Department of Chemistry and Physics, Arcadia University, Glenside, Pennsylvania 19038-3295, USA.
J Chem Phys. 2012 Feb 21;136(7):074104. doi: 10.1063/1.3685453.
We identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusion Monte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)(n)]. We show that the set (DDW)(n) provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)(n) can be solved deterministically. We use the potential energy set (DDW)(n) to explore and identify methods that can enhance the diffusion Monte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ≫ 100 using just 1 × 10(6) moves in classical simulations (DDW)(n). Finally, we prove that smart darting, when incorporated into the regular or the guided diffusion Monte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusion Monte Carlo algorithm.
我们确定了一组多维势能面，其复杂程度足以导致经典平行温度抽样和引导或无引导扩散蒙特卡罗方法的收敛效率过低，无法应用于实际。该数学模型构建为解耦双阱（DDW）（n）的线性组合。我们表明，集合（DDW）（n）为旨在解决随机模拟中稀有事件抽样的新方法提供了严格的测试。与这些情况下通常使用的数值测试不同，（DDW）（n）的热力学和量子动力学可以确定性地解决。我们使用势能集（DDW）（n）来探索和确定可以增强扩散蒙特卡罗算法的方法。我们证明，使用经典模拟（DDW）（n）中的 1 × 10（6）次移动，智能飞镖方法成功降低了 n ≫ 100 的准遍历性。最后，我们证明了将智能飞镖纳入常规或引导扩散蒙特卡罗算法中，可大大提高其收敛性。该新方法有望显著扩展可通过扩散蒙特卡罗算法计算处理的系统范围。
