Vibration external adsorbate-adsorbent

The response of the system concerned to an external electromagnetic field is conveniently described in terms of double-time Green s function (GF) which can be introduced in a variety of representations.144,218 221 In what follows we will involve the representation in Matsubara s frequency space218 which is accepted in the theory of anharmonic crystals197 and provides a number of exact solutions in the case of a single adsorbed molecule.I50,1 2 In this approach, the spectral line shape for high-frequency vibrations can be determined as follows 184... 

Fortunately, the same limiting conditions that validate the friction approximation can also be used with time-dependent density functional theory to give a theoretical description of rjxx. This expression was originally derived to describe vibrational damping of molecules adsorbed on surfaces [71]. It was later shown to also be applicable to any molecular or external coordinate and at any location on the PES, and thus more generally applicable to non-adiabatic dynamics at surfaces [68,72]. The expression is... 

Vibrational Frequency of CO Adsorbed on Pd Clusters. In the next example, we present results for the vibrational properties of a CO molecule on a Pd surface, modelled by a cluster of 14 transition metal atoms (32 3). Furthermore, the influence of an external electric field is investigated using a smaller cluster, Pd2CO (33,34). In both cases, CO is assumed to be bonded in the bridge position. The chemically inactive Pd core electrons are described by a relativistic model potential as described in detail in Ref. 14. 

Second, being quasibound Inside a potential barrier on the perimeter of the molecule, such resonances are localized, have enhanced electron density In the molecular core, and are uncoupled from the external environment of the molecule. This localization often produces Intense, easily studied spectral features, while suppressing non-resonant and/or Rydberg structure and, as discussed more fully below, has a marked Influence on vibrational motion. In addition, localization causes much of the conceptual framework developed for shape resonances In free molecules to apply equally well to photolonlzatlon and electron scattering and to other states of matter such as adsorbed molecules, molecular crystals, and Ionic solids. 

Calculations by semi-empirical quantum mechanics of the INS of water on nickel clusters also refer to the riding modes [10,11]. The cluster Niii(H20), comprising a single layer of 11 nickel atoms with the water molecule bound to the central nickel atom, was modelled. The water molecule on top of the central nickel atom was at an optimised distance of 0.22 nm it was not dissociated. The INS of nickel particles with adsorbed water molecules was assigned with the aid of the computed spectrum peaks above 350 cm, to two external and two internal vibrations of the adsorbed water molecules peaks below 350 cm, to adsorbent (i.e. nickel) vibrations enhanced by hydrogen atoms... 

Figure 12. Plots of the binding energy Eh, anharmonic vibrational frequency vm.a, static dipole moment /t, dynamic dipole moment /, Hitshfeld charge Oh, and equilibrium bond distance r, as a function of the external field for hollow-site adsorbed Na (diamonds), O (circles), C (squares), and I (triangles) on 13-atom Pt clusters. Reprinted with permission fi-om S. A. Wasileski e al., J. Chem. Phys., IIS, (2001) 8193. Copyright 2001, American Institute of Physics...

IR spectra of ammonia adsorbed on oxovanadium species supported on porous sihca are shown in Figure 2.33. Two kinds of interactions with hydroxyl groups are evident (282). The broad band at about 1470 cm corresponds to the bending vibrations of ammonium ions formed by reaction with addic vanadia hydroxyls. The band at 1635 cm is ascribed to the bending mode of ammonia molecules H-bonded to silanols. Simultaneously, a shift of the OH stretching modes of the silanol groups (external silanols at 3745 cm and terminal and H-bonded silanols in hydroxyl chains at 3710 and 3547 cm, respectively) by about —800 cm is observed. The bands at 3390 and 3330 cm are assigned to N-H modes. 

The heat of adsorption q is approximated by the interaction potential at minimum position Ve diminished by the zero point vibrational energy of the external motions of the adsorbate Eo and the change of the thermal energy upon adsorption Es-Eg... 

The vibrational frequency shift arises from the perturbation of the molecular eigenvalues by adsorption. The interaction potential depends on the internal stretching coordinate =(r-re)/re. The vibrational potential of the adsorbed molecule V(0 is composed of the internal potential of the free molecule and the external potential... 

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