Microcanonical unimolecular rate theory at surfaces. I. Dissociative chemisorption of methane on Pt(111)

Microcanonical treatment of HCl dissociative chemisorption on Au(111): Reactive dampening through inefficient translational energy coupling and an active surface

Microcanonical unimolecular rate theory is applied to Shirhatti and Wodtke's recent supersonic molecular beam experiments examining the activated dissociative chemisorption of HCl on Au(111). A precursor mediated microcanonical trapping (PMMT) model (where the surface vibrates and HCl rotations, vibration, and translation directed along the surface normal are treated as active degrees of freedom) gave dissociative sticking coefficient predictions that are several orders of magnitude higher than experimental values but in good accord with prior quantum and molecular dynamics simulations. Density functional theory (DFT) electronic structure calculations using the Perdew-Burke-Ernzerhof (PBE) functional served to fix the vibrational frequencies of the reactive transition state and the threshold energy for dissociation, E0 = 72.9 kJ/mol. To explore the possibilities of varying threshold energy, coupling to phonons, and dynamics, a three-parameter [E0, s, ɛn] dynamically biased (d-) PMMT model was fit to the experiments. A dynamical bias was introduced using an efficiency, ɛn, of normal translational energy to contribute to the active exchangeable energy capable of promoting reactivity. To achieve the low sticking probabilities observed in experiment, severe normal translational energy dampening (ɛn → 0.26) was imposed, leading to a large vibrational efficacy of ηv = εv/εn = 3.85. The optimal threshold energy for dissociation was E0 = 30.88 kJ/mol, some 40 kJ/mol below the PBE-DFT prediction, and the optimal number of Au surface oscillators was s = 1. The d-PMMT modeling indicates that HCl/Au(111) reactivity can be consistent with electronically adiabatic passage across a relatively low and late transition state that dynamically disfavors normal translational energy.

Diffraction of CH4 from a Metal Surface

Diffraction with matter waves has been reported since the beginning of quantum mechanics. In free space, diffraction effects have been observed even with objects as large as C₆₀ molecules. However, in scattering from a solid surface, pure elastic diffraction features have never been observed with molecules larger than D₂. Here we report the observation of pure molecular diffraction for CH₄ scattered off of an Ir(111) surface. These results prove that quantum coherence is preserved, despite the small separation between rotational levels and the interaction with surface phonons. Density functional theory calculations of the potential energy surface provide some clues to understand the larger corrugation sampled by CH₄ molecules in comparison to Ne atoms. Our results show that isotope separation of polyatomic molecules may be possible using gas-surface diffraction.

Low-energy methane scattering from Pt(111)

We have measured the temperature dependence of angular distributions of CH₄ from Pt(111) at an incident energy of 109 meV. A broad angular distribution has been observed along the two main symmetry directions, whereby the peak center shifts from the supra-specular position to the sub-specular position when the surface temperature increases from 120 K to 800 K. Different widths have been measured for the scattering patterns along the [ 1¯01 ] and the [ 2¯11 ] azimuthal directions. Based on calculations performed within the binary collision model, these differences have been ascribed to different corrugations of the CH₄-Pt(111) interaction potential along the two high-symmetry directions. This corrugation has been estimated from the model calculations to amount ∼0.03 Å, a factor of three larger than the one measured with helium diffraction.

Coherent quantum scattering of CH4 from Ni(111)

We have measured high-resolution angular distributions of methane scattered from a Ni(111) surface at incident energies between 68.9 meV and 108.6 meV. A sharp and intense specular peak has been observed, in addition to sharp features corresponding to rotationally inelastic diffraction (RID) peaks along the two main symmetry directions of Ni(111). The intensity of the most intense RID peaks is ca. 50% of the specular one. The observation of sharp, coherent elastic peaks at such low incident energies suggests that single scattering dominates over trapping at these energies, and that the depth of the van der Waals well should be lower than 60 meV. In contrast, a broad angular distribution shifted from the specular position is observed from a graphene-covered Ni(111) surface under identical incident conditions. These results open up the possibility of studying the physisorption well between CH₄ and a transition metal surface using high-resolution molecular beams.

Methane dissociation on Ni(111): A fifteen-dimensional potential energy surface using neural network method

In the present work, we develop a highly accurate, fifteen-dimensional potential energy surface (PES) of CH4 interacting on a rigid flat Ni(111) surface with the methodology of neural network (NN) fit to a database consisted of about 194 208 ab initio density functional theory (DFT) energy points. Some careful tests of the accuracy of the fitting PES are given through the descriptions of the fitting quality, vibrational spectrum of CH4 in vacuum, transition state (TS) geometries as well as the activation barriers. Using a 25-60-60-1 NN structure, we obtain one of the best PESs with the least root mean square errors: 10.11 meV for the entrance region and 17.00 meV for the interaction and product regions. Our PES can reproduce the DFT results very well in particular for the important TS structures. Furthermore, we present the sticking probability S0 of ground state CH4 at the experimental surface temperature using some sudden approximations by Jackson's group. An in-depth explanation is given for the underestimated sticking probability.

