Spin transfer models

There is a vast field in chemistry where the spin-boson model can serve practical purposes, namely, the exchange reactions of proton transfer in condensed media [Borgis et al. 1989 Suarez and Silbey 1991a Borgis and Hynes 1991 Morillo et al. 1989 Morillo and Cukier 1990]. 

Although the classical mapping formulation yields the correct quantum-mechanical level density in the special case of a one-mode spin-boson model, the classical approximation deteriorates for mulhdimensional problems, since the classical oscillators may transfer their ZPE. As a hrst example. Fig. 21a compares Nc E) as obtained for Model I in the limiting cases y = 0 and 1 (thin solid lines) to the exact quantum-mechanical density N E) (thick line). The classical level density is seen to be either much higher (for y = 1) or much lower (for y = 0) than the quantum result. Since the integral level density can be... 

The semiclassical mapping approach outlined above, as well as the equivalent formulation that is obtained by requantizing the classical electron-analog model of Meyer and Miller [112], has been successfully applied to various examples of nonadiabatic dynamics including bound-state dynamics of several spin-boson-type electron-transfer models with up to three vibrational modes [99, 100], a series of scattering-type test problems [112, 118, 120], a model for laser-driven... 

There is now fairly good evidence from EPR/ENDOR on the S2 state MLS that the observed signal and the 55Mn hyperfine structure results from a single Miu cluster with electron spin density distributed over all 4 Mn ions.462 465 In this work 55Mn ENDOR experiments, which deliver more precise hfc and nqc values463 and spectral simulations,462-466 have been of great importance. Independent support for the model came from simulations of the NH3-modified MLS that showed a spin redistribution in the Mm cluster rather than spin transfer to other atoms.462-463... 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

In most cases, carbon-centered radicals carry the unpaired electron in p(7t)-type orbitals. Since C isotopes are present at a very low percentage (natural abundance, 1.11%), the spin distribution is monitored by adjacent H nuclei. The spin from the p-type orbital of the C atom is transferred to the adjacent H atom (H ) via n-spin polarization (Fig. 7.2a) however, spin transfer to more distant protons follows the model of a hyperconjugation mechanism illustrated in Fig. 7.2b. The closer the Cp-Hp is oriented toward the z-axis of the C p orbital, (0 = 0°) the bigger becomes the Hp hfc. When 0 is equal to 90°, the Hp hfc reaches its minimum value. This behavior is described by an empirical formula ... 

Obviously, the interactions sketched in Fig. 7.2 are very helpful, yet rough, empirical models for efficient spin transfer. Substantially more precise hfc values... 

Fig. 17. Longitudinal H NMR relaxation parameters at 30 MHz for water adsorbed on lysozyme powders derived from the cross-relaxation model after setting the protein relaxation rate equal to 0. Tis the water proton relaxation time and 7", is the time constant characterizing spin transfer between the protein protons and the water protons. From Hilton etal. (1977).

Electron transfer processes, more generally transitions that involve charge reorganization in dielectric solvents, are thus shown to fall within the general category of shifted harmonic oscillator models for the thennal enviromnent that were discussed at length in Chapter 12. This is a result of linear dielectric response theory, which moreover implies that the dielectric response frequency a>s does not depend on the electronic charge distribution, namely on the electronic state. This rationalizes the result (16.59) of the dielectric theoiy of electron transfer, which is identical to the rate (12.69) obtained from what we now find to be an equivalent spin-boson model. 

The localization of the lowest-energy exciton in ionic solids like the alkali halides is such that neither the Frenkel nor Wannier approximation is valid. An early picture of the excitation by Hilsch and Pohl [58] was that absorption of a photon results in the transfer of an electron from one of the halogen ions to a neighboring alkali ion. This charge-transfer model of the exciton attributed observed double-absorption peaks to the spin-orbit splitting of the halide ion, and successfully predicted exciton energies by the empirical relation... 

In the case of covalency in a magnetic complex, charge transfer from ligand to partially filled metal orbitals results in a transfer of spin density in the opposite direction. The magnitude of the spin transfer, obtainable from LHFI, is directly related to the covalency parameters by the simple MO model (see Section II. B). 

Having understood the interplay between the excitation gap and the bond coupling delay effect, we can now present some other features of the model. This is done by reviewing topics in spin transfer reactions and by an application to a cycloaddition reaction (both reactions are defined as isovalent types). 

The processes we have considered thus far - extrusion, wire coating, and injection and compression molding - are dominated by shear between confined surfaces. By contrast, in fiber and film formation the melt is stretched without confining surfaces. It is still possible to gain considerable insight from very elementary flow and heat transfer models, but we must first parallel Section 2.2 and develop some basic concepts of extensional flow. The remainder of the chapter is then devoted to an analysis of fiber formation by melt spinning. 

MC path integral simulations have been performed on a spin-boson model of the RC. A phase diagram for the ET process has been compiled based on the results of many path integral simulations. This is shown in Figure 3. The solid lines show which combinations of 2 and H12 could have produced dynamics consistent with experimentally observed behaviors. There is a gap region between the sequential and the superexchange region in which no 1 -> 3 transfer consistent with experiment can be seen. 

A series of electron donors and acceptors together can form a charge transfer chain (CTC). Examples of these are found in some electron transfer proteins, Electron transport in ID CTCs has been studied using the spin-boson model with multiple tight-binding electronic states. The nature of the transport depends on the strength of the dissipation of the environment. 

Abstract Photoinduced processes in extended molecular systems are often ultrafast and involve strong electron-vibration (vibronic) coupling effects which necessitate a non-perturbative treatment. In the approach presented here, high-dimensional vibrational subspaces are expressed in terms of effective modes, and hierarchical chains of such modes which sequentially resolve the dynamics as a function of time. This permits introducing systematic reduction procedures, both for discretized vibrational distributions and for continuous distributions characterized by spectral densities. In the latter case, a sequence of spectral densities is obtained from a Mori/Rubin-type continued fraction representation. The approach is suitable to describe nonadiabatic processes at conical intersections, excitation energy transfer in molecular aggregates, and related transport phenomena that can be described by generalized spin-boson models. 

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