Chemistry of fast electronsSergey 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 � 0.5�1.3 eV) metalelectrons caused by moderately exothermic (1�3 eV) chemicalreactions over high work function (4�6 eV) metal surfaces. In thisreport, the relation between chemicurrent and surface chemistry iselucidated with a combination of top-down phenomenology andbottom-up atomic-scale modeling. Examination of catalytic COoxidation, an example which exhibits a chemicurrent, reveals 3constituents of this relation: The localization of some conductionelectrons to the surface via a reduction reaction, 0.5 O2 � �e�3O��

(Red); the delocalization of some surface electrons into a conduc-tion band in an oxidation reaction, O��

� CO3 CO2��3 CO2 � �e�

(Ox); and relaxation without charge transfer (Rel). Juxtaposition ofRed, Ox, and Rel produces a daunting variety of metal electronicexcitations, but only those that originate from CO2 reactive de-sorption are long-range and fast enough to dominate the chemi-current. The chemicurrent yield depends on the universality classof the desorption process and the distribution of the desorptionthresholds. This analysis implies a power-law relation withexponent 2.66 between the chemicurrent and the heat of ad-sorption, which is consistent with experimental findings for arange of systems. This picture also applies to other oxidation-reduction reactions over high work function metal surfaces.

heterogeneous catalysis � hot electrons � metal surfaces � surface science �transition metals

The significance of electronic excitations on metal surfaceswas probably first recognized within the photoelectric effect

(1, 2) and has been reaffirmed ever since. Photoelectrons areemitted into the vacuum from metal surfaces upon exposure tolight, the energy quantum of which exceeds an exit threshold—the work function. Just as light ejects photoelectrons that mapthe surface, chemical reactions of exothermicity exceeding thework function eject exoelectrons (3) that map the chemistry onlow work function (�3 eV) metal surfaces. Low work functionmetal substrates (e.g., groups IA, IIA, and IIIA) are too reactiveto be practical for catalysis unlike their noble or late transitiond-metal counterparts, which support rich chemistry, often ofindustrial significance. These more interesting substrates havework functions of 4�6 eV (4), too high for exoelectrons toemerge. But electronic excitations in metals are omnipresent:Any surface movement invokes, by virtue of Anderson’s orthog-onality catastrophe, sub-work function electronic excitations (5)that stay inside the metal—unseen unless looked for—andultimately dissolve in the sea of thermal conduction electrons,phonons, and photons.

Experimental evidence of internal metal excitations associ-ated with chemistry on high work function metal surfaces hasemerged only recently. A pattern in quenching of NO moleculesro-vibrationally excited by 2.9�3.8 eV near an Au(111) surface(6) alludes to the involvement of sub-work function electronicexcitations. Involvement of the Au(111) surface plasmon at 2.5eV (7) in the observed multiple NO vibrational quanta losses isnot unlikely. Furthermore, 2 research groups (those of refs. 3, 8,and 9 and those of refs. 10–12) have independently detectedelectronic excitations during exposure of thin metal film/semiconductor Schottky diodes to species that exothermicallyadsorb or chemically react on the metal film. Some of theseelectronic excitations reach the metal/semiconductor interface

where the exit threshold for electrons is significantly loweredfrom the work function to the Schottky barrier and then enter theconduction band of the semiconductor and give rise to thechemicurrent Ic, a measurable electric current that runs throughthe diode as a result of the surface chemical process. The ratioof the number of detected elementary charges constituting Ic tothe independently counted number of underlying surface eventsis the apparent yield, Yc. References 3, 8, and 9 report Yc �10�6�10�2 in Ag/n-Si diodes with Schottky barriers of0.2�0.5 eV during adsorption in ultrahigh vacuum of variousspecies with adsorption heats �4 eV. References 10–12 reportYc � 10�4�10�2 in Pt/n-TiO2, Pd/n -TiO2, and Pt/n-GaN diodeswith higher Schottky barriers of 0.9�1.3 eV during steady-statecatalytic carbon monoxide oxidation at atmospheric pressure.This exothermic by a 2.93 eV reaction [see National Institute ofStandards and Technology (NIST) chemistry WebBook (http://webbook.nist.gov/chemistry)] is essential to the operation ofautomotive catalytic exhaust converters. The experiments revealthe following signatures of chemicurrent: (H) Substrate elec-trons fast enough to cross the Schottky barrier determine Ic; (H�)Yc decays with film thickness; (L) Yc does not depend on the COoxidation 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 onthe heat of adsorption (9), which is reminiscent of the photo-electron yield from metals that follows a power-law dependenceon the excess photon energy above the work function, albeit witha smaller exponent of �2.0 (2); and (NP) surface plasmons areunlikely to affect the chemicurrent because the reaction heatsare below the plasma thresholds �3.7 eV on Ag-, Pt-, and Pd-lowindex surfaces (13).

