Reaction probability state-selected

The reactions of state-selected Co ions with propane in the gas phase have been studied C-C activation only occurs with excited state ions whereas C-H activation also occurs with ground state, Reactions of Co with primary amines give ammonia, probably by insertion into the C-N bond followed by P-elimination.i98... 

Figure B3.4.6. Reaction probabilities for the initial-state-selected process H2(v = 0,J = 0)+OH(v,y = 0) — H2O+H, for zero total angular momentum. Taken from [75] with pennission.

The methodology presented so far allows the calculations of state-to-state. S -matrix elements. However, often one is not interested in this high-level of detail but prefers instead to find more average infomiation, such as the initial-state selected reaction probability, i.e. the probability of rearrangement given an initial state Uq. In general, this probability is... 

At times, however, even the infomiation presented by "nis too detailed. If one wants to rigorously calculate the themial rate of rearrangement reactions, the initial vibrational state is not important. The relevant quantity is the sum of tire initial-state-selected probabilities... 

Differential scattering experiments with Ne and other beams state selected with a tuneable dye laser are near realization. Differences in the potential-energy curves and reaction probabilities for the iP2 and iP0 states will provide valuable insight into the role of the core ion on the collision dynamics and electronic structure as well as clarify the relative importance of the two states in macroscopic processes. Experiments using a metal-atom crossed beam, also currently in progress at Freiburg, promise a revealing contrast to the weak van der Waals interactions thus far studied. 

Figure 2 The initial dissociative sticking probability for D2 on Cu(l 1 1) extracted from the state selected measurements of desorbing molecules for various vibrational (A) and rotational (B) states of the molecule [19]. Vibrational energy couples effectively to the reaction coordinate, lowering the translational energy requirement for dissociation. Rotational energy initially hinders and then promoted dissociation. Similar effects of rotational energy are predicted in the trajectory calculations shown in (C) for molecules constrained to rotate in a plane perpendicular to the surface [29].

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... 

It can be concluded that, in many cases, solid state reactions proceed much faster and with increased selectivity than the solution reactions, probably because they bring into play a very high concentration of reactants. 

Once the initial state-selected total reaction probability is obtained from Eq. (95), one can calculate the integral cross section and thermal rate constant using standard... 

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. 

We can often understand the dynamics in greater detail by studying 7-specific state-selected reaction probabilities P n (E), which are related to 7-specific state-to-state reaction probabilities via... 

We also find it useful to define the corresponding densities of state-selected reaction probability p ( ) ... 

Assignment of the remaining fitted features was made [14] largely on the basis of densities of state-selected reaction probability, p° and pln, presented in Fig. 5. Each of the panels (b) through (e) and (g) through (j) displays densities of state-selected reaction probability for a given value of v or v and for each value of j or j open up to 1.9 eV. 

Many but not all of the quantized transition states observed in the densities of state-selected reaction probability are observed as peaks in the total density of reactive states. Some highly bend excited states (e.g., [0 12°], and [0 14°]) are observed as peaks only in the state-selected dynamics. If the closely spaced features in the stretch-excited manifolds for p(i are indicative of supernumerary transition states more closely spaced in energy than the variational transition states (which adiabatic transition state theory also suggests), then only some of the supernumerary transition states, in particular S[20°], 5[22°], 5[24°], 5[30°], 5[32°], 5[34°], and 5[36°], are observed in the total density, i.e., only some are of the first kind. The other supernumerary transition states identified in the state-selected dynamics are of the second kind. 

We discussed the implications of the O + H2 reaction s multiple bottleneck regions in terms of variational and supernumerary transition states. We related the observed features to the scattering results for asymmetrical Eckart potentials. We emphasized that global control is maintained to very high energy (1.9 eV) and very high levels of v2. We demonstrated the influence of quantized transition states at the level of state-selected reaction probability for this reaction. 

As was mentioned before, isomerisation of the substituted indoles does not occur under the conditions used in this study. The selectivity of the catalytic reaction should therefore only depend on the relative rates of formation of the enehydrazines 2 and 3 in the conformation which aliows their [3,3]-sigmatropic rearrangement to occur (which is the conformation drawn in Scheme 1). The sorption data and molecular geometries indicate that the formation of both enehydrazines 2 and 3 inside the channels of zeolite beta should be possible, but 2 is probably severely hindered in adopting the conformation required for indolization, given the fact that this conformation is even bulkier than the indole isomer 4 which is formed from it. The selective Fischer synthesis of 2-benzyl-3-methylindole 5 catalyzed by zeolite beta is therefore a true example of transition state selectivity. 

Some years later, aided by considerably more rapid computers than available to Wall and co-workers, Karplus, Porter, and Sharma reinvestigated the exchange reaction between H2 and H [24]. As with the earlier work, the twelve classical equations of motion were solved. In addition, discrete quantum-mechanical vibrational and rotation states were included in the total energy so that the trajectories were examined as a function of the initial relative velocity of the atom and molecule and the rotational and vibrational quantum numbers j and v of the molecule. The more sophisticated potential energy surface of Porter and Karplus was used [7], and the impact parameter, orientation and momentum of the reactants, and vibration phase were selected at random from appropriate distribution functions. This Monte Carlo approach was used to examine 200-400 trajectories for each set of VyJ, and v. The reaction probability P can be written as... 

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