Beryllium and tungsten species can form by plasma-induced erosion of the walls of a fusion reactor. Accurate and fast evaluation of energies and geometries of Be/W/H compounds is needed for direct molecular dynamics of the plasma-wall interface or for generating training data for potential energy surfaces. Density functional calculations can serve this purpose but within the magnitude of suggested functionals no single one is the obvious choice. We investigate the performance of compact linear combinations of density functionals on some Be/W/H compounds by statistical machine learning.

Equilibrium geometries and atomization energies of the neutral molecules Be_n, Be_nH_m, W_n, W_nBe_m, and W_nH_m with m+n≤4 from 16 density functionals were compared with their counterparts from coupled cluster calculations. A statistical learning method was used to find combinations of these functionals that can accurately reproduce the results of the much more costly coupled cluster method. Linear models of two or three functionals predict the coupled cluster data quite well with an accuracy of 98.2% and 99.7%, respectively, much better than any of the functionals alone. This simple procedure is, for example, useful for the calculation of species concentrations in reaction networks of molecules close to plasma facing components in a fusion device. Accurate molecular energies are crucial for determining the species concentrations which depend exponentially on their differences.

铍和钨物质可以通过等离子体引起的聚变反应堆壁腐蚀形成。等离子体-壁界面的直接分子动力学或生成势能表面的训练数据需要对 Be/W/H 化合物的能量和几何形状进行准确和快速的评估。密度泛函计算可以达到这一目的，但在建议泛函的范围内，没有一个是显而易见的选择。我们通过统计机器学习研究了密度泛函的紧凑线性组合对某些 Be/W/H 化合物的性能。

中性分子 Be _n、Be _n H _m、W _n、W _n Be _m和 W _n H _{m 的}平衡几何形状和原子化能将来自 16 个密度泛函的 m+n≤4 与来自耦合簇计算的对应物进行比较。使用统计学习方法来寻找这些泛函的组合，可以准确地重现成本更高的耦合聚类方法的结果。两个或三个泛函的线性模型很好地预测了耦合聚类数据，准确率分别为 98.2% 和 99.7%，比单独的任何泛函都要好得多。例如，这个简单的过程对于计算聚变装置中靠近面向等离子体的组件的分子反应网络中的物质浓度很有用。准确的分子能量对于确定依赖于它们的差异呈指数关系的物种浓度至关重要。