Chemistry of fast electrons

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Jul 14, 2009 - A chemicurrent is a flux of fast (kinetic energy. 0.5 1.3 eV) metal ... This picture also applies to other oxidation- reduction ...... This work was funded by the Helios Solar Energy Research Center, which is supported by the ...
Chemistry of fast electrons Sergey N. Maximoff1 and Martin P. Head-Gordon1 Department of Chemistry, University of California, and Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Edited by Gabor A. Somorjai, University of California, Berkeley, CA, and approved May 5, 2009 (received for review February 25, 2009)

A chemicurrent is a flux of fast (kinetic energy ⲏ 0.5ⴚ1.3 eV) metal electrons caused by moderately exothermic (1ⴚ3 eV) chemical reactions over high work function (4ⴚ6 eV) metal surfaces. In this report, the relation between chemicurrent and surface chemistry is elucidated with a combination of top-down phenomenology and bottom-up atomic-scale modeling. Examination of catalytic CO oxidation, an example which exhibits a chemicurrent, reveals 3 constituents of this relation: The localization of some conduction ⴚ electrons to the surface via a reduction reaction, 0.5 O2 ⴙ ␦eⴚ 3 O␦ (Red); the delocalization of some surface electrons into a conducⴚ ⴚ tion band in an oxidation reaction, O␦ ⴙ CO 3 CO2␦ 3 CO2 ⴙ ␦eⴚ (Ox); and relaxation without charge transfer (Rel). Juxtaposition of Red, Ox, and Rel produces a daunting variety of metal electronic excitations, but only those that originate from CO2 reactive desorption are long-range and fast enough to dominate the chemicurrent. The chemicurrent yield depends on the universality class of the desorption process and the distribution of the desorption thresholds. This analysis implies a power-law relation with exponent 2.66 between the chemicurrent and the heat of adsorption, which is consistent with experimental findings for a range of systems. This picture also applies to other oxidationreduction reactions over high work function metal surfaces. heterogeneous catalysis 兩 hot electrons 兩 metal surfaces 兩 surface science 兩 transition metals

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he significance of electronic excitations on metal surfaces was probably first recognized within the photoelectric effect (1, 2) and has been reaffirmed ever since. Photoelectrons are emitted into the vacuum from metal surfaces upon exposure to light, the energy quantum of which exceeds an exit threshold— the work function. Just as light ejects photoelectrons that map the surface, chemical reactions of exothermicity exceeding the work function eject exoelectrons (3) that map the chemistry on low work function (ⱗ3 eV) metal surfaces. Low work function metal substrates (e.g., groups IA, IIA, and IIIA) are too reactive to be practical for catalysis unlike their noble or late transition d-metal counterparts, which support rich chemistry, often of industrial significance. These more interesting substrates have work functions of 4⫺6 eV (4), too high for exoelectrons to emerge. But electronic excitations in metals are omnipresent: Any surface movement invokes, by virtue of Anderson’s orthogonality catastrophe, sub-work function electronic excitations (5) that stay inside the metal—unseen unless looked for—and ultimately dissolve in the sea of thermal conduction electrons, phonons, and photons. Experimental evidence of internal metal excitations associated with chemistry on high work function metal surfaces has emerged only recently. A pattern in quenching of NO molecules ro-vibrationally excited by 2.9⫺3.8 eV near an Au(111) surface (6) alludes to the involvement of sub-work function electronic excitations. Involvement of the Au(111) surface plasmon at 2.5 eV (7) in the observed multiple NO vibrational quanta losses is not unlikely. Furthermore, 2 research groups (those of refs. 3, 8, and 9 and those of refs. 10–12) have independently detected electronic excitations during exposure of thin metal film/ semiconductor Schottky diodes to species that exothermically adsorb or chemically react on the metal film. Some of these electronic excitations reach the metal/semiconductor interface 11460 –11465 兩 PNAS 兩 July 14, 2009 兩 vol. 106 兩 no. 28

