Connecting Small Molecule Reaction Dynamics to Catalysis Ian Harrison Department of Chemistry, University of Virginia Charlottesville, VA

Catalysis ↔ Surface Science  Pressure, materials, and non-equilibrium gaps P = Torr T s = K; T g ~300 K = ? Surface Science Model Single-crystal surface Real Catalyst Crystalline nanoparticle catalyst P = 10 atm (~10 4 Torr) T = 1000 K

Harnessing Dynamical Information  Non-equilibrium dissociative sticking coefficients can be high.   -TST model can harness this high S/N dynamical information.

Reactivity & Energy Flow at Surfaces ←Nonequilibrium & Equilibrium Nonequilibrium Expts (e.g. T g  T s ) Equilibrium Expts PC-MURT Transition State Properties DFTAb Initio Functional Development canonical-TST fast Experiments Kinetic Theory Electronic Structure Theory Master Equation - MURT ←Energy Flow ←Equilibrium only Improved Design and Engineering of Catalytic & Nanoscale Processes at Surfaces slow

Activation Energies for Surface Reactions A couple of multibillion-dollar-a-year surface reactions are:  Steam reforming of natural gas (methane dissociation on Ni catalysts).  Si homoepitaxy via UHV-CVD (silane dissociation on Si(100)). SiH 4 on Si(100) CH 4 on Ni Abbott et al., J. Chem. Phys. 121, 3792 (2004).Kavulak et al., J. Phys. Chem. B 109, 685 (2005).

Microcanonical Unimolecular Rate Theory  Molecule first interacts with only a few local surface atoms (oscillators).  Energy of the transient “physisorbed complex” (PC) is randomized by the initial collision and/or rapid intramolecular vibrational energy redistribution (IVR).   All states at E * become equally probable and react with common k i (E * )s.  PCs are approximately adiabatically isolated because thermalization is slow compared to the picosecond timescale for desorption at E * > E 0.

Physisorbed Complex – Microcanonical Unimolecular Rate Theory (PC-MURT) Using RRKM rate constants, the steady state approximation yields,  A purely statistical result! E 0,i = threshold energy for i

PC-MURT  Convolving the individual energy distributions gives the overall PC energy distribution,  The experimentally observed sticking coefficient is calculated as,  Predictions possible for any experiment

Dynamical Constraints  Typically, for smooth flat metal surfaces and alkanes  Normal translational energy scaling of S applies.  E n = E t cos 2 ; parallel momentum is approximately conserved.  Local normal energy scaling may apply for corrugated surfaces, e.g., SiH 4 /Si(100)-(2x1)  Introduces a new parameter  fixed independently by molecular beam experiments; = E t {(1-  ) cos  sin 2 . *  Certain rotational or vibrational modes may also be spectator degrees of freedom. * Xia and Engstrom, J. Chem. Phys. 101, 5329 (1994)

PC-MURT Parameters  Desorption ‡ → freely rotating molecule at ∞  Dissociation ‡ → 3 Adjustable Parameters {E 0, s, D }  E 0, the threshold energy for dissociative chemisorption.  s, the number of surface oscillators that freely exchange energy within the physisorbed complex.  D, a lumped frequency for the molecule-surface normal vibration and the 3 frustrated rotations at the reactive transition state.  Average Relative Discrepancy minimum fixes the 3 parameters

Synopsis of PC-MURT for CH 4 /Ni(100)  Dissociative sticking probabilities for:  Laser pumped and thermally populated molecular beam experiments.  Thermal “ bulb ” equilibrium experiments.  Extract transition state parameters for comparison to electronic structure theory. Abbott et al., J Chem Phys 121, 3792 (2004) E 0 = 65 kJ/mol D = 170 cm -1 s = 2  ARD = 43% Schmid et al., J. Chem. Phys. 117, 8603 (2002) Juurlink et al., Phys. Rev. Lett. 83, 868 (1999) Homblad et al., J. Chem. Phys. 102, 8255 (1995) Nielsen et al., Catal. Lett. 32, 15 (1995) Expts:

Comparison of T s = 475 K Experiments  7 order of magnitude difference in dissociative sticking coefficient

Application of PC-MURT to CH 4 /Ni(100): Comparison of f(E * )s at T s = 475 K  Nonequilibrium eigenstate resolved experiment (2 3, J = 2;  E t  = 93 kJ/mol).  Thermal bulb experiment at x higher pressure. Schmid et al., J. Chem. Phys. 117, 8603 (2002) Nielsen et al., Catal. Lett. 32, 15 (1995)  E *  = 169 kJ/mol; S Beam = 0.15  E *  = 17 kJ/mol; S T = 4.8 x 

