Aquilante Francesco, Pedersen Thomas Bondo, Lindh Roland
Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124, S-22100 Lund, Sweden.
J Chem Phys. 2007 May 21;126(19):194106. doi: 10.1063/1.2736701.
The authors propose a new algorithm, "local K" (LK), for fast evaluation of the exchange Fock matrix in case the Cholesky decomposition of the electron repulsion integrals is used. The novelty lies in the fact that rigorous upper bounds to the contribution from each occupied orbital to the exchange Fock matrix are employed. By formulating these inequalities in terms of localized orbitals, the scaling of computing the exchange Fock matrix is reduced from quartic to quadratic with only negligible prescreening overhead and strict error control. Compared to the unscreened Cholesky algorithm, the computational saving is substantial for systems of medium and large sizes. By virtue of its general formulation, the LK algorithm can be used also within the class of methods that employ auxiliary basis set expansions for representing the electron repulsion integrals.
作者提出了一种新算法“局部K”（LK），用于在使用电子排斥积分的Cholesky分解时快速评估交换福克矩阵。其新颖之处在于采用了每个占据轨道对交换福克矩阵贡献的严格上界。通过用定域轨道来表述这些不等式，计算交换福克矩阵的标度从四次方降低到二次方，同时仅产生可忽略不计的预筛选开销并实现严格的误差控制。与未筛选的Cholesky算法相比，对于中大型系统，计算量的节省是可观的。由于其通用的表述方式，LK算法也可用于采用辅助基组展开来表示电子排斥积分的一类方法中。
