On understanding the chemical origin of band gaps

Conceptual DFT and quantum chemical topology provide two different approaches based on the electron density to grasp chemical concepts. We present a model merging both approaches, in order to obtain physical properties from chemically meaningful fragments (bonds, lone pairs) in the solid. One way to do so is to use an energetic model that includes chemical quantities explicitly, so that the properties provided by conceptual DFT are directly related to the inherent organization of electrons within the regions provided by topological analysis. An example of such energy model is the bond charge model (BCM) by Parr and collaborators. Bonds within an ELF-BCM coupled approach present very stable chemical features, with a bond length of ca. 1 Å and 2[Formula: see text]. Whereas the 2[Formula: see text] corroborate classical views of chemical bonding, the fact that bonds always expand along 1 Å introduces the concept of geometrical transferability and enables estimating crystalline cell parameters. Moreover, combining these results with conceptual DFT enables deriving a model for the band gap where the chemical hardness of a solid is given by the bond properties, charge, length, and a Madelung factor, where the latter plays the major role. In short, the fundamental gap of zinc-blende solids can be understood as given by a 2[Formula: see text] bond particle asymmetrically located on a 1 Å length box and electrostatically interacting with other bonds and with a core matrix. This description is able to provide semi-quantitative insight into the band gap of zinc-blende semiconductors and insulators on equal footing, as well as a relationship between band gap and compressibility. In other words, merging these different approaches to bonding enables to connect measurable macroscopic behavior with microscopic electronic structure properties and to obtain microscopic insight into the chemical origin of band gaps, whose prediction is still nowadays a difficult task. Graphical Abstract Conceptual DFT couples to quatum chemcial topology to explain the band gap of zinc-blende solids.