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

Methane dissociative chemisorption and detailed balance on Pt(111): Dynamical constraints and the modest influence of tunneling S. B. Donald, J. K. Navin, and I. Harrison Citation: The Journal of Chemical Physics 139, 214707 (2013); doi: 10.1063/1.4837697 View online: http://dx.doi.org/10.1063/1.4837697 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/21?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The dissociative chemisorption of methane on Ni(100) and Ni(111): Classical and quantum studies based on the reaction path Hamiltonian J. Chem. Phys. 139, 194701 (2013); 10.1063/1.4829678 The temperature dependence of methane dissociation on Ni(111) and Pt(111): Mixed quantum-classical studies of the lattice response J. Chem. Phys. 132, 134702 (2010); 10.1063/1.3357415 Coverage dependence and hydroperoxyl-mediated pathway of catalytic water formation on Pt (111) surface J. Chem. Phys. 125, 054701 (2006); 10.1063/1.2227388 Microcanonical unimolecular rate theory at surfaces. III. Thermal dissociative chemisorption of methane on Pt(111) and detailed balance J. Chem. Phys. 123, 094707 (2005); 10.1063/1.2006679 The dynamics of the dissociative adsorption of methane on Pt(533) J. Chem. Phys. 118, 3334 (2003); 10.1063/1.1538184

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.174.255.116 On: Wed, 26 Nov 2014 17:19:35

THE JOURNAL OF CHEMICAL PHYSICS 139, 214707 (2013)

Methane dissociative chemisorption and detailed balance on Pt(111): Dynamical constraints and the modest influence of tunneling S. B. Donald, J. K. Navin, and I. Harrisona) Department of Chemistry, University of Virginia, Charlottesville, Virginia 22904-4319, USA

(Received 7 August 2013; accepted 18 November 2013; published online 6 December 2013) 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 Ts = 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 dPMMT model parameters of {E0 = 58.9 kJ/mol, s = 2, ηv = 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. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4837697] I. INTRODUCTION

The activated dissociative chemisorption of methane at catalytic metal surfaces can be a rate-limiting step1–5 in the catalytic reforming of methane (ca., 95% of natural gas) that is the industrially preferred process to produce hydrogen and synthesis gas. Development of quantitative models for methane dissociative chemisorption has been of long-standing interest6–16 given that such models might ultimately prove helpful in optimizing catalytic transformations of methane. Experimentally, the gas-surface reactivity of methane usually depends on both the surface temperature and the energy of the incident molecules, but not always in accord with statistical transition state theory. Vibrational mode-specific reactivity has been observed in laser-pumped supersonic molecular beam experiments14, 17, 18 where it has been found that vibrational energy in particular modes can be more or less efficacious in promoting reactivity as compared to molecular translational energy directed along the surface normal, En = Et cos 2 ϑ. The thermally averaged efficacy of vibrational energy, ηv , relative to En , for methane reactivity on Pt(111) is 0.40.19 For smooth, close-packed single crystal surfaces, methane dissociative sticking coefficients are found a) Electronic mail: [email protected]. Tel.: (434) 924-3639. Fax: (434)

924-3710.

0021-9606/2013/139(21)/214707/15/$30.00

to scale with En , not Et , and so molecular translations parallel to the surface have typically been treated as spectator, or ignored, degrees of freedom in microcanonical unimolecular rate theory11, 13, 19 or reduced dimensionality dynamical models.10, 20–24 A full dimensional quantum dynamical model recently developed by Jackson and Nave for methane on Ni surfaces15, 16 treats parallel translations using a sudden approximation to average over surface impact sites and treats rotational motions adiabatically. Recent comparisons19, 25 of the reactivity of methane incident on Pt(111) from effusive molecular beams and from supersonic molecular beams with very different molecular rotational energy distributions, characterized by different rotational temperatures, concluded that molecular rotations can be approximated as spectator degrees of freedom within a microcanonical model. This discernment was possible because molecules prepared in an effusive molecular beam have thermal energy distributions whose gas temperature, Tg = Tt = Tv = Tr , is shared by all molecular degrees of freedom,26 whereas methane molecules prepared in a supersonic beam with nozzle temperature TN suffer negligible vibrational cooling, Tv = TN , but substantial rotational cooling, Tr = 0.1 TN , due to inter-molecular collisions that occur during the supersonic expansion.27 In this paper, tunneling28 is incorporated into the dynamically biased (d-) precursor mediated microcanonical trapping (PMMT) model19 of activated dissociative chemisorption.

139, 214707-1

© 2013 AIP Publishing LLC


214707-2

Donald, Navin, and Harrison

J. Chem. Phys. 139, 214707 (2013)

The revised model is assessed in its ability to replicate a diverse variety of methane/Pt(111) dissociative chemisorption experiments, and by detailed balance, the methane product state distributions of the thermally driven reverse reaction, hydrogenation of adsorbed methyl radicals. Tunneling enabled kinetic isotope effects to be calculated at arbitrary temperatures and proved important to consider when modeling the methyl radical hydrogenation reactions which occurred at relatively low surface temperatures, Ts = 240 K,29 and 395 K.30 The methane product translational energy distribution, Pt (Et ), for the laser induced thermal reaction (LITR)30 CH3(c) + H(c) → CH4(g) is shown to be a useful tool for evaluating dynamical constraints on PMMT models of methane dissociative chemisorption. Several new CH4 /Pt(111) dissociative sticking coefficient measurements are reported using refined techniques that either demonstrate error bounds, or increase the dynamic range of the dissociative sticking measurements available. The unrivaled diversity of the experimental data available for the CH4 /Pt(111) reactive system makes it an important model system for evaluating emerging theoretical models16, 19, 31–34 of polyatomic gas-surface reactivity. II. METHODS A. Precursor mediated microcanonical trapping models

1. Dynamically biased (d-) PMMT

Details concerning the application of the statistical (s-) PMMT model13, 35, 36 and the d-PMMT model19 to activated dissociative chemisorption are available elsewhere. Briefly, the PMMT models assume that transiently formed gas-surface collision complexes with a pooled energy sufficient to react will have access to state-mixing regions of the reactive potential energy surface such that through the collision and/or intramolecular vibrational energy redistribution13 their energy will become microcanonically randomized, at least in a collective sense over the ensemble of collision complexes formed,11, 37, 38 and the molecules will be transiently trapped in the neighborhood of the precursor molecular adsorption well located between the transition states for reaction (dissociative chemisorption) and desorption. These precursor complexes (PCs), formed of an incident molecule and a few local surface oscillators, go on to react or desorb with RiceRamsperger-Kassel-Marcus (RRKM) rate constants, ki (E ∗ ) =

Wi (E ∗ ) , hρ(E ∗ )

(1)

where E∗ is the active exchangeable energy whose zero occurs for the reactants at rest at infinite separation, Wi (E ∗ ) is the sum of states for transition state i = D, R (for desorption and ∗ = 0 and ER∗ = E0 (see reaction) with threshold energies ED ∗ Fig. 1), ρ(E ) is the PC density of states, and h is Planck’s constant. Applying the steady state approximation to Fig. 1 kinetics scheme,11, 13 F0 f (E ∗ )

∗

kR (E ) −− −− −− −− → CH4(g) − ← − CH4(p) −−−−−→ CH3(c) + H(c) kD (E ∗ )

(2)

FIG. 1. Schematic depiction of the kinetics and energetics of methane dissociative chemisorption via precursor-mediated microcanonical trapping (PMMT). At energies sufficient to react, collisionally formed precursor complexes, PCs, comprised of a methane molecule interacting with s surface oscillators in the spatial vicinity of the physisorption well, are presumed to become transiently trapped between the transition states for desorption and reaction. Zero-point energies are implicitly included within the potential energy curve along the reaction coordinate. See text for further details.

yields the expression for the experimental dissociative sticking coefficient, ∞ S(E ∗ )f (E ∗ )dE ∗ , (3) S= 0

where S(E∗ ) is the microcanonical sticking coefficient, S(E ∗ ) =

kR (E ∗ ) WR (E ∗ ) = , ∗ ∗ kR (E ) + kD (E ) WR (E ∗ ) + WD (E ∗ )

(4)

and f (E∗ ) is the probability distribution for forming a PC with exchangeable energy E∗ , which is calculated by convolution over the molecular and surface energy distributions describing the particular experimental conditions of interest. The experimental sticking coefficient is the average of the microcanonical sticking coefficient over the experimental probability of forming a PC with energy E∗ . The microcanonical sticking coefficient is the ratio of the number of open channels to react to the total number of open channels to either react or desorb. S(E∗ ) is a statistical quantity derived solely from the quantum structure of the transition states. In the d-PMMT model developed here, rotations and translations parallel to the surface are taken to be spectator degrees of freedom, and a vibrational dynamical bias is introduced19 only during formulation of the PC exchangeable


214707-3


J. Chem. Phys. 139, 214707 (2013)

energy available to surmount the reaction barrier, E ∗ = En + ηv Ev + Es ,

(5)

where En , Ev , Es are the normal translational energy, vibrational energy, and surface energy, respectively, and ηv is the efficacy for vibrational energy to promote reaction relative to En . The probability distribution for forming PCs with exchangeable energy E∗ is calculated by convolution over the experimental molecular and surface energy distributions, E∗ E ∗ −En f (E ∗ ) = fn (En ) fs (Es ) 0

0

× fv ηv−1 (E ∗ − En − Es ) dEs dEn .

