Crystallographic Definition of Bonds

Crystallographic studies provide two grades of intemuclear distances R, between nuclei at special positions (frequently with a precision 0.005 to 0.002 A) determined by geometric coefficients times the unit cell parameters, and between two nuclei which are both (or at least one) on general positions (typically 10 times less precise). It should be noted that R values with 4 or 5 decimals 48) usually are derived from micro-wave rotational spectra, especially of gaseous diatomic molecules, giving the time average of R 2. The thermal vibrations at room temperature frequently have an amplitude of 0.05 to 0.1 A which would only be decreased by a factor around 2 or 3 at the absolute zero. 

If we plot the POO/r2 for many instances of two nuclei Zx and Z2 it is well-known that there are no very short intemuclear distances observed. There is a sharp maximum at a characteristic value r = R12. The peak is slightly asymmetric (it is much more frequent for an observed r to be 0.2 A longer than Rt2 than to be 0.2 A shorter) and its width is not much larger than the typical amplitude of thermal vibration at 

Under equal circumstances, the X-ray diffraction pattern shows an intensity proportional to ZtZ2 and by far the larger part of the intensity is due to the electrons in inner shells. It is very difficult to obtain reliable values for the density of the valence electrons 51) and even in the very favorable case of diamond (where only a-third of the electrons are in inner shells) the electron density around each C+4 core is almost exactly spherical, and certainly not four sausages connecting the closest neighbor atoms. For group-theoretical reasons, the first deviation from spherical symmetry allowed 16 has octupole symmetry (proportional to xyz) but the strength of this deformation is only a few percent of the spherically symmetric density. 

The question of valence-electron density has a specific significance 4 in the NaCl-type crystals NaF, KC1 and RbBr and the CsCl-type Csl which are known, within experimental uncertainty, to show the X-ray diffraction pattern of the corresponding types with identical atoms. However, if it comes to look for differences of about one electron between the two kinds of atoms, present-day experimentation is rather far from the goal.51) 

A special case of indeterminate N occurs4) in the cubic type (representing the common modification of Fe, Cr, Mo, W, Nb, Ta and the alkaline metals) corresponding to CsCl with identical atoms. In the three cubic binary halide types CuCl (AT = 4), NaCl (N = 6) and CsCl (N = 8) all atoms are on special positions, but 

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