where the exit threshold for electrons is significantly lowered from the work function to the Schottky barrier and then enter the conduction band of the semiconductor and give rise to the chemicurrent Ic, a measurable electric current that runs through the diode as a result of the surface chemical process. The ratio of the number of detected elementary charges constituting Ic to the independently counted number of underlying surface events is the apparent yield, Yc. References 3, 8, and 9 report Yc ⬃ 10 ⫺6 ⫺10 ⫺2 in Ag/n-Si diodes with Schottky barriers of 0.2⫺0.5 eV during adsorption in ultrahigh vacuum of various species with adsorption heats ⱗ4 eV. References 10–12 report Yc ⬃ 10⫺4⫺10⫺2 in Pt/n-TiO2, Pd/n -TiO2, and Pt/n-GaN diodes with higher Schottky barriers of 0.9⫺1.3 eV during steady-state catalytic carbon monoxide oxidation at atmospheric pressure. This exothermic by a 2.93 eV reaction [see National Institute of Standards and Technology (NIST) chemistry WebBook (http:// webbook.nist.gov/chemistry)] is essential to the operation of automotive catalytic exhaust converters. The experiments reveal the following signatures of chemicurrent: (H) Substrate electrons fast enough to cross the Schottky barrier determine Ic; (H⬘) Yc decays with film thickness; (L) Yc does not depend on the CO oxidation turnover rate in refs. 10–12 or on the adsorption/ desorption rate in refs. 3, 8, and 9; (PL) Yc, save for a few outliers, exhibits a power-law dependence with an exponent of ⬃2.7 on the heat of adsorption (9), which is reminiscent of the photoelectron yield from metals that follows a power-law dependence on the excess photon energy above the work function, albeit with a smaller exponent of ⬃2.0 (2); and (NP) surface plasmons are unlikely to affect the chemicurrent because the reaction heats are below the plasma thresholds ⲏ3.7 eV on Ag-, Pt-, and Pd-low index surfaces (13). Despite much theoretical work on excitations on metal surfaces (reviewed in refs. 13 and 14), the aspects of the relation between the surface and adsorbate that underlie the chemicurrent experiments have remained uncomfortably obscure. The spectrum of an adsorption system includes excitations intrinsic to its constituents: metal’s electron-hole pairs, interband transitions, phonons, and electronic collective modes, as well as the transitions within the molecular discrete and continuum spectra, but may also include features that have no analogue in the metal and adsorbate in separation, as in the adsorption of noble gases (4). Spectral line shapes of adsorbed molecules and metal electronic excitations during chemisorption have been treated within models that assume, explicitly or implicitly, that lowenergy electron-hole pairs primarily contribute to energy exchange at the active interface (15–17). In addition to the electron-hole pairs, the adsorbate’s electronic and vibrational excitations have been considered in refs. 18–20. None of these models, however, appears to imply PL. Author contributions: S.N.M. designed research; S.N.M. performed research; and S.N.M. and M.P.H.-G. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1To

whom correspondence may be addressed. E-mail: [email protected] or [email protected].

This article contains supporting information online at www.pnas.org/cgi/content/full/ 0902030106/DCSupplemental.

www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902030106

Phenomenological Examination Catalytic carbon monoxide oxidation over late transition fcc d-metal (Rh, Pd, Ir, and Pt) surfaces is a model catalytic process complex enough to be interesting but sufficiently understood to be illuminating. It includes events from the adsorption/ desorption of CO, O2, and CO2 gases to the transport of charge and heat. The nature of these events depends on the substrate, temperature, and partial pressures of the gases in an exceptionally complex manner. The surface may relax and reconstruct, multiple adsorption phases may coexist, island, and form filaments. The reaction mechanisms may differ within and along the islands (21, 22). Notwithstanding the above complexity, CO oxidation below ignition is driven by 3 constituent processes: The reductive dissociative O2 adsorption (22), and perhaps the formation of surface metal oxides (P1) (4, 23); oxidative or reductive—depending on the conditions—CO adsorption (4, 24), and perhaps the formation of surface carbon and unsaturated carbon oxides (P2) (25); and a surface reaction that culminates in oxidative CO2 desorption (P3). With intent to relate P1, P2, and P3 to the chemicurrent, conduct in a thought experiment the Langmuir–Hinshelwood process (26) over an active interface at given CO, excess O2, and negligible CO2 partial pressures in the temperature range below ignition. Ensure that CO does not dissociate and that the active interface does not reconstruct, as vicinal or closed Pt, Pd, Rh, and Ir surfaces do (4). Monitor CO, O2, and CO2 adsorption/desorption, charge, and heat flows over an active interface patch whose unit normal, n, points into the metal, and whose dimension exceeds that of atoms but not that of islands, island borders, filaments, or filament termination spots during the following cycle. Beginning at the clean active interface, ⭋, adsorb O2 dissociatively, withdraw the adsorption heat, adsorb CO, rapidly withdraw the adsorption heat to avoid reactive CO2 desorption, heat up until the reactive desorption is complete, withdraw the reactive desorption heat, and then repeat the whole sequence indefinitely. The chemicurrent Ic has to do with neither the active interface without the chemical reaction for, by L, Ic correlates with the reaction rate, nor with the chemical reaction without the active interface, for Ic is directional in space, but a free chemical reaction is not. Rather, Ic has to do with a relation—which needs to be determined—between the chemical reaction and the active interface, together constituting the surface chemical process. This relation, which is described concisely by the diagrams P1, P2, and P3 in Fig. 1, is a statement of directionality in space with respect to the active interface and directionality in time with respect to the irreversible progression of the chemical process. Maximoff and Head-Gordon