Despite much theoretical work on excitations on metal sur-faces (reviewed in refs. 13 and 14), the aspects of the relationbetween the surface and adsorbate that underlie the chemicur-rent experiments have remained uncomfortably obscure. Thespectrum of an adsorption system includes excitations intrinsic toits constituents: metal’s electron-hole pairs, interband transi-tions, phonons, and electronic collective modes, as well as thetransitions within the molecular discrete and continuum spectra,but may also include features that have no analogue in the metaland adsorbate in separation, as in the adsorption of noble gases(4). Spectral line shapes of adsorbed molecules and metalelectronic excitations during chemisorption have been treatedwithin models that assume, explicitly or implicitly, that low-energy electron-hole pairs primarily contribute to energy ex-change at the active interface (15–17). In addition to theelectron-hole pairs, the adsorbate’s electronic and vibrationalexcitations have been considered in refs. 18–20. None of thesemodels, 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: maximoff@berkeley.edu ormhg@cchem.berkeley.edu.

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

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This report is about the relation between chemicurrent and thechemistry supported by high work function metal surfaces. Theproperties H, H�, L, PL, and NP open this inquiry by pointing toquestions to be addressed: What requirements on the surfacechemical process must be met for chemicurrent to appear? Whydoes PL emerge for diverse species? To what extent is PLuniversal? How does the distribution of the fast electronssurpassing the Schottky barrier relate to the surface chemicalprocess? What parameters of the surface chemical process andthe metal substrate control the chemicurrent, and how?

In what follows, CO oxidation will be subject to initialphenomenological examination that arrives at a conjecture:Concerted motion of adsorbates and surface metal electronsduring surface oxidation-reduction processes acts as a near-critical 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 observablecharacteristics of the chemicurrent will be predicted and will beshown to satisfy PL. It will be further explained that thesuggested mechanism pertains to other oxidation-reduction re-actions over metal surfaces, including those of ref. 9.

Phenomenological ExaminationCatalytic carbon monoxide oxidation over late transition fccd-metal (Rh, Pd, Ir, and Pt) surfaces is a model catalytic processcomplex enough to be interesting but sufficiently understood tobe illuminating. It includes events from the adsorption/desorption of CO, O2, and CO2 gases to the transport of chargeand heat. The nature of these events depends on the substrate,temperature, and partial pressures of the gases in an exception-ally complex manner. The surface may relax and reconstruct,multiple adsorption phases may coexist, island, and form fila-ments. The reaction mechanisms may differ within and along theislands (21, 22). Notwithstanding the above complexity, COoxidation below ignition is driven by 3 constituent processes: Thereductive dissociative O2 adsorption (22), and perhaps theformation of surface metal oxides (P1) (4, 23); oxidative orreductive—depending on the conditions—CO adsorption (4,24), and perhaps the formation of surface carbon and unsatur-ated carbon oxides (P2) (25); and a surface reaction thatculminates in oxidative CO2 desorption (P3).

With intent to relate P1, P2, and P3 to the chemicurrent, conductin a thought experiment the Langmuir–Hinshelwood process (26)over an active interface at given CO, excess O2, and negligible CO2partial pressures in the temperature range below ignition. Ensurethat CO does not dissociate and that the active interface does notreconstruct, as vicinal or closed Pt, Pd, Rh, and Ir surfaces do (4).Monitor CO, O2, and CO2 adsorption/desorption, charge, and heatflows over an active interface patch whose unit normal, n, pointsinto the metal, and whose dimension exceeds that of atoms but notthat of islands, island borders, filaments, or filament terminationspots during the following cycle. Beginning at the clean activeinterface, �, adsorb O2 dissociatively, withdraw the adsorptionheat, adsorb CO, rapidly withdraw the adsorption heat to avoidreactive CO2 desorption, heat up until the reactive desorption iscomplete, withdraw the reactive desorption heat, and then repeatthe whole sequence indefinitely.

The chemicurrent Ic has to do with neither the active interfacewithout the chemical reaction for, by L, Ic correlates with thereaction rate, nor with the chemical reaction without the activeinterface, for Ic is directional in space, but a free chemicalreaction is not. Rather, Ic has to do with a relation—which needsto be determined—between the chemical reaction and the activeinterface, 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 withrespect to the active interface and directionality in time withrespect to the irreversible progression of the chemical process.

