An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood's superposition approximation. Detailed considerations of the peaks' shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system's dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids' dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid's structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

中文翻译：

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三重相关函数研究液态和玻璃态简谐排斥系统的结构

对液体结构的有效描述，特别是液体在过冷时发生的结构变化仍然是一个挑战。在这种情况下，由软粒子组成的系统特别有趣，因为它们经常展示不允许引入最近邻壳概念的非平凡局部顺序。出于这个原因，为原子液体的结构分析而开发的一些方法的使用对于软粒子系统是有问题的。在这里，我们报告了我们使用三重相关函数 (TCF) 对 3D 简谐排斥液体结构的研究，即不依赖最近邻概念的方法。液体被认为处于减压状态（P = 1。8) 在冷却时它表现出显着的抗结晶稳定性。已经证明，TCF 允许解决结构中取向相关性的发展，而这些结构不允许从键取向有序参数的研究中得出明确的结论。我们的结果表明，如果通过 TCF 中峰的高度来衡量，取向相关性在冷却时显着增加。Kirkwood 的叠加近似没有正确捕捉到这种定向排序的上升。对 TCF 中峰形状的详细考虑表明，在定向排序和系统动力学减慢之间存在联系。我们的研究结果支持这样的观点，即液体中取向相关性的发展可能在液体动力学中发挥重要作用，并且对分布函数的考虑可能不足以直观地理解液体在过冷时发生的所有结构变化. 总的来说，我们的结果表明，TCF 的考虑对于讨论液体对密度函数之外的结构以及解释使用键取向有序参数获得的结果是有用的。