Metal atomic bond lengths

Changes in the charge of the central atom also strongly affect the metal-ligand bond length and the ionic-covalent share in fluoride complexes, which in turn impact the vibration spectra. Fig. 46 shows the dependence of asymmetric valence vibrations on the charge of the central atom. The spectral data for Mo, W, Zr, Hf fluoride compounds were taken from [71,115,137]. 

We can determine the amount of empty space in the simple cubic (a space-filling model is shown in Figure 7.15) structure by considering it to have an edge length l, which will be twice the radius of an atom. Therefore, the radius of the atom is 1/2, so the volume of one atom is (4/3)7r(l/2)3 = 0.52413, but the volume of the cube is P. From this we see that because the cube contains only one atom that occupies 52.4% of the volume of the cube, there is 47.6% empty space. Because of the low coordination number and the large amount of empty space, the simple cubic structure does not represent an efficient use of space and does not maximize the number of metal atoms bonded to each other. Consequently, the simple cubic structure is not a common one for metals. 

Donor atom to metal-ion bond lengths which are shorter or longer than expected as well as unusual angular relationships between such bonds have all been documented in macrocyclic complexes. Such effects can be a prime cause of the unusual properties mentioned previously. Thus the... 

Furthermore, protonation results in a significant distortion of the coordination polyhedron, i.e., the metal ion is displaced from the plane formed by the four cyano ligand carbon atoms toward the oxo along the M = 0 axis by as much as 0.34 A, which represents about 20% of the total metal-oxo bond length. In spite of this distortion stronger metal-cyano bonds are observed crystallographically, suggesting a better n back-donation by the metal center to the cyano carbons since d-ff overlap is increased. This observation is in line with both the 13C and 15N chemical shift and kinetic data (Section V) for the protonated complexes (8). 

The ground-state distortion (Table I) from the normal octahedral geometry, i.e., the displacement of the central metal atom by up to 0.34 A toward the oxo from the plane formed by the four cyano carbon atoms, is in further agreement with this reasoning, indicative of more reactive complex with an increased metal-oxygen bond length. 

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