Department of Chemistry, Graduate School of Science, Tohoku University, Sendai, Miyagi 980-8578, Japan.
National Institutes for Quantum and Radiological Science and Technology, Kidzugawa, Kyoto 619-0215, Japan.
J Chem Inf Model. 2020 Mar 23;60(3):1376-1389. doi: 10.1021/acs.jcim.9b01063. Epub 2020 Mar 4.
Two types of implementation of the Hartree-Fock (HF) exchange energy were developed with the real-space grid approach for the purpose of achieving high efficiency in the parallel execution of the hybrid exchange functional in the density functional theory. First, a parallel implementation of the three-dimensional fast Fourier transform (FFT), referred to as PFFT, was adapted to solve the Poisson equations for the electrostatic potentials of the densities of the orbital pairs. In the other approach, the Poisson equations were solved iteratively through the conjugate gradient (CG) procedures where the operation of Laplacian was parallelized by the domain decomposition scheme. Comparison of the parallel performances for the exchange energy calculation was made between these two approaches, and it was revealed that the calculation with the FFT method is faster than that with CG. The method with FFT is more advantageous than CG because a larger bandwidth can be made available in the collective message passing interface communication associated with the parallel execution of FFT. We also implemented the projection operator to circumvent the laborious calculation of the exchange energy at every self-consistent field step, which made a significant contribution to expedite the convergence. To assess the accuracy of our implementation, the association energies of a hydrated ion were computed, which showed excellent agreement with those given by the Gaussian 09 program employing sophisticated basis sets.
为了在密度泛函理论中实现混合交换泛函的并行执行的高效率，开发了两种 Hartree-Fock（HF）交换能的实空间网格方法的实现。首先，适应了三维快速傅里叶变换（FFT）的并行实现，称为 PFFT，以解决轨道对密度的静电势的泊松方程。在另一种方法中，通过共轭梯度（CG）程序迭代求解泊松方程，其中拉普拉斯算子通过域分解方案并行化。比较了这两种方法的交换能计算的并行性能，结果表明 FFT 方法的计算速度比 CG 方法快。FFT 方法比 CG 更有利，因为在与 FFT 并行执行相关的集体消息传递接口通信中，可以提供更大的带宽。我们还实现了投影算子，以避免在每个自洽场步骤中繁琐的交换能计算，这对加快收敛速度有很大贡献。为了评估我们的实现的准确性，计算了水合离子的缔合能，与使用复杂基组的 Gaussian 09 程序给出的结果非常吻合。
