Maurer S A, Kussmann J, Ochsenfeld C
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany.
J Chem Phys. 2014 Aug 7;141(5):051106. doi: 10.1063/1.4891797.
We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N⁵) to O(N³) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.
我们提出了一种低前置因子、三次方缩放的反向自旋二阶莫勒-普列斯特定理微扰理论（SOS-MP2）方法，该方法非常适合图形处理单元（GPU）等大规模并行架构。通过在原子轨道基组中经由拉普拉斯变换对MP2表达式进行重新表述，并结合积分的单位分解（RI）近似以及用于三中心积分变换的高效稀疏代数，将缩放比例从O(N⁵)降低到了O(N³)。与之前在Hartree-Fock后计算中使用GPU的工作不同，我们并非简单地使用基于GPU的线性代数库来加速传统算法。相反，我们的重新表述允许用一种经过改进的J引擎算法替代速率决定的收缩步骤，该算法已被证明在GPU上具有很高的效率。因此，我们的SOS-MP2方案使我们能够在单个GPU服务器上以准确且高效的方式处理大型分子系统。