(6)

A statistical (s-) PMMT model is recovered in the limit ηv → 1. For comparative purposes, several calculations were made for alternate s-PMMT and d-PMMT models with active rotational degrees of freedom in which rotational energy, Er , was added to E∗ in Eq. (5), the experimental rotational distribution was convolved into f (E∗ ) in Eq. (6), and the state counts in S(E∗ ) of Eq. (4) were adjusted appropriately.19 The vibrational efficacy, ∂S −1 ∂S ηv ≡ , (7) ∂Ev Ej =v ∂En Ej =n may be measured experimentally in quantum-state-resolved dissociative sticking coefficient experiments as14 En ηv = , (8) Ev Sv where Sv is the change in S accompanying a Ev increase in vibrational energy at some particular En , and En is the change in En required to gain the same Sv change in S for molecules maintained in the lower energy vibrational state. Dissociative sticking calculations require specification of the transition states for desorption and reaction. The desorption transition state is taken to occur when the alkane is freely vibrating in the gas-phase, far from the s surface oscillators of the united PC. The surface oscillators are assumed to vibrate at the mean phonon frequency of the Pt metal [νs = ( 43 ) kB TDebye / hc = 122 cm−1 ] with only the component of the lattice vibrations normal to the surface contributing to the PC exchangeable energy (symmetric with the experimental finding that the dissociative sticking coefficient scales with only the normal component of the molecular translational energy). The desorption coordinate was taken to be the vibrational motion that ultimately becomes free molecular translation along the surface normal, and so that degree of freedom is missing from the desorption transition state (n.b., also missing are the spectator translational motions parallel to the surface and the rotations). The transition state for CH4 dissociative chemisorption on Pt(111) was taken to be the one calculated by Nave, Tiwari, and Jackson39 using generalized gradient approximation - density functional theory (GGA-DFT) electronic structure theory. The PMMT models used the transition state vibrational frequencies from these GGA-DFT calculations but the apparent threshold energy for reaction was treated as a free variable. Additional GGA-DFT

calculations were performed to determine transition state vibrational frequencies for CD4 dissociative chemisorption on Pt(111). Ultimately, only 3 parameters are required for dPMMT calculations, {E0 , ηv , s}, where E0 is the apparent threshold energy for dissociative chemisorption (see Fig. 1), ηv is the vibrational efficacy, and s is the number of surface oscillators involved in the PC. These parameters were fixed by minimizing the average relative discrepancy (ARD) between simulated theoretical and experimental dissociative sticking coefficients, |Stheory − Sexpt | , (9) ARD = min(Stheory , Sexpt ) for a limited subset of non-equilibrium supersonic molecular beam experiments performed by Luntz and Bethune at two different nozzle temperatures.27 The translational temperature of Luntz’s supersonic molecular beams was modeled as Tt = 25 K (relative to the average beam translational energy) based on his description that the translational energy dispersions of the beams were 10%–20% depending upon the nozzle conditions. Following standard assumptions,9, 13, 27 the vibrational and rotational temperatures of methane in the beams were modeled as Tv = TN and Tr = 0.1 TN where TN is the beam nozzle temperature. Once the d-PMMT model parameters were defined by these simulations it became possible to predict dissociative sticking coefficients for any experiment for which the initial energy distributions are adequately described. Whenever other PMMT models were considered in this paper their parameters were optimized in identical fashion against the same limited subset of non-equilibrium experiments. 2. Tunneling

To account for tunneling through the barrier to dissociative chemisorption [see Fig. 2(a)], the RRKM rate constant for dissociative chemisorption was written in its generalized form as28 E WR (E) = kR (E) = p(εt )kR (E, εt )dεt hρ(E) 0 E 1 = p(εt )ρR (E − εt )dεt , (10) hρ(E) 0 where E = E∗ + ZRe is the classical energy above the electronic potential energy surface whose zero is set by the wellseparated reactants at T = 0 K, ZRe is the zero-point energy of the reactants, εt is the translational energy along the reaction coordinate leading to separated products, p(εt ) is the barrier transmission probability, and ρ R (E − εt ) is the density of states, excluding the reaction coordinate mode, of the reactive transition state evaluated at the energy available to populate vibrational states of the transition state complex when tunneling occurs at εt .40, 41 The barrier to chemisorption was approximated by a 1D Eckart potential42, 43 whose height was Ec = E0 − (ZTS − ZRe ) while the curvature, ν rxn = 953i cm−1 , was fixed by GGA-DFT39 and the activation barrier for associative desorption of methane,44 Ea = 71 kJ/mol, was ultimately used to help define the exothermicity, rxn H = Ea (CH4 → CH3 + H) − Ea (CH3 + H → CH4 ) = −6 kJ/mol


214707-4


J. Chem. Phys. 139, 214707 (2013)

FIG. 2. (a) 1D Eckart potential for CH4 /Pt(111) dissociative chemisorption with curvature fixed by the GGA-DFT39 calculated reaction coordinate mode frequency of 953i cm−1 , d-PMMT optimized reaction threshold energy of E0 = 58.9 kJ/mol, and Ea = 71 kJ/mol activation energy for the reverse reaction, associative desorption of methane.44 The zero-point energies of the separated reactants and the transition state, ZRe and ZTS , as well as some other energies relevant to the RRKM and tunneling equations (10)–(14) are also labeled. (b) Microcanonical dissociative sticking coefficient, S(E∗ ), evaluated with and without tunneling.

(see Fig. 2(a)). For the range of Eo values explored, the overall reaction was always considered to be exothermic. The analytic expression42 for the tunneling transmission probability through a 1D Eckart barrier was used for p(εt ) where εt is the reaction coordinate translational energy above the classical electronic potential evaluated for the well-separated reactants, without regard to zero-point energies. The sum of states for the reactive transition state referenced to the E∗ energy scale can be written as E ∗ +ZRe p(εt )ρR (E ∗ + ZRe − εt )dεt , (11) WR (E ∗ ) = 0

where the argument of ρ R is the energy available to populate vibrational states of the transition state complex, taking in to account their vibrational zero-point energy. In the absence of tunneling, the barrier transmission probability would be 0, E < Ec + ZT S , (12) p(εt ) 1, E ≥ Ec + ZT S and given εt = εt∗ + ZRe , Eq. (11) reduces to the conventional non-tunneling expression, E ∗ +ZRe ∗ ρR (E ∗ + ZRe − εt )dεt WR (E ) =

Ecl +ZT S E∗

=

E0

ρR (E ∗ − εt∗ )dεt∗

E ∗ −E0

= 0

†

ρR (E ∗ − E0 − εt∗ )dεt∗

= WR (E ∗ − E0 ) =

E† 0

†

ρR (E † )dE † ,

(13)

where the arguments of the daggered quantities are referenced to the energy of the transition state above its zero-point energy, e.g., E† = E∗ − E0 = E − Ec − ZTS . To account for tunneling, it was operationally convenient to calculate the

convolution of Eq. (8) as E ∗ +ZRe † ∗ p(εt )ρR (E ∗ + ZRe − ZT S − εt )dεt WR (E ) = 0

(14) † using the Beyer-Swinehart algorithm for ρR (E † ). Tunneling was not relevant to desorption because the desorption barrier is infinitely thick and approached asymptotically, so that † WD (E ∗ ) = WD (E ∗ ). With sums of states calculated in these ∗ ways, S(E ) was evaluated. In particular simulations of experimental dissociative sticking coefficients where it was interesting to exclude tunneling pathways (i.e., by implementing Eq. (12) Heaviside conditions on p(εt )), S(E∗ ) was reduced † † † to WR (E ∗ − E0 )/[WR (E ∗ − E0 ) + WD (E ∗ )]. The effects of ∗ tunneling on S(E ) are illustrated in Fig. 2(b). 3. GGA-DFT calculations of transition state vibrational frequencies

Electronic structure theory calculations were performed using the DFT based Vienna ab initio Software Package45–48 (VASP) using a plane-wave basis set. Exchange and correlation effects were treated within the GGA of the Perdew-Becke-Ernzerhof (PBE)49, 50 functional. The calculations were performed using the projector-augmented wave (PAW)51, 52 method. A plane-wave cutoff of 400 eV was used. The metal substrate was modeled as four layers of a 4 × 4 unit cell, corresponding to 64 metal atoms, with periodic boundary conditions and a large vacuum space separating repeating images. Reaction pathways were searched with the dimer53 method. Calculations were considered converged when all forces were smaller than 0.05 eV/Å. The MedeA computational platform54 was used for visualization and the construction of VASP input files. VASP calculations were performed on the Stampede supercomputer of the National Science Foundation’s Extreme Science and Engineering Discovery Environment (XSEDE).


