扩散蒙特卡罗方法应用于水分子、二聚体和六聚体的性能评估
Assessing the Performance of the Diffusion Monte Carlo Method as Applied to the Water Monomer, Dimer, and Hexamer
摘要：
扩散蒙特卡罗（DMC）方法适用于水单体，二聚体和六聚体，使用q-TIP 4P/F，最简单的，经验的水模型与灵活的单体之一。研究了时间步长（$Δτ$）和总体大小（$N_w$）的偏倚。对于结合能，$Δτ$中的偏差几乎完全抵消，而$N_w$中的明显偏差仍然存在。然而，对于同位素位移（例如，在（H $_2$ O）$_2$和（D $_2$ O）$_2$之间的二聚体结合能中），$N_w$中的系统误差确实抵消。因此，后者的非常准确的结果（在$\sim 0.01$千卡/摩尔内）是用相对适度的数值努力（$N_w\sim 10^3$）获得的。对于水六聚体及其（D $_2$ O）$_6$同位素异构体，检查笼式和棱柱异构体的DMC结果作为$N_w$的函数。对于一个给定的异构体，步行人口泄漏出相应的吸引盆的问题是通过使用适当的几何约束。六聚体的群体大小偏差更严重，为了保持与二聚体相似的准确度，群体大小$N_w$必须增加约两个数量级。幸运的是，当采用笼和棱镜之间的能量差时，偏差消除，从而在使用$N_w=4.8\times 10^5$步行者群体时将系统误差降低到$\sim 0.01$ kcal/mol内。因此，也获得了非常准确的同位素位移结果。值得注意的是，棱镜笼能量差的量子效应和同位素效应都很小。
英文摘要：
The Diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer, using q-TIP4P/F, one of the most simple, empirical water models with flexible monomers. The bias in the time step ($Δτ$) and population size ($N_w$) is investigated. For the binding energies, the bias in $Δτ$ cancels nearly completely, while a noticeable bias in $N_w$ still remains. However, for the isotope shift, (e.g, in the dimer binding energies between (H$_2$O)$_2$ and (D$_2$O)$_2$) the systematic errors in $N_w$ do cancel. Consequently, very accurate results for the latter (within $\sim 0.01$ kcal/mol) are obtained with relatively moderate numerical effort ($N_w\sim 10^3$). For the water hexamer and its (D$_2$O)$_6$ isotopomer the DMC results as a function of $N_w$ are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and in order to maintain accuracy similar to that of the dimer, the population size $N_w$ must be increased by about two orders of magnitude. Fortunately, when the energy difference between cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within $\sim 0.01$ kcal/mol when using a population of $N_w=4.8\times 10^5$ walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and the isotope effects for the prism-cage energy difference are small.
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