Critical configuration

Hase W L 1972 Theoretical critical configuration for ethane decomposition and methyl radical recombination J. Chem. Rhys. 57 730-3... 

Large quantities of fissile isotopes, U and U, should be handled and stored appropriately to avoid a criticahty hazard. Clear and relatively simple precautions, such as dividing quantities so that the minimum critical mass is avoided, following adniinisttative controls, using neutron poisons, and avoiding critical configurations (or shapes), must be followed to prevent an extremely treacherous explosion (246). 

To implement the Doppler-selected TOF measurement, the initial relative velocity is arranged to be parallel to the propagation vector of the probe laser. This critical configuration can readily be achieved in this rotating sources machine.36 Under this configuration, each Doppler-sliced 2D distribution exhibits a cylindrical symmetry The slit in front of the TOF spectrometer allows only those products with a rather small vx to be detected. Hence, only the -distribution, obtained by the TOF measurement, is needed to completely characterize the Doppler-sliced 2D (vx — vy) distribution. 

Consider the dissociation of an ion AM" that may either dissociate to form the fragments and M or the INC [A", M] allowing free mutual rotation and thus reorientation of the particles. Within the INC, A" and M can recombine only if they attain a well-defined mutual orientation, i.e., the system has to freeze rotational degrees of freedom. Such a configuration allowing covalent bonds to be formed is termed locked-rotor critical configuration [169-171,177] and any reac-... 

The configuration of maximum PE is called the activated complex the transition state or the critical configuration and the unit (X——Y——Z) must attain this configuration before reaction can take place. Possessing the critical energy is not sufficient the fundamental requirement is attainment of this critical configuration. 

The vertical distance between a and the critical configuration gives the necessary PE for reaction, and the minimum total energy needed to attain the critical PE. 

Any change in the dimensions of the activated complex along the reaction coordinate leads to a decrease in PE, behaviour not found in molecules. The Morse curve shown earlier (Figure 4.19) demonstrates that for a molecule displacement from the equilibrium position always leads to an increase in PE. The activated complex should be regarded as merely a critical configuration. Changes in dimensions in all other directions result in an increase in PE, behaviour typical of vibration about an equilibrium intemuclear distance. 

Activated or energized molecules have energy equal to, or greater than, the critical energy. They can be anywhere on the surface, but can only become activated complexes by rearranging the relative positions of the atoms in the reaction unit (X—-Y—-Z) until the critical configuration is reached. 

Molecules with less than the critical energy also appear on the surface, but these can only alter in a manner allowed by their total energy. For these molecules the possibilities of alteration in configuration are limited. In particular, the critical configuration can never be reached. Quantum mechanical tunnelling allows the... 

It is vitally important to understand what a free translation means, and to be aware of the important consequences of motion through the critical configuration being a free translation. The force acting on a system is... 

If the PE is constant, then d(PE)/dr is zero, and the force is zero and there is no acceleration in the motion of the reaction unit as it passes through the critical configuration, i.e. through the region of the surface where the PE is constant. If there is no acceleration, then the reaction unit must pass over the barrier at a constant rate. This rate can be calculated from kinetic theory. 

If the PE is not constant, then d(PE)/dr is non-zero, and the rate of change of configuration over that region of the PE surface will vary depending on the value of d(PE)/dr. This happens at all points other than the critical configuration. 

The concentration of activated complexes is the total number of units (X——Y——Z) per unit volume which are in the critical configuration, no matter what their past history is. 

Answer. Along AB, rAB = rBC. The activated complex lies at the saddle-point lying on AB. The PE contour diagram is symmetrical about the critical configuration. The activated intermediate lies in the well of the elliptical contours and at configurations where rBC > rAB. There is a further activated complex as marked along the line PQ. 

This involves calculating the rate at which the reaction unit passes through the critical configuration. Since the PE is constant over the region of the surface occupied by the critical configuration, the rate at which it moves through the critical... 

If is the total number of activated complexes, then the number which pass through the critical configuration per unit time per unit volume is N v/Vb, and so the rate of reaction can be given as... 

The partition function calculation for the activated complex is more tricky. If the surface is known the quantities quoted above can be found from the dimensions and the curvature of the surface around the critical configuration. If this is not possible, then estimates of Qf can be made by analogy with a molecule of similar structure. The vital feature is that the free translation along the reaction coordinate has already been accounted for and must not be included in the calculation, and so the activated complex has one degree of vibrational freedom less than that for a molecule with the same number of atoms. 

The crucial step in the development of unimolecular theory was the postulate of a time lag between the activation and reaction steps in the master mechanism for all elementary reactions given in Chapter 1. During this time an activated molecule can either be deactivated in a deactivating energy transfer collision, or it can alter configuration to reach the critical configuration and react. All elementary reactions involve three steps, two energy transfer steps and one reaction step, and for unimolecular reactions... 

In the Hinshelwood theory the time lag corresponds to the time taken for the activated molecule to rearrange configuration into the critical configuration of the activated complex. The Kassel theory deals explicitly with this process, and imposes a much more severe restriction than does Hinshelwood. Before an activated molecule can react there must be a flow of energy at least 0 into a... 

Reactions on attractive surfaces with early barriers are promoted by high translational energy in the reactants, with vibrational energy playing a minor role. Selective enhancement by translational energy is easiest when there is a straight run up the entrance valley to the critical configuration. 

For the minimum energy path, rAB for the critical configuration at the col is close to OabIcc, but rBC is much larger than (rBC)eq. 

Such reactions are typified by the unimolecular decomposition of cyclopropane to give propene, where one molecule of reactant moves into the critical configuration and thence to products, with... 

For gases, Q, and Qb are readily found from spectroscopic data, but Qf for the activated complex can only be calculated if the potential energy surface is accurately known in the region of the critical configuration. It cannot be measured experimentally - the activated complex is merely a special critical configuration. 

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