Au20: A Tetrahedral ClusterJun Li, et al.Science 299, 864 (2003);DOI: 10.1126/science.1079879The following resources related to this article are available online atwww.sciencemag.org (this information is current as of March 25, 2007 ):Updated information and services, including high-resolution figures, can be found in the onlineversion of this article at:http://www.sciencemag.org/cgi/content/full/299/5608/864Supporting Online Material can be found at:http://www.sciencemag.org/cgi/content/full/299/5608/864/DC1This article cites 11 articles, 4 of which can be accessed for free:http://www.sciencemag.org/cgi/content/full/299/5608/864#otherarticlesThis article has been cited by 150 article(s) on the ISI Web of Science.This article has been cited by 3 articles hosted by HighWire Press; see:http://www.sciencemag.org/cgi/content/full/299/5608/864#otherarticlesThis article appears in the following subject collections:Chemistryhttp://www.sciencemag.org/cgi/collection/chemistryInformation about obtaining reprints of this article or about obtaining permission to reproducethis article in whole or in part can be found at:http://www.sciencemag.org/about/permissions.dtlDownloaded from www.sciencemag.org on March 25, 2007Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyrightc 2003 by the American Association for the Advancement of Science; all rights reserved. The title SCIENCE is aregistered trademark of AAAS.
R EPORTSand subsequent adiabatic expansion from 2 to3, (iii) establishment of thermal contact withthe entropy sink to effect isothermal compressionfrom 3 to 4 at temperature T c, and(iv) breaking of thermal contact and continuanceof adiabatic compression from 4 to 1.We define the efficiency of the photo-Carnot engine as (Q in Q out)/Q in(T hS 12 T cS 43)/T hS 12. In the high-temperature(kT ) and small expansion( 1 2) limits, S 12 S 43k/.Engine efficiency, when fueled by regularthermal atoms, is then given by 1 (T cS 34/T hS 12) 1 T c/T h. However,when the radiation working fluid is heatedby phase-coherent atoms, T h3 T and theCarnot efficiency is given by T cT h3n¯ bc cos (7)where ε 3 bc 1. Hence, when,for example, .We see from Eq. 7 that when T h T cand 3n bc, the photon engine produceswork from a single heat bath. The net workproduced, when T h T c,isW net T c S 12 n kTkT c n (8)where the “Rabi flopping” angle is the(small) tipping angle defined below.The atomic coherence can be generated,for example, by passage of the atoms througha microwave field (12), which may be approximatedby a coherent state that has amean photon number N 2 . If theresonant atom-field coupling frequency is g ,and the interaction time is , then bc exp(i )/3kT, where g andwe have taken the high-temperature limit cc bb/3kT. We may then write3n bcn /kT. Hence if we take reasonablevalues; 0.1, / 0.1, and n 10 3 , we find bc3 10 6 . Hence, for bc of order 10 5 , efficiencies are of afew percent (10, 11) even though T h T c.Heating effects governed by are unimportantin determining the temperature of thefield. The atomic density matrix after microwavepreparation is given by Eq. 6, where 2/kT is higher order in . Furthermore,the effects of cancel out as can beseen in Eq. 5 and if bbis replaced with P b and ccis replaced with P c. Hence, thephysics is contained in bc.We can estimate the microwave energy,W , necessary to produce coherence betweenb and c, given the preceding microscopicmodel of our QHE (10, 11). The importantpoint is that we find W 5W net, i.e., W W netin the present QHE.The quantum thermodynamics of systemsslightly out of equilibrium is an area of currentinterest (22). In the particular form ofnonequilibrium considered here, quantum coherence,the phase is found to be a demonesquecontrol parameter that allows work tobe extracted from a single bath. The totalsystem entropy is constantly increasing, andthe physics behind the second law is notviolated. However, quantum coherence doesallow certain features of engine operationbeyond the classical limit.References and Notes1. For an in-depth treatment, see K. Annamalai and I.Puri, Advanced Thermodynamic Engineering (CRCPress, Boca Raton, FL, 2001).2. M. O. Scully, M. S. Zubairy, Quantum Optics (CambridgePress, London, 