标题： 如何量化固体的能量景观 显示英文标题

标题： How to quantify energy landscapes of solids

摘要： 我们探讨化学系统中能量景观的拓扑结构是否遵循某些规则以及这些规则是什么。 为了解答这个问题及相关问题，我们使用了多种工具：(i) 降低的能量表面及其状态密度，(ii) 一种称为指纹函数的结构描述符，它可以表示为一维函数或抽象多维空间中的向量，(iii) 定义两个结构之间的“距离”，从而实现对能量景观的量化，(iv) 定义结构的有序度，(v) 定义准熵以量化结构多样性。 我们的方法可用于合理化大量晶体结构数据库，并调整结构预测的计算算法。 它能够对能量景观进行定量和直观的表示，并重新评估一些传统的化学概念和规则。 我们的分析证实了预期，即低能极小值聚集在配置空间的紧凑区域（“漏斗”）中，并且化学系统往往只有很少的漏斗，有时只有一个。 该分析可以应用于固体的物理性质，开辟了发现结构-性质关系的新途径。 我们定量地证明了晶体倾向于采用与其化学性质一致的几种最简单结构之一，为鲍林的第五条规则提供了热力学依据。 显示英文摘要

摘要： We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii) descriptor of structure called fingerprint function, which can be represented as a one-dimensional function or a vector in abstract multidimensional space, (iii) definition of a ''distance'' between two structures enabling quantification of energy landscapes, (iv) definition of a degree of order of a structure, and (v) definitions of the quasi-entropy quantifying structural diversity. Our approach can be used for rationalizing large databases of crystal structures and for tuning computational algorithms for structure prediction. It enables quantitative and intuitive representations of energy landscapes and reappraisal of some of the traditional chemical notions and rules. Our analysis confirms the expectations that low-energy minima are clustered in compact regions of configuration space ("funnels") and that chemical systems tend to have very few funnels, sometimes only one. This analysis can be applied to the physical properties of solids, opening new ways of discovering structure-property relations. We quantitatively demonstrate that crystals tend to adopt one of the few simplest structures consistent with their chemistry, providing a thermodynamic justification of Pauling's fifth rule.