Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
J Chem Phys. 2013 Apr 28;138(16):164111. doi: 10.1063/1.4801862.
A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Green's function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 10(8) Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.
提出了一种随机方法，可直接评估分子（即准粒子能量或相关的电离能和电子亲和能）的狄森自能的二阶微扰修正，而不是将其作为两个大噪声量之间的小差异。借助拉普拉斯变换，多体格林函数理论中二阶自能的通常求和积分表达式被重写为仅四个 13 维积分的和，其中 12 维部分通过蒙特卡罗积分进行评估。通过使用 Metropolis 算法和可分析积分的 12 维权重函数，可以实现有效的重要性采样，该权重函数处处为正，并完全且精确地消除积分项中的所有奇点。通过 10(8)个蒙特卡罗步骤，以几个毫电子伏特的精度再现了小分子的准粒子能量，与正确值相差无几。甚至对于这些小分子，也证明了计算成本的大小依赖性呈线性到二次方的比例关系。
