Reaction probability cumulative

A3.11.5.3 EXACT QUANTUM EXPRESSIONS FOR THE CUMULATIVE REACTION PROBABILITY... 

Zhang D H and Light J C 1996 Cumulative reaction probability via transition state wave packets J. Chem. Phys. 104 6184-91... 

N E) is called the cumulative reaction probability. It is directly related to the themial reaction rate k T) by... 

A major achievement [71, 82, 83, 84, 85, 86, 87 and 88] was the development of a simple quantum ( flux-flux ) expression for the cumulative reaction probability, N E), with the final result... 

Seideman T and Miller W H 1992 Calculation of the cumulative reaction probability via a discrete variable representation with absorbing boundary conditions J. Chem. Phys. 96 4412... 

Cumulative Reaction Probability via a Discrete Variable Representation with Absorbing Boundary Conditions. 

W. H. Miller I would like to ask Prof. Schinke the following question. Regarding the state-specific unimolecular decay rates for HO2 — H + O2, you observe that the average rate (as a function of energy) is well-described by standard statistical theory (as one expects). My question has to do with the distribution of the individual rates about die average since there is no tunneling involved in this reaction, the TST/Random Matrix Model used by Polik, Moore and me predicts this distribution to be x-square, with the number of decay channels being the cumulative reaction probability [the numerator of the TST expression for k(E)] how well does this model fit the results of your calculations ... 

The rate constant for a chemical reaction is conveniently expressed in terms of the cumulative reaction probability [1] (CRP) N(E),... 

Figure 2. Dotted lines are the eigen-reaction-probabilities p (E) for the collinear H + H2 reaction. The solid line is their sum, the cumulative reaction probability N(E).

Figure 3. Cumulative reaction probability for the H + H2 H2 + H reaction (a) collinear geometry (Ref. 3a) (fc) three-dimensional space for total angular momentum 7 = 0 (Ref. 3b).

One expects to observe a barrier resonance associated with each vibra-tionally adiabatic barrier for a given chemical reaction. Since the adiabatic theory of reactions is closely related to the rate of reaction, it is perhaps not surprising that Truhlar and coworkers [44, 55] have demonstrated that the cumulative reaction probability, NR(E), shows the influence barrier resonances. Specifically, dNR/dE shows peaks at each resonance energy and Nr(E) itself shows a staircase structure with a unit step at each QBS energy. It is a more unexpected result that the properties of the QBS seem to also imprint on other reaction observables such as the state-to-state cross sections [1,56] and even can even influence the helicity states of the products [57-59]. This more general influence of the QBS on scattering observables makes possible the direct verification of the existence of barrier-states based on molecular beam experiments. 

Figure 3.17 The cumulative reaction probability for./ = 0 F+HCl versus collision energy. The location of the HCl(v= 0,j> energetic threshold is indicated. For comparison, the QCT result is also shown.

Figure 5.18 A high-resolution view of the cumulative reaction probability (CRP) for J= 0 and J = 2. The resonance peaks in this range are assigned to the Cl-HF[V = l,j, k) postreac-tive states, where v is the quantum number for the low frequency vdW stretching mode.

V. Ryaboy, N. Moiseyev, Cumulative reaction probability from Siegert eigenvalues Model studies, J. Chem. Phys. 98 (1993) 9618. 

In order to proceed, we need to know the precise form of the cumulative reaction probability, and introduce the following approximation ... 

Abstract. The Chebyshev operator is a diserete eosine-type propagator that bears many formal similarities with the time propagator. It has some unique and desirable numerical properties that distinguish it as an optimal propagator for a wide variety of quantum mechanical studies of molecular systems. In this contribution, we discuss some recent applications of the Chebyshev propagator to scattering problems, including the calculation of resonances, cumulative reaction probabilities, S-matrix elements, cross-sections, and reaction rates. 

In studying reaction dynamics, one may only be interested in averaged properties such as cumulative reaction probabilities and thermal rate constants. These quantities can of course be obtained from state-to-state probabilities, but as shown by Miller and coworkers they can be calculated directly and more efficiently without knowledge of the S-matrix elements.[44,45] The cumulative reaction probability, for example, can be computed as follows ... 

We follow the correlation function formulation of Miller and Carrington, [52] which rewrites the cumulative reaction probability as follows ... 

We have tested this approach for the three-dimensional H + H2 exchange reaction (, 0) and found excellent agreement with the time-dependent results of Zhang and Light. [49] It was then used to calculate the cumulative reaction probabihty for the Li + HF -> LiF + H reaction, also with zero total angular momentum.[54] Figure 2 displays the cumulative reaction probability of this reaction below 0.65 eV. It can be readily seen that the cumulative reaction probability is dominated by numerous narrow resonances. These resonances are well known in state-resolved reaction probabihties... 

For the H-rCH4 H2+CH3PO] and O+CH4 OH+CHspI] reactions, accurate Multi Conhgurational Time Dependent Hartree (MCTDH) calculations have been performed. These calculations include all vibrational modes and are for a total angular niomcntum J = 0. The flux correlation function formalism[68. 69, 70] was employed to calculate cumulative reaction probabilities for J — 0. 

O.I. Tolstikhin, V. N. Ostrovsky, and H. Nakamura, Cumulative reaction probability without absorbing potentials. Phys. Rev. Lett., 80 41-44, 1998. 

Then we can obtain the cumulative reaction probability, Pcum( ), as an in-flux current to the resonant orbital, which is represented by the NEGF framework as follows ... 

Eq. (20.36) is a relation of (cumulative) reaction probability, that is, reaction dynamics, and hot electron dynamics. Because the rate of energy transfer is much higher in DIET than DIMET per single hot electron attachment, the eTST is suitable for a DIET process as a first approximation. 

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