The charge current is the flux of metal electrons, i � e je (e isthe electron charge), because desorption of negatively chargedparticles and cations is unlikely. The clean active interfaceseparates by the work function the nearly confined electronswithin the nearly freely moving CO and O2 molecules in the gasabove and the nearly freely moving electrons in the backgroundof the nearly confined metal ions below. The Schottky contactseparates metal and semiconductor conduction electrons by theSchottky barrier, 0.9 � �Sh � 1.3 eV. The Ohmic contactseparates conduction electrons within the catalyst film and thosewithin the lead. These interfaces are polarized and the chargecurrent is proportional to the rate of polarization change. Thepolarization of the active interface covered with adsorptionlayer, P, differs from intrinsic static polarization of the cleanactive interface, P�, by �P � P � P�. The average change in thesurface polarization, �P�n � �(1/4�e)��, during a surfacechemical process is estimated through the change in the work

Fig. 1. From top to bottom of the diagrams P1, P2, and P3, the parts of thecatalytic reactor are as follows: the gas phase, the adsorbate atomic cores, thesurface 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 leftto right which designates surface local sources of charge (i), entropy (s), andmass (je, jCO, and jO2). Meanwhile, spatial flows je, jCO, jO2, jCO2, i, and s—whichare related through balance conditions (41)—draw the transversal dashedlines. The vertical dotted lines designate a relation that unites the subsystemsof adsorbate atomic cores and the surface electrons into the adsorptionsystem. The orientation of the arrows is set by the direction of thermodynamictime, i.e., by the direction of growth in entropy. The entropy change near theactive interface, �S[s, i, R, Re, J] � �Schem � �Srelax � �Strans, includes 3contributions. The first contribution, �Schem, is due to the chemical transfor-mations between the electrons and adsorbate atomic cores within the activeinterface at the respective rates, Re and R. The second contribution, �Srelax, isdue to energy relaxation flow from the adsorbate atomic cores to the elec-trons within the active interface at the rate J during the chemical reaction. Thethird contribution, �Strans � (smetal � sgas) � n, is the entropy brought to or takenaway from the active interface by the entropy flux, smetal, due to adsorption/desorption of the metal electrons and the energy exchange with the metal aswell as by the entropy flux, sgas, due to adsorption/desorption of the gasmolecules and the energy exchange with the gas. From a subsurface point ofview, the cycle (seen in P1P2P3) corresponds to an electron pump, which drawselectrons from the Ohmic lead to the surface, and then reinjects them into thebulk where a fraction will surpass the Schottky barrier in the form of achemicurrent. This latter process is represented by the inner cycle of thediagram and is directly associated with the progress of the surface chemicalreaction, which is represented by the outer cycle.

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function, ��. Furthermore, the charge current incident to the activeinterface is estimated by the rate of the polarization change,therefore i � �(1/4�e)(d��/dt). Since the charge is conserved, i �i�n � �iSh � iOh; here iOh and iSh are the current densities incidentto the Ohmic and the Schottky contacts, respectively.

The work function changes are 0.3 � �� � 1.0 eV in P1, and�0.25 � �� � 1.0 eV in P2 (4), and �SP1,2

� 0. Therefore, iP1�

0, and the metal electrons accumulate at the active interface; itcan be that iP2

� 0 or iP2� 0, and the electrons are repelled from

or attracted to the active interface. A complementary oxidationor reduction reaction should reverse these changes in the surfaceelectron distribution. Reactive CO2 desorption, P3, which is aninverse of dissociative CO2 adsorption; O2 associative desorp-tion, which is an inverse of P1; and CO desorption, which is aninverse of P2, are possible complementary reactions. At therelevant 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 breakupthreshold, �: the minimum work that is required to free a gasmolecule or the maximum work that is produced upon localizingit to the active interface. � is the barrier for associative oxygendesorption, 1.1 � �O2

� 1.4 eV, in P1; the barrier for COdesorption, 1 � �CO � 1.5 eV in P2; and the barrier for reactiveCO2 desorption, 0.5 � �CO2

� 1.2 eV in P3; � is the adsorptionor desorption heat for species studied in ref. 9. The adsorptionatomic core phase is different from the gas phase for an energy,u, below �. In contrast, no distinction exists between adsorbedand gas phase CO2, CO, or O2 for u � �. The lack of thisdistinction means that subsystems of the adsorption system,eCO2

���CO2

, eCO ���CO, eO2

���O2

, whose energies are near theirrespective breakup thresholds are critical. For u away from a �,the correlation between events in the direction transversal to theactive interface should decay exponentially according to ahierarchy of relaxation times and lengths. Near �, this hierarchycollapses; the correlations’ decay becomes insensitive to the timeand length scale, i.e., it becomes a power law.

