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Vibrational cluster models

Espelid and B0rve [100] have recently explored the structure, stabihty, and vibrational properties of carbonyls formed at low-valent chromium boimd to sibca by means of simple cluster models and density fimctional theory (DFT) [101]. These models, although reasonable, do not take into consideration the structural situations discussed before but they are a useful basis for discussion. They foimd that the pseudo-tetrahedral mononuclear Cr(II) site is characterized by the highest coordination energy toward CO. [Pg.19]

The requirements for Raman resonance that must be fulfilled are the following (120,121) (a) total symmetry of the vibrations with respect to the absorbing center, and (b) same molecular deformation induced by the electronic and vibrational excitations. Quantum chemical calculations (41) of the vibrational frequencies and the electronic structure of shell-3 cluster models allowed the assignment of the main vibrational features, as shown in Fig. 7. The 1125 cm-1 band is unequivocally assigned to the symmetric stretching of the Ti04 tetrahedron. [Pg.43]

Just as in our abbreviated descriptions of the lattice and cell models, we shall not be concerned with details of the approximations required to evaluate the partition function for the cluster model, nor with ways in which the model might be improved. It is sufficient to remark that with the use of two adjustable parameters (related to the frequency of librational motion of a cluster and to the shifts of the free cluster vibrational frequencies induced by the environment) Scheraga and co-workers can fit the thermodynamic functions of the liquid rather well (see Figs. 21-24). Note that the free energy is fit best, and the heat capacity worst (recall the similar difficulty in the WR results). Of more interest to us, the cluster model predicts there are very few monomeric molecules at any temperature in the normal liquid range, that the mole fraction of hydrogen bonds decreases only slowly with temperature, from 0.47 at 273 K to 0.43 at 373 K, and that the low... [Pg.161]

Fig. 25. The vibrational eigenvalue spectrum from the cluster model (from Ref. 68>)... Fig. 25. The vibrational eigenvalue spectrum from the cluster model (from Ref. 68>)...
A new and efficient computational strategy has been presented, that simplifies the calculation of the vibrational frequencies of a molecular system adsorbed on moderate to large cluster models. This procedure is based on a certain hypothesis and assumption. Nevertheless, present results show that these do not affect the numerical accuracy of the calculated frequencies. An important consequence of this strategy is that largely simplifies the study of the effect of a uniform electric field on the frequencies of an adsorbed species. This is because it is not necessary to recalculate the normal coordinates at each value of the electric field. The method has been presented in connection to a cluster model representation of the surface, but it can be directly applied to periodical approaches without further modification. [Pg.224]

Alternatively, it is proposed that a comparison between theoretical frequencies obtained from cluster model calculations and experimental spectra is a worthwhile approach to study and assign the vibrational frequencies of oxy-anions adsorbed on single-crystal electrodes. [Pg.225]

We have followed a phenomenological approach and used the cluster model [18]. In this model the eg-type distortion interacts more strongly with the electronic state of an octahedral coordinated Cr3+ ion than the distortions of t2g symmetry. According to Ham [19], we assume that the continuum of vibrational modes with eg character can be approximated by a single mode with an effective frequency o>, mass /r and coupling constant V. The collective coordinates of the eg mode are conventionally known as Qe x2 — y2) and Qs ( 3z2 — r2). The linear Jahn-Teller Hamiltonian in equation (1) for the X state is [18] ... [Pg.533]

As mentioned above, HOSi(OA)3 may be taken as the simplest cluster model of the terminal hydroxyl group in silicas. Indeed, even with this cluster CNDO/BW provided a quite satisfactory description of the lower part of the curve representing potential energy as a function of the OH stretching vibration coordinate ROH (Fig. 2) (48,49). The respective experimental curve was plotted by Kazansky et al. (49) based on the analysis of the fundamental frequency vOH and the first overtone of the characteristic OH stretching vibration in terms of the Morse potential function. The frequencies of the second and third overtones were also determined in that work, and it was shown that the Morse potential reproduced well the potential curve within a rather wide range of ROH. [Pg.146]

The hydroxyl groups of the first kind are already absent in faujasites, quite in accordance with the cluster model predictions. Instead, two other bands with fundamental stretching vibration frequencies of 3640 and 3650 cm-1 were observed in Y zeolites. They were assigned to OH-II groups located within the large cavities (3650 cm 1) and to OH-II groups positioned inside the hexagonal prisms (3555 cm 1) (82). [Pg.164]

Our calculations also support the picture, already suggested by several experimental studies, of a significantly distorted adsorbate on the three metal surfaces there is a lengthening of the CC bond and a rehybridization of the carbon atoms from sp toward sp On these three surfaces, the a-donation is stronger than the d-rt backdonation, leading to positively charged species on the surface. The results obtained, also show that on platinum, palladium and nickel (100) surfaces the ethylene molecule adsorbs preferentially on the di-o mode. This conclusion is based not only on the adsorption energies (whose calculation is known to be the major problem of the cluster model approach) but also on a comparision between the calculated vibrational frequencies and the available experimental results. [Pg.237]

Adsorption energies, equilibrium distances and vibrational frequencies from Cl calculations on CH and H adsorbed at different sites on a cluster model of the Ni(lll) surface. Embedding theory... [Pg.146]


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