Fractional Energy Uptakes for Thermal Sticking of CH 4 /Ni(100)  Fractional energy uptakes are defined as  At T = 500 K,

Mode Selective Chemistry: CD 2 H 2 /Ni(100)  Mode selective chemistry is sometimes observed at surfaces!  Dissociative sticking coefficients for CD 2 H 2 rovibrational eigenstates and for a thermally populated molecular beam are shown at left.  CD 2 H 2 may have insufficient mode coupling  slow IVR/collisional state mixing.  Slow IVR requires a full dynamical theory.  The PC-MURT (lines) fails. Beck et al. Science 302, 98 (2003)

Effusive Beam S(T g,T s ) for CH 4 /Pt(111)  PC-MURT can also be used to predict S(T g, T s ) sticking for effusive molecular beams where T g = T t = T v = T r ; unlike in supersonic beams.  Note the many opportunities to measure “effective activation energies”, “E a ”(T s )  E a (T), in these non-equilibrium experiments.  Generally,

CH 4 Reactivity Induced by Surface & Gas E 0 = 49 kJ/mol D = 330 cm -1 s = 2  ARD = 41% K. DeWitt et al. J. Phys. Chem. B 110, 6705 (2006)

Alkane Dissociative Chemisorption Abbott et al., J. Chem. Phys. 119, 6407 (2003) [Ni] DeWitt et al., J. Phys. Chem. B 110, 6705, 6714 (2006) [Pt] Abbott & Harrison. J. Phys. Chem. B 109, (2005) [Ir] Abbott & Harrison. J. Catal. in press (2007) [Ru]  CH 4 below, C 2 H 6 above.  Reduction in E 0 from CH 4 to C 2 H 6 on Pt(111) is substantial; 52.5 ± 3 kJ/mol → 26.5 ± 3 kJ/mol.  DFT calculations for Pt(110) yield E 0 = 38.5 ± 2 kJ/mol for both CH 4 & C 2 H 6. *  C 2 H 6 E 0 : Final state effects, dynamics, energy transfer? PC-MURT Derived Threshold Energies * Anghel et al., Physical Review B 71, (2005); Chem. Phys. Lett. 413, (2005)

CH 4 Dissociation on Flat Metal Surfaces versus Nanocatalysts  PC-MURT predicts thermal dissociative sticking coefficients on flat metal surfaces many orders of magnitude higher than apparent values measured on nanocatalysts.  A surprising result since stepped surfaces, as found on high curvature nanocatalysts, are typically thought to be more active than flat surfaces.  Presumably, C build-up quickly limits the number of active sites available on the nanocatalysts. Not a bare surface limit.  There seems to be substantial opportunity for improving CH 4 reforming catalysts. Wei & Iglesia. J. Phys. Chem. B 108, 7253 (2004) [Ru] Carstens & Bell. J. Catal. 161, 423 (1996) [Ru] Wei & Iglesia. Angew. Chem. Int. Ed. 43, 3685 (2004) [Ir] Wei & Iglesia. J. Phys. Chem. B 108, 4094 (2004) [Pt] Wei & Iglesia. J. Catal. 224, 370 (2004) [Ni] Abbott & Harrison, J. Catal 254, (2008)

Dissociative Chemisorption & Associative Desorption Dynamics of H 2 /Cu(111) Can the PC-MURT provide at least a statistical baseline for the dissociative chemisorption/desorption dynamics? H 2(g) + Cu(111) ↔ 2 H (c)  Employ detailed balance at thermal equilibrium to predict the associative desorption fluxes. Two PC-MURT models:  2 parameter ( E 0 = 79 kJ/mol, s = 1 ) model with active rotations. *  3 parameter ( E 0 = 62 kJ/mol, D = 490 cm -1, s = 1 ) model with rotation as a spectator to the dissociation dynamics. † * Abbott & Harrison, J. Chem. Phys. 125, (2006); † Abbott & Harrison, J. Phys. Chem. A 111, 9871 (2007)

Detailed Balance at Thermal Equilibrium T = T g = T s Desorption Flux = Dissociative Sticking Flux D 0 = SF 0 Also applicable to state-resolved flux balances,