The mass, charge, and heat transport is fundamentally differ-ent for subsystems whose energy, u, is below or above a �.Above a �, desorption of fast, ro-vibrationally excited CO2(g)

� ,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 andcharge transport channel opens up, an electron leaving the activeinterface, after suffering losses, may be fast enough to overcome�Sh. That is, it may inject into the electron-deficient conductionband of the semiconductor, so that iSh � 0, whereas the flux ofthermal electrons, iOh � 0, from the electron-rich Ohmic lead,compensates the changes in the surface electron distribution. Ina sustained chemical process, the rates Re, R, and J need to bematched by the transport f luxes i, j, and s. The individualdiagrams can now be linked into a cycle P1P2P3 of an electronpump, shown in Fig. 1.

This phenomenological examination thus arrives at its goal: ahypothesis, whose validity is to be addressed, about the origin ofthe chemicurrent. The chemicurrent in CO oxidation includesthose 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 �� when the adsorbate and the conduction electrons engageupon adsorption and Yc (u � �)y� for u � � when theadsorbate leaves and the metal electrons disengage upon de-sorption; the threshold, �, is either �O2

, or �CO , or �CO2

, oranother breakup threshold; the critical exponents y and y�coincide for a given adsorption/desorption process.

Microscopic Paths That Contribute to ChemicurrentIn a computational experiment following up on the previoussection’s findings, O2(g) and CO(g) above Pt(111) become chemi-

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 tothe free molecules held at the points infinitely distant from theclean active interface and from each other. A pair of minima—both observed in the ultrahigh vacuum experiments and consis-tent with total energy models (ref. 27; ref. 28 and referencestherein)—correspond to CO(g) � O(a), the adsorption p(2 � 2) �O(fcc) pattern in register with Pt(111) and CO infinitely distantfrom the active interface, and CO(a) � O(a), the coadsorptionp(2 � 2) � Ofcc � COatop pattern in register with Pt(111).Another minimum that is found, the CO2(a) chemisorbed inp(2 � 2) � CO2 pattern, has not been experimentally observedon Pt(111). However, even if CO2(a) were a methodologicalartifact, it should still be considered. Its geometry is similar tothose 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 CO2

�. Furthermore, ref.29 reports a vibrationally silent CO2 desorption precursor—andCO2

� itself is vibrationally unconventional (30–32)—on Pt(111)surfaces precovered with oxygen and CO during reactive scat-tering of Cs� against the surface. Lowering the Pt(111) workfunction—e.g., by adsorbing an alkali metal—would stabilize theanionic chemisorbed CO2(a) if it were a reactive transient onPt(111). The energy also features a critical point (transitionstructure), CO2

, that deforms into CO2(a), O(a) � CO(a), andCO2(g) along apparently continuous minimum-energy pathsshown in Fig. 3A. The structure of the transition state can beinferred from energy- and angle-resolved reactive desorptionspectroscopy experiments (33, 34) that support a bent CO2

onPt(111) and other catalytic late transition d-metal surfaces.

Unlike neutrals and cations, all free anions have a finitenumber of discrete states below the ionization continuum (35).Free CO2

� has up to 3 discrete energy levels 12A�, 2A�, and 22A�

Fig. 2. The changes in the distribution of the adsorbed C and O atoms andin the distribution of the surface electrons between the energy stationarypoints 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 electrondensity relative to that of the decoupled adsorption layer and Pt(111). Thechanges in the energy and work function (both in eV) are shown above theupper and the lower arrows, respectively.

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(32, 36). As the distance OC���O� decreases and the angle �OCOstraightens along a reaction path, the bottom of the ionizationcontinuum of OC���O�, set by the ground-state adiabatic poten-tial of OC���O, descends upon the discrete anion levels to devourthem. No discrete anion electronic levels exist at configurationsclose to that of the product, the linear CO2 (see Fig. 3A). Thesurface states derived from the antibonding lowest unoccupiedmolecular orbital (LUMO), 1a�, of the transient CO2 in bentgeometry are substantially filled before CO2

but become vacantafter CO2

. As CO2 straightens, the LUMO rises well above theFermi level and ends up as the �g LUMO of CO2(g) (Fig. 4A). AfterCO2

along the reaction path, the rapidly increasing transportcontribution to the entropy (Fig. 4B), caused by irreversible emis-sion of fast electrons from the active interface into the emptyconduction band, indicates that the chemistry-induced irreversibleionization of the surface species is a very likely event.

