Vibrational frequencies free surface

The results of the DFT calculations for various stable C2H.V species and transitions states on Pt(lll) and Pt(211) are summarized in Table V, which also shows entropy changes for the various steps, as estimated from DFT calculations of the vibrational frequencies of the various adsorbed C2H species and transition states on 10-atom platinum clusters (55). Table V also includes estimates of the standard Gibbs free energy changes for the formation of stable C2H surface species and activated complexes responsible for C-C bond cleavage at 623 K. These estimates were made by combining... 

The free-energy surface was probed by varying the distance r between the carboxylate carbon and C6 iteratively, fully optimizing the other coordinates. At each point, the free energy was estimated as AE-TAS by including zero-point energies and entropies based on the unsealed vibrational frequencies. The area... 

Finally, there are several approaches to determine the specific component of the surface free energy of carbon materials [71-73]. Among these, that proposed by Donnet et al [73] uses the standard adsorption free energy which is plotted against (hr L) o-10 , where h is the Planck constant, is the characteristic vibration frequency of the electron and a is the deformation polarizability. The method seems to provide reasonable results, although it does not take into account the effect of the surface irregularities. 

It must be kept in mind, however, that the two-dimensional potential curves of Fig. 1 do not consider the possibility of a change in the interatomic distances r, in the molecule, due to the adsorption process. A chemisorption, in particular, implies an increase of the interatomic distance of those atoms which enter into covalent bonds with widely separated centers of the surface 14). The excitation process in the free molecule often leads to a loosening of the bonds manifested in decreased vibrational frequencies and, consequently, to increased interatomic distances. In the limit, for molecules like iodine, the absorption of photons near the band maximum corresponds to a dissociation into atoms separated on the surface by a distance definitely larger than that when they were bound in the ground state. 

In the equilibrium solvation path (ESP) approximation [74, 76], ve first find a potential of mean force surface for the primary subsystem in the presence of the secondary subsystem, and then we finish the calculation using this free energy surface. Notice a critical difference from the SES in that now we find the MEP on U rather than V, and we now find solute vibrational frequencies using U rather than V. 

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