214707-5


B. Dissociative sticking coefficient measurements

1. Experimental methods

The methodology for making alkane dissociative sticking coefficient measurements with dosing from an ambient gas or effusive molecular beam has been described elsewhere.26 Here we report on ambient gas dissociative sticking coefficients measured for CH4 /Pt(111) over a Ts range from 300 K to 1000 K using improved gas purification, as well as 700 K angle-resolved thermal dissociative sticking coefficient measurements with an effusive molecular beam doser of new design. Ambient gas dissociative sticking measurements were conducted by back dosing methane into the ultrahigh vacuum surface analysis chamber (base pressure = 1 × 10−10 Torr) through the molecular beam doser at Tg = 295 K, with the Pt crystal positioned such that the crystal face was not in the path of the direct molecular flux. The chamber temperature was 295 K for the ambient gas experiments. Angle-resolved thermal dissociative sticking coefficients were measured by directly dosing an amount of methane onto the crystal using the effusive molecular beam doser with temperatures adjusted so T = Tg = Ts = 700 K. Carbon deposition on the Pt surface from CH4 dissociative chemisorption was measured using Auger electron spectroscopy (AES) with a Phi model 15-255GAR double-pass cylindrical mirror electron energy analyzer. In angle-resolved experiments, AES was used to measure the C coverage across the surface as a function of distance (angle) away from the centerline of the effusive molecular beam intensity. Before experiments, the ion gauge and ion pumps were turned off or valved off to avoid formation of any extraneous reactive species.

2. Methane gas purification

Earlier ambient gas dissociative sticking coefficient measurements55, 56 found that as Ts was reduced measured dissociative sticking coefficients eventually approached an asymptotic value of ∼10–7 . This lower dissociative sticking coefficient limit was presumed to be due to small amounts (ca., 10−5 %) of highly reactive carbon-containing impurities in the methane gas. To improve the methane gas purity, a Supelco filter (Model 22450-U) was installed to filter the methane before dosing. This filter works to remove hydrocarbons larger than methane, saturated and unsaturated, as well as many other gases. With the methane gas purified in this manner it was possible to record ambient gas dissociative sticking coefficients as low as 7 × 10−8 with no evidence for approach towards an asymptotic minimum sticking coefficient imposed by gas impurities.

3. Improved effusive molecular beam doser design

Our previous effusive molecular beam doser, designated “Doser 1” and described by Cushing,26 was found to emit a detectable amount of potassium at Tg ≥ 900 K. This effect was attributed to an alumina binder that coated Doser 1 which contains the binding agent potassium silicate, K2 SiO3 . A new effusive beam doser design, designated “Doser 2” was

J. Chem. Phys. 139, 214707 (2013)

developed which was free of binding agents and allows for clean dosing over a gas temperature range that extends to Tg ≤ 1100 K. The Doser 2 design is a relatively straightforward evolution of the Doser 1 design26 with changes in only how the tungsten heating wire is insulated. The central dosing nozzle is a 316 stainless steel tube with a nominal diameter of 0.250 in. with a 316 stainless steel disk welded onto one end. The end disk is 0.003 in. thick and has a centered, laser drilled, hole of 0.5 mm diameter through which gas is dosed. On the opposite end of the tube, a 1/4 in. VCR fitting is welded which allows for easy attachment to a UHV conflat flange. A 6 in. long alumina tube (Aremco) with exterior threads is placed over the steel nozzle. A tungsten wire with a diameter of 0.25 mm and 99.95% purity (Goodfellow) is coiled around the threads of the alumina tube to allow for good thermal contact and to help hide the filament from ambient gas. A closely fitting alumina tube is then slid over the threaded alumina tube in order to thermally isolate the doser as well as to further hide the filament so that no radical species formed on the filament can strike the crystal surface. The tungsten wire is spot-welded to two copper electrical feedthroughs for resistive heating. Doser 2 was found to perform similar to Doser 1 but avoids the issue of K emission at Tg ≥ 900 K.

III. RESULTS AND DISCUSSION A. Dissociative chemisorption

Figure 3(a) compares methane dissociative sticking coefficients measured in supersonic molecular beam experiments9, 10, 27, 57 over a range of experimental conditions with d-PMMT simulations. Translational temperatures for the heated nozzle supersonic molecular beam experiments of the labs of Luntz and Bethune,27 Madix,9 and Beck57, 58 were taken to be Tt = 25 K, 25 K, and 10 K, respectively. PMMT parameters were determined by minimizing the ARD for simulations of Luntz and Bethune’s27 CH4 supersonic molecular beam experiments at two different nozzle temperatures, 680 K and 300 K, at Ts = 800 K. The d-PMMT model with {E0 = 58.9 kJ/mol, s = 2, ηv = 0.40}and spectator rotations quantitatively reproduce Luntz and Beck’s experiments of Fig. 3(a) but Madix’s experiments are underpredicted as was the case for a previous d-PMMT simulation without tunneling.19 The introduction of tunneling pathways to the d-PMMT model served to raise the reaction threshold energy by E0 = 1 kJ/mol but did not alter other parameters. The CD4 dissociative sticking coefficients measured at high translational energies are somewhat overpredicted by the d-PMMT simulations. The mean kinetic isotope effect, S(CH4 )/S(CD4 ), for Luntz’s high energy experiments is 2.7 and the d-PMMT simulations give 2.1. The surface temperature dependence of the dissociative sticking coefficients for supersonic molecular beam experiments10, 27 shown in Fig. 3(b), and Beck’s Fig. 3(c) results from heated nozzle and laser-pumped supersonic molecular beam experiments57 are closely replicated by the d-PMMT simulations. Beck’s eigenstate-resolved measurement of the CH4 (2ν 3 , J = 2) dissociative sticking coefficient allowed for his experimental


214707-6


J. Chem. Phys. 139, 214707 (2013)

FIG. 3. (a) and (b) Dissociative sticking coefficients for methane supersonic molecular beams incident on Pt(111). Experimental data (points) from the laboratories of Luntz,10, 27 Beck,57 and Madix9 are compared to dynamical (d-) PMMT simulations (lines) whose parameters were optimized to only Luntz’s CH4 experiments of panel (a). (c). Beck’s measurements57 (points) of dissociative sticking coefficients for thermal nozzle supersonic molecular beam and a (2ν 3 , J = 2) state-resolved supersonic molecular beam of CH4 incident on Pt(111) are compared to d-PMMT simulations (lines). (d) Dissociative sticking coefficients for thermal effusive molecular beams of CH4 incident on Pt(111) along the direction of the surface normal, Sn (Tg , Ts ), and for a 295 K ambient gas, S(Tg = 295 K, Ts ). The legend gives the impinging gas temperatures, Tg . Cushing’s Sn (Tg , Ts ) effusive beam experiments55, 56 (points) and our new S(Tg = 295 K, Ts ) ambient gas measurements (open points) are compared to d-PMMT simulations (lines).

determination, via Eq. (8) analysis, that ηv (2ν3 ) = 0.38 is the mode-specific vibrational efficacy for the 2ν 3 , J = 2 eigenstate. In contrast, the d-PMMT ηv must be considered as a vibrational mode averaged value, averaged over the vibrational state distributions present in Luntz’s Fig. 3(a) heated nozzle supersonic molecular beam experiments over which the dPMMT parameters were optimized. The mode-specific vibrational efficacy, ηv (eigenstate), typically varies with eigenstate for methane dissociative chemisorption on metals,14 but the only ηv (eigenstate) measured for CH4 /Pt(111) is ηv (2ν3 ). Although the d-PMMT model can provide useful information about the thermally mode-averaged vibrational efficacy, ηv , the model cannot generally be expected to predict the dissociative sticking for individual eigenstates very well.59, 60 The agreement between theory and the 2ν 3 , J = 2 experiments of Fig. 3(c) is particularly good because ηv (2ν3 ) happens to lie fortuitously close to the mode-averaged value, ηv = 0.40.

