Lambrecht Daniel S, Ochsenfeld Christian
Institut für Physikalische und Theoretische Chemie, Auf der Morgenstelle 8, Universität Tübingen, D-72076 Tübingen, Germany.
J Chem Phys. 2005 Nov 8;123(18):184101. doi: 10.1063/1.2079967.
We derive multipole-based integral estimates (MBIE) as rigorous and tight upper bounds to four-center two-electron integrals in order to account for the 1/R distance decay between the charge distributions, which is missing in the Schwarz screening commonly used in ab initio methods. Our screening criteria are valid for all angular momenta and can be formulated for any order of multipoles. We have found the expansion limited to dipoles to be sufficiently tight for estimating the integrals in Hartree-Fock and density-functional theories, while the screening effort is negligible. For, e.g., a DNA fragment with 1052 atoms and 10,674 basis functions (6-31G*) the exchange part is faster by a factor of 2.1 as compared to the Schwarz screening both within our linear exchange scheme, whereas a smaller factor of 1.3 is gained for the Coulomb part within the continuous fast multipole method. Most importantly, our new MBIE screening is perfectly suited to exploit the strong distance decay of electron-correlation effects of at least 1/R4 in atomic-orbital-based formulations of correlation methods.
我们推导了基于多极矩的积分估计（MBIE），作为四中心双电子积分的严格且紧密的上限，以考虑电荷分布之间的1/R距离衰减，这是从头算方法中常用的施瓦茨屏蔽所缺失的。我们的屏蔽标准对所有角动量均有效，并且可以针对任何多极矩阶数进行表述。我们发现，对于估计哈特里-福克和密度泛函理论中的积分而言，限于偶极矩的展开已经足够紧密，而屏蔽工作量可以忽略不计。例如，对于一个具有1052个原子和10674个基函数（6-31G*）的DNA片段，在我们的线性交换方案中，与施瓦茨屏蔽相比，交换部分的速度快2.1倍，而在连续快速多极矩方法中，库仑部分的速度提升因子为1.3。最重要的是，我们新的MBIE屏蔽非常适合利用基于原子轨道的相关方法中电子相关效应至少1/R4的强距离衰减。
