Weber John L, Vuong Hung, Devlaminck Pierre A, Shee James, Lee Joonho, Reichman David R, Friesner Richard A
Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States.
Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States.
J Chem Theory Comput. 2022 Jun 14;18(6):3447-3459. doi: 10.1021/acs.jctc.2c00111. Epub 2022 May 4.
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 because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, 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 exhibit high prefactors, making their 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 ph-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 that the method is computationally favorable even for small systems. We present results demonstrating 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 the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp). Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp), agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.
无相辅助场量子蒙特卡罗（ph-AFQMC）方法近来成为一种颇具前景的方法，可用于对中大型分子进行基准水平的模拟，这得益于其准确性以及随系统规模呈现出的良好多项式缩放特性。不幸的是，标准能量评估算法的内存占用量相当可观，这会对内存有限的图形处理单元（GPU）的计算时间产生显著影响。此前利用库仑积分的低秩结构来降低缩放比例的尝试虽已取得成功，但前置因子较大，致使其应用仅限于非常大的系统。在此，我们基于局域轨道间库仑相互作用的低秩特性，提出一种互补的立方缩放途径，以减少内存和计算缩放比例，重点关注其在ph-AFQMC中的应用。我们表明，由于这种近似（我们称之为局域轨道AFQMC，即LO-AFQMC）所导致的误差是系统性的，并且可通过单个变量进行控制，而且即便对于小系统，该方法在计算上也是有利的。我们给出的结果表明，对于因基于局域轨道的方法可能存在困难而选取的各种测试案例，包括从苯到并五苯的多并苯的单重态 - 三重态能隙、一组柏拉图式烃笼的生成热以及二茂铁Fe(Cp)的总能量，该方法与实验结果以及完整的ph-AFQMC相比，都能稳健地保持准确性。最后，我们重现了之前关于Ni(Cp)气相电离能的结果，在统计误差范围内与完整的ph-AFQMC结果一致，同时使用的计算时间不到其1/15。
