Multiple quantum statistical effects

Another defect of the cell model that we have already mentioned is the neglect of correlations. This appears very clearly in the limit of high densities and low temperatures. In this case we may use a harmonic oscillator cell potential. All molecules perform independent harmonic oscillations in their cells and the result is a specific heat curve of the Einstein type with an exponential decrease for T- 0 instead of a specific heat curve of the Debye type with a characteristic 7 law. Furthermore quantum statistical effects (exchange effects) cannot be introduced in a one-partide model. For this reason the cell model cannot be applied to problems in which such exchange effects play a dominant role (e.g. the X point of liquid He ). However, multiple cell occupations do take account of these correlations and exchange effects. IDgher multiple cell occupations prodde a continuous transition from a one-particle model to the correct 2V-partide model. 

Although the term theoretical techniques in relation to electronic effects may commonly be taken to refer to quantum-mechanical methods, it is appropriate also to mention the application of chemometric procedures to the analysis of large data matrices. This is in a way complementary to analysis through substituent constants based on taking certain systems as standards and applying simple or multiple linear regression. Chemometrics involves the analysis of suitable data matrices through elaborate statistical procedures,... 

Unfortunately, there have been only a few direct studies of the electronic dynamics. In a pioneering study, Tashiro and Schinke examined the quantum dynamics of the 0( P)- -02 reaction on the multiple electronic surfaces arising from the spin-orbit states of the oxygen atom. In a related study Yagi et al studied the quantum dynamics of the CH3 - - 0( P) reaction, but in only a two-dimensional framework. For both reactions, non-adiabatic effects were found to be of minimal importance. Nevertheless, it would be useful to examine these effects in other cases, particularly when statistical and adiabatic electronic treatments yield different estimates at low temperature. 

---