During the reductive steps, the delocalized conduction elec-trons fill (i � 0) the states localized at the active interface derivedfrom those vacant in the adsorbing CO(g) and O2(g). Theselocalized electrons are returned (i � 0) into the conduction bandduring the oxidative steps when no states capable of bindingelectrons at the active interface exists. In renormalization grouptheory language, the sign of i is a fixed-point property. Hence,the existence of cycles that are concatenated from a pair ofsegments with i � 0 and i � 0, like those described above, impliesthe existence of numerous comparable cycles. In turn, thisfinding implies their macroscopic significance, consistent withthe observed stability of the sign of the work function change onadsorption of CO and O2 on diverse transition metal substrates(4). Thus, there is an ensemble that is composed of those cyclesthat are localized before and delocalized after passing CO2

. Theensemble of all those eCO2

��� CO2

that are about to ionize-desorbis critical near the threshold, �CO2

, for the reactive desorption.The similarity in transition state geometries noted in Fig. 3A does

not then come as a surprise, because scale independence andself-similarity are signs of a critical transition.

Chemicurrent That Arises from the PathsThe stationary wave function, , of the closed adsorption systemis locally split into the variables describing the atomic cores, 3 �, and the electrons, 3 �, in the diagrams P1, P2, andP3 in Fig. 1. The vector � � (��) includes the translational andro-vibrational degrees of freedom of the adsorbate, and � �(�A) describes the necessarily finite number of localized discreteand the continuum states for an anionic form of the adsorbate,as well as the conduction bands in the metal. This splitting is notunique and has to be fixed by specifying the gauge potentials nearthe active interface: U, as well as the ‘‘nonadiabatic couplings’’A and A�, that may locally rotate the vectors � and �. Theobservables should be independent of the splitting, as should theaction governing the evolution of the electrons and atomic cores:

I �dt dx �i��� � � i��� � � � [�� A�vF � � iDAB � kF��B

�2

2mDBA�� A � DAB�B

�2

2MD����� � � D�����

VABCD�� A�B�� C�D U����� A�A]� .

The kinetic energy is given in terms of the covariant derivatives

DAB �AB� � iAAB for �,

and

D��� ���� � iA�� � for �.

The first order in D terms describe the ubiquitous electron-holepairs near the Fermi surface in the direction of a wave vector kF

and at the Fermi velocity vF (5). The quadratic in D termsaccount for the asymmetry between the electrons and holes aswell as the electronic kinetic energy near the adsorbate. The

Fig. 3. Progression of CO � O 3 CO2 along the reaction path. (A) Thedistribution of the geometries of the reacting CO relative to chemisorbed O.The angular coordinate is the �OCO, the linear coordinate is the longest of theC—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 lastactivated step for various mechanisms, surfaces, and metals (ref. 27; ref. 28 andreferences therein); the pink region encloses the transition structures within2 standard deviations in angular and radial coordinates. The solid blue linesdelineate the domains of a constant number of discrete levels in free CO2

�; thedotted line is an extrapolation. The color gradient from blue to white to redcorresponds to the increasing vertical energy of the emitted electron relativeto the ground state of the neutral CO2 in the domain where no discrete levelsexist. A minimum energy path is the green line. (B) An expansion of thediagrams in Fig. 1 arranged by �OCO.

Fig. 4. Changes in the electronic structure along the reaction path. (A) Densityof electronic states localized in the valence region of O���CO along the reactionpath 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 gradientfrombluetowhite toredcorresponds to increasingdensityof states.Thered linesindicate the molecular orbital energies of O���CO decoupled from Pt(111). (B) Acontribution to �Strans due to fast electrons undergoing irreversible electronemission into the conduction band (see SI Appendix).

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electron–electron interaction—VABCD at the scale of electronlocalization of lloc � 10�1 nm at the active interface—should bepivotal in compensating for the adsorbate’s angular momentumduring adsorption of 3� O2, and also in other low-energyprocesses involving the adsorbate’s energy levels crossing theFermi level; through nonperturbative two-electron events sim-ilar to those encountered in Kondo physics (37). The potential

U U��1��� U��

�2����� U����3� ������ U����

�4� �������� . . .

can be seen as potential energy (relative to the Fermi level),which restricts the adsorbate near the active interface. Thekinetic energy caused by motion of the adsorbate is quadratic inD�. Near an adsorption minimum, U � 0, � is confined by thefriction-like nonadiabatic potential A�, which channels the en-ergy from the adsorbate to the electrons.

