Crystal Orbital Displacement Analysis of Interactions in the Solid State. Application to the Study of Host…Guest Interactions in the Hofmann Clathrates

A crystal orbital displacement function (COD) is defined as the variation of the contribution of an atomic orbital (or atom, fragment, or fragment molecular orbital) to the density of states (DOS) on going from a sublattice to the complete crystal lattice, within the one-electron approximation of tight-binding band calculations. This simple definition allows one to abstract relevant information on weak interactions in solids, by discarding the large amount of noninteracting levels and the strong (covalent or metallic) interactions present in complex systems. The degree of charge transfer between donor and acceptor sublattices can be obtained as the integral of a COD function (ICOD) up to the Fermi level, Ω_i/(∊_F). The general shapes of the COD curves are described, and simple examples of interpretation of the COD and ICOD diagrams to well-known chemical systems are presented. Extended Hückel tight binding (EHTB) band calculations and the derived COD and ICOD curves are applied to the study of host-guest interaction in the Hofmann clathrate Ni(NH₃)₂Ni(CN)₄-2C₆H₆, and the role of the different building blocks of the host lattice in the host-guest interaction is discussed. The calculated barrier for the rotation of benzene around the molecular 6-fold axis, the predicted orientations of the guest molecules, changes in bond distances of the host and guest sublattices produced by enclathration, and variations of vibrational frequencies produced by enclathration are in agreement with a wealth of experimental data.