Interatomic surfaces often carry information related to the electron distribution in a molecule or crystal, not only being a visual aid but also enabling quantitative analyses. Under certain conditions, atomic Hirshfeld surfaces present a high resemblance to the interatomic surfaces obtained through the quantum theory of atoms in molecules (QTAIM), with the advantage of being easily calculated, even for crystal structures determined at low resolutions (i.e. when a charge-density refinement is not performed). Here an empirical relation between the curvedness property of the Hirshfeld surfaces and the electron density at the bond critical point for certain types of covalent and coordination interactions involving carbon atoms has been obtained. The exponential function was tested to estimate the electron density in different crystalline systems, and the highest deviation from reference values obtained through QTAIM was just 16%. Additionally, fine details of this fit may be salient to the difference in electronegativity of the atoms involved in the bond.

中文翻译：

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通过原子 Hirshfeld 表面估计键临界点处的电子密度

原子间表面通常携带与分子或晶体中的电子分布相关的信息，这不仅是一种视觉辅助，而且可以进行定量分析。在某些条件下，原子 Hirshfeld 表面与通过分子中原子的量子理论 (QTAIM) 获得的原子间表面高度相似，具有易于计算的优点，即使对于在低分辨率下确定的晶体结构（即当不进行电荷密度细化时）。这里已经获得了 Hirshfeld 表面的弯曲特性与某些类型的涉及碳原子的共价和配位相互作用的键临界点处的电子密度之间的经验关系。测试指数函数以估计不同晶体系统中的电子密度，通过 QTAIM 获得的参考值的最高偏差仅为 16%。此外，这种拟合的细节可能对参与键的原子的电负性差异很重要。