Effusive molecular beam and ambient gas dosing experiments are compared with d-PMMT simulations in Fig. 3(d). The “Tg = Ts ambient” entry in Fig. 3(d) legend is for simulations of the thermal equilibrium dissociative sticking coefficient appropriate to an ambient thermal gas above the surface. The Sn (Tg , Ts ) values derived from effusive beam experiments are closely replicated. However, theory overestimates the ambient gas S(Tg = 295K, Ts ) measurements by a mean factor of ∼4 over the surface temperature range from 1000 K to 600 K. It is not clear why these S(Tg = 295K, Ts ) measurements deviate from the simulations. Experimental measurements of the 700 K angle-resolved thermal dissociative sticking coefficient, S(ϑ; 700 K), conducted with Doser 1 (Ref. 25) and Doser 2 are compared with the d-PMMT simulation in Fig. 4 in an amplitude-scaled manner that highlights the angular variations. Error bars of one standard deviation are indicated for a few representative


214707-7


J. Chem. Phys. 139, 214707 (2013)

Doser 1 and Doser 2 measurements. Nevertheless, the similarity of the S(ϑ; 700 K) experimental measurements with two different dosers provides a measure of the reproducibility of the experimental method, validates the Doser 2 design, and confirms that Doser 1 operated cleanly at 700 K, consistent with the finding of no detectable K emission at Tg < 900 K for Doser 1.

B. Thermal associative desorption

FIG. 4. Effusive molecular beam measurements of the CH4 /Pt(111) angleresolved thermal dissociative sticking coefficient at 700 K (points and broken line fits) are compared to the d-PMMT simulation (solid line). The experiments and model simulation are well described by fits to the S(ϑ; T) = S0 cos n ϑ functional form.

experimental data points. The amplitude scaled d-PMMT simulation varies as cos 12.1 ϑ, with scaled ARDs of 2.94% and 5.82% with respect to the Doser 1 and Doser 2 sticking coefficients. The absolute S(ϑ; 700 K) values are in reasonable accord with one another. The d-PMMT S(ϑ; 700 K) is ∼35% smaller than the mean experimental S(ϑ; 700 K) = (7.6 ± 0.6) × 10−5 cos 12.8 ± 1.7 ϑ. A portion of the ±8% variation in the experimental measurements may lie in the replacement of the Stabil-Ion Bayard-Alpert gauge head (with ±6% accuracy) used for pressure measurement and flux calibration in the ultrahigh vacuum chamber during the time between the

Figure 5 compares d-PMMT detailed balance simulations for the product angular yields from the thermal associative desorption of CH3(c) + H(c) → CH4(g) from Pt(111) with experimental results from the laboratories of Ukraintsev and Harrison29 and Matsumoto.30 The d-PMMT model predicts that the product angular distribution should broaden as the reaction temperature for associative desorption increases. At the 240 K surface temperature of the Harrison thermal programmed reaction (TPR) experiments the d-PMMT predicts a cos 20 ϑ product angular distribution for CH4 associative desorption, broader than the experimentally observed cos 37 ϑ distribution. The d-PMMT prediction broadens for CD4 associative desorption at the 395 K surface temperature of Matsumoto’s laser-induced thermal reaction (LITR) experiments, but again is broader than the cos 31 ϑ distribution observed experimentally. Differences between the d-PMMT simulations and the experimental results are difficult to attribute to specific causes. The d-PMMT calculations are based on initial dissociative sticking coefficients extrapolated to vanishingly small adsorbate coverages, whereas the thermal associative desorption experiments were performed at close to saturation coverage of adsorbed species. The detailed balance simulations should therefore best apply to thermal associative desorption at low coverages, but there may be little coverage dependence to the reactivity.61 The chemisorbed methyl radicals were produced by 193 nm photofragmentation of physisorbed methane in Matsumoto’s experiments whereas in Harrison’s experiments methyl radicals were formed by 308 nm photoinduced

FIG. 5. Detailed balance d-PMMT simulations with (solid lines) and without19 (dashed lines) tunneling are compared to experimental data (points with dotted line fits) product angular distributions for (a) thermally induced methyl radical hydrogenation on Pt(111) at a 240 K,29 and (b) the LITR CD3(c) + D(c) → CD4(g) on Pt(111) assumed to occur at the calculated reaction peak surface temperature of 395 K.30


214707-8


J. Chem. Phys. 139, 214707 (2013)

FIG. 6. Experimental data30 (points) and detailed balance theoretical simulations (lines) are compared for the CD4(g) product translational energy distributions derived from time-of-flight spectra of the laser induced thermal reaction CD3(c) + D(c) → CD4(g) on Pt(111). (a) s-PMMT simulation with active rotations and no vibrational biasing. (b) d-PMMT simulation with active rotations and vibrational efficacy parameter, ηv . (c) s-PMMT simulation with rotation as a spectator and no vibrational biasing. (d) d-PMMT simulations with rotation as a spectator and vibrational efficacy parameter, ηv . Model parameters were determined by optimization to only Luntz’s CH4 experiments of Fig. 3(a).

dissociative electron attachment to physisorbed methyl bromide and so some co-adsorbed bromine photofragments were unavoidably present in the subsequent associative desorption TPR experiments. For dissociative chemisorption systems yielding polyatomic chemisorbed products, the applicability of detailed balance for the reverse reaction as studied under an ultrahigh vacuum environment will be degraded if product decomposition or other parallel reactions significantly compete with the thermally driven associative desorption. For the purposes of d-PMMT simulations, it was simply assumed that detailed balance applies to the CH3(c) + H(c) → ← CH4(g) equilibrium on Pt(111). This assumption must be considered cautiously when applied to associative desorption studies performed under ultrahigh vacuum conditions if other methyl reaction pathways or decomposition are significant. Campbell’s recent studies on methyl iodide decomposition found the reaction pathways from adsorbed methyl to methylidyne and coadsorbed hydrogen atoms, CH3(c) → ← CH(c) + 2H(c) , at temperatures up to 320 K and in the low coverage limit, ϑ < 0.1 ML, have an

equilibrium constant shifted far to the left,62 such that low coverages of methyl radicals are relatively stable which bolsters the prospects for detailed balance applicability. Figure 6 compares experimental CD4 LITR associative desorption translational energy distributions, Pt (Et ), with detailed balance simulations by several PMMT models with increasing dynamical constraints. The parameters of the various PMMT models were all optimized by minimizing the ARD of simulations to Luntz’s CH4 dissociative sticking experiments of Fig. 3(a). As the rotational and vibrational energy available to promote dissociative chemisorption in the PMMT models diminishes, the mean translational energy of the molecules which successfully react (associatively desorb) increases from 17.4 to 35.5 kJ/mol, tending towards the experimental value of 40.5 kJ/mol. While the usual d-PMMT model with spectator rotations best replicates the experimental Pt (Et ), the model overpredicts the molecular probability at low Et and underpredicts the tail at high Et . In the experimental LITR time-offlight spectra, molecules forming the low Et tail of the Pt (Et ) distribution are harder to detect using the number density


214707-9


J. Chem. Phys. 139, 214707 (2013)

detecting mass spectrometer than are more energetic molecules (i.e., n(t) ∝ t−2 Pt (Et ), where Et = (1/2)m(s/t)2 is the translational energy of the desorbing molecules, s is the distance between the mass spectrometer ionizer and crystal, and t is the time required to reach the ionizer) which makes it more difficult to accurately assess the low Et behavior of the experimental Pt (Et ). Noteworthy is that the LITR associative desorption Pt (Et ) provides a useful tool for evaluating dynamical constraints on PMMT models of methane dissociative chemisorption. Figure 6 makes clear that a fully statistical PMMT model is inadequate to describe CH4 /Pt(111) dissociative chemisorption, in accord with Matsumoto’s conclusion,30 but Fig. 6 also provides strong support for the d-PMMT model which is independent of its ability to replicate the dissociative sticking coefficients measured by supersonic and effusive molecular beam experiments. If tunneling was not incorporated into the PMMT models, detailed balance simulations of the LITR Pt (Et ) could exhibit some unphysical spiky undulations due to the sparseness of the transition state density of states which were smoothed out by tunneling (i.e., Fig. 2(b)). An example of the LITR Pt (Et ) simulated using the d-PMMT model without tunneling19 is available in the supplementary material.73 One way to investigate the translational energy dependence of the thermal dissociative sticking coefficient is to divide the associative desorption product translational energy distribution by a flux-weighted Maxwell Boltzmann distribution to recover a relative dissociative sticking coefficient.63, 64 Under thermal equilibrium conditions, detailed balance requires the net associative desorption flux, D(T) must balance the dissociative chemisorption flux, S(T) Fo , where S(T) and √ Fo = p/ 2π mkB T are the thermal dissociative sticking coefficient and the incident molecular flux, respectively, D(T ) = S(T ) Fo .

