The Anomalous Manganese Radius

The selenium-selenium and tellurium-tellurium distances observed in the manganese compounds provide further evidence for this structural interpretation. They correspond to radii that agree more satisfactorily with the normal-valence radii than with the tetrahedral radii of the nonmetallic atoms, indicating that the atoms are not forming tetrahedral covalent bonds  

Some years ago, in the course of a discussion of interatomic distances in metals, an equation for interatomic distances of fractional bonds, bonds with bond number less than 1, was proposed.55 This equation is 

Here D(n) is the bond length for bond number n (less than 1) and d( 1) is the bond length for a single bond of similar type (using similar bond orbitals). 

The equation wras formulated in the following way. In Section 7-6 it was pointed out that the dependence of bond length on bond order n9 over the range n9 = 1, 2, 3 is D(n9) D(l) — 0.71 log n. This equation might be used also for values of nf less than 1 for example, for a bond with bond order it makes the bond length 0.21 A greater than it is for a single bond. 

The relation between n9 and n as discussed in Section 7-6, is such that a bond with a given bond number n is expected to be shorter than 

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Conclusion. There is no need to multiply examples of the type considered, especially since our knowledge of the principles determining the structures of covalent crystals is still so incomplete that we can offer no explanation for the anomalous manganese radius indeed, even the observed arrangement1) of the bonds formed by sulfur in sulvanite, Om3FS4, was entirely unexpected and has been given only an ad hoc explanation. 

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