Fig. 1. From top to bottom of the diagrams P1, P2, and P3, the parts of the catalytic reactor are as follows: the gas phase, the adsorbate atomic cores, the surface electrons, the Ohmic contact (Oh), and the Schottky contact (Sh). During an instant of P1, P2, and P3, each part draws a horizontal line from left to right which designates surface local sources of charge (i), entropy (s), and mass (je, jCO, and jO2). Meanwhile, spatial flows je, jCO, jO2, jCO2, i, and s—which are related through balance conditions (41)— draw the transversal dashed lines. The vertical dotted lines designate a relation that unites the subsystems of adsorbate atomic cores and the surface electrons into the adsorption system. The orientation of the arrows is set by the direction of thermodynamic time, i.e., by the direction of growth in entropy. The entropy change near the active interface, ⌬S[s, i, R, Re, J] ⫽ ⌬Schem ⫹ ⌬Srelax ⫹ ⌬Strans, includes 3 contributions. The first contribution, ⌬Schem, is due to the chemical transformations between the electrons and adsorbate atomic cores within the active interface at the respective rates, Re and R. The second contribution, ⌬Srelax, is due to energy relaxation flow from the adsorbate atomic cores to the electrons within the active interface at the rate J during the chemical reaction. The third contribution, ⌬Strans ⫽ (smetal ⫺ sgas) 䡠 n, is the entropy brought to or taken away from the active interface by the entropy flux, smetal, due to adsorption/ desorption of the metal electrons and the energy exchange with the metal as well as by the entropy flux, sgas, due to adsorption/desorption of the gas molecules and the energy exchange with the gas. From a subsurface point of view, the cycle (seen in P1P2P3) corresponds to an electron pump, which draws electrons from the Ohmic lead to the surface, and then reinjects them into the bulk where a fraction will surpass the Schottky barrier in the form of a chemicurrent. This latter process is represented by the inner cycle of the diagram and is directly associated with the progress of the surface chemical reaction, which is represented by the outer cycle.

The charge current is the flux of metal electrons, i ⫽ e je (e is the electron charge), because desorption of negatively charged particles and cations is unlikely. The clean active interface separates by the work function the nearly confined electrons within the nearly freely moving CO and O2 molecules in the gas above and the nearly freely moving electrons in the background of the nearly confined metal ions below. The Schottky contact separates metal and semiconductor conduction electrons by the Schottky barrier, 0.9 ⱗ ␹Sh ⱗ 1.3 eV. The Ohmic contact separates conduction electrons within the catalyst film and those within the lead. These interfaces are polarized and the charge current is proportional to the rate of polarization change. The polarization of the active interface covered with adsorption layer, P, differs from intrinsic static polarization of the clean active interface, P⭋, by ␦P ⫽ P ⫺ P⭋. The average change in the surface polarization, ␦P䡠n ⫽ ⫺(1/4␲e)␦␹, during a surface chemical process is estimated through the change in the work PNAS 兩 July 14, 2009 兩 vol. 106 兩 no. 28 兩 11461

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This report is about the relation between chemicurrent and the chemistry supported by high work function metal surfaces. The properties H, H⬘, L, PL, and NP open this inquiry by pointing to questions to be addressed: What requirements on the surface chemical process must be met for chemicurrent to appear? Why does PL emerge for diverse species? To what extent is PL universal? How does the distribution of the fast electrons surpassing the Schottky barrier relate to the surface chemical process? What parameters of the surface chemical process and the metal substrate control the chemicurrent, and how? In what follows, CO oxidation will be subject to initial phenomenological examination that arrives at a conjecture: Concerted motion of adsorbates and surface metal electrons during surface oxidation-reduction processes acts as a nearcritical electron pump that is responsible for the chemicurrent. Microscopic paths in support of this conjecture will be presented, their macroscopic significance will be shown, and observable characteristics of the chemicurrent will be predicted and will be shown to satisfy PL. It will be further explained that the suggested mechanism pertains to other oxidation-reduction reactions over metal surfaces, including those of ref. 9.

