A simple general method for obtaining selection rules for the ro-vibronic states of reactant and product molecules connected in a reactive collision is discussed. Neglecting only the coupling with nuclear spin, rather stringent restrictions are found to occur in systems involving three and more identical nuclei. Several radical and ion molecule reactions of current interest are used to illustrate this finding. Even more restrictive selection rules are found when assuming weak coupling (‘ incomplete exchange of identical nuclei ’) in the intermediate reaction complex. These include the well-known selection rules for inelastic collisions of molecules with several identical nuclei, but less trivial examples with chemical reaction are also presented. The symmetry corrections and nuclear spin statistics in statistical theories of scattering (including the prior distributions for the information-theoretic approach) are derived. Further applications are discussed briefly.

Detailed symmetry selection rules for reactive collisions

Energy disposal and energy consumption in elementary chemical reactions. Information theoretic approach

The information-theoretic maximal-entropy procedure for the analysis of collision processes is derived as a consequence of the dynamics, be they quantal or classical. The method centers attention on the minimal number of operators (the "dynamic constraints") whose expectation values are both necessary and sufficient to completely characterize the collision dynamics. For a given Hamiltonian and initial state, the constraints required to obtain an exact solution of the equations of motion are determined by a purely algebraic procedure. It is furthermore found possible to derive equations of motion for the conjugate Lagrange parameters. Immediate applications are noted, e.g., a family of similar reactions is shown to have a common set of dynamic constraints and simple illustrative applications are provided. The determination of the scattering matrix is discussed, with examples. The general formalism consists in solving the scattering problem in two stages. The first is purely algebraic. At the end of this stage one obtains the functional form of, say, the scattering matrix or of the density matrix after the collision expressed in terms of parameters whose number equals the number of dynamic constraints. The end result of this algebraic stage suffices to analyze the scattering pattern for any initial state. The second stage is the predictive procedure. Explicit coupled first-order nonlinear differential equations are obtained for the parameters.

Connection between the maximal entropy and the scattering theoretic analyses of collision processes

Detailed experimental and theoretical information on the distribution of product energy states resulting from reactive molecular collisions are characterized by their entropy deficiency and temperature. Explicit algorithms are developed both for the case of ultimate resolution (both angular and internal state distribution) which provides the intrinsic (i.e., maximal) entropy deficiency and for the more realistic situations (e.g., chemiluminescence, molecular beam velocity analysis) where only averaged distributions are available and the entropy deficiency is therefore smaller. Twelve ``known'' product distributions are analyzed. The largest values of the entropy deficiency are found for reactions where there is significant deviation from a simple equilibrium distribution of products. A temperature parameter is introduced as a measure of the deviation from equilibrium. Inverted populations are characterized by a negative value of this temperature. Consideration of a number of isotopic reactions indicate that this temperature is essentially invariant under isotopic substitution. The new temperature parameter introduced in this work is the one appropriate for a finite system and differs from the more familiar (but special) form appropriate for a system coupled to an infinite heat bath. Two new tools are thus proposed for characterizing the deviation of an observed product state distribution (or a computational simulation thereof) from an equilibrium, microcanonical one. These are the temperature parameter (a differential measure) and the entropy deficiency (an integral one). They measure, respectively, the local and the average deviation between observed and equilibrium distributions.

Entropy and Chemical Change. II. Analysis of Product Energy Distributions: Temperature and Entropy Deficiency

State‐to‐state rate constants for vibrational energy transfer (both V–V and V–T) are characterized using an ’’exponential gap’’ representation. The collisions analyzed include experimental results for both V–T and V–V transfer rates, trajectory computations for V–T transfer rates (via both inelastic and reactive, atom exchange, collisions) and quantal computations for V–V transfer rates. The results are analyzed in terms of the surprisal, a measure of deviation of the actual rate from the prior (or reference) rate. The prior rates are computed on the basis of the assumption that (at a given collision energy) all final states are equally probable. For almost all cases the surprisal could be characterized by a single parameter. The magnitude of this parameter (and its temperature dependence) could be predicted using bulk averages only. Such predictions are demonstrated for both experimental and trajectory computed rates. The link between the microscopic dynamics and macroscopic kinetics is forged by the use of sum rules (which provide constraints on the rates) and of the principle of maximal entropy (which is used to determine the least biased set of rate constants subject to the constraints).

Vibrational energy transfer in molecular collisions: An information theoretic analysis and synthesis

Applications of the principle of microscopic reversibility are considered for reaction rates measured in experiments that reveal some of the dependence on the rotational, vibrational, and/or translational states of the reactants or products. Each type of measurement establishes a characteristic set of quantum states for the reactants and products, suggesting that removal of trivial statistical factors (densities of states) from the data to retrieve a purely dynamical quantity ω(E), the state‐to‐state reaction rate suitably averaged over the initial and final sets of states at fixed total energy E. This quantity is fully symmetric with respect to the direction of the reaction—either the forward or reverse rate coefficient can be obtained by multiplying ω with the proper density of final states. Thus ω reflects the intrinsic probability of the process, disregarding the statistical bias introduced by the nature of the experiment itself. Methods of accurate computation of state densities appropriate to sev...

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James L. Kinsey

Papers

Microscopic Reversibility for Rates of Chemical Reactions Carried Out with Partial Resolution of the Product and Reactant States