Dissociation probability time-dependent

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

The small and weakly time-dependent CPG that persisLs at longer delays can be explained by the slower diffusion of excitons approaching the localization edge [15]. An alternative and intriguing explanation is, however, field-induced on-chain dissociation, a process that does not depend on the local environment but on the nature of the intrachain state. The one-dimensional Wannier exciton model describes the excited state [44]. Dissociation occurs because the electric field reduces the Coulomb barrier, thus enhancing the escape probability. This picture is interesting, but so far we do not have any clear proof of its validity. 

Henriksen, N.E. (1988). The equivalence of time-independent and time-dependent calcu-lational techniques for photo dissociation probabilities, Comments At. Mol. Phys. 21, 153-160. 

In principle, one can induce and control unimolecular reactions directly in the electronic ground state via intense IR fields. Note that this resembles traditional thermal unimolecular reactions, in the sense that the dynamics is confined to the electronic ground state. High intensities are typically required in order to climb up the vibrational ladder and induce bond breaking (or isomerization). The dissociation probability is substantially enhanced when the frequency of the field is time dependent, i.e., the frequency must decrease as a function of time in order to accommodate the anharmonicity of the potential. Selective bond breaking in polyatomic molecules is, in addition, complicated by the fact that the dynamics in various bond-stretching coordinates is coupled due to anharmonic terms in the potential. 

The temperature dependence of S0 measured at normal incidence and Ex = 0.39 eY is reported in Fig. 11 for Ag(2 10) ( ) and compared with the behaviour observed at the same E and 0 for Ag(l 0 0) (dashes) and Ag(l 1 0) (solid line) at the same E and 0. The data for Ag(41 0) are reported, too ( , O, x) for two different 0, corresponding to similar values of S0. We notice that all surfaces show a smooth T dependence except for Ag(l 0 0), for which S0 drops abruptly beyond T = 170 K [100], i.e. as soon as desorption from the molecular well becomes important over the time scale of the experiment (0.3 sec). The Ag(4 1 0) and Ag(l 1 0) curves have the same behaviour up to 350 K, at which temperature S0(T) becomes steeper for Ag(41 0). Such difference is due to the dissociation process, which occurs only at steps for Ag(41 0) and takes place at regular sites for Ag(l 1 0). When the lifetime in the chemisorbed precursor becomes shorter than the time needed to search for the defect, the dissociation probability for Ag(41 0) decreases more rapidly with respect to a situation where no searching for an active site is necessary. The S0(T) curve of Ag(2 10), on the other hand, nearly perfectly overlaps with the one of Ag(l 1 0). The decrease of S0(T) on Ag(2 1 0) tells us further that the dissociation mechanism is mediated also in this case by a short lived molecular precursor, which has the choice between desorbing and dissociating. 

Van Bentham and Davis ° demonstrated the presence of vibrationally excited I2 in a flowing I2/02(a) system using LIF detection. Population of the 33 < u < 44 levels was observed, and a comparison of the time dependent profiles for I2 and I indicated that I2 could be the intermediate from which I waa produced. Van Bentham and Davis ° briefly discussed the origin of the 4 detected in their experiment. Conditions were such that dissociation was probably initiated by reactions (8) and (9), but in the region where spectra for were recorded the concentration of I was high enough for reaction (10) to be the dominant local source of I2. Van Bentham and Davis ° examined the qualitative effect of the He carrier gas on the I2 vibrational level population distribution. As expected, vibrational relaxation was observed as the He pressure increased. 

For the particular example in Fig. 4, the lowest resonance state is found at E = 8.75 - i0.05, while the next one has the energy E = 18.01 — iO.45. The positive real parts of the eigenenergies, ReE = Eq, indicate that these states are unbound with energies high above the dissociation limit, E — 0. The imaginary parts, which will be denoted —F/2, are related to the decay probability in a unit time interval, k [18]. Indeed, the time dependence of the wave function x(- ) is given by... 

The initial state-selected total dissociation probability of the diatom is obtained by projecting out the energy-dependent reactive flux. If i /,) denotes the time-independent (TI) full scattering wavefunction, where the labels i and E denote the initial state and energy, the total dissociation probability from an initial state i can be obtained by the flux formula (95). We choose the diatomic distance r to be the 5 coordinate in Eq. (96). The full TI scattering wave function is normalized as (if/,) NV/. ) = 2/nhh(E - E ). The total dissociation probability, according to Eq. (98), is given by... 

K. Kulander, Collision induced dissociation in collinear H + H2 Quantum mechanical probabilities using the time-dependent wavepacket approach. J. Chem. Phys. 69 5064 (1978). 

In this framework, the time-dependent dissociation probability is... 

Kelley and Rentzepis [297] have recently studied the recombination of iodine atoms in liquid and fluid xenon over times to 150 ps after photolysis. The iodine molecule can be biphotonically dissociated through the state to produce geminate pairs with larger initial separations. Some degree of spin relaxation of excited iodine atoms ( Pi/2) produced by biphotonic excitation may occur and reduce the probability of recombination. There is also evidence that the 11 state of I2 may be collisionally predissociated and that recombination may be more rapid than the rate of vibrational relaxation of the excited 12 state in polyatomic solvents (see also ref. 57). Despite these complications, several workers have attempted to model the time dependence of the recombination (or survival) probability of iodine atom reactions. The simple diffusion equation analysis of recombination probabilities [eqn. 

When there exist multiple paths with different decay times, the dissociation processes would exhibit multiexponential decay. In Figure 3.17, the time dependences of the remaining probabilities of wave packets are shown for different values of y [17], This finding indicates that the dissociation consists of two processes with different decay times. The faster one corresponds to the homoclinic intersection, and the slower one to the heteroclinic intersection. 

The purified peanut enzyme is homogeneous on electrophoresis, has a pi value of 4.65, and is very unstable at acid pH. Molecular weight determinations by a variety of techniques gave ranges from 50,000, in the presence of dissociating agents, to over 200,000. A time-dependent dissociation to a minimum of 20,000 was noted. The active enzyme is probably a complex (Heller etal., 1974). 

Fig. 8.9 Summary of the coupled electron and nuclear dynamics during the dissociation. The black vertical line indicates the time of recollision, 1.7 fs after ionization at the maximum electric field, (a) Temporal evolution of the electric field, (b) Time-dependent populations of the E n, and iPn states of CO+ after recoUision excitation ( solid CEP = 0, dotted CEP = 7r). (c) Temporal evolution of the probability of measuring a C+ fragment Pc+ for the dissociative ionization of CO+ after recoUision (black CEP = 0, gray CEP = it). Reprinted from [66] with copyright permission of APS...

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