Frustrated translation

The reaction coordinate that describes the adsorption process is the vibration between the atom and the surface. Strictly speaking, the adsorbed atom has three vibrational modes, one perpendicular to the surface, corresponding to the reaction coordinate, and two parallel to the surface. Usually the latter two vibrations - also called frustrated translational modes - are very soft, meaning that k T hv. Associative (nondissociative) adsorption furthermore usually occurs without an energy barrier, and we will therefore assume that A = 0. Hence we can now write the transition state expression for the rate of direct adsorption of an atom via this transition state, applying the same method as used above for the indirect adsorption. 

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. 

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. 

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... 

Comparing with the normal mode calculation and the experimentally determined value for CO/Pt(lll) below, it seems likely that for the ontop bonded molecules the anharmonic coupling is to the frustrated translation. As expected, d(o is then negative as the C—O stretch vibration frequency decreases when going away from the ontop position. 

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.

We present in Section 2 the formalism giving the equations for the reduced density operator and for competing instantaneous and delayed dissipation. Section 3 presents matrix equations in a form suitable for numerical work, and the details of the numerical procedure used to solve the integrodiffer-ential equations with the two types of dissipative processes. In Section 4 on applications to adsorbates, results are shown for quantum state populations versus time for the dissipative dynamics of CO/Cu(001). The fast electronic relaxation to the ground electronic state is shown first without the slow relaxation of the frustrated translation mode of CO vibrations, for comparison with previous work, and this is followed by results with both fast and slow relaxation. In Section 5 we comment on the general conclusions that can be reached in problems involving both vibrational and electronic relaxation at surfaces. 

After the adsorbed CO rapidly relaxes to its ground electronic state g due to electronic dissipation, the s-region reaches equilibrium at a temperature T, but the p-region is yet found in a distribution of vibrational states r, with r = vg = 0,1,2,. The kernel matrix for delayed dissipation of vibrational energy has been given in terms of the dimensionless CO displacement q = h1/2/(mCooJv)1/2 x for a frustrated translation of frequency wy and mass rrico in the p-region. 

Fig. 1 Energy levels for CO/Cu 001) showing the energy bands of the substrate and potential energy functions of the adsorbate CO with its axis perpendicular to the surface. The variable x refers to the frustrated-translation vibration of the center of mass of CO parallel to the surface, and q here is the distance from the center of mass of CO to the surface. Following an initial substrate photoexcitation, its de-excitation transfers energy into the adsorbate, which relaxes to the ground vibronic states.

The excitation of higher states in the frustrated translation mode, eventually leading to the translation of the molecule, can be calculated by numerically evaluating the matrix element (0 5Qi m) for the frustrated translation mode. If the harmonic case would exclusively apply here, only transitions exciting the m = 1 mode (plus the rest of the N-H stretch... 

When anharmonic terms of the vibrational potential are introduced in the calculation, the probability of reaching each level m directly upon N-H stretch decay (points in Fig. 7) becomes non-negligible. Above 300 meV the molecule can translate classically into other sites. The classical threshold is attained at m = 30 state of the anharmonic frustrated translation mode. The change in wavefunction above the threshold leads to an extra kink in the decay rate function. The probability of populating states above the 300 meV diffusion barrier is in the order of 10 5, compatible with yield values found in experiments [43]. 

Apart from the 32 meV and the 40 meV modes, a further intense loss is observed for 0/Ag(2 1 0) at 56 meY. This mode is much more intense than the above discussed peak at 69 meY present for Ag(4 1 0) and, in our opinion, is not compatible with the excitation of a frustrated translation. Its energy is too high for an adatom vibration and we assign it therefore to a subsurface oxygen species [97]. We shall come back to this important effect later on in the paper. 

If the solid is molecular, the molecules (considered to be formed by M atoms, where M = N/r and r is the number of molecules in the smallest Bravais cell) can be treated as for the gas phase, so giving rise to 3M- 6 (or 3M- 5 if linear) vibrations for each molecule. The degrees of freedom associated with the external modes of every molecular unit (6r for non-linear molecules and 5r for linear molecules) give rise to lattice vibrations ( frustrated translations and rotations ) and to three acoustic modes. On the other hand, the internal vibrations of each molecules should in principle give rise to r-fold splitting, owing to the coupling of the vibrations within its primitive unit cell as a whole. 

The flow of energy from laser-heated snbstrate electrons into the adsorbate results in the excitation of adsorbate vibrational modes. For desorption of diatomics from various surfaces, it has been snggested that excitation of the frustrated rotation is responsible for the desorption process [9,14, 39]. Our results are consistent with those observations. We cannot, strictly speaking, dismiss (a contribution from) the Pt-CO stretch vibration, but the frustrated translational mode can be exclnded based on the independently determined electron-coupling times found to be 2.5 and 4 ps for terrace-and step-adsorbed molecnles, respectively (see the Sect. 10.3.2). These coupling times are much longer than those describing the very rapid desorption process. 

This sequence of events, excitation of the substrate electrons, energy transfer to the frustrated translation of the CO molecnles and the associated changes in the C-0 stretch vibration, can be described again with the friction model [50], the result of which is shown as black lines in Fig. 10.6. To reproduce the data in Fig. 10.6, coupling times of Tj=2.5 0.5 ps and 4 0.5 ps for terrace and step, respectively, are required. The simple one-dimensional model fully reproduces the time-dependent width and central frequency. 

Hence, excitation of the fmstrated rotation is pivotal for CO hopping, in agreement with our experimental observations. For diffusion on a flat surface, frustrated rotation is most likely crucial. Because of the atomic corrugation of the surface, the frustrated translational mode always involves rotation of the molecular axis with respect to the surface normal. This rotation has to be compensated in order for the molecule to settle on the neighbouring site, which can only be achieved by excitation of the frustrated rotational mode. Our findings illustrate the intricacies of mode coupling at surfaces contrary to common belief, the frustrated rotational mode is strongly coupled to the coordinate for diffusion, and, in our case, dominates the diffusion away from step sites. 

Fig. 10.8 Reaction pathways for the diffusion of CO from the step sites to the upper terrace obtained with DPT calculations (calculated for the situation in which initially 75% of all step sites are occupied). To go from the initial state (is) to the final state (fs) the CO molecule must pass two transition states (tsl and ts2) and a reaction intermediate (ri). Whereas initially the motion is dominated by the frustrated translation, the molecule has to perform a rotational motion as well to overcome tsl. After passing tsl the molecule arrives in the reaction intermediate (ri) consisting of a bridge state. Before reaching the final state (fs), CO bound atop on the terrace site, the molecule performs again a translational and rotational motion. Note that experimentally a significant tilt angle away from the surface normal has been concluded for CO on step sites [55]. Nevertheless, even for tilted molecules the crucial step over the transition state is still the frustrated rotation to reach the final position the Pt-C bond has to be broken and reformed in the new position on the terrace requiring a rotation of the molecule. An initial change in the tilt angle can be achieved by a translation motion. Reprinted with permission from [1]. Copyright 2005 AAAS...

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