(15)

A more microscopically detailed version of Eq. (15) is D(Et , ϑ; T ) = S(Et , ϑ; T ) F0

cos ϑ fMB (Et ; T ), π

(16)

where cos ϑ/π is the angular distribution and fMB (Et ; T) is the flux-weighted Maxwell-Boltzmann translational energy distribution of the incident molecules, fMB (Et ; T ) =

Et e−Et /kb T . (kb T )2

(17)

The translational energy resolved associative desorption flux is balanced by the dissociatively chemisorbing flux according to detailed balance, and the former should be proportional to the thermally driven associative desorption product translational energy distribution, Pt (Et , ϑ), that can be measured experimentally, cos ϑ fMB (Et ; T ) ∝ Pt (Et , ϑ). π (18) Consequently, a relative thermal dissociative sticking as a function of translational energy can be determined as63 D(Et , ϑ; T ) = S(Et , ϑ; T )F0

Srel (Et , ϑ; T ) =

Pt (Et , ϑ) ∝ S(Et , ϑ; T ). fMB (Et ; T )

(19)

The relative dissociative sticking coefficient can be scaled to recover an approximation to the absolute S(Et , ϑ; T) based on the idea that at sufficiently high Et S(Et , ϑ; T) → 1 or by recognizing that S(Et , ϑ; T) is normalized according to ∞ S(ϑ; T ) = S(Et , ϑ; T )fMB (Et ; T )dEt , (20) 0

where S(ϑ; T) is the angle-resolved thermal dissociative sticking coefficient that can be calculated theoretically or measured experimentally in effusive molecular beam experiments.25 Further averaging over the angular distribution of the incident molecules yields the thermal dissociative sticking coefficient, cos ϑ d . (21) S(T ) = S(ϑ; T ) π In this detailed balance formalism, Pt (Et , ϑ) = ∞ 0

D(Et , ϑ; T ) D(Et , ϑ; T ) = D(ϑ; T ) D(Et , ϑ; T )dEt

S(Et , ϑ; T )fMB (Et ; T ) = S(ϑ; T )

(22)

and so the measured Pt (Et , ϑ) should be equivalent to the Et -resolved flux distribution of those molecules from a thermal gas that successfully dissociatively chemisorb when incident on the surface at angle ϑ. Figure 7(a) compares the S(Et , 0◦ ; 395 K) simulation of the d-PMMT model to its estimation derived from the LITR derived Srel (Et , 0◦ ; 395 K) normalized to the d-PMMT calculation of S(0◦ ; 395 K) = 2.8 × 10−8 . Experimental translational energies above 100 kJ/mol were considered to be at the level of noise and were not included in the Srel (Et , 0◦ ; 395 K) normalization. It is worth noting that if an effusive molecular beam measurement of S(0◦ ; 395 K) were available an all experimental determination of S(Et , 0◦ ; 395 K) would be possible. The d-PMMT S(Et , 0◦ ; 395 K) rolls over at higher Et more sharply than the experimental prediction. According to detailed balance arguments, Fig. 7(a) shows that the thermal dissociative sticking coefficient is strongly activated by normal translational energy, whereas the experimental Pt (Et , 0◦ ) of Fig. 6 gives the Et -resolved flux distribution of those molecules that successfully dissociatively chemisorb from the 395 K thermal distribution of molecules incident on the surface under equilibrium conditions. Figure 7(b) gives d-PMMT predictions for the mean energies for the successfully dissociatively chemisorbing reagents at 395 K as a function of angle of incidence that can be compared to the mean translational energies calculated from the associative desorption experiments. Mean energies were calculated as ∞ Ei Pi (Ei , ϑ)dEi Ei (ϑ)R = 0 ∞ , (23) 0 Pi (Ei , ϑ)dEi where i = v, t, s and the relevant reactive flux distributions Pi (Ei , ϑ) are defined as in Eq. (22). The mean normal translational energy of the reactive dissociative chemisorption flux is simply En (ϑ)R = Et (ϑ)R cos 2 ϑ. The mean total active (i.e., non-spectator) energy, Etot (ϑ)R = En (ϑ)R


214707-10


J. Chem. Phys. 139, 214707 (2013)

FIG. 7. (a) The Srel (Et , 0◦ ; 395 K) dissociative sticking coefficient (points) for CD4 /Pt(111) derived from Eq. (19) analysis of Fig. 6 experimental CD4 Pt (Et , 0◦ ) for associative desorption,30 normalized to the d-PMMT calculation of S(0◦ ; 395 K) is compared to the d-PMMT simulation of S(Et , 0◦ ; 395 K) (line). (b) d-PMMT simulations (lines) of the mean energies, Ej (ϑ)R , for the jth degrees of freedom of the successfully reacting reagents (products) of thermal dissociative chemisorption (associative desorption), CD4(g) → ← CD3(c) + D(c) , at T = 395 K as a function of angle, and Et (ϑ) experimental values30 (points).

+ Ev (ϑ)R + Es (ϑ)R , for the successfully reacting precursor complexes is also shown. Molecular vibrations are predicted to supply very little energy to the reacting molecules when incident at any angle. The surface phonon and normal translational motion of the molecules contribute about equally to the mean exchangeable energy of the successfully reacting molecules at zero degrees, but the surface phonon contribution increases dramatically as the incidence angle increases. Experimentally derived mean translational energies,30 Et (ϑ)R ≈ 40.1 kJ/mol, show negligible variation with angle up to the limit of detection, ϑ ≈ 25◦ , whereas the d-PMMT predictions fall from Et (0◦ )R = 35.5 kJ/mol to Et (25◦ )R = 25.1 kJ/mol, over the same range. Figures 6(d) and 7(b) indicate the molecules that successfully dissociatively chemisorb under thermal equilibrium conditions at 395 K have somewhat less translational energy according to d-PMMT calculations than what associative desorption experiments predict. The successfully dissociatively chemisorbing molecules come primarily from the high energy tail of the thermal Boltzmann distribution of the incident molecules and so it can be anticipated that the d-PMMT will overpredict the experimental S(T) at this temperature. Unfortunately, there is no measurement of S(T) at 395 K, but the d-PMMT calculates a value of 9.7 × 10−6 for S(T) at 700 K which compares to the experimental value of 1.0 × 10−5 , obtained by averaging the two S(ϑ; 700 K) measurements of Fig. 4 over angles according to Eq. (21). Although the d-PMMT model replicates the relatively high energy supersonic molecular beam and effusive molecular beam results of Fig. 3 quite well there is an unusually high ARD for the ambient gas S(Tg = 295K, Ts ) measurements of Fig. 3(d), with the discrepancy increasing as Ts decreases. Figure 3(b) shows that as the translational energy of the incident molecules decreases the sensitivity of the dissociative sticking coefficient to changes in Ts increases. Extrapolating to the ambient gas S(Tg = 295K, Ts ) experiments one anticipates that the effect of the surface (Ts ) will be particularly strong under more en-

ergy starved conditions. One way to resolve some of the remaining discrepancies between theory and experiment may be to introduce an additional d-PMMT parameter, a surface efficacy, ηs , that is less than one. This additional dynamical bias would further constrain the active exchangeable energy which would shift the simulation of the Pt (Et , 0◦ ) of Fig. 6 to higher Et , sharpen the angular yield distributions of Fig. 5, and presumably decrease the low energy dissociative sticking coefficients more profoundly than the higher energy ones. However, within the confines of this paper we have limited consideration of PMMT models to those with two or three parameters fit only to Luntz’s CH4 data of Fig. 3(a). Our expectation based on Fig. 4 is that the current d-PMMT model provides a relatively good description of the thermal dissociative chemisorption of CH4 /Pt(111) at the high temperatures of catalytic interest.

