筛选高斯基函数上两中心和三中心短程库仑积分的紧距离依赖估计
Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions
摘要：
我们推导了短程库仑势$\textrm{erfc}(ωr_{12})/r_{12}$上两中心和三中心电子排斥积分的距离依赖估计。这些估计比基于Schwarz不等式的估计更严格，可以被视为对四中心短程库仑积分和两中心和三中心完全库仑积分的距离相关估计的补充。由于短程库仑势常用于固态计算，包括HSE功能和我们最近推出的范围分离周期高斯密度拟合，我们测试我们的估计器上的周期性系统使用范围广泛的范围分离参数$ω$。这些测试表明，我们的估计，然后使用积分筛选计算周期性的三个中心的短程库仑积分与系统大小的线性缩放的鲁棒性紧密。
英文摘要：
We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $\textrm{erfc}(ωr_{12})/r_{12}$. These estimators are much tighter than one based on the Schwarz inequality and can be viewed as a complement to the distance-dependent estimators for four-center short-range Coulomb integrals and for two-center and three-center full Coulomb integrals previously reported. Because the short-range Coulomb potential is commonly used in solid-state calculations, including those with the HSE functional and with our recently introduced range-separated periodic Gaussian density fitting, we test our estimators on a diverse set of periodic systems using a wide range of the range-separation parameter $ω$. These tests demonstrate the robust tightness of our estimators, which are then used with integral screening to calculate periodic three-center short-range Coulomb integrals with linear scaling in system size.
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