Redox Potential and Crystal Chemistry of Hexanuclear Cluster Compounds

Most of TM6-cluster compounds (TM = transition metal) are soluble in polar solvents, in which the cluster units commonly remain intact, preserving the same atomic arrangement as in solids. Consequently, the redox potential is often used to characterize structural and electronic features of respective solids. Although a high lability and variety of ligands allow for tuning of redox potential and of the related spectroscopic properties in wide ranges, the mechanism of this tuning is still unclear. Crystal chemistry approach was applied for the first time to clarify this mechanism. It was shown that there are two factors affecting redox potential of a given metal couple: Lever’s electrochemical parameters of the ligands and the effective ionic charge of TM, which in cluster compounds differs effectively from the formal value due to the bond strains around TM atoms. Calculations of the effective ionic charge of TMs were performed in the framework of bond valence model, which relates the valence of a bond to its length by simple Pauling relationship. It was also shown that due to the bond strains the charge depends mainly on the atomic size of the inner ligands.

The crystal structure of Cu2GeSe3 and the structure-types of the I2-IV-VI3 family of semiconducting compounds

Almost 50 years after the initial report, the crystal structure of Cu2GeSe3, a I2-IV-VI3 semiconductor, has been revised using modern single-crystal X-ray diffraction data. The structure of this material can be properly described in the monoclinic space group Cc (No. 9) with unit-cell parameters a = 6.7703 (4) Å, b = 11.8624 (5) Å, c = 6.7705 (4) Å, β = 108.512 (6)°, V = 515.62 (5) Å3, Z = 4, rather than in the orthorhombic space group Imm2 (No. 44) with unit-cell parameters a = 11.860 (3), b = 3.960 (1), c = 5.485 (2) Å, V = 257.61 Å3, Z = 2, as originally proposed [Parthé & Garín (1971). Monatsh. Chem. 102, 1197–1208]. Contrary to what was observed in the orthorhombic structure, the distortions of the tetrahedra in the monoclinic structure are consistent with the distortions expected from considerations derived from the bond valence model. A brief revision of the structures reported for the I2-IV-VI3 family of semiconducting compounds (I: Cu, Ag; IV: Si, Ge, Sn; and VI: S, Se, Te) is also presented.

Metal–Metal Bond in the Light of Pauling’s Rules

About 70 years ago, in the framework of his theory of chemical bonding, Pauling proposed an empirical correlation between the bond valences (or effective bond orders (BOs)) and the bond lengths. Till now, this simple correlation, basic in the bond valence model (BVM), is widely used in crystal chemistry, but it was considered irrelevant for metal–metal bonds. An extensive analysis of the quantum chemistry data computed in the last years confirms very well the validity of Pauling’s correlation for both localized and delocalized interactions. This paper briefly summarizes advances in the application of the BVM for compounds with TM–TM bonds (TM = transition metal) and provides further convincing examples. In particular, the BVM model allows for very simple but precise calculations of the effective BOs of the TM–TM interactions. Based on the comparison between formal and effective BOs, we can easily describe steric and electrostatic effects. A possible influence of these effects on materials stability is discussed.

A revisit of the bond valence model makes it universal

The application of Pauling's principles to any type of chemical bond can be validated using recent quantum chemistry data (bond orders), thus making them universal.

A priori bond-valence and bond-length calculations in rock-forming minerals

Within the framework of the bond-valence model, one may write equations describing the valence-sum rule and the loop rule in terms of the constituent bond valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond valences. A priori bond valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences of the ion at each site in the structure, and the bond-topological characteristics of the structure (i.e. the ion connectivity). The a priori bond valences are calculated for selected rock-forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro-phlogopite, phlogopite, fluoro-tremolite, tremolite, albite) to finish with epidote (= 4.187 bits per atom). The effects of weak bonds (hydrogen bonds, long Na+—O2− bonds) on the calculation of a priori bond valences and bond lengths are examined. For the selected set of minerals, a priori and observed bond valences and bond lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences between the a priori and observed bond lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond lengths for the same ion-pair in different bond topologies.