Umbrella mode

In the "scissors mode" of H2O, the protons move parallel to the surface and the oscillation frequency is almost unaffected. For NH3, on the other hand, the so called "umbrella mode" is drastically stiffened by the surface because the protons move against the surface and suffer a strong Coulomb repulsion. Here again the dynamical dipole moment is dp/da = 2 Pj, slnda. For NHj, where Pjj = 0.53 a.u., the enhancement of the aynamlc dipole by the surface is compensated by the smaller oscillation amplitude. 

The methanol trimer is arguably one of the most interesting clusters. The unexpected structure in its O—H stretching spectrum [65, 75, 77, 173] has only recently found a consistent explanation [16]. It is not related to structural isomers [64, 75, 195, 219, 220] but rather to simultaneous excitation and de-excitation of low-frequency methyl umbrella modes [16, 65], that is, a... 

Figure 6. The complex OH stretching spectrum of methanol trimer (bottom) can be explained by sum (v5), difference (vD), and hot bands (vH) involving the OH fundamental (vF) and two umbrella modes of the methyl groups, which are nearly degenerate in the ground state but soften and split after OH stretching excitation. vR is the predominantly Raman active concerted stretching mode [16].

Fig. 1. The highest occupied molecular orbital for the closing umbrella mode.

Inelastic tunnelling electrons can also be used to selectively induce either the translation over a metallic surface or desorption from the metallic surface of individual molecules, as has been shown for NH3 on Cu(lOO) surfaces (Pascual et al, 2003). Activation of either the stretching vibration of ammonia ( 408 meV) leading to lateral translation on the surface, or the inversion of its pyramidal structure (umbrella mode s(NH3) 139 meV) leading to desorption, can be achieved by adjusting 7t and Vt. 

Table 9.4 compares to experiment the isotropic h.f.s. values computed for and H in the methyl radical at the UMP2/6-311G(d,p) level both (i) at the UHF/6-31G(d) equilibrium geometry and (ii) as the expectation value over the umbrella mode vibrational wave function computed at this level. Also included are data for the monofluoromethyl radical CHiF, which is even more affected by vibrational averaging because it has a very shallow doublewell potential along the umbrella mode (i.e., the equilibrium structme is pyramidal, but the barrier to inversion is less than 1 kcal mol ), so that its vibrational wave function has large amplitude around a planar structure with smaller h.f.s. than for the equilibrium structure. 

M. Shapiro Prof. Neumark, in general, I was struck by the similarity between your data on the CH3O radical and the photodissociation of CH3I, which we analyzed many years ago. In particular, it is interesting to note that the degree of excitation of the umbrella mode is similar and appears to increase with increasing excitation of the parent molecule. Obviously the exit channel dynamics dominate here. 

In modelling the vibrational umbrella mode for ammonia, the potential energy function V = i/cx2 + be cx is commonly used, where b and c are constants (see Figure 2.11). 

The computation is confined to RHF-6-311 + +G(2d,2p) level [16]. At one side, the limitation to the RHF is imposed by the actual availability of analytical second derivatives to this level only, but is also justified from other perspectives. A practical reason for the RHF scheme is clearly seen if translate to the same relative position (with /J3/, reference point as origin) the relaxed potential energy surfaces for the umbrella mode of NH3 computed at different levels (RHF, MP2, CCSD(T), B3LYP/6-311 + + G(2d,2p)). Figure 1 shows that the very different methods give... 

Fig. 6.10. Measured (Felder 1990) and calculated vibrational state distributions for the C-F3 umbrella mode ( 2) in the dissociation of CF3I at 248 nm.

The photodissociation of trifluoromethyl iodide, CF3I —> CF3 + I/I, which was briefly discussed in Section 6.4, seems to illustrate case (a) of Figure 9.4 while the photo dissociation of methyl iodide, CH3I —> CH3 + I/I, appears more to represent case (b). In both examples, the 1/2 umbrella mode, in which the C atom oscillates relative to the Irrespectively F3-plane, is predominantly excited. Following Shapiro and Bersohn (1980) the dissociation of CH3I and CF3I may be approximately treated in a two-dimensional, pseudo-linear model in which the vibrational coordinate r describes the displacement of the C atom from the H3-/F3-plane and the dissociation coordinate R is the distance from iodine to the center-of-mass of CH3/CF3 (see Figure 9.6).t... 

Fig. 9.7. (a) Final vibrational state distribution in the umbrella mode of CH3... 

Fig. 14.2. Raman spectrum for CH3I obtained by excitation at 266 nm. 3n stands for the nth eigenstate of the 1/3-mode, for example. 1/3 and v2 are the C-I and the CEb-umbrella mode, respectively. Reproduced from Imre, Kinsey, Sinha, and Krenos (1984).

Richard Zare and coworkers found that excitation of the umbrella mode of NH(T selectively enhances the proton transfer reaction however, in this case the projection of the nuclear motion onto the reaction coordinate is not as obvious. 

In the case of vibrational excitation of NH3 at a metal surface a very different dependence has been observed [119]. In this case, the vibrational excitation could be attributed to mechanical excitation of the NH3 umbrella mode in the collision with the surface. Finally, it is worth mentioning that at much higher energies, way into the domain of tens of eV s, mechanical excitation will lead to molecular vibrational excitation and dissociation for all molecules, see e.g. [120]. 

The RBU model can be used to study the effect of exciting the vibrational modes treated within the model. For the reactions X (X=C1, 0 and H) + CH4 HX + CH3 we find that exciting a vibrational inode results in a lower threshold to reaction. It was also found that exciting the reactive C-H stretch enhances the reactivity more than exciting the CH4 umbrella mode. Vibrational enhancements for the umbrella and C-H stretch vibrations have also been found in other studies of the dynamics[75, 80] and in canonical variational transition state theory (C T) calculations [84]. Enhancement of the Cl + CH4 reaction due to vibrational excitation of the H-CH3 stretch has also been confirmed b experimental measurements by Zare and coworkers[85]. 

For Cl f CH4 reacting out of the vibrational ground state to form j)ioducts in the vibrational ground state we find predominantly sideways and backward scattering. Also, the umbrella mode of the CH3 product is not excited. These calculated results are in good agreement with the experimental measurements. 

In summary, the agreement with the experimental results is good except in one case. This is for the normal isotope reaction out of CH4 with one (luantum in a stretch vibration giving ground state HCl. In this case the calculations gives more umbrella mode excitation than the experiments. 

Wang, M.L. and Zhang, J.Z.H. (2002) Generahzed semirigid vibrating rotor target model for atom-polyatom reaction Inclusion of umbrella mode for the H + CH4 reaction, J. Chem. Phys. 

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