Assessing a microcanonical theory of gas-surface reactivity: Applicability to thermal equilibrium, nonequilibrium, and eigenstate-resolved dissociation of methane on Ni(100)

SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OF H2 ON METAL SURFACES

The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form.

Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0) H 2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H 2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100) H2 reacts depending on its vibrational state. Future theoretical studies of H 2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H 2 with complex metal surfaces.

Using Effusive Molecular Beams and Microcanonical Unimolecular Rate Theory to Characterize CH4 Dissociation on Pt(111)

The dissociative sticking coefficient for CH4 on Pt(111) has been measured as a function of both gas temperature (Tg) and surface temperature (Ts) using effusive molecular beam and angle-integrated ambient gas dosing methods. The experimental results are used to optimize the three parameters of a microcanonical unimolecular rate theory (MURT) model of the reactive system. The MURT calculations allow us to extract transition state properties from the data as well as to compare our data directly to other molecular beam and thermal equilibrium sticking measurements. We find a threshold energy for dissociation of E0 = 52.5 +/- 3.5 kJ mol(-1). Furthermore, the MURT with an optimized parameter set provides for a predictive understanding of the kinetics of this C-H bond activation reaction, that is, it allows us to predict the dissociative sticking coefficient of CH4 on Pt(111) for any combination of Ts and Tg even if the two are not equal to one another, indeed, the distribution of molecular energy need not even be thermal. Comparison of our results to those from recent thermal equilibrium catalysis studies on CH4 reforming over Pt nanoclusters ( approximately 2 nm diam) dispersed on oxide substrates indicates that the reactivity of Pt(111) exceeds that of the Pt nanocatalysts by several orders of magnitude.

Effusive Molecular Beam Study of C2H6 Dissociation on Pt(111)

The dissociative sticking coefficient for C2H6 on Pt(111) has been measured as a function of both gas temperature (Tg) and surface temperature (Ts) using effusive molecular beam and angle-integrated ambient gas dosing methods. A microcanonical unimolecular rate theory (MURT) model of the reactive system is used to extract transition state properties from the data as well as to compare our data directly with supersonic molecular beam and thermal equilibrium sticking measurements. We report for the first time the threshold energy for dissociation, E0 = 26.5 +/- 3 kJ mol(-1). This value is only weakly dependent on the other two parameters of the model. A strong surface temperature dependence in the initial sticking coefficient is observed; however, the relatively weak dependence on gas temperature indicates some combination of the following (i) not all molecular excitations are contributing equally to the enhancement of sticking, (ii) that strong entropic effects in the dissociative transition state are leading to unusually high vibrational frequencies in the transition state, and (iii) energy transfer from gas-phase rovibrational modes to the surface is surprisingly efficient. In other words, it appears that vibrational mode-specific behavior and/or molecular rotations may play stronger roles in the dissociative adsorption of C2H6 than they do for CH4. The MURT with an optimized parameter set provides for a predictive understanding of the kinetics of this C-H bond activation reaction, that is, it allows us to predict the dissociative sticking coefficient of C2H6 on Pt(111) for any combination of Ts and Tg even if the two are not equal to one another.

Microcanonical unimolecular rate theory at surfaces. III. Thermal dissociative chemisorption of methane on Pt(111) and detailed balance

A local hot spot model of gas-surface reactivity is used to investigate the state-resolved dynamics of methane dissociative chemisorption on Pt(111) under thermal equilibrium conditions. Three Pt surface oscillators, and the molecular vibrations, rotations, and the translational energy directed along the surface normal are treated as active degrees of freedom in the 16-dimensional microcanonical kinetics. Several energy transfer models for coupling a local hot spot to the surrounding substrate are developed and evaluated within the context of a master equation kinetics approach. Bounds on the thermal dissociative sticking coefficient based on limiting energy transfer models are derived. The three-parameter physisorbed complex microcanonical unimolecular rate theory (PC-MURT) is shown to closely approximate the thermal sticking under any realistic energy transfer model. Assuming an apparent threshold energy for CH(4) dissociative chemisorption of E(0)=0.61 eV on clean Pt(111), the PC-MURT is used to predict angle-resolved yield, translational, vibrational, and rotational distributions for the reactive methane flux at thermal equilibrium at 500 K. By detailed balance, these same distributions should be observed for the methane product from methyl radical hydrogenation at 500 K in the zero coverage limit if the methyl radicals are not subject to side reactions. Given that methyl radical hydrogenation can only be experimentally observed when the CH(3) radicals are kinetically stabilized against decomposition by coadsorbed H, the PC-MURT was used to evaluate E(0) in the high coverage limit. A high coverage value of E(0)=2.3 eV adequately reproduced the experimentally observed methane angular and translational energy distributions from thermal hydrogenation of methyl radicals. Although rigorous application of detailed balance arguments to this reactive system cannot be made because thermal decomposition of the methyl radicals competes with hydrogenation, approximate applicability of detailed balance would argue for a strong coverage dependence of E(0) with H coverage--a dependence not seen for methyl radical hydrogenation on Ru(0001), but not yet experimentally explored on Pt(111).

