State crossings

Baer M, Faubel M, Martinez-Haya B, Rusin L Y, Tappe U and Toennies J P 1998 A study of state-to-state differential state cross-sections for the F + 02(0.= 0,jl) —> DF(u y ) + D reactions a detailed comparison between experimental and three dimensional quantum mechanical results J. Chem. Phys. 108 9694... 

The motivation comes from the early work of Landau [208], Zener [209], and Stueckelberg [210]. The Landau-Zener model is for a classical particle moving on two coupled ID PES. If the diabatic states cross so that the energy gap is linear with time, and the velocity of the particle is constant through the non-adiabatic region, then the probability of changing adiabatic states is... 

A simple method for predicting electronic state crossing transitions is Fermi s golden rule. It is based on the electromagnetic interaction between states and is derived from perturbation theory. Fermi s golden rule states that the reaction rate can be computed from the first-order transition matrix and the density of states at the transition frequency p as follows ... 

The golden rule is a reasonable prediction of state-crossing transition rates when those rates are slow. Crossings with fast rates are predicted poorly due to the breakdown of the perturbation theory assumption of a small interaction. 

We counted the contribution of only those trajectories that have a positive momentum at the transition state. Trajectories with negative momentum at the transition state are moving from product to reactant. If any of those trajectories were deactivated as products, their contribution would need to be subtracted from the total. Why Because those trajectories are ones that originated from the product state, crossed the transition state twice, and were deactivated in the product state. In the TST approximation, only those trajectories that originate in the reactant well are deactivated as product and contribute to the reactive flux. We return to this point later in discussing dynamic corrections to TST. 

The reverse reaction, closure of butadiene to cyclobutene, has also been explored computationally, using CAS-SCF calculations. The distrotatory pathway is found to be favored, although the interpretation is somewhat more complex than the simplest Woodward-Hoffinann formulation. It is found that as disrotatory motion occurs, the singly excited state crosses the doubly excited state, which eventually leads to the ground state via a conical intersection. A conrotatory pathway also exists, but it requires an activation energy. 

Stimulated emission is quantified by the (wavelength dependent) excited state cross-section other processes are important, stimulated emission leads directly to amplification of light. In a material with a volume density fVcxc of excited 5 -states this amplification can be described by... 

Category 5. Hydrogen Atom Abstraction. When benzophenone is irradiated in isopropyl alcohol, the initially formed Si state crosses to the Ti state, which abstracts hydrogen from the solvent to give the radical 7. Radical 7 then abstracts another hydrogen to give benzhydrol (8) or dimerizes to benzpinacol (9) ... 

The study of quantum yields. The quantum yield is the fraction of absorbed light that goes to produce a particular result. There are several types. A primary quantum yield for a particular process is the fraction of molecules absorbing light that undergo that particular process. Thus, if 10% of all the molecules that are excited to the state cross over to the T state, the primary quantum yield for that process is 0.10. However, primary quantum yields are often difficult to measure. A product quantum yield (usually designated ) for a product P that is formed from a photoreaction of an initially excited molecule A can be expressed as... 

Blancafort L, Robb MA (2004) Key role of a threefold state crossing in the ultrafast decay of electronically excited cytosine. J Phys Chem A 108 10609... 

Fig. 14 are the simulated distributions including the different parent rotational levels. An interesting observation from these distributions is that the shape of the multiplet peak corresponding to each 011 (/I) rotational level for the perpendicular polarization is not necessarily the same as that for the parallel polarization see for example the peak labelled v = 0, N = 22. From the simulations, relative populations are determined for the OH (A) product in the low translational energy region from H2O in different rotational levels for both polarizations. The anisotropy parameters for the OH product from different parent rotational levels are determined. Experimental results indicate that the ft parameters for the 011 (/I) product from the three parent H2O levels Ooo, loi, I11, are quite different from each other. Most notably, for the 011 (/I, v 0, N = 22) product the ft parameter from the foi H2O level is positive while the ft parameters from the Ooo and In levels are negative, indicating that the parent molecule rotation has a remarkable effect on the product anisotropy distributions of the OH(A) product. The state-to-state cross-sections have also been determined, which also are different for dissociation from different rotational levels of H2O. 

In conclusion, we stress that the complementary NLO characterization techniques of pump-probe, Z-scan, and 2PF allow for the unambiguous determination of nonlinear optical processes in organic materials. The important molecular parameters of 2PA cross section, fluorescence efficiency, reorientation lifetimes, excited state cross sections, etc. can be determined. 

In radiolysis, a significant proportion of excited states is produced by ion neutralization. Generally speaking, much more is known about the kinetics of the process than about the nature of the excited states produced. In inert gases at pressures of a few torr or more, the positive ion X+ converts to the diatomic ion X2+ very rapidly. On neutralization, dissociation occurs with production of X. Apparently there is no repulsive He2 state crossing the He2+ potential curve near the minimum. Thus, without He2+ in a vibrationally excited state, dissociative neutralization does not occur instead, neutralization is accompanied by a col-lisional radiative process. Luminescences from both He and He2 are known to occur via such a mechanism (Brocklehurst, 1968). 

We (as well as many others (4-8), for reviews see (9,10)) have been interested for some time (11,12) in the effect of spin-state changes on reactivity. In particular, we have used computational methods to explore these effects in transition metal chemistry ((13-15), for reviews see (10,16)). The key factor affecting reactivity is the relative energy at which the zeroth-order potential energy surfaces corresponding to the individual spin-states cross (Scheme 2). This factor will determine, among other things, whether spin-forbidden reactivity is competitive with... 

The NRT description of TS complexes is closely related to the general two-state valence bond model of Shaik and Pross.93 This model emphasizes the coupled changes in two adiabatic states that evolve from distinct diabatic valence-bond (VB) configurations r and states cross in energy at s = s, ... 

Canned motor pumps, 27 76-78 Canned pet foods, 70 849 Cannel coal, 6 705 Cannizzaro reaction, 72 110 solid-state crossed, 76 574 Cannon-Fenske viscometer, 27 728 Canoe fragrances, 75 360 Canonical ensemble, 7 33 Cans, two- and three-piece, 75 37-38. 

Solids retention time (SRT), 25 900 Solids separation, in solid-liquid separation, 11 342, 344 Solids suspension(s), 7 272t, 16 692-696 degrees of, 16 693 occurrences of, 7 273t Solid-state hydrogen, 13 850 Solid-state crossed Cannizzaro reactionp, 16 574... 

A connection between microscopic quantities such as state-to-state cross sections, state-to-state rate constant and macroscopic quantities such as overall rate constant k(T) is summarized in Flow Chart 1. 

One of the first approaches to study the microscopic kinetics i.e. state-to-state cross sections and reaction probabilities of a chemical reaction was the crossed molecular beam experiments. The principle of the method consists of intersecting two beams of the reactant molecules in a well-defined scattering volume and catching the product molecules in a suitable detector (Fig. 9.33). 

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