Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Monitoring structural transformations in crystals. 8. Monitoring molecules and a reaction center during a solid-state Yang photocyclization

Structural changes taking place in a crystal during an intramolecular photochemical reaction [the Yang photocyclization of the α-methylbenzylamine salt with 1-(4-carboxybenzoyl)-1-methyladamantane] were monitored step-by-step using X-ray structure analysis. This is the first example of such a study carried out for an intramolecular photochemical reaction. During the photoreaction, both the reactant and product molecules change their orientation, but the reactant changes more rapidly after the reaction is about 80% complete. The distance between directly reacting atoms in the reactant molecule is almost constant until about 80% reaction progress and afterwards decreases. The torsion angle defined by the reactant atoms that form the cyclobutane ring also changes in the final stages of the photoreaction. These phenomena are explained in terms of the influence of many product molecules upon a small number of reacting molecules. The adamantane portion shifts more than the remaining part of the anionic reactant species during the reaction, which is explained in terms of hydrogen bonding. The structural changes are accompanied by changes in the cell constants. The results obtained in the present study are compared with analogous results published for intermolecular reactions.

Applications and Extensions of Statistical Theories

The RRKM rate constant as given by equation (6.73) in the previous chapter is expressed as a ratio of the sum of states in the transition state and the density of states in the reactant molecule. An accurate calculation of this rate constant requires that all vibrational anharmonicity and vibrational/rotational coupling be included in calculating the sum and density.

State Preparation and Intramolecular Vibrational Energy Redistribution

The first step in a unimolecular reaction involves energizing the reactant molecule above its decomposition threshold. An accurate description of the ensuing unimolecular reaction requires an understanding of the state prepared by this energization process. In the first part of this chapter experimental procedures for energizing a reactant molecule are reviewed. This is followed by a description of the vibrational/rotational states prepared for both small and large molecules. For many experimental situations a superposition state is prepared, so that intramolecular vibrational energy redistribution (IVR) may occur (Parmenter, 1982). IVR is first discussed quantum mechanically from both time-dependent and time-independent perspectives. The chapter ends with a discussion of classical trajectory studies of IVR. A number of different experimental methods have been used to energize a unimolecular reactant. Energization can take place by transfer of energy in a bimolecular collision, as in . . . C2H6 + Ar → C2H6* + Ar . . . . . . (4.1) . . . Another method which involves molecular collisions is chemical activation. Here the excited unimolecular reactant is prepared by the potential energy released in a reactive collision such as . . . F + C2H4 → C2H4F* . . . . . . (4.2) . . . The excited C2H4F molecule can redissociate to the reactants F + C2H4 or form the new products H + C2H3F. Vibrationally excited molecules can also be prepared by absorption of electromagnetic radiation. A widely used method involves initial electronic excitation by absorption of one photon of visible or ultraviolet radiation. After this excitation, many molecules undergo rapid radiationless transitions (i.e., intersystem crossing or internal conversion) to the ground electronic state, which converts the energy of the absorbed photon into vibrational energy. Such an energization scheme is depicted in figure 4.1 for formaldehyde, where the complete excitation/decomposition mechanism is . . . H2CO(S0) + hν → H2CO(S1) → H2CO*(S0) → H2 + CO . . . . . . (4.3) . . . Here, S0 and S1 represent the ground and first excited singlet states.