Integral reaction probability

The classical integrated reaction probability is then given by... 

I 6 Single and Multiple Hydrogen/Deuterium Tranter Reactions in Liquids and Solids the quantum mechanical integrated reaction probability by... 

Figure 1 Integral reaction probability for the reaction o/D with cyc/oCsHi2 as a function of the initial energy ofD...

Photolysis at 298 nm of HI mixed with CH3O or CHsBr yidds CH4 as a result of the attraction and substitution reactions (71) and (72). The sum of the integral reaction probabilities of reactions (71) and (72) for atoms of initial energy... 

Nitrous Oxide. For the reaction of H with N2O two paths, (80) and (81), arc possible. Integral reaction probabilities for both processes have been determined... 

Integral reaction probabilities have been determined for numerous reactions of photochemically generated hot H or D atoms. The experiments of Kuppermann and White/ on the reaction... 

Figure 5. Reaction probabilities for a given instance of the noise as a function of the total integration time Tint for different values of the anharmonic coupling constant k. The solid lines represent the forward and backward reaction probabilities calculated using the moving dividing surface and the dashed lines correspond to the results obtained from the standard fixed dividing surface. In the top panel the dotted lines display the analytic estimates provided by Eq. (52). The results were obtained from 15,000 barrier ensemble trajectories subject to the same noise sequence evolved on the reactive potential (48) with barrier frequency to, = 0.75, transverse frequency co-y = 1.5, a damping constant y = 0.2, and temperature k%T = 1. (From Ref. 39.)...

Reaction probabilities have been extensively measured in many laboratories all round the world, and in particular at the California Institute of Technology under the guidance of William Fowler. But whenever experimental data is lacking, nuclear reaction rates can be estimated theoretically. In this way, reaction rates have been fully tabulated as a function of temperature, ready to be integrated into numerical codes for stars or the Big Bang, and made available to the whole astrophysical community. 

Samuel and Magee [436] suggested that the reaction probability between two such radicals both formed at r0, t0 is the volume integral of the product of the density of one radical times that of the other... 

In the line-of-centers model, the collision s effectiveness depends on the impact parameter, b. In general, the reaction probability is a function of energy and impact parameter, P (b, e). An integral over all possible impact parameters... 

Since the reaction probability Pr in the integral is given as a function of the original variables, and not of the primed variables, we need to express the old variables in terms of the primed variables. This is achieved by an integration of the relations in Eq. (4.82) ... 

For any dynamical simulation, a continuous representation of the PES is mandatory since the potential and the gradients are needed for arbitrary configurations. One can in fact perform ab initio molecular dynamics simulations in which the forces necessary to integrate the classical equations of motion are determined in each step by an electronic structure calculations. There have been few examples for such an approach [35-37], However, in spite of the fact that electronic structure calculations can nowadays be performed very efficiently, still there is a significant numerical effort associated with ab initio calculations. This effort is so large that in the ab initio dynamics simulations addressing molecular adsorption and desorption at surfaces the number of calculated trajectories has been well below 100, a number that is much too low to extract any reliable reaction probabilities. 

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