The ground state of free O2 and CO approaching the activeinterface corresponds to �dloc � 0 and U (�dloc) � 0. When thefree translational motion localizes during the adsorption, �loc 0 because of the zero-point motion, and U(�loc) � 0. During theCO2 reactive desorption, the frustrated translations of O � CO,�loc 0 , become free translations of CO2

�, �dloc � 0, after �

is overcome. The field � formally corresponds to the N-vectormodel, which is known to undergo a symmetry-breaking, i.e., acritical transition at u � � (38). For u � �, the action dependson the direction of � because the molecules are localized to theactive interface, i.e., the symmetry is broken. The preferentialdirection disappears above � because no molecules are local-ized anymore, i.e., the symmetry is reestablished.

The evolution of the field � around the classical value in thepotential U induces the evolution in �. The delocalized conduc-tion 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 localizedcomponents in � changes by 1 when the 1a� wave function ofCO2

enters the ionization continuum coupled to a vacantconduction band. For a fast electron to inject into the semicon-ductor, its range needs to exceed the typical separation, ldloc �10�100 lloc (12), between the active interface and the Schottkycontact, and its kinetic energy incident to the Schottky contactneeds to exceed �Sh. The lower-energy and shorter-range elec-trons should thermalize within the metal film. These long-rangedelocalized electrons of interest may arise whenever the chargestate of the adsorbate changes. The concentration of the delo-calized electrons should be low at energies of order �Sh; there-fore, Fermi statistics become irrelevant away from the activeinterface, i.e., � can be treated as a vector of commutingnumbers away from the active interface.

The chemicurrent yield, i.e., the long-range, high-energy partof i per desorbing CO2(g), is the time-dependent current–currentcorrelation function Yc �i iSh�. It is determined by the criticaldynamics of � near �. The latter for the near-critical N-vectormodel, under the constraint of charge conservation, and in therelaxation regime is known. It belongs to the Hohenberg–Halperin dynamic universality class B (39). This observationimplies a specific scaling behavior of the rate of change inelectron density at the active interface past the transition stateon the energy difference from �. The relaxation rate scalesinversely with the critically slow relaxation time, ��1 ��z, where� �u � ���� is the scaling of the decay length for the correlationfunction. The dynamic critical index is z � 4 � � in this case (39);� � 0.672 � 0.007 and � � 0.033 � 0.004 for the (N � 2)-vectormodel are known (38). Thus,

i ��1 ��z �u � ���z �u � ��2.66,

and

iSh �u � ��vzjco2 ,

in agreement with PL and L. More detailed analysis or simula-tions would be required to go beyond this schematic estimate.The relaxation experiments (9) for adsorption and desorption,which involve symmetry-breaking around the desorption energydue to frustration of translational motion and concomitantchange in the adsorbate charge state, agree with the prediction.

Further Discussion and ImplicationsNothing singles out catalytic CO oxidation among other surfacechemical processes except the following 3 building blocks: asurface reduction (i � 0), which is a chemical reaction thatoxidizes the substrate through localization of some conductionelectrons (Red); a surface oxidation (i � 0), which is a chemicalreaction that reduces the substrate through delocalization of thesurface electrons previously localized in Red (Ox); and a relax-ation process (i.e., i � 0 in the reversible limit), which is a purelydissipative component that is present in any surface chemicalprocess (Rel). These building blocks define an electron pumpwhose reduction leg (cathode) localizes the slow electrons andwhose oxidation leg (anode) releases fast electrons that maycontribute to the chemicurrent.

Several characteristics control operation of the electron pump.First is the pump’s capacity to displace the electrons at the activeinterface during the reductive or oxidative adsorption steps.Surface oxides, which are likely to form over defects or steps orsurfaces more open than Pt(111), feature higher (�1 e) thanchemisorbed oxygen (�0.1 e) surface electron concentrations(4). Second is the pump’s capacity to displace back the surfaceelectrons into fast metal electrons during oxidative or reductivedesorption steps. The energy available to the fast electrons isestimated by the excess of the reaction heat over an activationbarrier for reactive desorption. The yield of fast electrons scaleswith respect to the available excess energy as Yc (u � �)2.66,a scaling law characteristic of a different universality class thanthe 2.0 power law (Fowler law) observed for photoelectron yieldin light absorption. The locality of the electron–electron inter-action in metals implies that the near-threshold estimates shouldalso hold above the thresholds (38). Third is the pump’s capacityto excite low-energy electron-hole pairs and substrate phonons[vibrational quanta � 0.025 eV (4)], resulting in nonuniversalcontributions to the excitation spectrum. The surface chemicalprocess depends on the bulk mass, charge, and energy fluxes, andcan therefore be controlled by adjusting these fluxes. Bulk ioniccurrents are absent in gas-phase surface chemistry. It would bedifferent in an ionic liquid environment where not only electroncurrents, but also ionic currents, contribute to the chargetransport.

