A most basic and puzzling enigma in surface science is the description of the
dissociative adsorption of O2 at the (111) surface of Al. Already for the
sticking curve alone, the disagreement between experiment and results of
state-of-the-art first-principles calculations can hardly be more dramatic. In
this paper we show that this is caused by hitherto unaccounted spin selection
rules, which give rise to a highly non-adiabatic behavior in the O2/Al(111)
interaction. We also discuss problems caused by the insufficient accuracy of
present-day exchange-correlation functionals.Comment: 4 pages including 3 figures; related publications can be found at
  http://www.fhi-berlin.mpg.de/th/th.htm

A. Hellman

Bernard Delley

E. Wigner

G. Herzberg

Jörg Behler

Karsten Reuter

Matthias Scheffler

Sönke Lorenz

English

arXiv

Crossref

Dissociation of
                    
                      
                        O

Behler, J.

Delley, B.

Lorenz, S.

Reuter, K.

Scheffler, M.

MPG.PuRe

arXiv:cond-mat/0412534v1  [cond-mat.mtrl-sci]  20 Dec 2004(Phys. Rev. Lett., in press)Dissociation of O2 at Al(111): The Role of Spin Selection RulesJo¨rg Behler,1 Bernard Delley,2 So¨nke Lorenz,1 Karsten Reuter,1 and Matthias Scheffler11Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany2Paul-Scherrer-Institut, HGA/123, CH-5232 Villigen PSI, Switzerland(Received 28 October 2004)A most basic and puzzling enigma in surface science is the description of the dissociative adsorptionof O2 at the (111) surface of Al. Already for the sticking curve alone, the disagreement betweenexperiment and results of state-of-the-art first-principles calculations can hardly be more dramatic.In this paper we show that this is caused by hitherto unaccounted spin selection rules, which giverise to a highly non-adiabatic behavior in the O2/Al(111) interaction. We also discuss problemscaused by the insufficient accuracy of present-day exchange-correlation functionals.PACS numbers: 82.20.Kh, 82.20.Gk, 68.35.JaOxygen-metal interactions are responsible for every-day phenomena like corrosion, and form the atomic-scalebasis behind numerous technological applications like ox-idation catalysis. It is therefore most discomforting thatdespite several decades of research in surface science, theinitial step in the oxygen-metal interaction, namely thedissociation process of O2 molecules over metal surfaces,is not yet understood. This is in particular so for whatis often called the most simple metal surface, namelyAl(111): a close-packed surface of a nearly-free electronmetal. For the initial interaction of O2 with Al(111) ex-periments have consistently shown [1, 2] that the initialdissociative sticking probability for thermal O2 is verylow (about 2%). Density-functional theory (DFT) cal-culations, on the other hand, found that dissociation isnot hindered by energy barriers [3], which implies thatthe initial sticking coefficient should be very high (about100%). Another intriguing aspect of the O2/Al(111) sys-tem is that at very low coverages the distribution of ad-sorbed oxygen atoms is random, even when adsorptionis performed at temperatures at which thermal diffusioncan not play a significant role [2]. Thus, it is impossibleto trace back which two adatoms stem from the samemolecule. Initially this led to the suggestion that the ad-sorption energy is used to trigger the diffusion of “hotadatoms” [2]. More recently, a different explanation hasbeen suggested (“abstraction”), where only one O-atomis adsorbed and the other one is repelled back into thevacuum [4]. Again, theoretical work, so far, does not givea clue why this may be so. Thus, one may ask, what wecan trust in surface science when understanding of sucha most basic and simple system for molecule-surface in-teractions is so clearly lacking.Figure 1 summarizes the experimental data for the ini-tial sticking coefficient as function of the kinetic energyof incoming O2 molecules for a molecular beam at nor-mal incidence (full diamonds) [1], as well as the result,of what has hitherto been the standard theoretical treat-ment (labeled as “theory-adiabatic”). Also shown is theresult of the approach taken in the present paper (labeled0.0 0.2 0.4 0.6 0.8 1.0E (eV)020406080100S 0 (%)theory-adiabatictheory-tripletexperimentFIG. 