Graphyne and its family are new carbon allotropes in 2D form with both sp and sp² hybridization. Recently, the graphyne with different structures have attracted great attentions from both experimental and theoretical communities, especially because the first successful synthesis of graphdiyne, which is a typical member of the graphyne family. In this review, recent theoretical progresses in the research of the graphyne family are summarized. More specifically, we systematically introduce the structural, mechanical, band, electronic transport, and thermal properties of graphyne and its family, as well as their possible applications, such as gas separation, water desalination and purification, anode material for ion battery, H₂ storage, and catalysis application. Several related theoretical methods are also reviewed. The coexistence of sp and sp² hybridization and the unique atom arrangement of the graphyne family members bring many novel properties and make them promising materials for many potential applications.

中文翻译：

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石墨烯及其家族：最新理论进展

Graphyne及其家族是具有sp和sp ²杂交的2D形式的新型碳同素异形体。最近，具有不同结构的石墨烯受到了实验界和理论界的极大关注，特别是因为首次成功合成了石墨烯家族的典型成员-石墨二炔。本文综述了石墨烯家族研究的最新理论进展。更具体地说，我们系统地介绍了石墨烯及其家族的结构，机械，能带，电子输运和热性质，以及它们的可能应用，例如气体分离，水脱盐和净化，离子电池阳极材料，H ₂储存和催化应用。还回顾了几种相关的理论方法。sp和sp ²杂交的共存和石墨烯家族成员的独特原子排列带来了许多新颖的特性，并使它们成为具有许多潜在应用前景的材料。