1997).3. Reviews of LWI are to be found in (23–25). Thepresent scheme is closest to the lasing without inversionmodel of (26).4. For example (27, 28).5. H. Linke et al., Science 286, 2314 (1999).6. Two classic papers on information erasure and relatedsubjects are (29, 30).7. M. Scully, Phys. Rev. Lett. 87, 220601 (2001).8. , Phys. Rev. Lett. 88, 050602 (2002).9. S. Lloyd, M. Scully, in preparation.10. M. Scully, in Quantum Limits to the Second Law, D.Sheehan, Ed. (AIP Press, New York, 2002), pp. 83–91.11. M. S. Zubairy, in Quantum Limits to the Second Law,D. Sheehan, Ed. (AIP Press, New York, 2002), pp.92–97.12. Y. Rostovstev, Z. Sariyianni, M. Scully, in preparation.13. N. Ramsey, Phys. Rev. 103, 20 (1956).14. H. Skovil, E. Schultz-Dubois, Phys. Rev. Lett. 2, 262(1959).15. See, for example (31–33)and references therein.16. C. Bender, D. Brody, and B. Keister, Proc. R. Soc.London A 458, 1519 (2002).17. T. Opatrny, M. Scully, Fortschr. Phys. 50, 657 (2002).18. M. H. Lee, Am. J. Phys. 69, 874 (2001).19. D. Meschede, H. Walther, G. Muller, Phys. Rev. Lett.54, 551 (1985). For discussion of cavity QED, see (34,35). For the quantum theory of a micromaser, see(36). For the first demonstration of the microlaser,see (37).20. M. Kim, F. Narducci, M. O. Scully, M. S. Zubairy, inSpectroscopy of Systems with Spatially ConfinedStructures, B. Di Bartolo, Ed. (Kluwer, Netherlands2002).21. A complication arises as the cavity resonant frequencycontinuously changes during the passage of atomsthrough the cavity: the atoms may go out of resonance.To preserve resonance, we needed to continuouslychange the level spacing of the atoms. Thiscan be accomplished in several ways, but for thepresent purposes we will simply take such atomicfine tuning as a given. Further discussion will be givenelsewhere.22. See, for example, the conference proceedings on thesubject referred to in (10, 11)and references therein.23. O. Kocharovskaya, Phys. Rep. 219, 175 (1992).24. E. Arimondo, Prog. Opt. 35, 257 (1996).25. S. Harris, Phys. Today 50, 36 (1997).26. M. Scully, S.-Y. Zhu, A. Gavrielides, Phys. Rev. Lett. 62,2813 (1989).27. H. S. Leff, A. F. Rex, Eds., Maxwell’s Demon (AdamHilger, Bristol, 1990).28. H. C. von Baeyer, Warmth Disperses and Time Passes(Random House, New York, 1999).29. C. Bennett, Sci. Am. 257, 108 (1987).30. S. Lloyd, Phys. Rev. A 39, 5378 (1989).31. , Phys. Rev. A 56, 3374 (1997).32. T. Freedmann et al., Phys. Rev. E 61, 4774 (2000).33. R. Kosloff, E. Geva, J. Gordon, J. Appl. Phys. 87, 8093(2000).34. S. Haroche, D. Kleppner, Phys. Today 42 (no. 1), 24(1989).35. P. R. Berman, Ed., Cavity Quantum Electrodynamics(Academic Press, Boston, 1994), p. 57.36. P. Filipowicz, J. Javanainen, P. Meystre, J. Opt. Soc.Am. B 3, 906 (1986).37. K. An, J. J. Childs, R. R. Desari, M. S. Feld, Phys. Rev.Lett. 73, 3375 (1994).38. M.O.S. wishes to thank N. Ramsey for many stimulatingand helpful discussions. This paper is an outgrowthof QHE discussions with D. Kleppner, F. Narducci,T. Opatrny, and N. Ramsey at the TAMU-ONR2001 workshop. Useful conversations on the subjectof radiation thermodynamics with G. Baym, P. Martin,P. Meystre, and W. Phillips are gratefully acknowledged,as are helpful discussions on the presentmanuscript with K. Annamalai, K. Chapin, R. Curl, D.Depatie, B.-G. Englert, E. Fry, R. Hulet, C. Joachain, K.Kapale, V. Kocharovsky, S. Lloyd, A. Muthukrishnan, T.Opatrny, M. Pilloff, Y. Rostovtsev, Z. Sariyianni, andG. Sussmann. We thank R. Haden, the Texas EngineeringExperiment Station, the Office of Naval Research,the DARPA-QuIST program, and the WelchFoundation for supporting this research.1 October 2002; accepted 16 December 2002Published online 2 January 2003;10.1126/science.1078955Include this information when citing this paper.Au 20 : A Tetrahedral ClusterJun Li, 1 Xi Li, 1,2 Hua-Jin Zhai, 1,2 Lai-Sheng Wang 1,2*Photoelectron spectroscopy revealed that a 20-atom gold cluster has an extremelylarge energy gap, which is even greater than that of C 60, and an electronaffinity comparable with that of C 60. This observation suggests that the Au 20cluster should be highly stable and chemically inert. Using relativistic densityfunctional calculations, we found that Au 