1: Initial sticking curve of O2 at Al(111), based onthe adiabatic (empty triangles) and the spin-triplet (emptycircles) potential-energy surfaces using the RPBE functional.The experimental data (solid diamonds) are from ref. [1].as “theory-triplet”), which will be detailed below. Obvi-ously, there is hardly any similarity between the “theory-adiabatic” curve and the experimental result. Thoughwe called this the “standard theoretical treatment”, wenote that already the calculations behind the “theory-adiabatic” curve (and also behind the “theory-triplet”curve) are much more elaborate and advanced than typ-ical approaches to obtain the initial sticking coefficient:All theoretical results presented in this paper were ob-tained from extensive all-electron DFT calculations usingthe DMol3 code [5]. This provided the six-dimensionalpotential-energy surface (PES) for the O2/Al(111) sys-tem at more than 1500 geometries of the two oxygenatoms, keeping the substrate frozen. These PES datapoints were then interpolated by a neural-network [6, 7],enabling us to perform molecular dynamics (MD) calcu-lations for about 100,000 trajectories, including all possi-ble initial molecular orientations. Thus, this approach [8]grants a controlled and good statistics, in contrast to “on-the-fly ab initio MD”, which gives (for a frozen substrate)the same trajectories, but where due to the high CPUcost at best only ∼ 50 trajectories could be performed2even on todays biggest computers.Still, “on-the-fly ab initio MD” has the advantage thatit can also be used beyond the frozen substrate approxi-mation. To check on the validity of our treatment, wetherefore performed 24 ab initio MD runs, where thefull dynamics of the Al surface atoms was taken into ac-count. These studies show that the adsorption energyis efficiently transferred to strong surface vibrations, andthat the oxygen adatoms do not move far. Thus, the“hot adatom” concept is not supported. In all studiedtrajectories the Al(111) surface got only affected, whenthe O2 was quite close to the surface, i.e. when O-Albonds were being formed and the O-O bond notablyweakened (at molecule-surface distances below ≈ 2.5 A˚).Before this point, the O2 trajectories were not changedby the substrate vibrations, and in particular all incom-ing O2 molecules are found to dissociate, fully confirm-ing the adiabatic result shown in Fig. 1. We also per-formed a systematic comparison using different exchange-correlation (xc) functionals, including the PBE [9] andRPBE [10]. The resulting PESs look different in somedetails, however, the resulting sticking curve is alwaysessentially the same as the “theory-adiabatic” curve inFig. 1. Hence, neither the approximate xc treatment,nor the frozen substrate approximation can account forthe dramatic disagreement between the theoretical andexperimental results. We therefore conclude that the ori-gin must be more fundamental, namely in the assumedadiabatic description, restricting the impinging moleculeto the electronic ground state of the combined O2/Al sys-tem at each point of the O2 trajectory. Based on less rig-orous studies, this had been suggested previously [11, 12].Inspecting the six-dimensional adiabatic PES revealsimmediately an obvious flaw of the adiabatic descrip-tion, independent of the employed xc functional: Evenat largest distances the electron chemical potentials ofthe O2 molecule and the Al(111) surface align, whichis achieved by some electron transfer towards the O2molecule. Obviously, in reality charge transfer will occuronly when the two systems are getting close for a suffi-ciently long period of time. Recently, Hellman et al. [11]considered the influence of charge transfer by employ-ing an approach, where they replaced the Al(111) sur-face by jellium and treated the kinetic-energy operatorin the Thomas-Fermi-Weizsa¨cker approximation. Then,two one-dimensional diabatic PESs were constructed, onewhere the O2 molecule was kept neutral and one where afull electron was transferred [11]. This description couldindeed account for the qualitative shape of the experi-mental sticking curve, as could Binetti et al. [12], follow-ing a comparable approach, but considering four differentdiabatic model PESs. Both treatments point therefore atthe possible importance of non-adiabatic effects, but dueto the arbitrary and severe approximations, doubts re-main about their conclusiveness.Our works starts from recognizing that chemical inter-actions are ruled by various selection rules, and for thepresent situation spin-conservation [13] is expected to berelevant. In gas-phase chemistry it is well known that O2,when in its triplet ground state, is rather inert when theother reactant and the product are spin singlets. Inter-estingly, this role of the O2 spin has not attracted muchattention in the O2/Al(111) interaction, although it wase.g. studied for the adsorption of oxygen on Si(100) [14].The appropriate theoretical modeling should then con-strain the spin to the O2 Hilbert subspace, preventingcharge transfer, as well as spin quenching before the sys-tems interact. Such a spin-constrained DFT approachhas neither been formulated nor evaluated for molecule-surface scattering so far. We will show that it not onlygives a good description of the sticking coefficient (cf.Fig. 1, empty circles), but may also explain the enig-matic abstraction mechanism.Let us briefly describe the theoretical method enablingus to study the dynamics of an O2 molecule that re-mains in its spin-triplet configuration. Only very closeto the surface transitions to other configurations of theO2/Al(111) system may set in. In order to calculate thespin-triplet PES we follow the work of Dederichs et al.[15], for which one must first define the Hilbert subspaceof the O2 molecule. As the DMol3 code employs an atom-centered basis set, we use for this all basis functions thatare also needed to provide a good description of the freeO2 molecule. Then, for any position of the O2 molecule,we request that the total electron spin in this Hilbert sub-space is one. In practice this approach involves the self-consistent filling of the four partial densities of states ofthe spin-up and spin-down, O2 and Al(111) sub-systems.This is formulated in terms of an auxiliary field in orderto properly include the effect of the spin-constraint onthe total energy [7].Before discussing the results obtained with this ap-proach, we remind of two general problems of present-dayKohn-Sham-DFT: First, even with gradient corrected xcfunctionals the description of the binding energy of thefree O2 molecule is rather bad. Going from the O2 spin-triplet ground state to two free oxygen atoms, each ofthem also in the spin-triplet ground state, the errors ofour calculated binding energies with respect to the ex-perimental value (5.1 eV [16]) are: 2.3 eV (LDA), 1.0eV (PBE), 0.6 eV (BLYP), and 0.5 eV (RPBE). Fortu-nately, for the part of the PES, that is important forthe sticking coefficient, we find that different function-als give results that differ by much less, indicating somefavorable error cancellation. Below we will therefore re-strict our discussion to the PBE and the RPBE, sincethey represent the extreme cases for the gradient cor-rected functionals, yielding the strongest and smallestoverbinding in the O2 molecule, respectively. A secondnoteworthy problem arises because the expectation valueof S2 is not defined in Kohn-Sham-DFT. For the presentcase this implies that the multiplet structure is not well35.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZX(a)r (A)Z (A)5.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZXr (A)Z (A)(f)5.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZXZ (A)r (A)(d)0.085.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZXZ (A)r (A)(b)0.275.