Distribution transition energy

Figure 22. Shown in panel (a) is the relation between the bare energy difference e between frozen-in structural states in a glass and the effective splitting e that is smaller due the level repulsion in the tunnehng center. Panel (b) depicts schematically the derivative of e with respect to e, which is used to compute the new effective distribution P(e) of the transition energies.

Kinetics on the level of individual molecules is often referred to as reaction dynamics. Subtle details are taken into account, such as the effect of the orientation of molecules in a collision that may result in a reaction, and the distribution of energy over a molecule s various degrees of freedom. This is the fundamental level of study needed if we want to link reactivity to quantum mechanics, which is really what rules the game at this fundamental level. This is the domain of molecular beam experiments, laser spectroscopy, ah initio theoretical chemistry and transition state theory. It is at this level that we can learn what determines whether a chemical reaction is feasible. 

Fig. 2.2 Intensity distribution /( ) for the emission of y-rays with mean transition energy Eq. The Heisenberg natural line width of the distribution, F = S/t, is determined by the mean lifetime T of the excited state (e)...

This effect allows one to monitor the perturbation of the tt-c lection system by interaction of the electrophilic phosphorus atom with a Lewis base. Following the same rationale, the still larger chemical shifts of neutral 1,3,2-diazaphospholes and 1,3,2-diazaphospholide anions are considered to reflect predominantly a reduction in n-n transition energy due to destabilization of the n(P) orbital with an increasing number of lone-pairs on the NPN-moiety rather than differences in the charge densities or n-electron distribution in the heterocyclic ring [16]. 

Bloch (1933a,b) first pointed out that in the Thomas-Fermi-Dirac statistical model the spectral distribution of atomic oscillator strength has the same shape for all atoms if the transition energy is scaled by Z. Therefore, in this model, I< Z Bloch estimated the constant of proportionality approximately as 10-15 eV. Another calculation using the Thomas-Fermi-Dirac model gives I tZ = a + bZ-2/3 with a = 9.2 and b = 4.5 as best adjusted values (Turner, 1964). This expression agrees rather well with experiments. Figure 2.3 shows the variation of IIZ vs. Z. 

The formidable problems that are associated with the interpretation of LP kinetic data for nonstatistical IM reactions can be entirely avoided if the reactions can be studied in the HPL of kinetic behavior. In the HPL, the energy content of the initially formed species, X and Y, in reaction (2) would be very rapidly changed by collisions with the buffer gas so that the altered species, X and Y, would have normal Boltzmann distributions of energy. Furthermore, those Boltzmann energy distributions would be continuously refreshed as the most energetic X and Y within the distributions move forwards or backwards along the reaction coordinate. The interpretation of rate constants measured in the HPL is expected to be relatively straightforward because conventional transition-state theory can then be applied. 

Transition Complexes. The numerous collisions between reactant molecules result in a wide distribution of energies among the individual molecules. This can result in strained bonds, unstable forms of molecules, or unstable association of molecules which can then either decompose to give products, or by further collisions return to molecules in the normal state. Such unstable forms are called transition complexes. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

---