通过在斯莱特行列式空间中进行随机动力学，全组态相互作用量子蒙特卡罗（FCIQMC）方法已经能够获得基本上没有系统误差的基组相关能的能量，在小的和系统可改进的误差条内。然而，弱指数缩放与基的大小使收敛的能量相对于基组昂贵，在较大的系统中，是不可能的。为了改善这些基组问题，我们采用微扰理论将FCIQMC波函数耦合到一个显式相关的强正交双子基上，遵循Valeev { \em et al.}的[2]_{ \textrm{R12} }方法.所需的一个和两个粒子的密度矩阵计算的飞行期间FCIQMC动态，使用的采样程序，这导致相对较少的额外的计算费用。的F12能量校正示出迅速收敛作为采样的函数，无论是在虚时间，和步行者的数量。碳二聚体的结合曲线，表现出很强的相关性效应，以及大量的基组依赖性，我们的试点计算表明，FCIQMC-F12方法的准确性超过了所有以前的FCIQMC计算，和F12校正提高精度相当于增加两个基数的单电子基础的质量。
英文摘要：
By performing a stochastic dynamic in a space of Slater determinants, the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable errorbars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wave function to an explicitly correlated strongly orthogonal basis of geminals, following the [2]_{\textrm{R12}} approach of Valeev {\em et al.}. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time, and number of walkers. Our pilot calculations on the binding curve for carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves accuracy equivalent to increasing the quality of the one-electron basis by two cardinal numbers.
Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlo
FU Berlin, Department of Mathematics and Computer Science（柏林自由大学数学与计算机科学系）；Microsoft Research AI4Science（微软研究院AI4Science）；FU Berlin, Department of Physics（柏林自由大学物理系）；Rice University, Department of Chemistry（莱斯大学化学系）