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZXZ (A)r (A)(c)5.04.03.02.01.01.0 1.4 1.8 2.2top view side viewYXZXZ (A)r (A)(e)0.85FIG. 2: Two-dimensional (elbow) cuts through the six-dimensional PESs calculated for three different situations, always usingDFT-RPBE (see text): adiabatic (a, d), triplet (b, e) and singlet PES (c, f). The energies are shown as a function of the O2bond length r and of the distance Z of the O2 center of mass from the surface. The angles and lateral positions are indicatedin the insets. The energy zero (green/yellow border) corresponds to a free triplet O2 molecule. Contour lines are drawn at0.2 eV intervals. Dissociation barriers (if present) are labeled (eV).described [17, 18]. In free O2 the many-body groundstate belongs to the triple degenerate 3Σ−g state whichis followed by two singlets, namely a doubly degenerate1∆g level (0.98 eV above the ground state), and a nondegenerate 1Σ+g level (1.63 eV above the ground state).While the total energy of the spin-triplet ground stateis described well, the 1∆g and1Σ+g states are not de-scribed appropriately, since here DFT with jellium-basedxc functionals describes a certain mixture of multiplets.A reasonable approximation to the true spin-singlet stateis instead obtained by a spin-unpolarized calculation [7],which is for PBE 1.1 eV (for RPBE 1.2 eV) higher thanthe spin-triplet ground state.Figure 2 shows two cuts through the calculated six-dimensional PESs for three situations: the adiabatic ap-proximation (discussed in the introduction), the spin-triplet PES (using constrained DFT) and the spin-unpolarized calculation, which is the best we can do todescribe the spin-singlet PES. Whereas the two elbowplots of the adiabatic PES (cf. Fig. 2 left panels) donot exhibit sizeable energy barriers toward dissociativeadsorption, we find clear barriers on the triplet PES (cf.Fig. 2 middle panels). In fact, inspecting the whole six-dimensional triplet PES there is always an energy barrier(the lowest one is 0.05 eV). The right panels of Fig. 2show the corresponding cuts through the singlet PES,which never exhibits any energy barriers. Clearly, an O2molecule prepared in the singlet state would thereforereact most efficiently with the Al(111) surface. Sincethe spin forbidden transition to the triplet ground statecan only proceed by scattering with another molecule,the long lifetime of a singlet O2 should render molecularbeam experiments possible to verify this proposition.The sticking coefficient for these PESs is calculated asdescribed above, i.e., using the “divide and conquer” ap-proach [6, 7, 8]. The results for the adiabatic and thetriplet PESs, using the RPBE functional, are given inFig. 1. Obviously, the spin-triplet PES gives a stick-ing curve in good agreement with the experimental re-sult. However, when the O2 and Al(111) wave func-tions overlap at close distances, spin transfer will occurwith a certain probability. Due to the uncertainty inthe description of the singlet-PES, it is at present notvery meaningful to perform a quantitative evaluation ofthese transition probabilities. A rough estimate of theimportance of transitions bringing the system away fromthe triplet-PES is instead provided by the width of the2pi∗ Kohn-Sham resonance, which is the level that car-ries the spin. At large distance the width is zero, andit gradually increases upon approach to the surface. For42.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6Z  (Å)-0.20.00.20.40.60.8energy (eV)theory-adiabatictheory-singlettheory-triplet2pi*  DOSCTPFIG. 3: Potential energy along the reaction path shown asdashed line in Figs. 2a, b, c (solid line = triplet PES, dottedline = singlet PES, dashed line = adiabatic PES). The red ar-row indicates the classical trajectory of a thermal O2 moleculeconstrained to the triplet PES, with CTP marking the classi-cal turning point. At this point the coupling, represented bythe width of the O 2p Kohn-Sham level (dash-dotted line), isonly just emerging.a one-dimensional cut through configuration space thisis shown in Fig. 3. The peak width remains quite nar-row and even at the point where the triplet and singletPESs cross it is only about 0.1 eV. In general, the life-time of the 2pi∗ electrons should be compared to the timethe molecule spends between the classical turning point(CTP) and ca. 5 A˚ away from the surface. For ther-mal molecules (cf. the arrow and the CTP point in Fig.3) the comparison is: lifetime ≈ 3 ps vs. time of pres-ence ≈ 1 ps. We therefore conclude that for thermal O2molecules (and even for all molecules with a kinetic en-ergy below ∼ 0.2 eV) transitions away from the tripletPES will not play a big role. Our results then suggestthat particularly these lowest energy molecules should berepelled by the barriers on the triplet PES, well beforethere is significant hybridization of wave functions, i.e.before relaxation towards the adiabatic ground state oc-curs. Only for higher kinetic energies, transitions willgradually become important, leading to higher stickingcoefficients than in the “theory-triplet” curve shown inFig. 