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

Abstract

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, S2,(e~). 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 Huckel 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. Inclusion compounds are in general formed by a host lattice with voids or tunnels in which guest molecules are enclathrated. The host-.guest interactions may vary from charge-transfer forces to weak van der Waals interactions to hydrogen bonds.' One of the best known families of inclusion compounds is that of the Hofmann clathrates and their analogues.* The prototype of this family was prepared in 1897 by Hofmann and Ki i s~e r t ,~ -~ with the formula Ni(CN)z.NH3-C6H6 (P4/m, a = 7.242 A, c = 8.277 A, 2 = 2). Generally speaking, the Hofmann clathrates correspond to the formula6v7 M(NH~)ZM'(CN)~.~G, with M = Mn, Fe, Co, Ni, Cu, Zn, or Cd; M' = Ni, Pd, or Pt, and G = benzene, pyrrole, thiophene, dioxane, aniline, or biphenyl.* A related family of clathrates is obtained by substituting M' by a metal ion with tetrahedral coordination (M' = Cd, Hg).9J0 Thegoal of thework presented here is toanalyze the host-.guest interactions at the orbital level by using extended Hfickel tight binding (EHTB) calculations. Such a study is expected to provide simple explanations for the effects of enclathration on the structural and spectroscopic parameters of the host lattice and the guest molecules. In addition, this case constitutes a rather t Universitat de Barcelona. 8 Cornell University. i Ben Gurion University of the Negev. 9 Abstract published in Advance ACS Abstracts, August 1, 1994. (1) Zubkus.V.E.:Tomau.E.E.:Belosludov.V.R.InAduancesinChemical Ph&; I. Prigogine, I., Ri&, S. A., Eds.; John Wiley & Sons: New York, (2) !wamoto, T. In Inclusion Compounds;Atwd, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: London, 1984; Vol. 1, pp 29-57. (3) Hofmann, K. A.; Kiispert, F. Z . Z . Anorg. Chem. 1897,15,204-207. (4) Hofmann, K. A.; HBchtlen, F. Chem. Ber. 1903, 36, 1149-1151. (5) Hofmann, K. A,; Arnoldi, H. Chem. Ber. 1906, 39, 339-344. (6) Iwamoto, T. Isr. J. Chem. 1979, 18, 240-245. (7) Iwamoto, T. J. Mol. Struct. 1981, 75, 51-65. (8) Iwamoto, T.; Miyoshi, T.; Sasaki, Y. Acta Crystollogr. 1974, 830, (9) Kiyoki, M.; Iwamoto, T.; Ohtsu, Y.; Takeshige-Kato, Y. Bull. Chem. (10) Kuroda, R. Inorg. Nucl. Chem. Lett. 1973,9, 13-18. 1992; Vol. 81, pp 269-359.