Kinetics of chemical reactions on high work function metalsurfaces has been traditionally studied within reversible modelson ground-state energy surfaces or within nearly reversiblemodels that account for omnipresent electron-hole pairs andphonons through a velocity-dependent damping. The mecha-nism that is presented in this report as a principal cause of thechemicurrent in CO oxidation (and likely in other oxidation-reduction reactions on metal surfaces) involves an irreversiblestep that triggers the product desorption above a threshold. Thisis an efficient channel for the removal from the catalyticinterface of the reaction products and the heat in the form of fastelectrons and the energetic gas molecules. This channel is neitherreducible to an electron-hole pair nor to phonon creation duringsurface chemical processes. Further implications of the existenceof this channel for modeling chemical reactions on high workfunction metal surfaces are yet to be fully appreciated.

A broader picture emerges. The Pt(111) catalyst is covered byislands of oxygen and carbon monoxide coadsorption phases (21,22). Reactive CO2 desorption barriers vary broadly (0.3�1.2 eV)

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with surface environment. Regions actively involved in reactivedesorption can be viewed as tiny electron pumps that inject fastelectrons at an active interface patch whenever u � �. Theelectrons then travel through the film, which is thick enough forthe short-range electronic excitations to die out but thin enoughto let the long-range electrons reach the exit side. One canimagine a matrix of conducting wells insulated from one anotherthat collects all electrons of incident kinetic energy within awindow around �Sh and allows the electrons to leave through awell. The current iSh is collected from each well, amplified, andimaged. As the energy filter window slides up, the image shouldchange. Lower-energy images should be nearly featureless be-cause lower-energy electron-hole pairs emerge in any localdynamic process and overlap with other low-energy excitations.The distribution of surface areas involved in reactive desorptionshould be seen in higher-energy images after low-energy exci-tations are filtered out. The local distribution of � could beextracted from the image energy contrast.

Work function measurements and reactive desorption spec-troscopy were fruitful in the early days of surface science (40).The spectroscopy of fast electrons, representing dynamic workfunction measurement or reactive ‘‘electron adsorption/desorption’’ spectroscopy—although still in its infant stage—promises to eventually develop. The existence of a systematiccorrelation between the known surface chemistry and the largelyunknown chemistry of subsurface metal electrons is a necessarycondition for a spectroscopic method and one of central impli-cations of this report.

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

1. Einstein A (1905) Generation and conversion of light with regard to a heuristic pointof view. Ann Phys 17:132–148.

2. Fowler RH (1931) The analysis of photoelectric sensitivity curves for clean metals atvarious temperatures. Phys Rev 38:45–56.

3. Nienhaus H (2002) Electronic excitations by chemical reactions on metal surfaces. SurfSci Rep 45:3–78.

4. Landolt-Bornstein (2005) Numerical Data and Functional Relationships in Science andTechnology: Group III Condensed Matter (Springer, Berlin).

5. Mahan GD (2000) Many-Particle Physics (Kluwer, New York).6. Nahler NH, White JD, LaRue J, Auerbach DJ, Wodtke AM (2008) Inverse velocity

dependence of vibraitonally promoted electron emission from a metal surface. Science321:1191–1194.

7. Politano A, Formoso V, Chiarello G (2008) Dispersion and damping of gold surfaceplasmon. Plasmonics 3:165–170.

8. Nienhaus H, et al. (1999) Electron-hole pair creation at Ag and Cu surfaces by adsorp-tion of atomic hydrogen and deuterium. Phys Rev Lett 82:446–449.

9. Gergen B, Nienhaus H, Weinberg WH, McFarland EW (2001) Chemically inducedelectronic excitations at metal surfaces. Science 294:2521–2523.

10. Ji XZ, Zuppero A, Gidwani JM, Somorjai GA (2005) The catalytic nanodiode: Gas phasecatalytic reaction generated electron flow using nanoscale platinum titanium oxideSchottky diodes. Nano Lett 5:753–756.

11. Ji XZ, Somorjai GA (2005) Continuous hot electron generation in Pt/TiO2, Pd/TiO2, andPt/GaN catalytic nanodiodes from oxidation of carbon monoxide. J Phys Chem B109:22530–22535.

12. Somorjai GA, Bratlie KM, Montano MO, Park JY (2006) Dynamics of surface catalyzedreactions; the roles of surface defects, surface diffusion, and hot electrons. J Phys ChemB 110:20014–20022.

