Dissociation probabilities

Figure A3.9.9. Dissociation probability versus incident energy for D2 molecules incident on a Cu(l 11) surface for the initial quantum states indicated (u indicates the mitial vibrational state and J the initial rotational state) [100], For clarity, the saturation values have been scaled to the same value irrespective of the initial state, although in reality die saturation value is higher for the u = 1 state.

Figure A3.9.10. The dissociation probability for O2 on W(110) [101] as a fiinction of the nonnal energy, (upper). Jg = 800 K 0 ( ) 0°, (a) 30° ( ) 45° and (O) 60° The nonnal energy scaling observed can be explained by combining the two surface comigations indicated schematically (lower diagrams).

Direct dissociation reactions are affected by surface temperature largely tlirough the motion of the substrate atoms [72]. Motion of the surface atom towards the incoming molecule mcreases the likelihood of (activated) dissociation, while motion away decreases the dissociation probability. For low dissociation probabilities, the net effect is an enliancement of the dissociation by increasing surface temperature, as observed in the system 02/Pt 100]-hex-R0.7° [73]. 

Figure A3.9.12. The dissociation probability of N2 on the W(IOO) surface as a fimction of the energy of the...

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

Looking at the trends in dissociation probability across the transition metal series, dissociation is favored towards the left, and associative chemisorption towards the right. This is nicely illustrated for CO on the 4d transition metals in Fig. 6.36, which shows how, for Pd and Ag, molecular adsorption of CO is more stable than adsorption of the dissociation products. Rhodium is a borderline case and to the left of rhodium dissociation is favored. Note that the heat of adsorption of the C and O atoms changes much more steeply across the periodic table than that for the CO molecule. A similar situation occurs with NO, which, however, is more reactive than CO, and hence barriers for dissociation are considerably lower for NO. 

To account for the fact that the dissociation probabilities measured in the beam experiments increased in the order n-butane < propane < ethane... 

Figure 9.6 Simulated CVD cluster morphology for coverages of -0.07 and 0.25 monolayer, showing the effect of differential dissociation probability, (a) and (b), versus the effect of a uniform dissociation probability, (c) and (d) the physisorbed precursor molecules are mobile in each case. Note, (c) and (d) are equivalent to the simulated morphology for growth by PVD. (Reproduced with permission from Reference [73].)...

Figure 3.5. 2D dissociation probability S0 (= S) as a function of translational energy and vibrational state v for H2 (D2) dissociation on a PES similar to (but not identical) to that of Figure 3.4(a). (a) Quantum dissociation probabilities plotted logarithmically, (b) Dotted lines are results of quasi-classical dynamics and solid lines are from quantum dynamics. From Ref. [222]. 

One attempt to remedy the limitations of the 2D model, and yet retain its simplicity, is the so-called hole model [25] which represents a simple static way to average over this distribution of barriers. If the variation of barrier height with these spectator variables is given as (X, Y, i), ), then the 6D dissociation probability S6D is approximated in terms of the 2D S2D as... 

After a molecule traps and thermally equilibrates in a molecularly adsorbed state, the net dissociation probability S is given by competition between the thermal... 

This section introduces the principal experimental methods used to study the dynamics of bond making/breaking at surfaces. The aim is to measure atomic/molecular adsorption, dissociation, scattering or desorption probabilities with as much experimental resolution as possible. For example, the most detailed description of dissociation of a diatomic molecule at a surface would involve measurements of the dependence of the dissociation probability (sticking coefficient) S on various experimentally controllable variables, e.g., S 0 , v, J, M, Ts). In a similar manner, detailed measurements of the associative desorption flux Df may yield Df (Ef, 6f, v, 7, M, Ts) where Ef is the produced molecular translational energy, 6f is the angle of desorption from the surface and v, J and M are the quantum numbers for the associatively desorbed molecule. Since dissociative adsorption and... 

Figure 3.22. Dissociation probability S of D2 on Cu(lll) plotted logarithmically vs. the normal component of incident energy En for various vibrational temperatures (Tv = Tn) as listed in the figure. The x labeled pure D2 is S for simply increasing Tv and En simultaneously of a pure D2 beam by increasing Tn. From Refs. [33,225]. Lines are S(En,Tv) calculated from associative desorption experiments measuring S(En, v, J) and detailed balance.

