Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators
Distance-including rigorous upper bounds and tight estimates for two-electron integrals over long- and short-range operators
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DOI：
10.1063/1.4994190
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发表时间：
2017-10-14
影响因子：
4.4
通讯作者：
Ochsenfeld, Christian
中科院分区：
文献类型：
--
作者：
Thompson, Travis H.;Ochsenfeld, Christian
我们引入了由包含距离的schwarz型不等式导出的四中心双电子积分的严格和非严格距离依赖积分估计。这些估计甚至比我们迄今为止最有效的距离依赖估计更容易实现。A. Maurer et al.， J. Chem。物理学报，136,144107(2012)]，此外，不需要分离良好的电荷分布。它们也适用于大范围的双电子算符，如在显式相关理论和短程杂化密度泛函中发现的那些。对于具有指数距离衰减的两个这样的算子[e（-r12）和erfc(0.11)]。r(12))/r(12)]，严格界比标准Schwarz估计要严格得多，几乎没有误差惩罚。非严格估计给出的结果非常接近于对这些操作符和远程1/r（12）操作符的精确筛选，其误差通过积分筛选阈值完全可控。此外，我们提出了一种非严格边界的替代形式，特别适合于改进PreLinK方法[J]。库斯曼和C. Ochsenfeld， J. Chem。物理学报，138,134114(2013)]。AIP出版社出版。
We introduce both rigorous and non-rigorous distance-dependent integral estimates for four-center two-electron integrals derived from a distance-including Schwarz-type inequality. The estimates are even easier to implement than our so far most efficient distance-dependent estimates [S. A. Maurer et al., J. Chem. Phys. 136, 144107 (2012)] and, in addition, do not require well-separated chargedistributions. They are also applicable to a wide range of two-electron operators such as those found in explicitly correlated theories and in short-range hybrid density functionals. For two such operators with exponential distance decay [e(-r12) and erfc(0.11 . r(12))/r(12)], the rigorous bound is shown to be much tighter than the standard Schwarz estimate with virtually no error penalty. The non-rigorous estimate gives results very close to an exact screening for these operators and for the long-range 1/r(12) operator, with errors that are completely controllable through the integral screening threshold. In addition, we present an alternative form of our non-rigorous bound that is particularly well-suited for improving the PreLinK method [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] in the context of short-range exchange calculations. Published by AIP Publishing.