C. Reactivity under thermal equilibrium conditions

Figure 8 provides d-PMMT predictions about the reactive flux distributions for thermal dissociative chemisorption of CH4 on Pt(111) at a temperature of catalytic interest, 873 K.2 Angle-resolved mean energies and flux distributions for the successfully dissociatively chemisorbing (or associatively desorbing) species are shown for the various degrees of freedom. Earlier calculations with an s-PMMT model of CH4 /Ni(100) thermal dissociative chemisorption showed that the angle-averaged reacting flux distributions for the different degrees of freedom could be well described as thermal distributions with “effective temperatures” elevated from the ambient thermal equilibrium temperature.35 Effective temperatures are conveniently calculated as those that would yield a thermal distribution with the same mean energy as the reactive flux distribution. For the statistical model, all the angleaveraged reacting flux distributions shared the same elevated effective temperature and so the successfully reacting PCs


214707-11


J. Chem. Phys. 139, 214707 (2013)

FIG. 8. (a) Mean energies, Ej (ϑ)R , of the successfully reacting reagents (products) of thermal dissociative chemisorption (associative desorption) of CH4 /Pt(111) at T = 873 K. The (b) angle averaged, (c) ϑ = 0◦ , and (d) ϑ = 89◦ reactive flux distributions for 873 K thermal dissociative chemisorption (associative desorption) as calculated by d-PMMT simulations. The surface reactive flux distributions, fs, R (Es ), are plotted upside down from their upper axis to enhance visibility.

were predicted to be simply a hotter subset selected from all the PCs formed. Dynamically biasing skews this simple description of the reactivity and the reactive flux distributions tend to only straddle thermal distributions at varying effective temperatures. Table I catalogues the different effective temperatures for the CH4 /Pt(111) reactive flux distributions of Fig. 8 for the different degrees of freedom. For the angle-averaged distribution, the effective temperature entry for “translation” relates to normal translation and the thermal angle-averaged normal translational energy flux distribution, 1 −En /kb T e fMB (En ; T ) = , kb T

(24)

whose mean energy is En = kB T. Effective temperatures for the angle-resolved reactive flux distributions of Fig. 8 at the two extreme angles effectively bracket the range of effective temperatures for the reacting molecules. The translational and surface effective temperatures are matched together for the angle integrated and 0◦ reactive distributions. This is because

TABLE I. Effective temperatures for the successfully reacting-reagent flux distributions for 873 K thermal dissociative chemisorption of methane on Pt(111) as calculated by comparison of the distributions’ mean energies to those of thermal Boltzmann distributions, evaluated for the reactive flux distributions predicted by the d-PMMT model and the s-PMMT model of Fig. 6(a). Exceptionally, the translational temperatures listed for the angleaveraged distributions relate to the normal translational energy. Effective temperatures (K) 0◦

89◦

Angle averaged

d-PMMT Vibration Translation Surface

1209 2437 2437

1348 875 4350

1270 3077 3077

s-PMMT Rotation Vibration Translation Surface

1431 1403 1431 1431

1631 1600 875 1631

1523 1493 1523 1523

Degrees of freedom


214707-12


J. Chem. Phys. 139, 214707 (2013)

FIG. 9. (a) Angle averaged mean energies Ej R for the successfully reacting precursor complexes formed in thermal dissociative chemisorption as a function of temperature, and (b) the fractional energy uptakes, fj = Ej R /Etot R , where Etot R = En R + Ev R + Es R is the mean total active (i.e., non-spectator) energy for the successfully reacting PCs.

the efficacies for promoting reaction are the same for normal translational energy and surface phonon energy in this d-PMMT model, and at 0◦ the translational energy is simply normal translational energy. At off-normal angles of molecular incidence, the role of translational energy is discounted as En = Et cos 2 ϑ, whereas at all angles the vibrational energy has an efficacy of ηv = 0.4. Consequently, effective temperatures for vibration, and for translation at off-normal incidence, are relatively low. For spectator degrees of freedom such as rotation, or translation in the limit that the molecules are incident at 90◦ , the effective temperatures are simply the thermal equilibrium temperature of the reagents, 873 K. For comparative purposes, Table I also provides effective temperatures for the CH4 /Pt(111) reactive distributions predicted by the statistical s-PMMT model of Fig. 6(a) with active rotations. For the angle-averaged reactive distributions, the d-PMMT model predicts normal translational and surface effective temperatures that are more than twice as hot as those for the s-PMMT distributions. Although the angle-averaged reactive distributions of the s-PMMT model all share the same effective temperature since the efficacies are all the same, for the d-PMMT model the ratio of the effective temperatures for vibrational energy relative to either normal translational or surface energy (1270 K/3077 K = 0.41) is a good approximation of the vibrational efficacy, ηv = 0.40. The temperature variation of the fractional energy uptakes, fj = Ej R /Etot R , for thermal dissociative chemisorption is illustrated in Fig. 9. The d-PMMT model contends that surface phonons provide a large fraction of the active energy used to overcome the activation barrier to dissociation. For the temperature range T ≤ 1000 K relevant to catalytic reforming of methane,2 fs ≥ 44%, fn ≥ 24%, and fv ≤ 32%. For temperatures less than 775 K, fs exceeds the net fractional energy uptake from the gas, fg = fn + fv , such that the surface, rather than the incident gas phase molecules supplies the majority of the energy necessary to react.

Thermal dissociative sticking coefficients for CH4 and CD4 calculated with the d-PMMT model are shown in Fig. 10(a) along with the kinetic isotope effect (KIE) in Fig. 10(b). Wei and Iglesia2 experimentally measured the dissociation of CH4 on 1.6 wt.% Pt/ZrO2 at 873 K and determined the kinetic isotope effect to be 1.58 at 873 K, somewhat smaller than the d-PMMT prediction of 2.4. At sufficiently low temperatures the Arrhenius plots of S(T) eventually display the characteristic knee that is emblematic of tunneling and the KIE becomes very large. Figure 11(a) compares calculated CH4 S(T) curves for the d-PMMT model, for a s-PMMT model with the same {E0 = 58.9 kJ/mol, s = 2} parameters but ηv = 1, and the d-PMMT model without tunneling19 which has {E0 = 57.9 kJ/mol, s = 2, ηv = 0.40}. Also shown is the experimental value of S(T) at 700 K, equal to 1.0 × 10−5 , obtained by averaging the two S(ϑ; 700 K) measurements of Fig. 4 over angles according to Eq. (21). The 7-fold difference in the S(T) calculated by the d-PMMT and s-PMMT models provides a measure of the impact of vibrational dynamics on the thermal dissociative sticking. Of course, it is also important to know that parallel translations and rotations are spectator degrees of freedom. At the high temperatures of catalytic interest beyond about 500 K, the two d-PMMT models give the same S(T) results and tunneling is negligible. Fig. 11(b) provides a closer analysis of the fraction of the reactive flux in dissociative chemisorption that is predicted to have tunneled across the reaction barrier. Although tunneling is negligible at the higher temperatures relevant to catalysis, as the temperature drops the tunneling fraction increases steadily and by 200 K it reaches 95% for CH4 and 60% for CD4 . There is currently no compelling evidence that dissociative chemisorption occurs with greater frequency at steps, defects, or terrace sites dependent on whether the experiment involves thermal molecules or molecules incident on the surface from supersonic molecular beams with high translational


214707-13


J. Chem. Phys. 139, 214707 (2013)

FIG. 10. Kinetic isotope effect calculated for thermal dissociative sticking coefficients of methane on Pt(111).

energies. Given that the d-PMMT model parameters were set by optimization to only Luntz’s CH4 supersonic molecular beam data of Fig. 3(a), wherein En varied from 20 to 120 kJ/mol, the ability of the d-PMMT model to quantitatively predict the experimental S(T) and S(ϑ; T) at 700 K, and the thermal associative desorption product Pt (Et ) at 395 K, argues that there is no difference in the reactive sites sampled in the high translational energy beam and thermal equilibrium experiments. By detailed balance, the translational energy distribution of the molecules that successfully dissociatively chemisorb at thermal equilibrium at 395 K is given by the experimentally measured thermal associative desorption product Pt (Et ) of Fig. 6 whose mean En is 40.5 kJ/mol. Consequently, the successfully reacting molecules in thermal equilibrium and supersonic molecular beam dissociative sticking experiments often have similar translational energies. C cov-

erages accumulated in measurements of dissociative sticking coefficients using supersonic or effusive molecular beams are typically much greater than surface defect coverages (e.g., which can be less than 0.002 ML for a surface oriented to ±0.1◦ ) and so defects are likely quickly poisoned and the measured reactivity is believed to be representative of the terrace sites. D. Threshold energy

The CH4 /Pt(111) dissociative sticking coefficients scale exponentially with the apparent threshold energy for dissociative chemisorption, E0 = Ec + ZT S − ZRe (n.b., E0 ≈ Ec −10.25 kJ/mol; see the supplementary material73 ). Different electronic structure theory calculations38, 63–71 and different kinetic treatments of experimental data9, 11, 13, 54, 55, 61

FIG. 11. (a) Thermal dissociative sticking coefficient for CH4 on Pt(111) calculated by d-PMMT simulation with (solid line) and without19 (dashed line) tunneling through the reaction barrier, and with statistical treatment of the vibrational energy, ηv → 1 (dotted line). The experimental25 S(700 K) is shown as the open point. (b) d-PMMT calculation of the tunneling fraction of the reactive flux in the thermal dissociative sticking of methane on Pt(111) as a function of temperature.