20possesses a tetrahedral structure,which is a fragment of the face-centered cubic lattice of bulk gold with a smallstructural relaxation. Au 20is thus a unique molecule with atomic packingsimilar to that of bulk gold but with very different properties.Small clusters often have different physical andchemical properties than their bulk counterparts.Materials assembled from finite-sizedclusters have been intensively sought ever sincethe discovery of C 60(1). One of the criteria fora cluster to be used as a potential building blockfor cluster-assembled materials is its chemicalstability relative to other reagents and to otherclusters of the same material. A closed electronconfiguration with a large energy gap betweenthe highest occupied molecular orbital(HOMO) and the lowest unoccupied molecularorbital (LUMO) is a prerequisite for the chemicalstability of a cluster. Besides its high sym-Downloaded from www.sciencemag.org on March 25, 20078647 FEBRUARY 2003 VOL 299 SCIENCE www.sciencemag.org
R EPORTSmetry, the large HOMO-LUMO gap of C 60isresponsible for its chemical inertness and itsability to assemble into molecular crystals (2).Gold is undoubtedly an important material,and small clusters of gold have also attractedgreat attention. Although gold colloidshave been used for centuries to stainglass (3), more recently it has been shownthat gold clusters have unusual catalytic propertiesfor selective oxidation of CO (4–7), areoxidation-resistant (8), enable selective bindingof DNA (9), and have potential applicationsin nanoelectronics (10–16). Small Aucluster cations possess planar structures up toAu 7(17), whereas Au cluster anions areplanar up to at least Au 12–(18, 19). We haveprobed the electronic and geometrical structuresof small Au clusters using anion photoelectronspectroscopy (PES) and computersimulation. The improved instrumental resolution(20) and the ability to produce coldclusters (21) enabled us to obtain considerablymore detailed electronic structure informationthan was previously possible (22). Wefound that 20-atom gold clusters exhibit aHOMO-LUMO gap even greater than that ofC 60. Relativistic density functional calculationspredict that Au 20possesses a tetrahedralgeometry, similar to that of a fragment of thebulk face-centered cubic (fcc) crystal of gold.Details of our PES apparatus have beendescribed elsewhere (20, 23). Small Au n–clusters were produced by means of laservaporization of a pure gold target with ahelium carrier gas and were mass-analyzedwith time-of-flight mass spectrometry. PureAu 20–clusters were selected and deceleratedbefore photodetachment by a pulsed laserbeam. Figure 1 shows the PES spectra ofAu 20–at three photon energies. The 193-nmspectrum of Au 20–(Fig. 1C) displays a weakpeak around 2.7 eV (labeled X), followed bya large energy gap and more discrete transitionsat higher binding energies (A, B, C. . .).This spectral pattern suggests that neutralAu 20is a closed-shell molecule with a largeHOMO-LUMO gap.The extra electron that enters the LUMOof Au 20is removed upon photodetachment ofthe anion, yielding the neutral ground state (Xin Fig. 1). The feature A corresponds to thelowest triplet excited state of the neutral.Thus, the A-X separation, measured to be 1.77eV (Fig. 1B), represents the excitation energyof the first triplet excited state of neutral Au 20but is also an approximate experimental measureof the HOMO-LUMO gap. This energy1W. R. Wiley Environmental Molecular Sciences Laboratory,Pacific Northwest National Laboratory, PostOffice Box 999, Richland, WA 99352, USA. 2 Departmentof Physics, Washington State University, 2710University Drive, Richland, WA 99352, USA.*To whom correspondence should be addressed. E-mail: email@example.com.Fig. 1. Photoelectron spectra of Au 20 – .(A)At355 nm (3.496 eV ). (B)At 266 nm (4.661 eV ).