V r

Since dissociation of the molecule involves stretching of the H-H bond, it is natural to ask about the change in the PES when the bond extends. Far from the surface, this is simply the vibration of the molecule, and it is by changing the initial vibrational state of the molecule that experiment can probe the PES in this dimension. In gas-surface dynamics, this was done first by Hayden and Lamont [13], They showed that for the H2/Cu system when the temperature of a molecular beam is increased but the translational temperature is kept constant, the dissociation probability increases. Increasing the temperature of the beam increases the Boltzmann population of the vibrationally excited states of the molecule, therefore the conclusion of this work is that vibrationally excited molecules dissociate more readily. 

This simple model would lead one to conclude that H2 dissociation on transition metals, where the unfilled d-states produce a low and early barrier (or even zero barrier), will show no vibrational enhancement, whereas dissociation on simple and noble metals, for which the barrier is high and late, will have vibrationally enhanced dissociation. This appears to be borne out in molecular beam experiments there is no observable increase in dissociation with internal state temperature for H2 on Ni(l 1 1), Ni(l 1 0), Pt(l 1 1) or Fe(l 1 0) [16-19], whereas dissociation on all surfaces of Cu shows an 

After dissociation, the two atoms will be chemisorbed on the surface. For H2 on metals, the critical reaction barrier occurs when the molecule is oriented with the H-H axis parallel to the surface (the broadside orientation). For molecules oriented end-on to the surface, the reaction barrier is very much higher (several eV), because in this geometry the final state of one of the atoms lies in the gas-phase. In such circumstances, the dissociation probability will be less than 1 because molecules oriented end-on will not dissociate. A favourable dissociation trajectory will be one in which the bond axis remains approximately parallel to the surface during traversal of the barrier. 

Orientational hindrance does not occur only for molecules with angular momentum vectors parallel to the surface, i.e. cartwheel rotating molecules. The PES topography also depends strongly on the azimuthal orientation of the molecular bond. For example, in the H2/Cu(l 11) system the lowest dissociation barrier occurs at the bridge site when the H atoms are directed towards adjacent 3-fold hollow sites, but the barrier is substantially higher if the molecule is rotated 90° so that the atoms are directed towards atop sites. In this case, there is also substantial orientational hindrance of dissociation for helicopter states (those with angular momentum perpendicular to the surface). 

Late dissociation barriers influence the rotational (as well as vibrational) state dependence of the dissociation. As the molecule approaches the barrier, the H-H bond extends. This leads to an increase in the moment of inertia and concomitant reduction in the energy of each rotational state. The rotational energy released is channelled into further extending the bond, enhancing the dissociation probability 

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There can be subtle but important non-adiabatic effects [14, ll], due to the non-exactness of the separability of the nuclei and electrons. These are treated elsewhere in this Encyclopedia.) The potential fiinction V(R) is detennined by repeatedly solving the quantum mechanical electronic problem at different values of R. Physically, the variation of V(R) is due to the fact that the electronic cloud adjusts to different values of the intemuclear separation in a subtle interplay of mutual particle attractions and repulsions electron-electron repulsions, nuclear-nuclear repulsions and electron-nuclear attractions. 

Figure Al.2.1. Potential V(R) of a diatomic molecule as a fiinction of the intemuclear separation i . The equilibrium distance Rq is at the potential minimum.

Classically, the nuclei vibrate in die potential V(R), much like two steel balls coimected by a spring which is stretched or compressed and then allowed to vibrate freely. This vibration along the nuclear coordinated is our first example of internal molecular motion. Most of the rest of this section is concerned with different aspects of molecular vibrations in increasingly complicated sittiations. 

Despite the complexity of these expressions, it is possible to hrvert transport coefficients to obtain infomiation about the mtemiolecular potential by an iterative procedure [111] that converges rapidly, provided that the initial guess for V(r) has the right well depth. 

Defining EJh + oij, replacing v /(-co) by v r(0), since the difference is only a phase factor, which exactly cancels in the bra and ket, and assuming that the electric field vector is time independent, we find... 

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