论文标题
对周期系统中两中心高斯积分的有效评估
Efficient evaluation of two-center Gaussian integrals in periodic systems
论文作者
论文摘要
通过使用Poisson的求和公式，我们通过划分真实和相互空间之间的晶格求和来计算高斯基函数的周期积分，其中两个总和都与大指数呈指数级的汇总。我们证明可以有效地执行求和来计算各种内核上的2中心高斯积分，包括重叠，动力学和库仑。真实空间中的求和是使用McMurchie-Davidson复发关系（MDRR）的有效风味进行的。还会得出和实现在相互空间中执行求和的表达式。当使用具有大量指数的高度合同基础功能时，互惠空间求和的算法使我们能够重复使用多个术语，并导致效率的显着提高。我们发现，所得算法仅在5至15倍的范围之间慢于分子积分慢5到15倍，这表明在真实和相互空间求和中所需的术语数量很少。还提供了用于计算3中心库仑积分的算法的概述。
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large exponent. We demonstrate that the summation can be performed efficiently to calculate 2-center Gaussian integrals over various kernels including overlap, kinetic, and Coulomb. The summation in real space is performed using an efficient flavor of the McMurchie-Davidson Recurrence Relation (MDRR). The expressions for performing summation in the reciprocal space are also derived and implemented. The algorithm for reciprocal space summation allows us to reuse several terms and leads to significant improvement in efficiency when highly contracted basis functions with large exponents are used. We find that the resulting algorithm is only between a factor of 5 to 15 slower than that for molecular integrals, indicating the very small number of terms needed in both the real and reciprocal space summations. An outline of the algorithm for calculating 3-center Coulomb integrals is also provided.
