In this contribution we introduce an electronic-structure-theory-based approach to a quantum-chemical thermochemistry of solids. We first deal with local and collective atomic displacements and explain how to calculate these. The fundamental importance of the phonons, their dispersion relations, their experimental determination as well as their calculation is elucidated, followed by the systematic construction of the thermodynamic potentials on this basis. Subsequently, we provide an introduction for practical computation as well as a critical analysis of the level of accuracy obtainable. We then show how different solid-state chemistry problems can be solved using this approach. Among these are the calculation of activation energies in perovskite-like oxides, but we also consider the use of theoretical vibrational frequencies for determining crystal structures. The pressure and temperature polymorphism of elemental tin which has often been classically described is also treated, and we energetically classify the metastable oxynitrides of tantalum. We also demonstrate, using the case of high-temperature superconductors, that such calculations may be used for an independent evaluation of thermochemical data of unsatisfactory accuracy. Finally, we show the present limits and the future challenges of the theory.

The stabilities and electronic structures of several polymorphs of tantalum oxynitride, TaON, were studied quantum-chemically at density-functional level. Results obtained by complementary quantum-chemical techniques with wave-functions either expanded in atom-centered functions or in plane waves were compared. Close agreement was obtained for the relative stabilities of the baddeleyite, anatase, rutile, and fluorite phases of TaON. The effect 1157 of anion distribution on the structural parameters and the lattice energies of the anatase and rutile polymorphs was investigated. The calculated band structure of the polymorphs is compared with available experimental information.

We have performed electronic structure calculations from first principles (LDA & GGA, plane waves & muffin‐tin orbitals, pseudopotentials & all‐electron techniques) on the two reported polymorphs of TaON. For the experimentally well‐characterized β‐TaON adopting the baddeleyite structure type, there is excellent agreement between all accessible observables despite the supposedly correlated character of an oxynitride phase. Concerning hexagonal α‐TaON proposed first in 1966, one finds tremendous contradictions between theory and experimentally reported data (molar volume, total energy differences, electronic transport etc.) In combination with the communicated X‐ray diffraction diagram, α‐TaON is considered an erroneous entry in the solid‐state chemical literature that needs to be removed from the crystallographic databases.

Mistaken identity: The high‐pressure synthesis of PtN in the zinc blende structure type is refuted on the basis of first‐principles electronic‐structure calculations, which demonstrate that this low‐density phase is energetically unstable and cannot be produced at high pressure. The denser cooperite structure type is preferable for PtN (see picture; NPt4 tetrahedra are yellow).