function, ␦␹. Furthermore, the charge current incident to the active interface is estimated by the rate of the polarization change, therefore i ⫽ ⫺(1/4␲e)(d␦␹/dt). Since the charge is conserved, i ⫽ i䡠n ⫽ ⫺iSh ⫺ iOh; here iOh and iSh are the current densities incident to the Ohmic and the Schottky contacts, respectively. The work function changes are 0.3 ⱗ ␦␹ ⱗ 1.0 eV in P1, and ⫺0.25 ⱗ ␦␹ ⱗ 1.0 eV in P2 (4), and ⌬SP1,2 ⬎ 0. Therefore, iP1 ⬎ 0, and the metal electrons accumulate at the active interface; it can be that iP2 ⬍ 0 or iP2 ⬎ 0, and the electrons are repelled from or attracted to the active interface. A complementary oxidation or reduction reaction should reverse these changes in the surface electron distribution. Reactive CO2 desorption, P3, which is an inverse of dissociative CO2 adsorption; O2 associative desorption, which is an inverse of P1; and CO desorption, which is an inverse of P2, are possible complementary reactions. At the relevant experimental conditions, ⌬SP1,2,3 ⬎ 0, i.e., P1,2,3 occur (4). Another observable that describes an adsorbate in relation to the surface electrons within the active interface is a breakup threshold, ␹⫽: the minimum work that is required to free a gas molecule or the maximum work that is produced upon localizing it to the active interface. ␹⫽ is the barrier for associative oxygen desorption, 1.1 ⱗ ␹O2 ⱗ 1.4 eV, in P1; the barrier for CO desorption, 1 ⱗ ␹CO ⱗ 1.5 eV in P2; and the barrier for reactive CO2 desorption, 0.5 ⱗ ␹CO2 ⱗ 1.2 eV in P3; ␹⫽ is the adsorption or desorption heat for species studied in ref. 9. The adsorption atomic core phase is different from the gas phase for an energy, u, below ␹⫽. In contrast, no distinction exists between adsorbed and gas phase CO2, CO, or O2 for u ⬎ ␹⫽. The lack of this distinction means that subsystems of the adsorption system, ⫽ ⫽ ⫽ ⫽ ⫽ eCO2䡠䡠䡠CO⫽ 2 , eCO䡠䡠䡠CO , eO2䡠䡠䡠O2 , whose energies are near their respective breakup thresholds are critical. For u away from a ␹⫽, the correlation between events in the direction transversal to the active interface should decay exponentially according to a hierarchy of relaxation times and lengths. Near ␹⫽, this hierarchy collapses; the correlations’ decay becomes insensitive to the time and length scale, i.e., it becomes a power law. The mass, charge, and heat transport is fundamentally different for subsystems whose energy, u, is below or above a ␹⫽. ⴱ Above a ␹⫽, desorption of fast, ro-vibrationally excited CO2(g) , ⴱ ⴱ or CO(g) , or O2(g) , as well as simultaneous release of the surface electrons into the metal conduction band, become possible. During P3 above the threshold, when an efficient energy and charge transport channel opens up, an electron leaving the active interface, after suffering losses, may be fast enough to overcome ␹Sh. That is, it may inject into the electron-deficient conduction band of the semiconductor, so that iSh ⬎ 0, whereas the flux of thermal electrons, iOh ⬎ 0, from the electron-rich Ohmic lead, compensates the changes in the surface electron distribution. In a sustained chemical process, the rates Re, R, and J need to be matched by the transport fluxes i, j, and s. The individual diagrams can now be linked into a cycle P1P2P3 of an electron pump, shown in Fig. 1. This phenomenological examination thus arrives at its goal: a hypothesis, whose validity is to be addressed, about the origin of the chemicurrent. The chemicurrent in CO oxidation includes those fast electrons that arise during the cyclic process in Fig. 1. The transport rates at u ⫽ ␹⫽, and the chemicurrent yield, exhibits critical, i.e., power-law behavior Yc ⬀ (␹⫽ ⫺ u)y for u ⱗ ␹⫽ when the adsorbate and the conduction electrons engage upon adsorption and Yc ⬀ (u ⫺ ␹⫽)y⬘ for u ⲏ ␹⫽ when the adsorbate leaves and the metal electrons disengage upon de⫽ ⫽ ⫽ sorption; the threshold, ␹⫽, is either ␹O2, or ␹CO , or ␹CO2, or another breakup threshold; the critical exponents y and y⬘ coincide for a given adsorption/desorption process. Microscopic Paths That Contribute to Chemicurrent In a computational experiment following up on the previous section’s findings, O2(g) and CO(g) above Pt(111) become chemi11462 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902030106

