School of Physics & Astronomy, University Park, Nottingham, UK.
Phys Chem Chem Phys. 2019 Feb 6;21(6):3347-3359. doi: 10.1039/c8cp04390f.
A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bačić et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.
一个被 C60 富勒烯笼包裹的水分子的行为几乎像一个不对称转子，就像孤立的水分子一样。然而，非弹性中子散射（INS）实验表明，水分子与其环境之间存在相互作用的证据[Goh 等人，物理化学化学物理，2014 年，16，21330]。特别是，101 转动能级的 resolved splitting 分裂为 singlet 和 doublet 表明，水分子经历的环境具有低于 C60 笼的二十面体对称性的对称性。最近的计算表明，这种分裂可以用水分子与最近邻 C60 分子的电子云之间的静电四极相互作用来解释，这导致了 S6 对称性的有效环境[Felker 等人，物理化学化学物理，2017 年，19，31274 和 Bačić 等人，法拉第讨论，2018 年，212，547-567]。我们使用对称论证得到一个简单的代数表达式，该表达式表示为平移和旋转基函数的乘积的线性组合，该表达式描述了 S6 对称性任意势对水分子的影响。我们表明，我们可以仅使用两个未知参数来再现静电相互作用模型的结果，最高可达≈12 meV。得到的势具有可以很容易地用于未来计算的形式，而无需例如使用密度泛函理论（DFT）。如果将来获得能分辨更高能级转动分裂的实验结果，调整我们势中的参数将有助于确定是否存在其他降低对称性的相互作用。作为我们模型的另一个应用，我们表明，使用我们的模型也可以再现 DFT 计算中水分子在孤立 C60 分子笼内运动时能量变化的结果，其中水分子经历二十面体对称性的环境。
