Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France.
J Chem Phys. 2017 Jul 21;147(3):034101. doi: 10.1063/1.4992127.
A hybrid stochastic-deterministic approach for computing the second-order perturbative contribution E within multireference perturbation theory (MRPT) is presented. The idea at the heart of our hybrid scheme-based on a reformulation of E as a sum of elementary contributions associated with each determinant of the MR wave function-is to split E into a stochastic and a deterministic part. During the simulation, the stochastic part is gradually reduced by dynamically increasing the deterministic part until one reaches the desired accuracy. In sharp contrast with a purely stochastic Monte Carlo scheme where the error decreases indefinitely as t (where t is the computational time), the statistical error in our hybrid algorithm displays a polynomial decay ∼t with n = 3-4 in the examples considered here. If desired, the calculation can be carried on until the stochastic part entirely vanishes. In that case, the exact result is obtained with no error bar and no noticeable computational overhead compared to the fully deterministic calculation. The method is illustrated on the F and Cr molecules. Even for the largest case corresponding to the Cr molecule treated with the cc-pVQZ basis set, very accurate results are obtained for E for an active space of (28e, 176o) and a MR wave function including up to 2×10 determinants.
本文提出了一种混合随机-确定方法，用于计算多参考微扰理论（MRPT）中的二阶微扰贡献 E。我们混合方案的核心思想——将 E 重新表述为与 MR 波函数的每个行列式相关的基本贡献的和——是将 E 分为随机部分和确定部分。在模拟过程中，通过动态增加确定部分逐渐减少随机部分，直到达到所需的精度。与纯随机蒙特卡罗方案形成鲜明对比的是，在该方案中，误差随着时间 t（其中 t 是计算时间）无限减小，而在本文考虑的示例中，我们混合算法的统计误差呈多项式衰减∼t，n = 3-4。如果需要，可以继续进行计算，直到随机部分完全消失。在这种情况下，与完全确定计算相比，得到的是没有误差条且没有明显计算开销的精确结果。该方法在 F 和 Cr 分子上进行了说明。即使对于用 cc-pVQZ 基组处理的 Cr 分子的最大情况，对于包含多达 2×10 个行列式的（28e，176o）活性空间的 E，也可以得到非常精确的结果。
