论文标题
辅助场量子蒙特卡洛的局部轨道能量评估
A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo
论文作者
论文摘要
由于其准确性和具有系统尺寸的良好的多项式缩放,因此无浮力的辅助场量子蒙特卡洛(pH-AFQMC)最近成为一种有前途的基准级别模拟,作为中等大小分子的基准级别模拟的一种有前途的方法。不幸的是,标准能量评估算法的记忆足迹是非平凡的,这可能会严重影响记忆限制的图形处理单元(GPU)的时机。先前通过利用库仑积分的低等级结构来减少缩放的尝试已经成功,但受高预发剂的限制很大,从而使该实用程序限于非常大的系统。在这里,我们提出了一条互补的,立方缩放的途径,以根据局部轨道之间的库仑相互作用的低等级来减少记忆和计算缩放,重点是应用于无量的AFQMC。我们表明,由于这种近似而引起的误差,我们将其称为局部轨道AFQMC(LO-AFQMC),是通过单个变量进行系统和可控的,即使对于小型系统也是计算上的。 We present results demonstrating a robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized orbital based methods, including the singlet-triplet gaps of polyacenes benzene through pentacene, the heats of formation for a set of platonic hydrocarbon cages, and the total energy of ferrocene (Fe(Cp)$_2$).最后,我们将Ni(CP)$ _ 2 $的气相电离能的先前结果重现,同意全pH-AFQMC在统计误差之内,同时使用了不到计算机时间的十五个。
Phaseless Auxiliary-Field Quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium to large-sized molecules, due to its accuracy and favorable polynomial scaling with system size. Unfortunately the memory footprint of standard energy evaluation algorithms are non-trivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low rank structure of the Coulombic integrals have been successful, but are significantly limited by high prefactors, rendering the utility limited to very large systems. Here, we present a complementary, cubic scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to phaseless AFQMC. We show that the error due to this approximation, which we term Localized Orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable, and is computationally favorable even for small systems. We present results demonstrating a robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized orbital based methods, including the singlet-triplet gaps of polyacenes benzene through pentacene, the heats of formation for a set of platonic hydrocarbon cages, and the total energy of ferrocene (Fe(Cp)$_2$). Finally, we reproduce our previous result of the gas phase ionization energy of Ni(Cp)$_2$, agreeing with full ph-AFQMC to within statistical error while using less than a fifteenth of the computer time.