Capture model

In the equilibirum capture model, on the other hand, there is a dynamic equilibrium between the growing oligomers and the surface of the particles as well as the possibility of some interchange with the interior of the particles. 

For highly exothermic SN2 reactions, which have a central barrier significantly lower in energy than that of the reactants, association of the reactants may be the rate controlling step in TST.1 The SN2 rate constant can then be modeled by a capture theory9 such as VTST,10 average dipole orientation (ADO) theory,11 the statistical adiabatic channel model (SACM),12 or the trajectory capture model.13... 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

If crossing the central barrier is not rate-controlling in TST, then trapping in the ion-dipole complex must be incorporated into the statistical model and it is more difficult to represent the effect of central barrier recrossings correcting TST with the K factor is not sufficient. The recrossings and presence of both intermolecular and intramolecular complexes are expected to affect the k, kisom, and k rate constants in equation 6. The value for k should be smaller than that of a capture model, and kisom and k 8 should disagree with the predictions of RRKM theory. 

Capture Model and Total Reactive Cross Sections... 

The 7-shifting method depends on our ability to identify a unique bottleneck geometry and is particularly well suited to reactions that have a barrier in the entrance channel. For cases where there is no barrier to reaction in the potential energy surface, a capture model [149,150,152] approach has been developed. In this approach the energy of the centrifugal barrier in an effective onedimensional potential is used to define the energy shift needed in Eq. (4.41). For the case of Ai = 0, we define the one-dimensional effective potential as (see Ref. 150 for the case of AT > 0)... 

In both the 7-shifting model and the capture model it is assumed that the reaction probabilities are a function of the available energy, which is the energy... 

Lemon, K.P. Grossman, A.D. (2001) The extrusion-capture model for chromosome partitioning in bacteria. Genes Dev. 15, 2031-2041. 

Among those TDQM studies, exact quantum dynamical calculations were usually limited to the total angular momentum / = 0. For / > 0, most of the authors used a capture model (or L-shift model) [77] to estimate the reaction probability from the / = 0 results. Even the direct calculations of reaction probabilities for / > 0 were performed using the centrifugal sudden (CS) approximation. Carroll... 

The result of Eq. 11 agrees with Focrf obtained above by Ugelstad and Hansen [15]. Therefore, both Eq. 9 developed by Hansen and Ugelstad and Eq. 11 developed here can explain the value of kep/ em=10 found experimentally by Nomura et al. [14], although no direct experimental confirmation of the vahdity of these radical capture models have been reported yet. 

A critical assumption in the preceding formulation is Eq. (150), which assumes that a set of distinct models captures modeling uncertainty. Ideally, one would like to have a continuum of models such that the real plant is one point in that continuum. The continuum could be approximated by considering a very large number of distinct models, with the obvious trade-off of increase in the dimensionality of the on-line optimization problem. 

The fact that the O2+ measurements exceed the Langevin-Giomousis-Stevens (LGS) capture cross section raise a suspicion that these GIB cross sections may be too high. On the other hand, the simple LGS capture model may not be applicable in a case where rapidly dissociating states are produced, as is the case in the 02" " + Na system. Inspection of the O2/O2+ vibrational coordinates on a charge transfer energy scale... 

There are, in feet, two good analogues for the above two-step roll and capture model, periiaps appropriately called kiss and embrace in more antluopomorphic terms (i) the... 

The first study of this type in the Moerner lab explored the histidine kinase PleC, which localizes at one of the poles of the cell during the cell cycle. PleC fusions to EYFP were easily observed at the single-molecule level in C. crescentus cells, mostly diffusing via attachment to the inner membrane [114]. Because no directed transport or motional asymmetry was observed, the authors were able to conclude that a diffusion-to-capture model could explain the observed localization behavior. 

Capture model a,nd total reactive cross sections... 

Both in the J-shifting model and in the capture model, it is assumed that the reaction probabilities are a function of the available energy, which is the energy in excess of the barrier height. This function of the excess energy is assumed to be universal (i.e., the same for all J values). One can then take the results for some I)artieular J values and use them to define how reaction probability varies as a function of the excess energy. 

Figures 5A and 5B present the total reactive cross section for reaction N( D) + 0 2(X E ) —> O( P) -I- NO(X n) as a function of the initial relative translational energy [115] on its two lowest adiabatic surfaces (2 A and 1 A"). The Oo reactant is in its ground vib-rotational state in both cases. The cross sections have been calculated using the real wavepaeket [98] and the capture model approaches [112]. Figure 5A shows the total reactive cross section on the 2 A surface.

Gray, S.K.. Goldfield, E.M.. Schatz, G.C. and Balint-Kurti, G.G. (1999) Helidty decoupled quantum dynamics and capture model cross sections and rate constants... 

---