Chemical Bonding Analysis for Complex Solids in Real Space

在真实空间中进行的化学键分析作为传统的基于轨道的方法的替代，是一个积极发展的研究领域，在整个化学学界越来越受到欢迎。这些方法的主要优点是通用性（可以同样很好地应用于任何计算方法的结果），应用简单（分析不直接基于整个系统的一组大的离域单电子态）和坚实的理论背景（相应的形式通常基于约化密度矩阵）。这些方法对固体特别有用，因为固体通常有很多离域的单电子态和像平面波这样的非原子中心基集，很难清晰地分解成原子的贡献。最突出的可能是分子中原子的量子理论（QTAIM）和电子定位函数（ELF），但也存在其他强大的工具：其中包括电子定位指标（ELI，使连接实空间和轨道图像成为可能），离域指数（DI，表示电子在空间区域的定位程度），域平均费米空穴轨道（DAFHO，允许恢复许多基于轨道的键合概念）等等。无机合成的现代实验方法为发现具有复杂结构的新型固体提供了新的可能性，这些结构是由复杂的构建块（如冷凝混合金属团簇）形成的。这些受限金属在空间上通常像自然异质结构一样组织，但在较小的尺度上具有非凡的物理性质。对这些化合物中高度不平凡的键模式的初步分析是具有挑战性的。传统的基于轨道的方法，如带结构分析，也很难应用，因为大量的单电子态，特别是对于含有过渡金属的化合物。使用实空间指标的化学键分析应该是这种复杂系统的合适工具，它提供了独立于所研究系统复杂性的键合图像的紧凑和可视化的局部表示。该项目的目标是开发一种通用和有效的方法来分析复杂固体的实际空间键合，并利用它们来理解限制金属类化合物中的化学键合。它应该允许人们推导出结构原理，这可能有助于量身定制具有所需结构组织的新化合物的开发。同时，这也可以直接揭示“晶体结构-电子结构-物理性质”的相互关系，从而为新型材料的设计开辟道路。

The analysis of chemical bonding performed in real space as an alternative to the traditional orbital-based methods is an actively developing field of research, gaining more and more popularity in the whole chemical community. The main advantages of these methods are universality (can be equally well applied to the results of any calculation method), simplicity of applications (analysis is not directly based on a large set of one-electron states delocalized over the whole system) and firm theoretical background (corresponding formalism is usually based on reduced density matrices). These methods are especially beneficial for solids, where one usually has lots of delocalized one-electron states and non-atom-centered basis sets like the planewaves, which are difficult to cleanly decompose into atomic contributions. Probably the most prominent are the quantum theory of atoms in molecules (QTAIM) and the electron localization function (ELF) but other powerful tools also exist: among them are electron localizability indicators (ELI, making it possible to connect both real-space and orbital pictures), delocalization indices (DI, expressing the degree of electron localization in space region), domain-averaged Fermi hole orbitals (DAFHO, allowing to recover many orbital-based bonding concepts) and many more. Modern experimental methods of inorganic synthesis open new possibilities on discovering novel solids with complex structures formed itself by complex building blocks such as condensed mixed metal clusters. These confined metals are spatially often organized like natural heterostructures, but on the smaller scale and possess extraordinary physical properties. Tentative analysis of the highly nontrivial bonding patterns within these compounds is challenging. Traditional orbital-based methods like bandstructure analysis can also hardly be applied because of the large number of one-electron states especially in case of compounds containing transition metals. Chemical bonding analysis using real-space indicators should be a suitable tool for such complex systems providing compact and visual local representation of bonding pictures independently on the complexity of the system studied. It is the objective of the project to develop an universal and efficient approach to the real-space bonding analysis of complex solids and to use them to understand the chemical bonding in the confined metals class of compounds. It should allow one to derive the principles of construction, that may help to tailor the development of new compounds with desired structural organization. In the same time, this may also allow to reveal direct "crystal structure - electronic structure - physical properties" interrelations and thus open the way to the design of novel materials.