Model adiabatic

Quack M 1981 Faraday Discuss. Chem. Soc. 71 309-11, 325-6, 359-64 (Discussion contributions on flexible transition states and vibrationally adiabatic models statistical models in laser chemistry and spectroscopy normal, local, and global vibrational states)... 

Simons J 1989 Modified rotationally adiabatic model for rotational auto ionization of dipole-bound molecular anion J. Chem. Phys. 91 6858-68... 

Genera.1 Ca.se, The simple adiabatic model just discussed often represents an oversimplification, since the real situation implies a multitude of heat effects (/) The heat of solution tends to increase the temperature and thus to reduce the solubihty. 2) In the case of a volatile solvent, partial solvent evaporation absorbs some of the heat. (This effect is particularly important when using water, the cheapest solvent.) (J) Heat is transferred from the hquid to the gas phase and vice versa. (4) Heat is transferred from both phase streams to the shell of the column and from the shell to the outside or to cooling cods. 

If the tank has some headspace, as is usually the case, it is desirable to get a better estimate of the ac tual level, since tanks usually have some gas headspace even when filled with hquid. Two tank configurations are considered the gravity discharge tank (discharge is open to the atmosphere) and the pumped discharge tank. These calculations assume that the process is so rapid that an adiabatic model for the gas in the headspace is the correct choice. This is true when the drainage... 

The exchange reactions (6.20) and (6.21) have been among the basic objects of chemical-reaction theory for half a century. Clearly further investigation is needed, incorporating real crystal dynamics. It is worth noting that the adiabatic model, upon which the cited results are based, can prove to be insufficient because of the low frequency of the promoting vibrations. 

Since chemical reactions usually show significant nonadiabaticity, there are naturally quantitative errors in the predictions of the vibrationally adiabatic model. Furthermore, there are ambiguities about how to apply the theory such as the optimal choice of coordinate system. Nevertheless, this simple picture seems to capture the essence of the resonance trapping mechanism for many systems. We also point out that the recent work of Truhlar and co-workers24,34 has demonstrated that the reaction dynamics is largely controlled by the quantized bottleneck states at the barrier maxima in a much more quantitative manner than expected. 

In the meantime other experiments have also improved our range of observational results. For example, Watts et al. carried out experiments very similar to the NO/Ag(lll) experiments described above.32 A critical difference in this work was the substitution of Cu(110) in place of the Ag(lll). Despite the chemically distinct metal surface, nearly identical results were obtained as those in Refs. 24 and 25, including surface temperature and incidence energy dependence. While it is not unlikely that the bond softening of NO is similar on Ag(lll) and Cu(110), there is no a priori reason to believe that these two metals would exhibit the same incidence energy and surface temperature dependence in vibrational excitation experiments. More importantly, there has not been a theoretical attempt to explain why these two chemically distinct systems behave so similarly within the context of electronically adiabatic models. 

Levy, Healzer, and Abdollahian (1980) predicted the dryout flux in vertical pipes by a semiempirical adiabatic model (Levy and Healzer, 1980) for liquid film flow and entrainment. It starts with a heat balance along the flow direction and a mass balance perpendicular to the flow direction ... 

Finally, I refer back to the beginning of this paper, where the assumption of near-adiabaticity for electron transfers between ions of normal size in solution was mentioned. Almost all theoretical approaches which discuss the electron-phonon coupling in detail are, in fact, non-adiabatic, in which the perturbation Golden Rule approach to non-radiative transition is involved. What major differences will we expect from detailed calculations based on a truly adiabatic model—i.e., one in which only one potential surface is considered [Such an approach is, for example, essential for inner-sphere processes.] In work in my laboratory we have, as I have mentioned above,... 

Now, the global rate can be estimated at any conversion, since temperature can be calculated from eq. (5.232). Then, the conversion versus reactor depth or catalyst mass can be determined from the mass conservation equation (5.228). Only arithmetic solutions of the adiabatic model are possible. 

The most extensive potential obtained so far with experimental confirmation is that of Le Roy and Van Kranendonk for the Hj — rare gas complexes 134). These systems have been found to be very amenable to an adiabatic model in which there is an effective X—Hj potential for each vibrational-rotational state of (c.f. the Born Oppenheimer approximation of a vibrational potential for each electronic state). The situation for Ar—Hj is shown in Fig. 14, and it appears that although the levels with = 1) are in the dissociation continuum they nevertheless are quasi bound and give spectroscopically sharp lines. 

Another way of calculating the distribution of product states would be to apply an extension of RRKM that Wardlaw, Klippenstein, and I developed. However, judging from your observations, the reaction is highly vibrationally nonadiabatic, considering, for example, the considerable difference in vibrational quantum number vco in HCO and CO and the major change in bending — rotational state. In that case a Franck-Condon approach would seem to be much more appropriate than any adiabatic or near-adiabatic or statistically adiabatic model. 

For this adiabatic model, the LE to CT interconversion occurs on a single potential energy surface. The methods for describing charge transfers of this type have recently made major progress (see Section III.B). 

In summary, an adiabatic model for the first excited state of BA is able to account well for the equilibrium absorption and emission properties of BA. It seems reasonable to assume that many of the dual fluorescent molecules would be well described by an adiabatic model of this type. In the following section we show the dynamic properties of BA are also well described by an adiabatic model. Indeed, the results are revealing from the standpoint of understanding small barrier charge transfer reactions in general. 

It is useful to introduce the factors kd and kq to show explicitly the departure from the adiabatic model.3 Specifically we may write the dipole and quadrupole energies of Eqs. (17.15) and (17.16) in a form equivalent to the adiabatic forms. Explicitly... 

The adiabatic model predicts 4snf-4sng intervals a factor of 2 too high and the nonadiabatic model predicts intervals 10% lower than the measured frequencies. 

The 10% difference is probably due to core penetration in the 4snf states, which is not taken into account, and, according to the theoretical work of Vaidyanathan and Shorer12 should be of the same approximate size as the discrepancy. In any case, it is clear that the nonadiabatic core polarization model reproduces the observed intervals quite well, while the adiabatic model is substantially in error. 

Vibrationally adiabatic model an ultra simple model 123... 

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