13. Liebsch A (1997) Electronic Excitations at Metal Surfaces (Plenum, New York).14. Tully JC (2000) Chemical dynamics at metal surfaces. Annu Rev Phys Chem 51:153–178.15. Persson M, Hellsing B (1982) Electronic damping of adsorbate vibrations on metal-

surfaces. Phys Rev Lett 49:662–665.16. Trail JR, Graham MC, Bird DM, Persson M, Holloway S (2002) Energy loss of atoms at

metal surfaces due to electron-hole pair excitations: First-principles theory of ‘‘chemi-currents’’. Phys Rev Lett 88:166802.

17. Gadzuk JW (2002) On the detection of chemically-induced hot electrons in surfaceprocesses: From X-ray edges to Schottky barriers. J Phys Chem B 106:8265–8270.

18. Kasemo B, Tornquist E, Nørskov JK, Lundqvist BI (1979) Photon and electron emissionas indicators of intermediate states in surface reactions. Surf Sci 89:554–565.

19. Gadzuk JW (1983) Vibrational excitation in molecule-surface collision due to tempo-rary negative molecular ion formation. J Chem Phys 79:6341–6348.

20. Shenvi N, Roy S, Parandekar P, Tully J (2006) Vibrational relaxation of NO on Au(111)via electron-hole pair generation. J Chem Phys 125:154703.

21. Wintterlin J, Volkening S, Janssens TVW, Zambelli T, Ertl G (1997) Atomic and macro-scopic reaction rates of a surface-catalyzed reaction. Science 278:1931–1934.

22. Zambelli T, Barth JV, Wintterlin J, Ertl G (1997) Complex pathways in dissociativeadsorption of oxygen on platinum. Nature 390:495–497.

23. Ackermann MD, et al. (2005) Structure and reactivity of surface oxides on Pt(110)during catalytic CO oxidation. Phys Rev Lett 95:255505.

24. Blyholder G (1964) Molecular orbital view of chemisorbed carbon monoxide. J PhysChem 68:2772–2777.

25. McCrea KR, Parker JS, Somorjai GA (2002) The role of carbon deposition from COdissociation on platinum crystal surfaces during catalytic CO oxidation: Effects onturnover rate, ignition temperature, and vibrational spectra. J Phys Chem B106:10854–10863.

26. Langmuir I (1922) The mechanism of the catalytic action of platinum in the reactions2CO�O2�2CO2 and 2H2�O2�2H2O. Faraday Soc Trans 17:621–654.

27. Eichler A (2002) CO oxidation on transition metal surfaces: Reaction rates from firstprinciples. Surf Sci 498:314–320.

28. Li W, Hammer B (2005) Reactivity of a gas/metal/metal-oxide three-phase boundary:CO oxidation at the Pt(111)-c(4 x 2)-2CO/�-PtO2 phase boundary. Chem Phys Lett409:1–7.

29. Han SJ, Lee CW, Yoon H, Kang H (2002) Discovery of CO2 precursor in the reaction ofCO and O on Pt(111). J Chem Phys 116:2684–2687.

30. Field D, Jones NC, Lunt SL, Ziesel JP (2001) Experimental evidence for a virtual state ina cold collision: Electrons and carbon dioxide. Phys Rev A 64:022708.

31. Allan M (2002) Vibrational structures in electron-CO2 scattering below the 2�u shaperesonance. J Phys B 35:L387–L395.

32. Sommerfeld T, Meyer HD, Cederbaum LS (2004) Potential energy surface of the CO2�

anion. Phys Chem Chem Phys 6:42–45.33. Allers KH, Pfnur H, Feulner P, Menzel D (1994) Fast reaction products from the

oxidation of CO on Pt(111): Angular and velocity distributions of the CO2 productmolecules. J Chem Phys 100:3985–3998.

34. Nakao K, Ito S, Tomishige K, Kunimori K (2005) Structure of activated complex of CO2

formation in a CO�O2 reaction on Pd(110) and Pd(111). J Phys Chem B 109:17553–17559.35. Hunziker W, Sigal IM (2000) The quantum N-body problem. J Math Phys 41:3448–3510.36. Vanroose W, Zhang ZY, McCurdy CW, Rescigno TN (2004) Threshold vibrational exci-

tation of CO2 by slow electrons. Phys Rev Lett 92:053201.37. Nozieres P, Blandin A (1980) Kondo effect in real metals. J Physique 41:193–211.38. Zinn-Justin J (1993) Quantum Field Theory and Critical Phenomena (Oxford Sci,

Oxford).39. Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod

Phys 49:435–479.40. Somorjai GA (1994) Introduction to Surface Chemistry and Catalysis (Wiley, New York).41. de Groot SR (1951) Thermodynamics of Irreversible Processes (Interscience, New York).

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