Atomic theory, varying interpretations

No attempt has been made to correlate the value of probability factor p with the structure and properties of the reacting molecules and it is also not possible to interpret the abnormally high rates that we sometimes observe. The value of p has been found to vary from unity to 10 9 when we move from simple atomic reaction to reactions involving complex molecules. There is no explanation in terms of collision theory for such a wide variation in the value of p. 

Hume-Rothery (12,13) has pointed out that in some alloys the structure of the intermetallic phases are determined by the electron concentration (E.C.). The work of Hume-Rothery and others has shown that the series of changes (i.e. a phase —> (3 phase —> 7 phase — phase), which occurs as the composition of an alloy is varied continuously, takes place at electron-atom ratios of 3/2, 21/13, and 7/4, respectively. The interpretation of these changes in terms of the Brillouin zone theory has been made by H. Jones (14) and can be understood from the A (E)-curves for typical face centered cubic (a) and body centered cubic (6) structures as... 

The choice of a single function from either set (36) or (37) does not permit such a useful physical interpretation, and may indeed lead to difficulties as the internuclear distance is varied. Thus if one chooses just the perfectly paired function from the set (36), as -R-> 00 one finds each N atom is described by a curious non-stationary state - the so-called valence state of the atom, about which there has been so much discussion in the literature.18 The choice of the set of functions (36) in which orbitals participating in a bond are directly coupled to each other is just the VB theory as proposed by Slater and Pauling,19 whereas the set (37) formed from atoms in specific L-S coupled states corresponds to the spin-valence theory employed by Heitler.20... 

Comparison with Theoretical Calculations. It appears that the polymer valence bands are (very) difficult to interpret without the aid of a theoretical basis, or a model, or of the use of a reference spectrum obtained from a model compound. Indeed, Quantum Chemical theory is nowadays able to calculate band structure and density of states for polymers, to simulate the limited resolution of the spectrometer, and to modulate these theoretical density of states to account for the photoionization cross sections that vary considerably for valence bands of polymers containing different types of atoms, and electrons with various symmetries. Consequently, one is able now to predict theoretically the energies of the various molecular orbitals, but also... 

Thus when the two energy levels coexist, the density contains a term which varies periodically with time. This term has not a frequency equal to that of either of the separate values EJh or EJh but one equal to E —E jh. Thus we obtain a link between the wave-mechanical theory of the atom and the classical theory of the field which is formally very striking, though, in the light of any statistical interpretation of the electric density, it cannot be said that the problem is entirely free from mystery. 

---