Chemical Bonding Analysis for Complex Solids in Real Space

在真实空间进行的化学键分析作为传统的基于轨道的方法的替代，是一个正在蓬勃发展的研究领域，在整个化学界得到了越来越多的欢迎。这些方法的主要优点是普适性(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中一大组离域的单电子态)和坚实的理论背景(相应的形式通常基于约化的密度矩阵)。这些方法对固体特别有利，因为固体中通常有许多离域的单电子态和非原子中心的基组，如平面波，它们很难被干净地分解为原子贡献。可能最突出的是分子中原子的量子理论(QTAIM)和电子局域函数(ELF)，但也存在其他强大的工具：其中包括电子局域性指标(ELI，使之能够连接真实空间和轨道图像)、离域指数(DI，表示电子在空间区域的局域化程度)、区域平均费米空穴轨道(DAFHO，允许恢复许多基于轨道的成键概念)以及更多。现代无机合成的实验方法为发现具有复杂结构的新型固体开辟了新的可能性，这些固体是由浓缩的混合金属团簇等复杂的构造块形成的。这些受限金属通常像自然异质结构一样在空间上组织起来，但规模较小，并具有非凡的物理性质。试探性地分析这些化合物中高度不平凡的成键模式是具有挑战性的。传统的基于轨道的方法，如能带结构分析，也很难应用，因为有大量的单电子态，特别是在含有过渡金属的化合物的情况下。使用真实空间指示剂的化学键合分析应该是适用于这种复杂系统的工具，提供与所研究系统的复杂性无关的紧凑和可视的局部键合图像表示。该项目的目标是开发一种通用而有效的方法来进行复杂固体的真实空间成键分析，并使用它们来理解受限金属类化合物中的化学键。它应该允许人们推导出结构原理，这可能有助于定制具有所需结构组织的新化合物的开发。同时，这也可以揭示直接的“晶体结构-电子结构-物理性质”的相互关系，从而为新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.