1. We also note that the PESs of the PBE andRPBE functionals are similar, but quantitatively differ-ences exist. These differences have noticeable influenceon the calculated sticking curve only for kinetic transla-tional energies below 0.2 eV. As the RPBE gives a betterdescription for free O2 we place a higher credibility onits PES. Details will be discussed elsewhere [7].Analyzing the approaching O2 molecule in greaterdetail reveals finally another interesting feature. Formolecules that approach in an orientation perpendicu-lar to the surface (or close to this) the spin is shiftedto the atom that is further away from the surface. Webelieve this to be the onset of adsorption by the abstrac-tion mechanism. In this way one O atom can adsorb ina singlet state, while the spin is efficiently carried awaywith the other O atom that is either repelled back intothe vacuum or to a distant place at the surface. Calcu-lating the full dynamics of this process, i.e. going beyondthe onset of dissociation important for the sticking coef-ficient, requires the explicit consideration of forces on theAl atoms, which we are implementing at present.In summary, we have shown that spin selection rulescan play an important role for O2 scattering at metals.They imply that O2 molecules should travel in a spin-triplet configuration up to distances close to the surfacewhere hybridization with metal-surface states becomessignificant. This is particularly important for systemswith a low DOS at the Fermi level; for transition metalswe expect that the high density of d-states at the Fermilevel can more easily take up the spin. At Al(111) spinselection leads to a very low sticking probability for ther-mal O2 molecules in the triplet ground state, while O2molecules prepared in the singlet configuration shouldadsorb with high probability. Similar effects as thosediscussed in this paper should just as well play a role forother substrates with a low jellium-like density of statesat the Fermi level, and for other molecules with a high-spin ground state.[1] L. O¨sterlund, I. Zoric´, and B. Kasemo, Phys. Rev. B 55,15452 (1997).[2] H. Brune et al., Phys. Rev. Lett. 68, 624 (1992).[3] K. Honkala and K. Laasonen, Phys. Rev. Lett. 84,705 (2000); Y. Yourdshahyan, B. Razaznejad, and B.I.Lundqvist, Phys. Rev. B 65, 75416 (2002).[4] A.J. Komrowski et al., Phys. Rev. Lett. 87, 246103(2001).[5] DMol3 - academic version, B. Delley, J. Chem. Phys. 92,508 (1990). Employed basis set: 9 bohr real space cutofffor the basis functions, “all” basis set for O and “dnd”basis set for Al, (4× 4× 1) Monkhorst-Pack k-mesh.[6] S. Lorenz, A. Groß, and M. Scheffler, Chem. Phys. Lett.395, 210 (2004); S. Lorenz, PhD Thesis, TU Berlin(2001).[7] J. Behler et al., (to be published).[8] A. Groß and M. Scheffler, Phys. Rev. B 57, 2493 (1998).[9] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. 77, 3865 (1996).[10] B. Hammer, L.B. Hansen, and J. Nørskov, Phys. Rev. B59, 7413 (1999).[11] A. Hellman et al., Surf. Sci. 532-535, 126 (2003).[12] M. Binetti et al., Chem. Phys. Lett. 373, 366 (2003).[13] E. Wigner, Nachr. Ges. Wiss. Goett., Math.-Phys. Kl.,375 (1927)[14] K. Kato, T. Uda, and K. Terakura, Phys. Rev. Lett. 80,2000 (1998).[15] P.H. Dederichs et al., Phys. Rev. Lett. 53, 2512 (1984).[16] G. Herzberg, Can. J. Phys. 30, 185 (1952).[17] O. Gunnarsson and R. O. Jones, J. Chem. Phys. 72, 5357(1980).5[18] U. von Barth, Phys. Rev. A 20, 1693 (1979).

Dissociation of O2 at Al(111): The Role of Spin Selection Rules

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