(C)At 193 nm (6.424 eV ). The 355- and 266-nm photons were from a Nd–yttrium-aluminum-garnetlaser, and the 193-nm photonswere from an ArF excimer laser. Photoelectronswere analyzed with a magnetic bottle–typephotoelectron spectrometer and calibrated usingthe known spectrum of Rh – . The electronkinetic energy resolution was about 2.5%; thatis, 25 meV for 1-eV electrons.gap in Au 20is very large, about 0.2 eVgreater than that in C 60(1.57 eV) (24) (Fig.2). However, electron signals were observedin the HOMO-LUMO gap region in the 266-nm spectrum (Fig. 1B), owing to autodetachment,as a result of a photoexcited Au 20–*upon absorption of a 266-nm photon. Similarautodetachment signals were also observedpreviously in C 60–(Fig. 2A) (24). The 355-nm spectrum of Au 20–revealed a very sharppeak at the ground state transition (autodetachmentsignals were also observed at thisdetachment energy), suggesting that there isvery little geometry change between theground states of Au 20–and neutral Au 20. Thisis different from C 60–, whose PES spectraexhibit vibrational features due to structuraldistortions of the anion ground state (25). The355-nm spectrum yielded a vertical detachmentenergy of 2.751 0.010 eV and anadiabatic detachment energy of 2.745 0.015 eV for Au 20–. The latter is the electronaffinity (EA) of Au 20: a measure of howtightly the cluster can bind an electron. TheEA of Au 20is higher than that of C 60(2.689eV) (24), so Au 20is even more electronegativethan C 60.According to the electron shell model(26), Au 20with 20 valence electrons shouldrepresent a major shell closing. What is surprisingis the magnitude of the HOMO-LUMO gap. With the exception of Au 2andAu 6, the HOMO-LUMO gap observed forAu 20is the largest among all known coinagemetalclusters (22). It is also larger than thatobserved in the recently discovered 18-electronicosahedral W@Au 12cluster (27, 28).The large HOMO-LUMO gap suggeststhat Au 20should be very inert and may possessa highly symmetric geometry. To elucidateits structure and bonding, we carried outan extensive structural search for neutral andnegatively charged Au 20, using relativisticdensity functional calculations (29–33). Westarted from the highest symmetry possible[the Platonic dodecahedron with icosahedral(I h) symmetry and octahedron with octahedral(O h) symmetry] to their various importantsubgroups, as well as the ring and bowlstructures known for C 20(34) (Table 1 andFig. 3). We also tested a capped decahedron(C 2v) structure (Fig. 3C) and an amorphous(C 1) structure (Fig. 3B), which were found as“global” minima in previous calculations (35,36). The I hand O hAu 20structures are openshellstructures and would be subject to Jahn-Fig. 2. Comparison of the photoelectron spectraof Au 20 – with those of C 60 – .(A)The 266-nmspectrum of C 60 – . “AD” stands for autodetachmentsignals. (B)The 266-nm spectrum ofAu 20 – .(C)The 193-nm spectrum of C 60 – .(D)The 193-nm spectrum of Au 20 – .C 60 – data arefrom (24).Downloaded from www.sciencemag.org on March 25, 2007www.sciencemag.org SCIENCE VOL 299 7 FEBRUARY 2003 865
R EPORTSTable 1. Optimized molecular structures, point group symmetries, electronic configurations, HOMO-LUMO energy gaps (E HL), relative scalar-relativistic energies (E SR), and EAs of Au 20. The relativescalar-relativistic energies of the optimized anions are also listed [E SR(anion)]. All energies are in eV. Thetotal energies of the various isomers of Au 20and Au 20–are relative to those of the neutral tetrahedralAu 20.Structure Group Configuration E HLE SRE SR(anion)EATetrahedral pyramid T d(t 2) 6 (e) 4 (t 2) 0 1.818 0 –2.612 2.612No symmetry C 1(a) 2 (a) 2 (a) 0 0.495 1.395 –1.767 3.162Capped decahedron C 2v(a 1) 2 (a 1) 2 (b 2) 0 0.204 1.779 –1.616 3.395Planar C 2h(a g) 2 (b u) 2 (b u) 0 0.689 2.063 –1.636 3.699Octahedron O h(a 1g) 2 (e g) 2 (t 1u) 0 0 2.509 –0.484 2.993String-bag cage D 2h(a 1g) 2 (b 2u) 2 (b 3g) 0 0.170 2.898 –0.729 3.627Dodecahedron I h(h g) 10 (g u) 2 (t 2u) 0 0 8.466 4.842 3.624Bowl C 5v(e 2) 4 (e 1) 4 (e 1) 0 0.087 10.504 6.176 4.328Ring D 5h(e 1) 4 (a 2) 2 (a 1) 0 0.737 11.520 7.249 4.271Chain C v() 2 () 4 () 4 () 0 0.003 17.625 12.101 5.524Fig. 3. Selected optimized Au 20 structures. (A)Tetrahedral structure (T d).(B)Amorphous structure(C 1).(C)Capped decahedron (C 2v).(D)Planar structure (C 2h).(E)Octahedral structure (O h).