Fig. 2. The changes in the distribution of the adsorbed C and O atoms and in the distribution of the surface electrons between the energy stationary points during P1,2,3 at given coverages [(1/4)C and (1/2)O per surface Pt atom] are displayed in the upper and lower registers of each diagram, respectively. The contours encode depletion (red) and build-up (blue) of the electron density relative to that of the decoupled adsorption layer and Pt(111). The changes in the energy and work function (both in eV) are shown above the upper and the lower arrows, respectively.

sorbed O(a) and CO(a) during P1,2, and then become CO2(g) during P3 as shown in Fig. 2. The total energy features 5 minima. A pair of minima, CO(g) ⫹ 0.5 O2(g) and CO2(g), correspond to the free molecules held at the points infinitely distant from the clean active interface and from each other. A pair of minima— both observed in the ultrahigh vacuum experiments and consistent with total energy models (ref. 27; ref. 28 and references therein)—correspond to CO(g) ⫹ O(a), the adsorption p(2 ⫻ 2) ⫺ O(fcc) pattern in register with Pt(111) and CO infinitely distant from the active interface, and CO(a) ⫹ O(a), the coadsorption p(2 ⫻ 2) ⫺ Ofcc ⫺ COatop pattern in register with Pt(111). Another minimum that is found, the CO2(a) chemisorbed in p(2 ⫻ 2) ⫺ CO2 pattern, has not been experimentally observed on Pt(111). However, even if CO2(a) were a methodological artifact, it should still be considered. Its geometry is similar to those of precursors to CO2 dissociative adsorption on Fe, Ru, Rh, and Ni surfaces that are more electropositive than Pt(111) (4), and also to that of free long-living CO⫺ 2 . Furthermore, ref. 29 reports a vibrationally silent CO2 desorption precursor—and CO⫺ 2 itself is vibrationally unconventional (30–32)—on Pt(111) surfaces precovered with oxygen and CO during reactive scattering of Cs⫹ against the surface. Lowering the Pt(111) work function—e.g., by adsorbing an alkali metal—would stabilize the anionic chemisorbed CO2(a) if it were a reactive transient on Pt(111). The energy also features a critical point (transition structure), CO⫽ 2 , that deforms into CO2(a), O(a) ⫹ CO(a), and CO2(g) along apparently continuous minimum-energy paths shown in Fig. 3A. The structure of the transition state can be inferred from energy- and angle-resolved reactive desorption spectroscopy experiments (33, 34) that support a bent CO⫽ 2 on Pt(111) and other catalytic late transition d-metal surfaces. Unlike neutrals and cations, all free anions have a finite number of discrete states below the ionization continuum (35). 2 2 2 Free CO⫺ 2 has up to 3 discrete energy levels 1 A⬘, A⬙, and 2 A⬘ Maximoff and Head-Gordon

(32, 36). As the distance OC䡠䡠䡠O⫺ decreases and the angle ⬔OCO straightens along a reaction path, the bottom of the ionization continuum of OC䡠䡠䡠O⫺, set by the ground-state adiabatic potential of OC䡠䡠䡠O, descends upon the discrete anion levels to devour them. No discrete anion electronic levels exist at configurations close to that of the product, the linear CO2 (see Fig. 3A). The surface states derived from the antibonding lowest unoccupied molecular orbital (LUMO), 1a⬘, of the transient CO2 in bent geometry are substantially filled before CO⫽ 2 but become vacant after CO⫽ 2 . As CO2 straightens, the LUMO rises well above the Fermi level and ends up as the ␲g LUMO of CO2(g) (Fig. 4A). After CO⫽ 2 along the reaction path, the rapidly increasing transport contribution to the entropy (Fig. 4B), caused by irreversible emission of fast electrons from the active interface into the empty conduction band, indicates that the chemistry-induced irreversible ionization of the surface species is a very likely event. During the reductive steps, the delocalized conduction electrons fill (i ⬎ 0) the states localized at the active interface derived from those vacant in the adsorbing CO(g) and O2(g). These localized electrons are returned (i ⬍ 0) into the conduction band during the oxidative steps when no states capable of binding electrons at the active interface exists. In renormalization group theory language, the sign of i is a fixed-point property. Hence, the existence of cycles that are concatenated from a pair of segments with i ⬍ 0 and i ⬎ 0, like those described above, implies the existence of numerous comparable cycles. In turn, this finding implies their macroscopic significance, consistent with the observed stability of the sign of the work function change on adsorption of CO and O2 on diverse transition metal substrates (4). Thus, there is an ensemble that is composed of those cycles that are localized before and delocalized after passing CO⫽ 2 . The ⫽ ensemble of all those eCO2䡠䡠䡠 CO⫽ 2 that are about to ionize-desorb ⫽ is critical near the threshold, ␹CO2, for the reactive desorption. The similarity in transition state geometries noted in Fig. 3A does Maximoff and Head-Gordon