Figure 3.26. (a) The experimental dissociation probability S for N2 on Ru(0001) plotted logarithmically vs. the incident normal energy E = En for three different N2 vibrational temperatures as noted in the legend. The squares varied both En and Tv simultaneously. From Ref. [244]. (b) First principles predictions of the logarithim of the dissociation probability at two vibrational temperatures as noted in the legend. The solid points are from 3D (Z, R, q) quasi-classical dynamics and the open points are from 6D quasi-classical dynamics. The latter are from Ref. [27]. 

Figure 3.29. CH4 dissociation probability SQ (or S in this chapter) on Ni(100) plotted logarithmically vs. the normal kinetic energy En. (a) as a function of vibrational temperature Tv as noted in the figure. The lines are the fits of eq. (3.2) to the experiments. From Refs. [267,268]. (b) is for vibrationally state-resolved dissociation measurements, with CH4 in the Vj (solid triangles facing upwards), 2v3(open squares), v3 (open downward facing traingles) and v = 0 (solid circles) vibrational states. From Ref. [117].

Figure 3.30. Natural logarithm of the CH4 dissociation probability S0 (= S) on Pt(lll) vs. 1/TS for different incident energies at normal incidence ( = En). If the Ts dependence was due to precursor-mediated dissociation, it would be Arrhenius (a straight line with slope independent of e ) and hence is due to lattice coupling.

Figure 3.31. (a) Experimental dissociation probability S0(= S) for D2 on Pt(l 11) as a function of Et and 0,. From Ref. [292]. (b) Points connected by lines are some of the experimental results of (a) re-plotted at fixed parallel incident energy Epar(= ). The pure solid, dashed and dotted lines are the equivalent results from 6D first principles dynamics. From Ref. [300]. 

Figure 3.36. Nitrogen dissociation on W(100). (a) Experimental measurements of the dissociation probability S as a function of En and Ts. (b) Experimental measurements of only the direct component of dissociation probability S as a function of Et and 6f. (a) and (b) from Ref. [339]. (c) Dissociation probability S from first principles classical dynamics, separated into a dynamic trapping fraction and a direct dissociation fraction, (d) Approximate reaction path for dynamic trapping mediated dissociation from the first principles dynamics. The numbers indicate the temporal sequence, (c) and (d) from Ref. [343].

Elementary substances, if polyatomic in the molecule, will dissociate under conditions of sufficient energy. Chlorine and iodine, which are diatomic, are half dissociated at 1700 C and I200 C, respectively. Just above the boiling point the molecule of sulfur is Sj. Its molecular weight decreases from 250 at 450°C to 50 at 2070°C. Thus there are some monatomic sulfur molecules at 2070 C. The dissociation probably takes place in reversihle steps and can be represented by the equation ... 

Henriksen, N.E. (1988). The equivalence of time-independent and time-dependent calcu-lational techniques for photo dissociation probabilities, Comments At. Mol. Phys. 21, 153-160. 

In principle, one can induce and control unimolecular reactions directly in the electronic ground state via intense IR fields. Note that this resembles traditional thermal unimolecular reactions, in the sense that the dynamics is confined to the electronic ground state. High intensities are typically required in order to climb up the vibrational ladder and induce bond breaking (or isomerization). The dissociation probability is substantially enhanced when the frequency of the field is time dependent, i.e., the frequency must decrease as a function of time in order to accommodate the anharmonicity of the potential. Selective bond breaking in polyatomic molecules is, in addition, complicated by the fact that the dynamics in various bond-stretching coordinates is coupled due to anharmonic terms in the potential. 

Here 3/, = Ex — av = tuox — (Ek + ))/2. The second term in Eq. (5.47), in brackets, is a function of TxSEfi. If two bound state levels dominate the pump excitation, then this term contributes a scaling characteristic to control plots. That is, if we plot contours of constant dissociation probability as a function of A, and 5E.k then, barring the first term, plots with different Tx will appear similar, with a new range scaled by 5E, = (Tx/T )2SEjt. >... 

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