214707-14


J. Chem. Phys. 139, 214707 (2013)

have given rise to a wide range of E0 values extending from 43 kJ/mol to 121 kJ/mol. Earlier s-PMMT model (assuming active rotations) analyses of supersonic molecular beam experiments gave E0 = 61.3 kJ/mol,11 58.9 kJ/mol,13 and lower values of E0 = 49 kJ/mol,65 48.2 kJ/mol56 for analyses of different effusive molecular beam experiments. The d-PMMT model assuming rotation as a spectator was the first to allow for simultaneous reproduction of the results of both supersonic and effusive molecular beam experiments with values of 57.9 kJ/mol without tunneling,19 and E0 = 58.9 kJ/mol with tunneling. Recent GGA-DFT calculations of E0 (Ec ) values include 79.3 (89.5) kJ/mol calculated39 using the PBE functional and 63.7 (73.9) kJ/mol calculated66 using the Perdew Wang (PW-91) functional.67, 68 The accuracy of GGA-DFT energies calculated with these and other popular functionals has been reviewed by Truhlar69 where an “averaged error for catalytic energies” of 33 kJ/mol was determined for the PBE and PW-91 functionals which tend to systematically underestimate reaction barrier heights. Recent single crystal adsorption calorimetry studies by the Campbell group have established that the standard heat of reaction for the forward reaction kf

−−− −− → CH4(g) ← − CH3(c) + H(c)

(25)

kb

on Pt(111) is r H0 = −14 ± 20 kJ/mol.70 Zaera has measured the activation energy for the back reaction occurring at 240 K in thermal programmed reaction44 to be Ea,b = 71± 4 kJ/mol which makes it possible to calculate Ea,f for the forward reaction according to the thermodynamic formulation of canonical transition state theory (TST).71 The standard volume of activation needs to be accounted for in the forward reaction because it involves a gaseous reactant but it is negligible for the back reaction and so Ea,f = † Hf0 + 2RT and Ea,b = † Hb0 + RT , where † Hf0 is the standard change in enthalpy from the reactants to transition state in the forward direction. Given the transition state is the same for both reactions, it follows that for the forward reaction, r H 0 = † Hf0 − † Hb0 = Ea,f − Ea,b − RT . The forward rate constant of Eq. (25) that is appropriate to concentration-based kinetics (i.e., [CH4 ]) has an activation energy that is 1/2 RT more than the activation energy for the dissociative sticking coefficient, Ea,f = Ea + 12 RT .72 Altogether this leads to an expression for the activation energy for the thermal dissociative sticking coefficient of Ea = r H 0 + Ea,b + 12 RT ,

(26)

which evaluated at 240 K yields Ea = 58 kJ/mol. This calculation assumes the validity of the thermodynamic TST treatment of the rate constants which does not admit the possibility of tunneling through the reaction barrier.71 The d-PPMT value of Ea evaluated at 240 K (see Fig. 11(a)) is 57.3 kJ/mol without tunneling and 46.4 kJ/mol with tunneling. Tunneling is predicted to be substantial (ca., 80%) for CH4 dissociative sticking at 240 K according to Fig. 11(b). Nevertheless, consistent agreement is found that Ea ∼ 58 kJ/mol at 240 K based on those theoretical models that do not admit tunneling and with parameters derived from experiments. As discussed above, recent GGA-DFT calculations are consistent

with E0 [i.e., Ea (T → 0)] values of 79.3 kJ/mol using the PBE functional39 and 63.7 kJ/mol using the PW-91 functional.66 IV. CONCLUSIONS

Tunneling was introduced into PMMT models of dissociative chemisorption for the first time and was found to have negligible impact on the CH4 /Pt(111) reactivity at temperatures above ∼500 K. Incorporation of tunneling allowed kinetic isotope effects to be calculated more realistically at low temperatures and improved simulations of the Et -resolved reactive flux distributions for thermal dissociative sticking, Pi (Ei , ϑ), that were compared by detailed balance to measured methane product translational energy distributions from thermal associative desorption. The d-PMMT model, with vibrational efficacy of ηv = 0.40, and with rotations and parallelto-the-surface translations taken as spectator degrees of freedom, was largely successful in replicating the varied dissociative sticking and associative desorption experimental results. However, the new measurements of ambient gas dissociative sticking coefficients, S(Tg = 295K, Ts ), and the associative desorption experiments provide some indications that closer agreement between theory and experiment might be achieved if a surface efficacy less than one was introduced into the dPMMT model as a further dynamical constraint. ACKNOWLEDGMENTS

This work was supported by National Science Foundation (NSF) Grant No. CHE-1112369 and an AES Graduate Fellowship in Energy Research for J.K.N. Electronic structure calculations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF Grant No. OCI-1053575, and the Stampede supercomputing system at TACC/UT Austin, funded by NSF Grant No. OCI-1134872. 1 J.

M. Wei and E. Iglesia, J. Catal. 224, 370 (2004). M. Wei and E. Iglesia, J. Phys. Chem. B 108, 4094 (2004). 3 J. G. Jakobsen, T. L. Jorgensen, I. Chorkendorff, and J. Sehested, Appl. Catal., A 377, 158 (2010). 4 J. G. Jakobsen, M. Jakobsen, I. Chorkendorff, and J. Sehested, Catal. Lett. 140, 90 (2010). 5 G. Jones, J. G. Jakobsen, S. S. Shim, J. Kleis, M. P. Andersson, J. Rossmeisl, F. Abild-Pedersen, T. Bligaard, S. Helveg, B. Hinnemann, J. R. Rostrup-Nielsen, I. Chorkendorff, J. Sehested, and J. K. Norskov, J. Catal. 259, 147 (2008). 6 C. N. Stewart and G. Ehrlich, J. Chem. Phys. 62, 4672 (1975). 7 C. T. Rettner, H. E. Pfnur, and D. J. Auerbach, Phys. Rev. Lett. 54, 2716 (1985). 8 M. B. Lee, Q. Y. Yang, S. L. Tang, and S. T. Ceyer, J. Chem. Phys. 85, 1693 (1986). 9 G. R. Schoofs, C. R. Arumainayagam, M. C. Mcmaster, and R. J. Madix, Surf. Sci. 215, 1 (1989). 10 J. Harris, J. Simon, A. C. Luntz, C. B. Mullins, and C. T. Rettner, Phys. Rev. Lett. 67, 652 (1991). 11 V. A. Ukraintsev and I. Harrison, J. Chem. Phys. 101, 1564 (1994). 12 J. H. Larsen and I. Chorkendorff, Surf. Sci. Rep. 35, 163 (1999). 13 A. Bukoski, D. Blumling, and I. Harrison, J. Chem. Phys. 118, 843 (2003). 14 L. B. F. Juurlink, D. R. Killelea, and A. L. Utz, Prog. Surf. Sci. 84, 69 (2009). 15 B. Jackson and S. Nave, J. Chem. Phys. 135, 114701 (2011). 16 B. Jackson and S. Nave, J. Chem. Phys. 138, 174705 (2013). 17 L. B. F. Juurlink, P. R. McCabe, R. R. Smith, C. L. DiCologero, and A. L. Utz, Phys. Rev. Lett. 83, 868 (1999). 2 J.


214707-15 18 M.