Quantum dynamics of polyatomic dissociative chemisorption on transition metal surfaces: mode specificity and bond selectivity

Recent advances in quantum dynamical characterization of polyatomic dissociative chemisorption on accurate global potential energy surfaces are critically reviewed.

Methane dissociative chemisorption and detailed balance on Pt(111): dynamical constraints and the modest influence of tunneling

A dynamically biased (d-) precursor mediated microcanonical trapping (PMMT) model of the activated dissociative chemisorption of methane on Pt(111) is applied to a wide range of dissociative sticking experiments, and, by detailed balance, to the methane product state distributions from the thermal associative desorption of adsorbed hydrogen with coadsorbed methyl radicals. Tunneling pathways were incorporated into the d-PMMT model to better replicate the translational energy distribution of the desorbing methane product from the laser induced thermal reaction of coadsorbed hydrogen and methyl radicals occurring near T(s) = 395 K. Although tunneling is predicted to be inconsequential to the thermal dissociative chemisorption of CH4 on Pt(111) at the high temperatures of catalytic interest, once the temperature drops to 395 K the tunneling fraction of the reactive thermal flux reaches 15%, and as temperatures drop below 275 K the tunneling fraction exceeds 50%. The d-PMMT model parameters of {E0 = 58.9 kJ/mol, s = 2, η(v) = 0.40} describe the apparent threshold energy for CH4/Pt(111) dissociative chemisorption, the number of surface oscillators involved in the precursor complex, and the efficacy of molecular vibrational energy to promote reaction, relative to translational energy directed along the surface normal. Molecular translations parallel to the surface and rotations are treated as spectator degrees of freedom. Transition state vibrational frequencies are derived from generalized gradient approximation-density functional theory electronic structure calculations. The d-PMMT model replicates the diverse range of experimental data available with good fidelity, including some new effusive molecular beam and ambient gas dissociative sticking measurements. Nevertheless, there are some indications that closer agreement between theory and experiments could be achieved if a surface efficacy less than one was introduced into the modeling as an additional dynamical constraint.

Vibrationally promoted dissociation of water on Ni(111)

Water dissociation on transition-metal catalysts is an important step in steam reforming and the water-gas shift reaction. To probe the effect of translational and vibrational activation on this important heterogeneous reaction, we performed state-resolved gas/surface reactivity measurements for the dissociative chemisorption of D2O on Ni(111), using molecular beam techniques. The reaction occurs via a direct pathway, because both the translational and vibrational energies promote the dissociation. The experimentally measured initial sticking probabilities were used to calibrate a first-principles potential energy surface based on density functional theory. Quantum dynamical calculations on the scaled potential energy surface reproduced the experimental results semiquantitatively. The larger increase of the dissociation probability by vibrational excitation than by translation per unit of energy is consistent with a late barrier along the O-D stretch reaction coordinate.

An effusive molecular beam technique for studies of polyatomic gas-surface reactivity and energy transfer

An effusive molecular beam technique is described to measure alkane dissociative sticking coefficients, S(T(g), T(s); ϑ), on metal surfaces for which the impinging gas temperature, T(g), and surface temperature, T(s), can be independently varied, along with the angle of incidence, ϑ, of the impinging gas. Effusive beam experiments with T(g) = T(s) = T allow for determination of angle-resolved dissociative sticking coefficients, S(T; ϑ), which when averaged over the cos (ϑ)/π angular distribution appropriate to the impinging flux from a thermal ambient gas yield the thermal dissociative sticking coefficient, S(T). Nonequilibrium S(T(g), T(s); ϑ) measurements for which T(g) ≠ T(s) provide additional opportunities to characterize the transition state and gas-surface energy transfer at reactive energies. A resistively heated effusive molecular beam doser controls the T(g) of the impinging gas striking the surface. The flux of molecules striking the surface from the effusive beam is determined from knowledge of the dosing geometry, chamber pressure, and pumping speed. Separate experiments with a calibrated leak serve to fix the chamber pumping speed. Postdosing Auger electron spectroscopy is used to measure the carbon of the alkyl radical reaction product that is deposited on the surface as a result of alkane dissociative sticking. As implemented in a typical ultrahigh vacuum chamber for surface analysis, the technique has provided access to a dynamic range of roughly 6 orders of magnitude in the initial dissociative sticking coefficient for small alkanes on Pt(111).

Microcanonical Transition State Theory for Activated Gas−Surface Reaction Dynamics: Application to H2/Cu(111) with Rotation as a Spectator

A microcanonical unimolecular rate theory (MURT) model incorporating quantized surface vibrations and Rice-Ramsperger-Kassel-Marcus rate constants is applied to a benchmark system for gas-surface reaction dynamics, the activated dissociative chemisorption and associative desorption of hydrogen on Cu(111). Both molecular translation parallel to the surface and rotation are treated as spectator degrees of freedom. MURT analysis of diverse experiments indicates that one surface oscillator participates in the dissociative transition state and that the threshold energy for H2 dissociation on Cu(111) is E0 = 62 kJ/mol. The spectator approximation for rotation holds well at thermally accessible rotational energies (i.e., for Er less than approximately 40 kJ/mol). Over the temperature range from 300 to 1000 K, the calculated thermal dissociative sticking coefficient is ST = S0 exp(-Ea/kBT) where S0 = 1.57 and Ea = 62.9 kJ/mol. The sigmoid shape of rovibrational eigenstate-resolved dissociative sticking coefficients as a function of normal translational energy is shown to derive from an averaging of the microcanonical sticking coefficient, with threshold energy E0, over the thermal surface oscillator distribution of the gas-surface collision complexes. Given that H2/Cu(111) is one of the most dynamically biased of gas-surface reactive systems, the simple statistical MURT model simulates and broadly rationalizes the H2/Cu(111) reactive behavior with remarkable fidelity.