H 2 /Cu(111) PC-MURT: Rotation as a Spectator State-Averaged Chemisorption Experiments  Absolute dissociative sticking coefficients for thermally populated molecular beams of H 2 & D 2 at specified nozzle temperatures. Rettner et al. J. Chem. Phys. 102, 4625 (1995); Michelsen et al. J. Chem. Phys. 98, 8294 (1993) E 0 = 62 kJ/mol D = 490 cm -1 s = 1 ARD = 570%

H 2 /Cu(111) PC-MURT: Rotation as a Spectator State-Averaged Desorption Experiments  Angular distributions and cos n fits for H 2 & D 2 recombinative desorption at various surface temperatures.  5D quantum calculations * predict cos 25 for H 2 on Cu(111) at T s = 1000 K. Rettner et al. J. Chem. Phys. 94, 7499 (1991) * Gross et al. Phys. Rev. Lett. 73, 3121 (1994) with E 0 = 70 kJ/mol; E 0 = 48.5 kJ/mol is recent DFT expectation. E 0 = 62 kJ/mol D = 490 cm -1 s = 1 ARD = 24%

D 2 /Cu(111) PC-MURT: Rotation as a Spectator State-Averaged Desorption Experiments  5D quantum calculations, * like the 1-D van Willigen model, † predict increasing with.  Catastrophe for 1-D model as →90°.  PC-MURT behaves correctly as →90°. Comsa & David Surf. Sci. 117, 77 (1982) * Gross et al. Phys. Rev. Lett. 73, 3121 (1994) with E 0 = 70 kJ/mol. † van Willigen, Phys. Lett. 28A, 80 (1968)

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Eigenstate-Resolved Desorption Experiments By detailed balance, Hodgson’s desorption experiments yield: Murphy & Hodgson J. Chem. Phys. 108, 4199 (1998)

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Eigenstate-Resolved Desorption Experiments For one surface oscillator, the PC-MURT analytically requires, Thus, and expts show, at the lowest E t s.

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Eigenstate-Resolved Desorption Experiments Hodgson’s experiments clearly demonstrate that the surface is not a spectator! Later, we will show that the fractional energy uptakes for surmounting the thermal activation energy for dissociation at 925 K are roughly: f t = 42% f s = 41% f v = 17% So, the surface plays an essential role in the dissociation dynamics.

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Rotationally-averaged, vibrationally-resolved P(E t )  Qualitative agreement  Averaged over rotational states, J = 0 – 6 Rettner et al. J. Chem. Phys. 102, 4625 (1995); Michelsen et al. J. Chem. Phys. 98, 8294 (1993) E 0 = 62 kJ/mol D = 490 cm -1 s = 1

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Eigenstate-Resolved Desorption Experiments  Mean translational energies for H 2 & D 2 as a function of rotational state agree well with PC-MURT for J ≤ 6. These are the key J states at thermal energies.  Divergence for J ≥ 7 shows that rotational energy begins to facilitate sticking at high J and E r ≥ 40 kJ/mol (n.b., at 925 K, = k B T = 7.7 kJ/mol). Rettner et al. J. Chem. Phys. 102, 4625 (1995); Michelsen et al. J. Chem. Phys. 98, 8294 (1993) E 0 = 62 kJ/mol D = 490 cm -1 s = 1 ARD = 16 %

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Eigenstate-Resolved Desorption Experiments  Arrhenius fit lines through PC-MURT rotational energy distributions for recombinative desorption of H 2 & D 2 are for T r = T s = 925 K. E 0 = 62 kJ/mol D = 490 cm -1 s = 1 ARD = 221 %

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Vibrational Energy Distribution for Desorption JExpt (%)PC-MURT(%) H2H ∑P  J D2D ∑P  J  Somewhat less vibrational energy in associatively desorbed hydrogen than theoretically predicted.

Early rather than Late Barrier for Dissociation!  Experiments show more translational energy and less vibrational energy release in the associatively desorbing hydrogen than the PC-MURT predicts.  By detailed balance, dissociative chemisorption favors translational energy over vibrational energy as compared to the statistical PC-MURT predictions.  The measured vibrational efficacy for dissociative chemisorption is only 50% of the translational efficacy. *  Appropriate to an early transition state on the dissociative potential energy surface according to the Polanyi rules. † * Rettner et al. J. Chem. Phys. 102, 4625 (1995) † J.C.Polanyi, Acc. Chem Res. 5, 161 (1972)