(F)Dodecahedral structure (I h).Teller instability; a string-bag–like cage, abowl, and a ring structure are closed-shell butare highly unstable, with small HOMO-–LUMO gaps (Table 1). Because smaller Au n(n 13 atoms) clusters prefer planar geometries(18, 19), we also calculated a planarAu 20structure (Fig. 3D), as well as a linearAu 20chain, which has recently been formedon a NiAl surface and studied with scanningtunneling microscopy (STM) (37). Althoughless stable than the tetrahedral structure, theplanar structure was found to be more stablethan any other isomers except the amorphouscluster (Fig. 3B) and the capped decahedron(Fig. 3C). The linear chain is highly unstable,with almost no HOMO-LUMO gap, which isconsistent with its metallic behavior observedby STM (37). The most stable structure wefound was the ideal tetrahedral (T d) structure,which is more stable than the previouslysuggested “global minima” C 1and C 2vstructures by 1.4 and 1.8 eV, respectively.The T dAu 20structure is closed-shell, witha HOMO-LUMO gap of 1.8 eV, in excellentagreement with the experiment. TheAu-Au distances (0.268, 0.271, 0.283,0.297, and 0.312 nm) in the calculated T dAu 20structure are close to those in bulkgold (0.288 nm), yielding a tetrahedral edgearound 1 nm. Frequency calculations for theT dAu 20structure confirmed that it is a minimumon the potential energy surface.To facilitate comparison with experimentalresults, we also optimized the geometriesof the anions for all the isomers (Table 1).Consistent with the experiment, very littlestructural change was observed upon electronaddition to T dAu 20: The Jahn-Teller distortionenergy (0.02 to 0.04 eV for distortionto the D 2dand C 3vsymmetries) is muchsmaller than the spin-orbit coupling energy(0.16 eV), so that the geometry distortion isquenched. The total energy difference betweenthe anion and the neutral defines thetheoretical EA. The calculated EA for T dAu 20is 2.61 eV. However, when spin-orbitcoupling is included, we obtain a theoreticalEA of 2.741 eV, which is in excellent agreementwith the experimental value of 2.745eV, whereas the calculated EAs for all otherFig. 4. The simulated photoelectron spectrumof Au 20 – . The simulated spectrum was constructedby fitting the distribution of the calculateddetachment transition energies withunit-area Gaussian functions of 0.05 eV at fullwidth at half maximum.structures deviate considerably from the experimentalmeasurement (Table 1).Because the X-A gap (Fig. 1) representsthe excitation energy of the lowest tripletexcited state, we also calculated this quantityfor T dAu 20. The calculated excitation energyfor the lowest triplet state ( 3 A 1) is 1.777 eV,in close agreement with the experimentallydetermined value of 1.77 eV. The excellentagreement between the calculated EA andexcitation energy and the experimental measurementscan probably be attributed to thefact that very little change in geometry existsbetween the anion ground state and the neutralground and excited states, and it confirmsunequivocally that Au 20possesses a tetrahedralstructure. Further confirmation of the T dstructure is provided by the theoretical detachmentspectrum (Fig. 4), which shows thatmajor PES features are all well reproduced inthe simulated spectrum for T dAu 20–(38).Tetrahedral Au 20is a small piece of bulkgold with a small relaxation. Each of the fourfaces represents a (111) surface of fcc gold. Ithas a very high surface area (all the atoms areon the cluster surface) and a large fraction ofcorner sites with low coordination. The threedifferent kinds of atoms in the T dstructure, 4 atthe apexes, 4 at the center of each face, and 12along the edges (Fig. 3A), have different coordinationenvironments and may provide idealsurface sites to bind different molecules forcatalysis (such as CO, O 2, and CO 2)(39). Thelarge HOMO-LUMO gap of Au 20suggests thatit is a highly inert and stable molecule and maypossess novel chemical and physical properties;its unique tetrahedral structure makes Au 20anideal model for gold surfaces.References and Notes1. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, R. E.Smalley, Nature 318, 162 (1985).2. W. Krätschmer, L. D. Lamb, K. Fostiropoulos, D. R.Huffman, Nature 347, 354 (1990).3. M. A. Hayat, Ed., Colloidal Gold: Principles, Methods,and Applications (Academic Press, New York, 1989).Downloaded from www.sciencemag.org on March 25, 20078667 FEBRUARY 2003 VOL 299 SCIENCE www.sciencemag.org