not then come as a surprise, because scale independence and self-similarity are signs of a critical transition. Chemicurrent That Arises from the Paths The stationary wave function, ⌿, of the closed adsorption system is locally split into the variables describing the atomic cores, ⌿ 3 ␸, and the electrons, ⌿ 3 ␺, in the diagrams P1, P2, and P3 in Fig. 1. The vector ␸ ⫽ (␸␣) includes the translational and ro-vibrational degrees of freedom of the adsorbate, and ␺ ⫽ (␺A) describes the necessarily finite number of localized discrete and the continuum states for an anionic form of the adsorbate, as well as the conduction bands in the metal. This splitting is not unique and has to be fixed by specifying the gauge potentials near the active interface: U, as well as the ‘‘nonadiabatic couplings’’ A and A⬘, that may locally rotate the vectors ␺ and ␸. The observables should be independent of the splitting, as should the action governing the evolution of the electrons and atomic cores: I⫽

冕 再

៮ 䡠 ␺ ˙ ⫹ iប ␸៮ 䡠 ␸ dt dx iប␺ ˙ ⫺ [␺៮ AបvF 䡠 共iDAB ⫺ kF兲 ␺ B



ប2 ប2 DBA␺៮ A 䡠 DAB␺ B ⫹ D⬘ ␸៮ 䡠 D⬘␤␣␸ ␤ 2m 2M ␤␣ ␣



⫹ V ABCD␺៮ A␺ B␺៮ C␺ D ⫹ U共 ␸兲 ␺៮ A␺ A] . The kinetic energy is given in terms of the covariant derivatives DAB ⫽ ␦ ABⵜ ⫺ iAAB for ␺, and D⬘␣␤ ⫽ ␦ ␣␤ⵜ ⫺ iA⬘␣ ␤ for ␸. The first order in D terms describe the ubiquitous electron-hole pairs near the Fermi surface in the direction of a wave vector kF and at the Fermi velocity vF (5). The quadratic in D terms account for the asymmetry between the electrons and holes as well as the electronic kinetic energy near the adsorbate. The PNAS 兩 July 14, 2009 兩 vol. 106 兩 no. 28 兩 11463

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Fig. 3. Progression of CO ⫹ O 3 CO2 along the reaction path. (A) The distribution of the geometries of the reacting CO relative to chemisorbed O. The angular coordinate is the ⬔OCO, the linear coordinate is the longest of the C—O bonds. The yellow dots are the energy minima: CO(a) ⫹ O(a), the CO2(a), and the CO2(g). The pink dots are the transition-state structures for the last activated step for various mechanisms, surfaces, and metals (ref. 27; ref. 28 and references therein); the pink region encloses the transition structures within 2 standard deviations in angular and radial coordinates. The solid blue lines delineate the domains of a constant number of discrete levels in free CO2⫺; the dotted line is an extrapolation. The color gradient from blue to white to red corresponds to the increasing vertical energy of the emitted electron relative to the ground state of the neutral CO2 in the domain where no discrete levels exist. A minimum energy path is the green line. (B) An expansion of the diagrams in Fig. 1 arranged by ⬔OCO.

Fig. 4. Changes in the electronic structure along the reaction path. (A) Density of electronic states localized in the valence region of O䡠䡠䡠CO along the reaction path that connects CO(a) ⫹ O(a) (left) to the CO2(g) and the clean active interface (right). The binding energy, ⑀, is relative to the Fermi level (red horizontal line). The positive binding energies correspond to vacant states. The color gradient from blue to white to red corresponds to increasing density of states. The red lines indicate the molecular orbital energies of O䡠䡠䡠CO decoupled from Pt(111). (B) A contribution to ⌬Strans due to fast electrons undergoing irreversible electron emission into the conduction band (see SI Appendix).

