Reactive collision, probabilities

Neuhauser, D., Baer, M., Judson, R.S. and Kotiri, D.J. (1990) A time-dependent wave packet approach to atom diatom reactive collision probabilities - theory and application to H -P H2 (J=0) system,, 7. Chem. Phys. 93, 312-322. 

Fig. 2. Reactive collision probabilities Pfrom ground state of the reactants, calculated by Truhlar and Kuppermann (1972), as functions of total energy E and relative kinetic energy E0. Arrows indicate vibrational thresholds. Crosses are results of Mortensen and Gucwa (1962) for P 0o), shifted to the left by 0-057 eV.

Neuhauser D, Baer M, Judson RS, Kouri DJ (1990) A time-dependent wave packet approach to atomdiatom reactive collision probabilities theory and application to the H -F H2 (/ = 0) system. J Chem Phys 93(1) 312... 

Marcus R A 1970 Extension of the WKB method to wave functions and transition probability amplitudes (S-matrix) for inelastic or reactive collisions Chem. Phys. Lett. 7 525-32... 

The evidence in Figure 2 for a kinetic energy threshold for reaction of excited H2+ with He does not support the assumption of a kinetic energy transfer process for the excitation of reactant H2+ with v < 5 in reactive collisions with He. If such processes were probable, a drastic change in the maximum value of Q or k might be expected. The transfer of less than 0.5 e.v. of kinetic to internal energy would add quantum states with v = 3 and 4 to the inventory of available H2 + reactant and increase the maximum value of k by a factor of 2. 

This formulation assumes that the continuum diffusion equation is valid up to a distance a > a, which accounts for the presence of a boundary layer in the vicinity of the catalytic particle where the continuum description no longer applies. The rate constant ky characterizes the reactive process in the boundary layer. If it approximated by binary reactive collisions of A with the catalytic sphere, it is given by kqf = pRGc(8nkBT/m)1 2, where pR is the probability of reaction on collision. 

The second term on the right-hand side is the recombination probability, — q(z). Now, X2B a0b is the doublet density f2n and hence the recombination probability is the negative of the integral (or average) over all wave vectors, q, and velocities of A and B (vj and v2) of the reactive collision operator, TAB, and the doublet distribution of A and B, fAB. 

The expression (2.1) is not the precise number of reactive collisions, but the average. The actual number fluctuates around it and we want to find the resulting fluctuations in the rij around the macroscopic values determined by (2.2). In order to describe them one needs the joint probability distribution P(n, t). Although it is written as a function of all rij, it is defined on the accessible sublattice alone. Alternatively one may regard it as a distribution over the whole physical octant, which is zero on all points that are not accessible. 

We demonstrate the method on the following concrete - if somewhat trivial - example. A swarm of particles is moving freely in space, but each particle has a probability a per unit time to disappear, through spontaneous decay or through a reactive collision. To cover the latter possibility we allow a to depend on v. The (r, u)-space is decomposed in cells A and nx is the number of particles in cell X. The joint probability distribution P( nx, t) varies through decay and through the motion of the particles. The decay is described by... 

An electronically excited molecule can lose its energy by non-reactive collisions in the gas phase or by deactivating collisions with surfaces, and in laboratory studies both processes are probably of importance ... 

Quantum mechanically, the reactive dynamics is expressed in a more wavelike language. By solving Schrodinger s equation, we treat the problem where an initial probability wave of reactants is sent in towards the activation barrier from reactants. When the wave hits the barrier, part of it is reflected and part of it is transmitted. The reflected part of the wave corresponds to non-reactive collision events, and the transmitted part corresponds to reaction. 

The conformational orientation between the excited CNA and CHD should be restricted very much to produce a photocycloadduct in the collision complex indicated in the scheme 1. In the fluid solvents like hexane, the rotational relaxation times of the solute molecules are rather fast compared to the reaction rate, which increases the escape probability of the reactants from the solvent cavity due to the large value of ko. On the other hand, the transit time in the reactive conformation, probably symmetrical face to face, may be longer in the liquid paraffin. This means that the observed kR may be expressed as a function of the mutual rotational relaxation time of reactants and the real reaction rate in the face-to-face conformation. In this sense, it is very important to make precise time-dependent measurements in the course of geminate recombination reaction indicated in Scheme 2, because the initial conformation after photodecomposition of cycloadduct is considered to be close to the face-to-face conformation. The studies on the geminate processes of the system in solution by the time resolved spectroscopy are now progress in our laboratory. 

High available energy is only one reason for the new chemistry that is made possible in the hot and compressed cluster. The simulations show that equally important is that collisions in the cluster necessarily occur with rather low impact parameters. (Two molecules moving relative to one another with a high impact parameter will collide with other molecules before they can collide with each other.) The same is true for nonadiabatic transitions. The computed probability of crossing to the upper electronic state decreases rapidly with increasing impact parameter. It is because the cluster favors low impact parameter collisions that the yield of reactive collisions is high. 

These strong non-adiabatic effects observed in the cone-states of the upper sheet contrast with the absence of any significant effect in the H-I-H2 reactive collision. Eor instance, Mahapatra et al. [69] examined the role of these effects in the H -f H2 (v = 0, = 0) reaction probability for / = 0 and found negligible nonadiabatic coupling effects in the initial state selected probability. Subsequently, Mahapatra and co-workers [70] reported initial state-selected ICS and thermal rate constants of H -I- H2(HD) for total energies up to the three body dissociation. Again, they... 

As an illustration of the construction of these reactive collision operators, we first consider the simplest case. Suppose that when an AB pair collides there is a probability that reaction to form CD will take place. For... 

Consider first a gas phase bimolecular reaction (A + B -> C + D). If we consider that the reagents are approaching each other with a relative velocity v, then the total flux of A moving toward B is just vC where Cj is the concentration of A (number of A per unit volume (or per unit length in one dimension)). If u is the integral cross section for reaction between A and B for a given velocity v (a is the reaction probability in one dimension), then for every B, the number of reactive collisions per unit time is The total number of... 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

The collision fraction law fails in competitive q>eriments in which the reactive collision energy probability density distribution is strongly dependent on sample composition. Such behavior arises when the excitation functions for nonthermal reactions exhibit dissimilar collision energy dependences (7,9,10,19-26). Despite diis caveat, the simple collision fraction rule exhibits good utility for many types of competitive systems (9,23). 

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