Physisorption well

Another PES topology for molecular dissociation occurs when an intermediate molecularly chemisorbed state lies parallel to the surface between the physisorption well and the dissociated species as shown in Figure 3.2(b). This molecular state is usually described in terms of a diabatic correlation to a state formed by some charge transfer from the surface to the molecule [16]. In this case, there can be two activation barriers, V] for entry into the molecular chemisorption state of depth Wx and barrier V2 for dissociation of the molecularly chemisorbed state. This PES topology is relevant to the dissociation of some it bonded molecules such as 02 on metals, although this is often an oversimplification since distinct molecularly adsorbed states may exist at different sites on the surface [17]. In some cases, V < 0 so that no separate physisorbed state exists [18]. If multiple molecular chemisorption... 

Figure 3.34. Schematic ID PES and dynamics for 02 dissociation on Pt(lll). Eiigh incident energies allow adsorption directly into the molecularly chemisorbed states, which then act as precursors to dissociation. At lower incident energies, 02 first adsorbs in the physisorption well and then proceeds through sequential precursors to dissociation. From Ref. [320].

Since no physisorption well is present, the question has to be considered how the inclusion of a physisorption state would alter the trapping dynamics. Physisorption wells are created by a combination of the attractive van der Waals interaction with Pauli repulsion caused by the overlap of molecular and substrate wave functions. While the former effect is not reproduced by the DFT calculation, the repulsion due to wave function overlap is well described by present DFT functionals. Hence, the calculated PES would only become more attractive if van der Waals forces were correctly included. For a more quantitative description of the trapping process at kinetic energies below 0.05 eV certainly the physisorption channel has to be included. 

Ethylene molecules are known to physisorb at low crystal temperature. The binding energy in this state was estimated to be 0.25 eV from isothermal desorption experiments on Ag(l 0 0) [84]. Near edge X-rays absorption fine structure showed that the admolecules occupy the fourfold hollows on Ag(l 0 0) with the axis parallel to the surface [85, 86]. The sticking probability into the physisorption well is inhibited for rotationally excited gas-phase molecules [84]. 

A weak physisorption well at far distances from the surface (Z 7 bohr here) with r ... 

However, the accuracy of the detailed calculations is still not sufficient for chemical accuracy, 1 kcal/mole for instance, and the computational expense still prohibits calculation of enough points to map out the full multidimensional PES. The use of a reaction path Hamiltonian formalism (Miller et al. 1980) would reduce the number of required points but may not be particularly appropriate since the depth of the physisorption well can often reach 0.2-0.4eV. This accelerates the molecule and thus prevents following the reaction path even at extremely low initial kinetic energies. For example, on the contour plot in Fig. 17, the well M of nearly 0.4 eV will cause acceleration along Z and not along r, even though the latter is close to the reaction coordinate near point D. 

Using experimental information on the physisorption well depth of 0.27eV (Yates et al. 1976) and by comparison of dynamical simulations with molecular-beam scattering data on So( i,0i) (Pfniir et al. 1986), the values of (Ann,Anw) = ( —0.369,0.241) were found for (I>nw> nw nw) = (6.18eV, 1.05bohr S 2.32 bohr). The latter values differ very slightly from those found by fitting the N-W calculated interaction potential in Fig. 21. 

A major breakthrough in the study of gas—solid interactions was the development by Lennard-Jones [20] in 1924 of a potential curve for the interaction. For a gas—metal system where the interaction is strong enough to form a chemisorbed species, it was shown that an incoming molecule passes through two minima, the first a broad, shallow well (the physisorption well attributed to van der Waals forces) and the second a deeper well corresponding to the formation of a chemical bond. 

The physisorption well was originally calculated by summing the 6 12 potentials between the incoming species and each surface atom... 

Two schematic combined potential energy wells for the interaction of a gaseous species with a surface are shown in Fig. 2, illustrating the importance of the crossover point of the chemisorption and physisorption wells for adsorption and desorption kinetics. In the first case, adsorption is activated in the second, it is non-activated. (There are, in fact, only a few well-documented cases of activated chemisorption.) Recently, Lundqvist et al. [43] have made detailed calculations of the potential interaction between H2 and a magnesium surface which substantiate the presence of two minima. Their work is reviewed elsewhere [44]. It must be borne in mind that diagrams such as Fig. 2 grossly oversimplify the... 

The implication is that, either the trapping probability, oc, is smaller ( 0.82) on hydrogen-saturated areas of the surface than on clean areas ( 0.97), or a proportion of the incident molecules which would have been elastically reflected in the absence of the chemisorbed potential energy will pass directly into the chemisorbed state on the clean or j32-covered surface. The latter is probably the correct explanation, particularly as the physisorption well depth for H2 is small, so that one would anticipate... 

The isolated H2 molecule possesses an occupied lOg, bonding level well below the bottom of most metal bands and a luu, antibonding level above Ep. At large distances from the metal surface, the electronic stmcture of H2 is little affected by the presence of the surface. The physisorption well is determined by the dynamic polarization properties of H2 (van der Waals attraction) and the steep rise in energy due to Pauli repulsion as the separation is reduced. H2 acts as a neutral but polarizable adsorbate. A physisorbed state of that nature is expected on all simple and noble metal surfaces. The corresponding potential energy curves were calculated for the simple metals Al, Mg, Li, Na and K and for the noble metals Cu, Ag and Au [101-106]. They compare weU with the few available experimental results [107,108]. 

The value of k can be obtained by fitting for a given surface the physisorption well or the bound states of the He-metal potential. In Fig. 21 is drawn this potential for He/Ag(l1l). 

When a closed shell molecule approaches a metal surface, a Pauli repulsion becomes effective due to overlapping between orbitals of the molecule and Bloch functions of the metal surface. The physisorption well results when the repulsion is combined with the van der Waals attraction. 

Figure 3.6 The Lennard-Jones curve-crossing model for dissociative chemisorption, left without and right with an energy barrier. The undissociated A2 molecule is physisorbed at the surface. The A atoms are chemisorbed. The energy of the two new metal—A bonds suffices to compensate for the A-A bond energy e and the depth of the physisorption well. Therefore the interaction potential of the undissociated A2 molecule with the surface is asymptotically lower, by the A—A bond energy. But near the surface this potential curve is crossed by the interaction of two A atoms with the surface. The limitation of the two-body point of view is evident in this plot. The A—A bond distance, that is surely a key variable, is not represented in this simple view. More on this topic in Chapter 12.

Extensive information on weakly bound, physisorbed atoms on solids is available from bound state resonance data obtained from beam scattering experiments. Strong changes in the scattering intensities are observed when selective adsorption in the physisorption well occurs (see, for instance, ref. [113]). The resonance positions yield the eigenvalues E of the potential V(z). These satiesfies to a good approximation the Bohr-Sommerfeld quantization condition... 

The physisorption wells are in the meV range and the atoms are physisorbed at some value of the distance z 2-4 A from the surface. For a discussion of the systematic trends in atom-surface potentials, see also ref. [120]. 

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