Orbital-based bonding analysis in solids.

As of today, there is certainly no doubt about the quantum character of the atomistic world, most straightforwardly calculated by using wave mechanics and Schrödinger's fundamental equation from 1926. Even though one century has passed, the paramount importance of the wave function, which determines everything down to the last detail, remains unchanged, and the wave function is most conveniently approximated by a combination of orbitals, one-electron wave functions for atoms, molecules, and also solids. And it is precisely this "orbital basis" that serves as a gateway to understanding the very interactions that cause atoms to condense into solids, just like for molecules. The analysis of quantum-chemical interactions and the nature of the chemical bonding between atoms in solids by use of orbitals will be our topic in this perspective, starting with the glorious past, going over to the current practice and, of course, the magnificent prospects for the future. As electronic structures for periodic solids are most often calculated using plane waves (instead of orbitals), for simple reasons of translational symmetry and Bloch's fundamental theorem, a unitary transformation to atomic or molecular orbitals is needed for final inspection, technically solved by the LOBSTER quantum-chemistry package. LOBSTER allows for the calculation of wave function-based atomic charges, various population analyses and periodic bonding indicators, first-principles bond orders, two- and multi-centre bonding analysis, fragment-molecular analysis, and a lot more. All those techniques are illustrated from three solid-state systems deriving from carbonate chemistry.