Adiabatic energy transfer

Adiabatic energy transfer occurs when relative collision velocities are small. In this case the relative motion may be considered a perturbation on adiabatic states defined at each intermolecular position. Perturbed rotational states have been introduced for T-R transfer at low collision energies and for systems of interest in astrophysics.A rotational-orbital adiabatic basis expansion has also been employed in T-R transfer,as a way of decreasing the size of the bases required in close-coupling calculations. In T-V transfer, adiabatic-diabatic transformations, similar to the one in electronic structure studies, have been implemented for collinear models.Two contributions on T-(R,V) transfer have developed an adiabatical semiclassical perturbation theory and an adiabatic exponential distorted-wave approximation. Finally, an adiabati-cally corrected sudden approximation has been applied to RA-T-Rg transfer in diatom-diatom collisions. 

Quantum dynamical calculations are reviewed, in different approximations and for sudden and adiabatic energy transfer. The inverse scattering problem is briefly covered, as well as the many-body approach to molecular collisions. 

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,... 

How are the energy transfer requirements for the process best accomplished Should one operate isothermally, adiabatically, or in accord with an alternative temperature protocol ... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

In the formulation of the boundary conditions, it is presumed that there is no dispersion in the feed line and that the entering fluid is uniform in temperature and composition. In addition to the above boundary conditions, it is also necessary to formulate appropriate equations to express the energy transfer constraints imposed on the system (e.g., adiabatic, isothermal, or nonisothermal-nonadiabatic operation). For the one-dimensional models, boundary conditions 12.7.34 and 12.7.35 hold for all R, and not just at R = 0. 

Chen KY, Hsieh CC, Cheng YM et al (2006) Tuning excited state electron transfer from an adiabatic to nonadiabatic type in donor-bridge-acceptor systems and the associated energy-transfer process. J Phys Chem A 110 12136-12144... 

Kiefer PM, Hynes JT (2002) Nonlinear free energy relations for adiabatic proton transfer reactions in a polar environment. I. Fixed proton donor—acceptor separation. J Phys Chem A... 

FIGURE 6.6 Potential energy diagram for the theory of electron transfer reactions. The activated complex is at S. For reasonably fast reactions, the reactant adheres to the lower curve and slithers into the product curve through the activated complex—that is, an adiabatic electron transfer occurs. 

From the above discussion, we can see that the purpose of this paper is to present a microscopic model that can analyze the absorption spectra, describe internal conversion, photoinduced ET, and energy transfer in the ps and sub-ps range, and construct the fs time-resolved profiles or spectra, as well as other fs time-resolved experiments. We shall show that in the sub-ps range, the system is best described by the Hamiltonian with various electronic interactions, because when the timescale is ultrashort, all the rate constants lose their meaning. Needless to say, the microscopic approach presented in this paper can be used for other ultrafast phenomena of complicated systems. In particular, we will show how one can prepare a vibronic model based on the adiabatic approximation and show how the spectroscopic properties are mapped onto the resulting model Hamiltonian. We will also show how the resulting model Hamiltonian can be used, with time-resolved spectroscopic data, to obtain internal... 

In the ensuing discussion, the energy dependence of the rate constants for proton transfer within a variety of substituted benzophenone-lV, /V-dimethylaniline contact radical ion pairs is examined only the data for the nitrile solvents are discussed. This functional relationship is examined within the context of theories for non-adiabatic proton transfer. Finally, these results are viewed from the perspective of other proton-transfer studies that examine the energy dependence of the rate constants. 

Calhoun and Voth also utilized molecular dynamic simulations using the Anderson-Newns Hamiltonian to determine the free energy profile for an adiabatic electron transfer involving an Fe /Fe redox couple at an electrolyte/Pt(lll) metal interface. This treatment expands upon their earlier simulation by including, in particular, the influence of the motion of the redox ions and the counterions at the interface. 

Pig. 2-37. Redox reaction cycle FeJ5 - Fejj + ei iD, - FeJ in aqueous solution solid arrow=adiabatic electron transfer, dotted arrow = hydrate structure reorganization X = reorganization energy ered.d = most probable donor level eox.a = most probable acceptor level. 

For reference purposes, we consider first adiabatic population transfer in a subset of three states decoupled from the full manifold of states. This adiabatic transfer can be driven by STIRAP. The subset of states we consider consists of 1200000), 1300000) and 200020), and the population transfer is from 200000) to 1200020). In the following paragraph, we refer to these states as 11), 5 ), and 6), respectively. We note that state 210011) with energy 5658.1828 cm is nearly degenerate with state 1200020) with energy 5651.5617 cm . We refer to 1210011) as state 9). Since the transition moment coupling states 11) and 6) is one order of... 

The examples of CDF-aided vibrational energy transfer we have discussed modify the STIRAP process. Broadly put, the goal of an assisted adiabatic process is the complete transfer of population from an initial state to a selected target... 

---