Blunt Nick S, Thom Alex J W, Scott Charles J C
Department of Chemistry, Lensfield Road , Cambridge CB2 1EW , United Kingdom.
J Chem Theory Comput. 2019 Jun 11;15(6):3537-3551. doi: 10.1021/acs.jctc.9b00049. Epub 2019 May 15.
We propose the use of preconditioning in FCIQMC which, in combination with perturbative estimators, greatly increases the efficiency of the algorithm. The use of preconditioning allows a time step close to unity to be used (without time-step errors), provided that multiple spawning attempts are made per walker. We show that this approach substantially reduces statistical noise on perturbative corrections to initiator error, which improve the accuracy of FCIQMC but which can suffer from significant noise in the original scheme. Therefore, the use of preconditioning and perturbatively corrected estimators in combination leads to a significantly more efficient algorithm. In addition, a simpler approach to sampling variational and perturbative estimators in FCIQMC is presented, which also allows the variance of the energy to be calculated. These developments are investigated and applied to benzene (30e, 108o), an example where accurate treatment is not possible with the original method.
我们建议在费米子连续时间量子蒙特卡罗（FCIQMC）中使用预处理，它与微扰估计器相结合，能极大地提高算法效率。使用预处理允许使用接近1的时间步长（无时间步长误差），前提是每个游走者进行多次产生尝试。我们表明，这种方法能大幅降低对初始误差微扰校正的统计噪声，这提高了FCIQMC的精度，但在原方案中可能存在显著噪声。因此，将预处理与微扰校正估计器结合使用会得到一种效率显著更高的算法。此外，还提出了一种在FCIQMC中对变分和微扰估计器进行采样的更简单方法，这也能计算能量的方差。对这些进展进行了研究，并应用于苯（30个电子，108个轨道），这是一个用原方法无法进行精确处理的例子。
