Energy deviations from full

Explicit results are only presented by MWT for NO/Ag(l 11). To the extent that the relationship AE/kTg scales with ., deviations from full accommodation might be expected for NO/Pt(lll) at Ts>750K. An additional mechanism for reducing the rotational energy of the desorbed species arises... 

The operation of Eq. (3.3) is illustrated by the results given in Table 2 out of 48 molecules of the cc-pVTZ set. They are listed in order of increasing correlation energy. The first column of the table lists the molecule. The next 6 columns show how many orbitals and orbital pairs of the various types are in each molecule, i.e. the numbers Nl, Nb, Nu, Nlb etc. The seventh column lists the CCSD(T)/triple-zeta correlation energy and the eight column lists the difference between the latter and the prediction by Eq. (3.3). The mean absolute deviation over the entire set of cc-pVTZ data set is 3.14 kcal/mol. For the 18 molecules of the CBS-limit data set it is found to be 1.57 kcal/mol. The maximum absolute deviations for the two data sets are 11.29 kcal/mol and 4.64 kcal/mol, respectively. Since the errors do not increase with the size of the molecule, the errors in the estimates of the individual contributions must fluctuate randomly within any one molecule, i. e. there does not seem to exist a systematic error. The relative accuracy of the predictions increases thus with the size of the system. It should be kept in mind that CCSD(T) results can in fact deviate from full Cl results by amounts comparable to the mean absolute deviation associated with Eq. (3.3). 

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

Energies for a selection of homolytic bond dissociation reactions of two-heavy-atom hydrides are provided in Table 6-2. These have been drawn from a larger collection found in Appendix A6 (Tables A6-1 to A6-8). A summary of mean absolute deviations from G3 calculations (based on the full collection) is provided in Table 6-3. 

For molecular desorption, laser spectroscopic studies of the desorbing molecule can give full internal state distributions, Df Ef, 6f, v, J, f M ), Ts), where f M ) is some distribution function describing the rotational orientation/alignment relative to the surface normal. For thermal desorption in non-activated systems, most atoms/molecules have only modest (but important) deviations from a thermal distribution at Ts. However, in associative desorption of systems with a barrier, the internal state distributions reveal intimate details of the dynamics. Associative desorption results from the slow thermal creation of a transition state, with a final thermal fluctuation causing desorption. Partitioning of the energy stored in V into... 

The final total energy is effectively at the QCISD(T,FULL)/G3Large level if the different additivity approximations work well. The average absolute deviation from experiment of G3 theory for the G2/97 test set is 1.01 kcal/mol (see Table 5). For the subset of 148 neutral enthalpies of formation the average absolute deviation is 0.93 kcal/mol. The corresponding deviations for G2 theory are 1.49 and 1.56 kcal/mol, respectively. The improvement over G2 theory is shown in Figure 3 for different types of molecule in the G2/97 test set. 

Here the full Eq. (12.11) should be considered with potentially much larger deviations from the energies of the true Forster cycle transitions. 

If the diabatic coupling matrix element, He, is -independent, this d/dR matrix element between two adiabatic states must have a Lorentzian H-depen-dence with a full width at half maximum (FWHM) of 46. Evidently, the adiabatic electronic matrix element We(R) is not - independent but is strongly peaked near Rc- Its maximum value occurs at R = Rc and is equal to 1/46 = a/4He. Thus, if the diabatic matrix element He is large, the maximum value of the electronic matrix element between adiabatic curves is small. This is the situation where it is convenient to work with deperturbed adiabatic curves. On the contrary, if He is small, it becomes more convenient to start from diabatic curves. Table 3.5 compares the values of diabatic and adiabatic parameters. The deviation from the relation, We(i )max x FWHM = 1, is due to a slight dependence of He on R and a nonlinear variation of the energy difference between diabatic potentials. When We(R) is a relatively broad curve without a prominent maximum, the adiabatic approach is more convenient. When We (R) is sharply peaked, the diabatic picture is preferable. The first two cases in Table 3.5 would be more convenient to treat from an adiabatic point of view. The description of the last two cases would be simplest in terms of diabatic curves. The third case is intermediate between the two extreme cases and will be examined later (see Table 3.6). 

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