法，并在基于Slater类型轨道（STO）基于Amsterdam的密度功能（ADF）电子结构代码中描述了其实现。我们在一系列具有高达432个原子和7776个基础函数的水簇上证明了算法的可伸缩性，并具有控制距离距离远程质量的渐近性二次缩放，以控制距离距离效果和三重$ $ $ζ$（TZ）的基集以及双极性质量。同样，由于一个很小的预制剂，这些设置的这些簇中最大的$ G_0W_0 $计算仅需240个CPU小时。在四倍体 - $ζ$级别上的GW100数据库中的Homo Energies的错误为0.24 eV，我们的实现不如使用较大的DEF2-QZVP GTO-TPYE基集的规范全电子实现。除了基集误差之外，这与使用分析延续技术的GW时空方法的众所周知的缺点以及准确代表分散型AO产品的PADF相关的数字问题有关。我们推测，通过使用优化的辅助拟合集具有具有更高角动量的更分散函数，可以克服这些困难。尽管存在这些缺点，但对于GW5000数据库中的中和大分子的子集，使用TZ和增强DZ质量的方法的误差随系统尺寸而降低。在增强的DZ水平上，我们在一组20个大的有机分子中繁殖了规范，完整的基集限制外推参考值，其精度为80 MEV。我们预计我们的算法（当前形式）将在研究大量有机系统（例如发色团和受体分子）的单粒子特性中非常有用。
We derive a low-scaling $G_0W_0$ algorithm for molecules, using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO) based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-$ζ$ (TZ) plus double polarization quality. Also owing to a very small prefactor, with these settings a $G_0W_0$ calculation for the largest of these clusters takes only 240 CPU hours. With errors of 0.24 eV for HOMO energies in the GW100 database on the quadruple-$ζ$ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-tpye basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF-approach of accurately representing diffuse AO-products. We speculate, that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented DZ quality is decreasing with system size. On the augmented DZ level we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.