Methane dissociative adsorption on the Pt(111) surface over the 300-500 K temperature and 1-10 Torr pressure ranges

The dissociative adsorption of methane on the Pt(111) surface has been investigated and characterized over the 1-10 Torr pressure and 300-500 K temperature ranges using sum frequency generation (SFG) vibrational spectroscopy and Auger electron spectroscopy (AES). At a reaction temperature of 300 K and a pressure of 1 Torr, C-H bond dissociation occurs in methane on the Pt(111) surface to produce adsorbed methyl (CH(3)) groups, carbon, and hydrogen. SFG results suggest that C-C coupling occurs at higher reaction temperatures and pressures. At 400 K, methyl groups react with adsorbed C to form ethylidyne (C(2)H(3)), which dehydrogenates at 500 K to form ethynyl (C(2)H) and methylidyne (CH) species, as shown by SFG. By 600 K, all of the ethylidyne has reacted to form the dissociation products ethynyl and methylidyne. Calculated C-H bond dissociation probabilities for methane, determined by carbon deposition measured by AES, are in the 10(-8) range and increase with increasing reaction temperature. A mechanism has been developed and is compared with conclusions from other experimental and theoretical studies using single crystals.

Seven-dimensional microcanonical treatment of hydrogen dissociation dynamics on Cu(111): Clarifying the essential role of surface phonons

A simple picture of the hydrogen dissociation/associative desorption dynamics on Cu(111) emerges from a two-parameter, full dimensionality microcanonical unimolecular rate theory (MURT) model of the gas-surface reactivity. Vibrational frequencies for the reactive transition state were taken from density functional theory calculations of a six-dimensional potential energy surface [Hammer et al., Phys. Rev. Lett. 73, 1400 (1994)]. The two remaining parameters required by the MURT were fixed by simulation of experiments. These parameters are the dissociation threshold energy, E(0)=79 kJmol, and the number of surface oscillators involved in the localized H(2)Cu(111) collision complex, s=1. The two-parameter MURT quantitatively predicts much of the varied behavior observed for the H(2) and D(2)Cu(111) reactive systems, including the temperature-dependent associative desorption angular distributions, mean translational energies of the associatively desorbing hydrogen as a function of rovibrational eigenstate, etc. The divergence of the statistical theory's predictions from experimental results at low rotational quantum numbers, J < or approximately 5, suggests that either (i) rotational steering is important to the dissociation dynamics at low J, an effect that washes out at high J, or (ii) molecular rotation is approximately a spectator degree of freedom to the dissociation dynamics for these low J states, the states that dominate the thermal reactivity. Surface vibrations are predicted to provide approximately 30% of the energy required to surmount the activation barrier to H(2) dissociation under thermal equilibrium conditions. The MURT with s=1 is used to analytically confirm the experimental finding that partial differential "E(a)(T(s))" partial differential E(t)= -1 for eigenstate-resolved dissociative sticking at translational energies E(t)<E(0)-E(v)-E(r). Explicit treatment of the surface motion (i.e., surface not frozen at T(s)=0 K) is a relatively novel aspect of the MURT theoretical approach.

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).

Comparative study of C-H stretch and bend vibrations in methane activation on Ni(100) and Ni(111)

State-resolved measurements on clean Ni(100) and Ni(111) surfaces quantify the reactivity of CH4 excited to v = 3 of the nu4 bend vibration. A comparison with prior data reveals that 3nu4 is significantly less effective than the nu3 C-H stretch at promoting dissociative chemisorption, even though 3nu4 contains 30% more energy. These results contradict statistical theories of gas-surface reactivity, provide clear evidence for vibrational mode specificity in a gas-surface reaction, and point to a central role for C-H stretching motion along the reaction path to dissociative chemisorption.

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.

Nonequilibrium Activated Dissociative Chemisorption: SiH4 on Si(100)

A three-parameter local hot spot model of gas-surface reactivity is employed to analyze and predict dissociative sticking coefficients for SiH4 incident on Si(100) under varied nonequilibrium conditions. Two Si surface oscillators and the molecular vibrations, rotations, and translational energy directed along the local surface normal are active degrees of freedom in the 15 dimensional microcanonical kinetics. The threshold energy for SiH4 dissociative chemisorption is found to be 19 kJ/mol, in quantitative agreement with recent GGA-DFT calculations. A simple scheme for increasing the rate of chemical vapor deposition of silicon from SiH4 at low surface temperatures is modeled.

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.