electron–electron interaction—VABCD at the scale of electron localization of lloc ⬃ 10⫺1 nm at the active interface—should be pivotal in compensating for the adsorbate’s angular momentum during adsorption of 3⌸ O2, and also in other low-energy processes involving the adsorbate’s energy levels crossing the Fermi level; through nonperturbative two-electron events similar to those encountered in Kondo physics (37). The potential 2兲 共3兲 共4兲 ␸␣␸␤ ⫹ U␣␤␥ ␸␣␸␤␸␥ ⫹ U␣␤␥␦ ␸␣␸␤␸␥␸␦ ⫹ . . . U ⫽ U共␣1兲␸␣ ⫹ U共␣␤

can be seen as potential energy (relative to the Fermi level), which restricts the adsorbate near the active interface. The kinetic energy caused by motion of the adsorbate is quadratic in D⬘. Near an adsorption minimum, U ⬍ 0, ␸ is confined by the friction-like nonadiabatic potential A⬘, which channels the energy from the adsorbate to the electrons. The ground state of free O2 and CO approaching the active interface corresponds to ␸dloc ⫽ 0 and U (␸dloc) ⫽ 0. When the free translational motion localizes during the adsorption, ␸loc ⫽ 0 because of the zero-point motion, and U(␸loc) ⬍ 0. During the CO2 reactive desorption, the frustrated translations of O ⫹ CO, ␸loc ⫽ 0 , become free translations of COⴱ2, ␸dloc ⫽ 0, after ␹⫽ is overcome. The field ␸ formally corresponds to the N-vector model, which is known to undergo a symmetry-breaking, i.e., a critical transition at u ⫽ ␹⫽ (38). For u ⬍ ␹⫽, the action depends on the direction of ␸ because the molecules are localized to the active interface, i.e., the symmetry is broken. The preferential direction disappears above ␹⫽ because no molecules are localized anymore, i.e., the symmetry is reestablished. The evolution of the field ␸ around the classical value in the potential U induces the evolution in ␺. The delocalized conduction bands in ␺ couple to the initially half-filled antibonding, ␲g,O2(␶), of dissociating 3⌸ O2, and to the unfilled antibonding, 2␲CO(␶), of 1⌺ CO states during P1,2. The number of the localized components in ␺ changes by 1 when the 1a⬘ wave function of CO⫽ 2 enters the ionization continuum coupled to a vacant conduction band. For a fast electron to inject into the semiconductor, its range needs to exceed the typical separation, ldloc ⲏ 10⫺100 lloc (12), between the active interface and the Schottky contact, and its kinetic energy incident to the Schottky contact needs to exceed ␹Sh. The lower-energy and shorter-range electrons should thermalize within the metal film. These long-range delocalized electrons of interest may arise whenever the charge state of the adsorbate changes. The concentration of the delocalized electrons should be low at energies of order ␹Sh; therefore, Fermi statistics become irrelevant away from the active interface, i.e., ␺ can be treated as a vector of commuting numbers away from the active interface. The chemicurrent yield, i.e., the long-range, high-energy part of i per desorbing CO2(g), is the time-dependent current–current correlation function Yc ⬀ 冬i iSh冭. It is determined by the critical dynamics of ␸ near ␹⫽. The latter for the near-critical N-vector model, under the constraint of charge conservation, and in the relaxation regime is known. It belongs to the Hohenberg– Halperin dynamic universality class B (39). This observation implies a specific scaling behavior of the rate of change in electron density at the active interface past the transition state on the energy difference from ␹⫽. The relaxation rate scales inversely with the critically slow relaxation time, ␶⫺1 ⬀ ␰⫺z, where ␰ ⬀兩u ⫺ ␹⫽兩⫺␯ is the scaling of the decay length for the correlation function. The dynamic critical index is z ⫽ 4 ⫺ ␩ in this case (39); ␯ ⫽ 0.672 ⫾ 0.007 and ␩ ⫽ 0.033 ⫾ 0.004 for the (N ⫽ 2)-vector model are known (38). Thus, i ⬀ ␶⫺1 ⬀ ␰⫺z ⬀兩u ⫺ ␹⫽兩␯z ⬀兩u ⫺ ␹⫽兩2.66, and 11464 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902030106