P. Schmid, P. Maroni, R. D. Beck, and T. R. Rizzo, J. Chem. Phys. 117, 8603 (2002). 19 S. B. Donald and I. Harrison, Phys. Chem. Chem. Phys. 14, 1784 (2012). 20 A. P. J. Jansen, and H. Burghgraef, Surf. Sci. 344, 149 (1995). 21 M. N. Carré and B. Jackson, J. Chem. Phys. 108, 3722 (1998). 22 Y. Xiang, J. Z. H. Zhang, and D. Y. Wang, J. Chem. Phys. 117, 7698 (2002). 23 G. P. Krishnamohan, R. A. Olsen, G. J. Kroes, F. Gatti, and S. Woittequand, J. Chem. Phys. 133, 144308 (2010). 24 B. Jiang and H. Guo, J. Phys. Chem. C 117, 16127 (2013). 25 J. K. Navin, S. B. Donald, D. G. Tinney, G. W. Cushing, and I. Harrison, J. Chem. Phys. 136, 061101 (2012). 26 G. W. Cushing, J. K. Navin, L. Valadez, V. Johánek, and I. Harrison, Rev. Sci. Instrum. 82, 044102 (2011). 27 A. C. Luntz and D. S. Bethune, J. Chem. Phys. 90, 1274 (1989). 28 W. H. Miller, J. Am. Chem. Soc. 101, 6810 (1979). 29 V. A. Ukraintsev and I. Harrison, Surf. Sci. 286, L571 (1993). 30 K. Watanabe, M. C. Lin, Y. A. Gruzdkov, and Y. Matsumoto, J. Chem. Phys. 104, 5974 (1996). 31 K. G. Prasanna, R. A. Olsen, A. Valdes, and G. J. Kroes, Phys. Chem. Chem. Phys. 12, 7654 (2010). 32 M. Sacchi, D. J. Wales, and S. J. Jenkins, J. Phys. Chem. C 115, 21832 (2011). 33 A. K. Tiwari, S. Nave, and B. Jackson, J. Chem. Phys. 132, 134702 (2010). 34 B. Jiang, R. Liu, J. Li, D. Q. Xie, M. H. Yang, and H. Guo, Chem. Sci. 4, 3249 (2013). 35 H. L. Abbott, A. Bukoski, and I. Harrison, J. Chem. Phys. 121, 3792 (2004). 36 A. Bukoski, H. L. Abbott, and I. Harrison, J. Chem. Phys. 123, 094707 (2005). 37 D. L. Bunker and W. L. Hase, J. Chem. Phys. 59, 4621 (1973). 38 S. H. P. Bly, L. W. Dickson, Y. Nomura, J. C. Polanyi, I. W. M. Smith, P. N. Clough, M. Kneba, U. Wellhausen, J. Wolfrum, P. E. Siska, R. J. Wolf, C. S. Sloane, W. L. Hase, L. Holmlid, K. Rynefors, K. Luther, M. Quack, K. Freed, W. M. Jackson, R. Naaman, R. N. Zare, G. Hancock, R. Walsh, J. Troe, D. M. Lubman, G. Atkinson, D. W. Setser, M. R. Levy, M. Mangir, H. Reisler, M. H. Yu, C. Wittig, C. M. Miller, F. M. G. Tablas, M. N. R. Ashfold, A. J. Roberts, I. Veltman, A. Durkin, D. J. Smith, R. Grice, D. R. Herschbach, G. M. McClelland, and K. L. Kompa, Faraday Discuss. 67, 221–254 (1979). 39 S. Nave, A. K. Tiwari, and B. Jackson, J. Chem. Phys. 132, 054705 (2010). 40 W. Forst, Unimolecular Reactions: A Concise Introduction, 1st ed. (Cambridge University Press, Cambridge, UK, 2003). 41 T. Baer, and W. L. Hase, Unimolecular Reaction Dynamics (Oxford University Press, New York, NY, 1996). 42 H. S. Johnston and J. Heicklen, J. Phys. Chem. 66, 532 (1962). 43 J. A. Booze, K. M. Weitzel, and T. Baer, J. Chem. Phys. 94, 3649 (1991). 44 F. Zaera, Surf. Sci. 262, 335 (1992). 45 G. Kresse and J. Furthmuller, Comput. Mater. Sci. 6, 15 (1996).

J. Chem. Phys. 139, 214707 (2013) 46 G.

Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996). Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994). 48 G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). 49 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 50 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997). 51 P. E. Blochl, Phys. Rev. B 50, 17953 (1994). 52 G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 53 G. Henkelman and H. Jonsson, J. Chem. Phys. 111, 7010 (1999). 54 MedeA 2.8, Materials Design Inc., Angel Fire, NM, 2012. 55 G. W. Cushing, J. K. Navin, S. B. Donald, L. Valadez, V. Johanek, and I. Harrison, J. Phys. Chem. C 114, 17222 (2010). 56 G. W. Cushing, J. K. Navin, S. B. Donald, L. Valadez, V. Johánek, and I. Harrison, J. Phys. Chem. C 114, 22790 (2010). 57 R. Bisson, M. Sacchi, T. T. Dang, B. Yoder, P. Maroni, and R. D. Beck, J. Phys. Chem. A 111, 12679 (2007). 58 M. P. Schmid, P. Maroni, R. D. Beck, and T. R. Rizzo, Rev. Sci. Instrum. 74, 4110 (2003). 59 B. A. Waite and W. H. Miller, J. Chem. Phys. 73, 3713 (1980). 60 W. H. Miller, Chem. Rev. 87, 19 (1987). 61 H. Mortensen, L. Diekhoner, A. Baurichter, and A. C. Luntz, J. Chem. Phys. 116, 5781 (2002). 62 E. M. Karp, T. L. Silbaugh, and C. T. Campbell, J. Phys. Chem. C 117, 6325 (2013). 63 M. J. Murphy and A. Hodgson, J. Chem. Phys. 108, 4199 (1998). 64 A. Hodgson, Prog. Surf. Sci. 63, 1 (2000). 65 K. M. DeWitt, L. Valadez, H. L. Abbott, K. W. Kolasinski, and I. Harrison, J. Phys. Chem. B 110, 6705 (2006). 66 R. Zhang, L. Song, and Y. Wang, Appl. Surf. Sci. 258, 7154 (2012). 67 J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 68 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992). 69 K. Yang, J. J. Zheng, Y. Zhao, and D. G. Truhlar, J. Chem. Phys. 132, 164117 (2010). 70 E. M. Karp, T. L. Silbaugh, and C. T. Campbell, J. Am. Chem. Soc. 135, 5208 (2013). 71 K. J. Laidler, Chemical Kinetics, 3rd ed. (Harper and Row, New York, 1987). 72 C. T. Rettner, H. A. Michelsen, and D. J. Auerbach, Faraday Discuss. 96, 17 (1993). 73 See supplementary material at http://dx.doi.org/10.1063/1.4837697 for (i) a theoretical simulation of the CD4 product translational energy distribution for the laser induced thermal reaction CD3(c) + D(c) → CD4(g) on Pt(111) using a d-PMMT model without incorporation of tunneling pathways,19 and (ii) a table of GGA-DFT calculated transition state vibrational frequencies for the dissociative chemisorption of CH4 and CD4 on Pt(111) and a list of experimental vibrational frequencies for gas-phase methane that were used in the d-PMMT calculations. 47 G.


First-principles quantum dynamical theory for the dissociative chemisorption of H2O on rigid Cu(111).

Dissociative chemisorption of methane on Ni and Pt surfaces: mode-specific chemistry and the effects of lattice motion.

The dissociative chemisorption of methane on Ni(100) and Ni(111): classical and quantum studies based on the reaction path Hamiltonian.

The dissociative chemisorption of water on Ni(111): Mode- and bond-selective chemistry on metal surfaces.

Dynamics of water dissociative chemisorption on Ni(111): effects of impact sites and incident angles.

Rotational and steric effects in water dissociative chemisorption on Ni(111).

Temporal constraints on hydrate-controlled methane seepage off Svalbard.

Influence of temperature on methane hydrate formation.

Conciliating synchronicity with spatial discretization, exclusion, interactions, and detailed balance.

Validity of the site-averaging approximation for modeling the dissociative chemisorption of H2 on Cu(111) surface: a quantum dynamics study on two potential energy surfaces.

Balancing cognitive control: how observed movements influence motor performance in a task with balance constraints.

Metalated nucleotide chemisorption on hydroxyapatite.

Six-dimensional quantum dynamics for dissociative chemisorption of H2 and D2 on Ag(111) on a permutation invariant potential energy surface.

Ultrafast 2DIR probe of a host-guest inclusion complex: structural and dynamical constraints of nanoconfinement.

Detailed Balance Limit of Efficiency of Broadband-Pumped Lasers.

The influence of accuracy constraints on EMG and kinetic variables during gait initiation.

Influence of conditioning agents and enzymic hydrolysis on the biochemical methane potential of sewage sludge.

Long-Term Dynamical Constraints on Pharmacologically Evoked Potentiation Imply Activity Conservation within In Vitro Hippocampal Networks.

Aortic Stiffening and Dilation: Influence on Coronary Supply-Demand Balance.

The influence of upper body fatigue on dynamic standing balance.

Quantum modelling of hydrogen chemisorption on graphene and graphite.

Influence of age and sagittal balance of the spine on the value of the pelvic incidence.

The role of task constraints in relating laboratory and clinical measures of balance.

Influence of Fermi arc states and double Weyl node on tunneling in a Dirac semimetal.