Bloch’s rule

This relationship, known as Bloch s rule, applies in the localized-electron limit where the interatomic spin-spin interaction is described by the superexchange perturbation theory of eq. (23) with 7n J J is the Heisenberg exchange energy. Calculations by Shrivastava and... 

Jaccarino (1976) and by Smith (1969) have given a bca r n with n 2.5-3.0 for an equilibrium M-O bond length r. If U and A of eq. (23) are pressure-independent, it follows that 7 n r 10 V-3-3. If the compressibility K = — V ldV/dP remains constant, the pressure dependence of 7n should conform to Bloch s rule. Therefore, any deviation from Bloch s rule would be an indication that either the superexchange perturbation approach breaks down or the assumption that U and A are pressure-independent is not valid. 

In addition to the reinterpretation of Pauling s rules developed by Burdett and McLarnan (1984), there have been a number of other studies related to various aspects of these standard rules. Due to the substantial number of errors in classifying AB compounds in terms of ionic radius ratio (e.g., Phillips, 1970 Tossell, 1980b), there have been numerous attempts to create structure maps that have two atomic quantities as coordinates and that can provide a unique separation of the different structure types. Such atom quantities may be related primarily to size or energy or to some combination of the two. Some of the most important such approaches are those of Mooser and Pearson (1959), Phillips (1970), and Simons and Bloch (1973). 

Amorphous materials exhibit special quantum properties with respect to their electronic states. The loss of periodicity renders Bloch s theorem invalid k is no longer a good quantum number. In crystals, structural features in the reflectivity can be associated with critical points in the joint density of states. Since amorphous materials cannot be described by k-states, selection rules associated with k are no longer appropriate. Reflectivity spectra and associated spectra are often featureless, or they may correspond to highly smoothed versions of the crystalline spectra. 

Bloch therefore suggested isoprene units could be condensed first to give squalene and then cholesterol, an extension of Ruzicka s isoprene rule for the biosynthesis of linear and cyclic terpenoids. It was then necessary to show that selectively labeled 14C-acetate could get incorporated into squalene with the correct distribution of 14C and that this squalene could give rise to cholesterol, also with the appropriate position of the 14C label. 

In 1931 Hiickel published the first in a series of four papers in which he applied the new quantum mechanics to the benzene problem using for the first time the VB method for aromatic compounds. Little reference is now made to this part of Hiickel s paper. In the second part of this same paper, he applied to aromatics a method that Bloch had used for crystal lattices. In this method electrons are placed into orbitals that extend over the entire molecule instead of being localized on a single atom. These molecular orbitals may in turn be constructed as linear combinations of atomic orbitals, and such an approach is usually called the Hund—Mulliken—Huckel (HMH) or molecular orbital (MO) method. Huckel s work in this second part of the paper leads to the famous 4/7 -f 2 rule for monocyclic conjugated hydrocarbons, though we do not find it explicitly stated here. 

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