iSh ⬀ 兩u ⫺ ␹ ⫽兩 vzjco2 , in agreement with PL and L. More detailed analysis or simulations would be required to go beyond this schematic estimate. The relaxation experiments (9) for adsorption and desorption, which involve symmetry-breaking around the desorption energy due to frustration of translational motion and concomitant change in the adsorbate charge state, agree with the prediction. Further Discussion and Implications Nothing singles out catalytic CO oxidation among other surface chemical processes except the following 3 building blocks: a surface reduction (i ⬎ 0), which is a chemical reaction that oxidizes the substrate through localization of some conduction electrons (Red); a surface oxidation (i ⬍ 0), which is a chemical reaction that reduces the substrate through delocalization of the surface electrons previously localized in Red (Ox); and a relaxation process (i.e., i ⫽ 0 in the reversible limit), which is a purely dissipative component that is present in any surface chemical process (Rel). These building blocks define an electron pump whose reduction leg (cathode) localizes the slow electrons and whose oxidation leg (anode) releases fast electrons that may contribute to the chemicurrent. Several characteristics control operation of the electron pump. First is the pump’s capacity to displace the electrons at the active interface during the reductive or oxidative adsorption steps. Surface oxides, which are likely to form over defects or steps or surfaces more open than Pt(111), feature higher (⬇1 e) than chemisorbed oxygen (⬇0.1 e) surface electron concentrations (4). Second is the pump’s capacity to displace back the surface electrons into fast metal electrons during oxidative or reductive desorption steps. The energy available to the fast electrons is estimated by the excess of the reaction heat over an activation barrier for reactive desorption. The yield of fast electrons scales with respect to the available excess energy as Yc ⬀ (u ⫺ ␹⫽)2.66, a scaling law characteristic of a different universality class than the 2.0 power law (Fowler law) observed for photoelectron yield in light absorption. The locality of the electron–electron interaction in metals implies that the near-threshold estimates should also hold above the thresholds (38). Third is the pump’s capacity to excite low-energy electron-hole pairs and substrate phonons [vibrational quanta ⱗ 0.025 eV (4)], resulting in nonuniversal contributions to the excitation spectrum. The surface chemical process depends on the bulk mass, charge, and energy fluxes, and can therefore be controlled by adjusting these fluxes. Bulk ionic currents are absent in gas-phase surface chemistry. It would be different in an ionic liquid environment where not only electron currents, but also ionic currents, contribute to the charge transport. Kinetics of chemical reactions on high work function metal surfaces has been traditionally studied within reversible models on ground-state energy surfaces or within nearly reversible models that account for omnipresent electron-hole pairs and phonons through a velocity-dependent damping. The mechanism that is presented in this report as a principal cause of the chemicurrent in CO oxidation (and likely in other oxidationreduction reactions on metal surfaces) involves an irreversible step that triggers the product desorption above a threshold. This is an efficient channel for the removal from the catalytic interface of the reaction products and the heat in the form of fast electrons and the energetic gas molecules. This channel is neither reducible to an electron-hole pair nor to phonon creation during surface chemical processes. Further implications of the existence of this channel for modeling chemical reactions on high work function metal surfaces are yet to be fully appreciated. A broader picture emerges. The Pt(111) catalyst is covered by islands of oxygen and carbon monoxide coadsorption phases (21, 22). Reactive CO2 desorption barriers vary broadly (0.3⫺1.2 eV) Maximoff and Head-Gordon

with surface environment. Regions actively involved in reactive desorption can be viewed as tiny electron pumps that inject fast electrons at an active interface patch whenever u ⲏ ␹⫽. The electrons then travel through the film, which is thick enough for the short-range electronic excitations to die out but thin enough to let the long-range electrons reach the exit side. One can imagine a matrix of conducting wells insulated from one another that collects all electrons of incident kinetic energy within a window around ␹Sh and allows the electrons to leave through a well. The current iSh is collected from each well, amplified, and imaged. As the energy filter window slides up, the image should change. Lower-energy images should be nearly featureless because lower-energy electron-hole pairs emerge in any local dynamic process and overlap with other low-energy excitations. The distribution of surface areas involved in reactive desorption should be seen in higher-energy images after low-energy excitations are filtered out. The local distribution of ␹⫽ could be extracted from the image energy contrast.

ACKNOWLEDGMENTS. Thanks to Gabor Somorjai, Russ Renzas, Jeong Park, Yimin Li, and Antoine Hervier for numerous stimulating discussions; Konstandin Kudin for his help with QuantumEspresso code; and John Tully for stimulating conversations. The calculations in this work were done on highperformance computer clusters at the Department of Energy’s National Energy Research Scientific Computing Center under a grant of computer time. This work was funded by the Helios Solar Energy Research Center, which is supported by the Director, Office of Science, Office of Basic Energy Sciences of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

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Maximoff and Head-Gordon

PNAS 兩 July 14, 2009 兩 vol. 106 兩 no. 28 兩 11465

CHEMISTRY

Work function measurements and reactive desorption spectroscopy were fruitful in the early days of surface science (40). The spectroscopy of fast electrons, representing dynamic work function measurement or reactive ‘‘electron adsorption/ desorption’’ spectroscopy—although still in its infant stage— promises to eventually develop. The existence of a systematic correlation between the known surface chemistry and the largely unknown chemistry of subsurface metal electrons is a necessary condition for a spectroscopic method and one of central implications of this report.