Dissociative chemisorption and energy transfer for methane on Ir(111)

A 3-parameter local hot spot model of gas-surface reactivity is employed to analyze and predict dissociative sticking coefficients for CH(4) incident on Ir(111) under varied nonequilibrium and equilibrium conditions. One Ir surface oscillator and the molecular vibrations, rotations, and translational energy directed along the surface normal are treated as active degrees of freedom in the 14 dimensional microcanonical kinetics. The threshold energy for CH(4) dissociative chemisorption on Ir(111) derived from modeling molecular beam experiments is E(0) = 39 kJ/mol. Over more than 4 orders of magnitude of variation in sticking, the average relative discrepancy between the beam and theoretically derived sticking coefficients is 88%. The experimentally observed enhancement in dissociative sticking as beam translational energies decrease below approximately 10 kJ/mol is consistent with a parallel dynamical trapping/energy transfer channel that likely fails to completely thermalize the molecules to the surface temperature. This trapping-mediated sticking, indicative of specific energy transfer pathways from the surface under nonequilibrium conditions, should be a minor contributor to the overall dissociative sticking at thermal equilibrium. Surprisingly, the CH(4) dissociative sticking coefficient predicted for Ir(111) surfaces at thermal equilibrium, based on the molecular beam experiments, is roughly 4 orders of magnitude higher than recent measurements on supported nanoscale Ir catalysts at 1 bar pressure, which suggests that substantial improvements in catalyst turnover rates may be possible.

Microcanonical unimolecular rate theory at surfaces. II. Vibrational state resolved dissociative chemisorption of methane on Ni(100)

A three-parameter microcanonical theory of gas-surface reactivity is used to investigate the dissociative chemisorption of methane impinging on a Ni(100) surface. Assuming an apparent threshold energy for dissociative chemisorption of E(0)=65 kJ/mol, contributions to the dissociative sticking coefficient from individual methane vibrational states are calculated: (i) as a function of molecular translational energy to model nonequilibrium molecular beam experiments and (ii) as a function of temperature to model thermal equilibrium mbar pressure bulb experiments. Under fairly typical molecular beam conditions (e.g., E(t)>/=25 kJ mol(-1), T(s)>/=475 K, T(n)</=400 K), sticking from methane in the ground vibrational state dominates the overall sticking. In contrast, under thermal equilibrium conditions at temperatures T>/=100 K the dissociative sticking is dominated by methane in vibrationally excited states, particularly those involving excitation of the nu(4) bending mode. Fractional energy uptakes f(j) defined as the fraction of the mean energy of the reacting gas-surface collision complexes that derives from specific degrees of freedom of the reactants (i.e., molecular translation, rotation, vibration, and surface) are calculated for thermal dissociative chemisorption. At 500 K, the fractional energy uptakes are calculated to be f(t)=14%, f(r)=21%, f(v)=40%, and f(s)=25%. Over the temperature range from 500 K to 1500 K relevant to thermal catalysis, the incident gas-phase molecules supply the preponderance of energy used to surmount the barrier to dissociative chemisorption, f(g)=f(t)+f(r)+f(v) approximately 75%, with the highest energy uptake always coming from the molecular vibrational degrees of freedom. The predictions of the statistical, mode-nonspecific microcanonical theory are compared to those of other dynamical theories and to recent experimental data.

Preference for Vibrational over Translational Energy in a Gas-Surface Reaction

State-resolved gas-surface reactivity measurements revealed that vibrational excitation of nu3 (the antisymmetric C-H stretch) activates methane dissociation more efficiently than does translational energy. Methane molecules in the vibrational ground state require 45 kilojoules per mole (kJ/mol) of translational energy to attain the same reactivity enhancement provided by 36 kJ/mol of nu3 excitation. This result contradicts a key assumption underlying statistical theories of gas-surface reactivity and provides direct experimental evidence of the central role that vibrational energy can play in activating gas-surface reactions.

Vibrational Mode-Specific Reaction of Methane on a Nickel Surface

The dissociation of methane on a nickel catalyst is a key step in steam reforming of natural gas for hydrogen production. Despite substantial effort in both experiment and theory, there is still no atomic-scale description of this important gas-surface reaction. We report quantum state-resolved studies, using pulsed laser and molecular beam techniques, of vibrationally excited methane reacting on the nickel (100) surface. For doubly deuterated methane (CD2H2), we observed that the reaction probability with two quanta of excitation in one C-H bond was greater (by as much as a factor of 5) than with one quantum in each of two C-H bonds. These results clearly exclude the possibility of statistical models correctly describing the mechanism of this process and attest to the importance of full-dimensional calculations of the reaction dynamics.