Early not Late Barrier! GGA-DFT: late barrier  b ‡ > 33% b eq LDA-DFT: early barrier  b ‡ < 10% b eq b Z GGA-DFT invariably predicts late barriers for the dissociation of diatomic molecules but the H 2 /Cu(111) dynamics provide evidence for an early barrier. Impact on Br ø nsted-Evans-Polanyi correlations: where  0.5 for late barriers. E 0 = 62 kJ/mol D = 490 cm -1 s = 1 E 0 = 48 kJ/mol D = 405 cm -1 GGA-DFTPC-MURT Transition State Characteristics

H 2 /Cu(111) PC-MURT: Rotation as a Spectator Thermal & Effusive Beam Sticking  More than an order of magnitude variation in S T if rotations are active. Dynamics matter!  Rettner employed an erf-model with over 100 parameters to predict the 925 K thermal sticking for D 2 /Cu(111) based on his eigenstate-resolved desorption experiments. *  The 3-parameter PC-MURT is in good agreement with the S T (925 K) for D 2 /Cu(111) and the H 2 /Cu(110) measurements. † D 2 /Cu(111) S T (925) expt = 3.29 x S T (925) PC-MURT = 2.16 x (no rotations) S T (925) PC-MURT = 1.4 x (with rotations) * Rettner et al. Faraday Discuss. 96, 17 (1993) † Campbell et al., JVST A 9, 1693 (1991)

Energy Uptake in Thermal Sticking of H 2 /Cu(111)  Mean energies and fractional energy uptakes, f i =  E i  R /  E *  R, calculated by PC-MURT are shown for thermal sticking from an ambient gas.  Molecular normal translational energy contributes most to overcoming E 0.  More than 40% of the reactive energy comes from surface phonons!

PC-MURT Predictions with Active Rotation: D 2 /Cu(111) Associative Desorption  Rotational temperatures predicted by the PC-MURT are T r ~ 6000 K. Lines through the experimental solid points are for T r = T s = 925 K.  The Boltzmann plots of the experimental data indicate that rotation is a spectator until E r ~ 40 kJ/mol is exceeded.  The initial rise of the experimental with J seems to be a modest dynamical effect, the subsequent fall in can be rationalized by the statistical PC-MURT predictions. E 0 = 79 kJ/mol s = 1 Abbott & Harrison, J. Chem. Phys. 125, (2006)

H 2 /Cu(111) Dynamics: Rotation as a Spectator  The dissociation dynamics appear to transition from rotation as a spectator for E r 40 kJ/mol.  Consequently, at thermally accessible energies, rotation is effectively a spectator degree of freedom and dynamical steering is of negligible importance. Abbott & Harrison, J. Phys. Chem. A 111, 9871 (2007)

Summary  The MURT local hot spot model was used to explain and simulate a variety of activated dissociative chemisorption/associative desorption dynamics.  Benchmark transition state characteristics can be extracted by low parameter MURT analysis of diverse experiments with high dynamic range.  MURT may be helpful in closing the “nonequilibrium gap” between surface science and catalysis (e.g., CH 4 beam experiments and thermal catalysis).  Most of the energy for thermal activated dissociative chemisorption comes from the gas but surface phonons cannot be neglected – even for H 2 on Cu(111)!  Dynamical effects can sometimes produce order of magnitude changes in dissociative sticking coefficients (e.g., if rotation is a spectator) and hence are vital to know about. The MURT can provide statistical baseline predictions against which dynamical effects can be identified when they occur (e.g., early transition states;  < 0.5 in Br ø nsted-Evans-Polanyi correlations).

Acknowledgements  National Science Foundation  American Chemical Society Petroleum Research Fund For a brief description of MURT and references: Heather AbbottLeticia Valadez and Kristy DeWitt Prof. Kurt Kolasinski (West Chester University) MURT Kinetics Alumni: Dr. Heather Abbott – Humboldt Fellow, FHI, Berlin Dr. Alex Bukoski – Resident, Veterinary Anesthesiology, U. Florida Dr. Kristy DeWitt – Optical Air Data Systems Dan Blumling – Ph.D. student, Penn State Dave Kavulak – Ph.D. student, UC Berkeley

Synopsis of PC-MURT for CO 2 /Rh(111)  CO 2 dissociative sticking in thermal bulb.  CO oxidation dynamics by detailed balance. Goodman et al., Surf. Sci. 140, L239 (1984) Sibner et al., J. Chem. Phys. 89, 1163 (1989); 103, 6677 (1995) Coulston & Haller, J. Chem. Phys. 95, 6932 (1991) E 0 = 73 kJ/mol s = 2 Rotation a spectator Frequencies from GGA-DFT Abbott & Harrison, J. Phys. Chem. C 111, (2007)

