Frustrated rotation

In general a nonlinear molecule with N atoms has three translational, three rotational, and 3N-6 vibrational degrees of freedom in the gas phase, which reduce to three frustrated vibrational modes, three frustrated rotational modes, and 3N-6 vibrational modes, minus the mode which is the reaction coordinate. For a linear molecule with N atoms there are three translational, two rotational, and 3N-5 vibrational degrees of freedom in the gas phase, and three frustrated vibrational modes, two frustrated rotational modes, and 3N-5 vibrational modes, minus the reaction coordinate, on the surface. Thus, the transition state for direct adsorption of a CO molecule consists of two frustrated translational modes, two frustrated rotational modes, and one vibrational mode. In this case the third frustrated translational mode vanishes since it is the reaction coordinate. More complex molecules may also have internal rotational levels, which further complicate the picture. It is beyond the scope of this book to treat such systems. 

A noteworthy feature of the photoacoustic spectra shown in Figure 2 Is the presence of water librations. These are frustrated rotations and have been observed for ice (24) by infrared spectroscopy, as well as for water adsorbed on Ft and Ag surfaces by electron energy loss spectroscopy (25-27). The three libration modes have been associated with the bands at 600, 538 and 468 cm" > this set of peaks occurs for water adsorbed on both the hydroxylated and methoxylated silica. 

The low-frequency shift and the broadening of the CO spectra at 0 ps suggest that the low-frequency modes of adsorbed CO, that is, stretching, frustrated rotation, and frustrated translation modes of Pt-CO, were thermally excited by pump pulses, as reported by Bonn et al. [82] Thus, it is concluded that the transient site migration of adsorbed CO on the Pt electrode surface was caused by a transient rise in the surface temperature of Pt induced by pump pulses. 

Park YS, Widawsky JR, Kamenetska M, Steigerwald ML, Hybertsen MS, Nuckolls C, Venkataraman L (2009) Frustrated rotations in single-molecule junctions. J Am Chem Soc 131 10820-10821... 

In contrast to Eq. (3.13) of Ref. 1 where ur(r0+ur)s mO, we assume that the force constant kg of the frustrated rotation with the changing angle 6 is independent of ur). On substituting values (4.3.20) in Eq. (4.3.18) and accounting for the doubled contribution from two modes rop mutually perpendicular in the surface plane, we obtain ... 

Fig. 6. Schematic representation of the normal modes of an adsorbed diatomic molecule neglecting the surface structure, after Richardson and Bradshaw . In parentheses the experimentally measured values for CO in the ontop position on Pt(lll). (a) A frustrated translation (60 cm (b) A frustrated rotation (not yet detected), (c) The metal-molecule stretch (460cm ) . (d) The intramolecular stretch model (2100cm" ) . ...

The important conclusion is that we get a very good fit to the experimental data assuming an anharmonic coupling to one specific low frequency mode. The normal mode calculation of CO bridgebond on Ni by Richardson and Bradshaw estimates for the frustrated translation to = 76 cm and for the frustrated rotation m = 184 cm " while it is known from EELS data that the metal-molecule stretch is found at 400 cm The calculated values should... 

For surface species one or more of the rotational degrees of freedom may be restricted. Such frustrated rotations are better described as vibrations. 

Fig. 1 displays a series of SFG spectra of CO/Pt(l 11) for selected pump-IR probe delays. In this work, we only present a general discussion of spectrum analysis. A more detailed report will be presented elsewhere. A red shift and broadening of the CO band (as already observed for CO/Pt(l 11) at a ps time scale [4], and for C0/Ru(0001 [2]), and variations of the spectral shape, are observed. This does not indicate an excitation of the internal stretch itself (there is no indication that v=l is populated). The spectral changes rather reflect the excitation of other modes which perturb the internal stretch through anharmonic coupling. Among the three possible modes, frustrated translation and frustrated rotation can be considered. The CO-Pt stretch is ignored because it is expected to produce a blue shift. 

Fig. 2. CO internal stretch frequency and width as a function of time, as extracted from the numerical simulation of the spectra. Contributions of the frustrated rotation and the frustrated translation are also shown.

Fig. 3. Three temperature model pump pulse temporal profile, and variation of the temperatures of electrons, phonons, frustrated rotation and frustrated translation.

Fig. 2. (a) Frustrated rotational motion of C2H2 adsorbed on a Cu(001) surface induced... 

Now we consider the desorption process combined with the molecular vibration of the adsorbate using a simple model. If we assume that a diatomic molecule sits on the on-top site with an upright geometry on the metal surface, we consider what knowledge is obtained from state-selective detection and the angular distribution of desorbed molecules. The vibrational modes characteristic of the adsorbate are frustrated rotation, which is the bending vibration of the molecule at the center of the adsorbate... 

Only the modes with peak intensities larger than 0.003 are shown. Pt-NO str. 1 and Pt-NO str. 2 represent the Pt-NO stretching modes of the fee hollow and on-top species, respectively. NO rot. represents the frustrated rotational mode of the on-top NO species. The corresponding modes of the hollow NO species have zero intensity because of the upright geometry. N-O str. 1 and N-O str. 2 correspond to the N-O stretching modes of the fee and hep hollow species, respectively, while N-O str. 3 corresponds to that of the on-top species. 

The mean amplitude of molecular vibration can be calculated from the vibrational frequency [74] and vice versa. For the frustrated rotation of an upright diatomic molecule adsorbed on heavy substrate atoms and a vibrational mode which is doubly degenerate, the mean square amplitude at equilibrium temperature Ts is given by [68]... 

The angular frequency of the frustrated rotation in the excited state coe can be estimated from the vibrational amplitude, if the amplitude obtained from the turning angle of 4> = 46° is used. Since the present case is non-equilibrium, the v = 0 v" = 0 transition is dominant in the single-photon... 

Then, a very low wave number ve = Mq/Itsc 4 cm-1 is obtained, and the excited-state PES for the frustrated rotation of NO adsorbed on the fee hollow site of Pt(l 1 1) is regarded as having a nearly flat form. However, if desorption takes place by the two-step model, ve may be much larger than 4 cm-1, i.e. the excited-state PES for the frustrated rotation is not flat. 

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