恒等二阶松原格林函数理论的随机解析

Stochastic resolution of identity second-order Matsubara Green's function theory.

作者信息

Takeshita Tyler Y, Dou Wenjie, Smith Daniel G A, de Jong Wibe A, Baer Roi, Neuhauser Daniel, Rabani Eran

机构信息

Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, USA.

Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA.

出版信息

J Chem Phys. 2019 Jul 28;151(4):044114. doi: 10.1063/1.5108840.

DOI:10.1063/1.5108840

PMID:31370516

Abstract

We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N) to O(N) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10 electrons and more.

摘要

我们开发了一种用于二阶松原格林函数（sRI - GF2）理论的恒等表示的随机分解方法。通过对库仑积分进行随机分解，GF2中的二阶玻恩自能被解耦并简化为矩阵乘积/收缩，这将计算成本从O(N)降低到了O(N)（其中N是原子轨道的数量）。当前方法可视为我们之前关于恒等表示二阶莫勒 - 普莱塞特微扰理论工作的扩展 [T. Y. Takeshita等人，《化学理论与计算杂志》13, 4605 (2017)]，并为之前的随机GF2公式 [D. Neuhauser等人，《化学理论与计算杂志》13, 5396 (2017)] 提供了一种替代方案。我们表明，对于小系统，sRI - GF2恢复了确定性GF2的结果；对于N > 80，它在计算上比确定性GF2更快，并且是描述具有10个及以上电子的系统中弱相关性的一种实用方法。