Synopsis of PC-MURT for SiH 4 /Si(100)  Dissociative sticking probabilities for  Thermally populated molecular beam experiments  Thermal nonequilibrium experiments (UHV-CVD)  Corrugated Si(100)-(2x1) surface Engstrom et al. J. Vac Sci. and Tech. A 13, 2651 (1995) For other references see: Kavulak et al. J. Phys. Chem. B 109, 685 (2005) E 0 = 19 kJ/mol D = 230 cm -1 s = 2  ARD = 15%

Synopsis of PC-MURT for CH 4 /Ni(100)  Dissociative sticking probabilities for:  Laser pumped and thermally populated molecular beam experiments.  Thermal “ bulb ” equilibrium experiments.  Extract transition state parameters for comparison to electronic structure theory. Abbott et al., J Chem Phys 121, 3792 (2004) E 0 = 65 kJ/mol D = 170 cm -1 s = 2  ARD = 43% Schmid et al., J. Chem. Phys. 117, 8603 (2002) Juurlink et al., Phys. Rev. Lett. 83, 868 (1999) Homblad et al., J. Chem. Phys. 102, 8255 (1995) Nielsen et al., Catal. Lett. 32, 15 (1995) Expts:

Synopsis of PC-MURT for CH 4 /Pt(111)  Dissociative sticking probabilities for thermally populated supersonic molecular beam experiments by Luntz & Bethune.  Extract transition state parameters for comparison to electronic structure theory. (E 0 = 43, 64, 75, and 81 kJ/mol are EST calculations) E 0 = 56 kJ/mol D = 125 cm -1 s = 3  ARD = 34% Luntz & Bethune J. Chem. Phys. 90, 1274 (1989); Harris et al. Phys. Rev. Lett. 67, 652 (1991) For details see: Bukoski et al. J Chem Phys 118, 843 (2003)

Synopsis of PC-MURT for CH 4 /Ir(111) E 0 = 39 kJ/mol D = 185 cm -1 s = 1  ARD MB = 88% Seets et al. J. Chem. Phys. 107, (1997) Jachimowski et al. Surf. Sci. 393, 126 (1997)  Dissociative sticking probabilities for:  Thermally populated molecular beam experiments.  Thermal equilibrium and nonequilibrium experiments. [c.f., EST calculations of E 0 = 15 and 76 kJ/mol] Abbott & Harrison, J. Phys. Chem. B 107, (2005)

Synopsis of PC-MURT for CH 4 /Ru(0001) E 0 = 59 kJ/mol D = 155 cm -1 s = 2  ARD = 316%  Dissociative sticking probabilities for:  Thermally populated molecular beam experiments.  Thermal bulb experiments.  Supported catalysts. Luntz et al., J. Chem. Phys. 116, 5781 (2002) Chorkendorff et al., J. Chem. Phys. 110, 2637 (1999) Egeberg et al., Surf. Sci. 497, 183 (2002) Wu & Goodman, J. Chem. Phys. 110, 2637 (1999) Abbott & Harrison, J. Catal 254, (2008)

C 2 H 6 /Pt(111): Effusive Beam Experiments DeWitt et al., J. Phys. Chem. B 110, 6714 (2006) E 0 = 24 kJ/mol D = 215 cm -1 s = 10 ARD = 53 % E 0 = 29 kJ/mol D = 90 cm -1 s = 2 ARD = 556 % Angle- Integrated ARD = 13 %

C 2 H 6 /Pt(111): Supersonic Beam Expts Schoofs et al., Surf. Sci. 215, 1 (1989); Newell et al., Faraday Discuss. 105, 193 (1996) E 0 = 24 kJ/mol D = 215 cm -1 s = 10 ARD = 3032 % E 0 = 29 kJ/mol D = 90 cm -1 s = 2 ARD = 48 % Increasing T nozzle increases S.

Recommended Transition State Parameters for C 2 H 6 on Pt(111) E 0 = 26.5 ± 3 kJ mol -1 D = 153 ± 63 cm -1 s = 2 (or 10) Translational, vibrational, and surface energy certainly help facilitate dissociation. The role of rotational energy is less clear – rotation might even inhibit dissociation. Rodriguez & Goodman, J. Phys. Chem. 94, 5342 (1990)