PHYSICAL REVIEW BVOLUME 53, NUMBER 1215 MARCH 1996-IIElectronic structure of small copper oxide clusters: From Cu 2 OtoCu 2 O 4Lai-Sheng Wang,* Hongbin Wu, and Sunil R. DesaiDepartment of Physics, Washington State University, Richland, Washington 99352and Environmental Molecular Sciences Laboratory, Pacific Northwest Laboratory, MS K2-14, P.O. Box 999, Richland, Washington 99352Liang LouRice Quantum Institute and Departments of Chemistry and Physics, Rice University, Houston, Texas 77251Received 25 October 1995; revised manuscript received 21 November 1995We study the electronic structure of copper oxide clusters, Cu 2 O x x1–4, using anion photoelectronspectroscopy and density-functional calculations. The experiment is used to successfully guide a computationalsearch for the cluster geometries. The predicted electron affinities at the obtained cluster structures reproduceexactly the trend observed experimentally. The definitive determination of the cluster structures enables adetailed analysis of the chemical bonding and electronic structure involving Cu atoms in different oxidationstates exhibited by these clusters.The study of atomic clusters is attractive because theyoffer the opportunity to examine how atomic or molecularproperties evolve into that of the condensed phases, and representinteresting molecular species that often exhibit remarkablephysical and chemical properties. 1 Their finite sizesmake more accurate ab initio calculations possible, and provideideal models to study local effects taking place on surfacesand in the bulk. 2 Despite considerable experimentaladvances in the last decade, there is yet no direct experimentalmethod to determine the structures of free clusters. On theother hand, theoretical approaches that have been provenhighly accurate for determining molecular structures can beused to obtain definitive cluster structural information incombination with experimental studies. 3–5 In particular, ithas recently been shown that cluster structures can be obtainedby comparing first-principles simulations with photoelectronspectroscopy of size-selected anion clusters. 5 Metaloxide clusters, at which few efforts have been directed, 6 areinteresting due to the scientific and technological importanceof oxide materials. 7 We are interested in understanding theelectronic and geometric structures of copper oxide clustersand their chemical bonding properties. These clusters areparticularly important because they may provide bettermodel systems to understand the electronic structure of copperoxide materials relevant to the copper oxidesuperconductors. 7In this paper, we present a combined study of a series ofcopper oxide clusters, Cu 2 O x x1–4, using anion photoelectronspectroscopy PES and ab initio density-functionaltheory DFT calculations. Detailed electronic and vibrationalinformation of these clusters is revealed from the PESexperiment. We determine the cluster structures by comparingthe experimental observable, such as the electron affinitiesand the vibrational frequencies, with the DFT calculations.We found that from Cu 2 O to Cu 2 O 3 each O atombridge bonds to the Cu 2 dimer, accompanied by a systematicincrease of the electron affinity. Cu 2 O 4 at which there is noelectron affinity increase, assumes a hexagonal planner structurewith two O 2 units bridge bonded to the Cu 2 dimer. Thecopper atoms in these systems are sequentially oxidized froman oxidation state of 1 inCu 2 Oto3inCu 2 O 3 , at whichthe oxidation is saturated, leading to two O-O units inCu 2 O 4 . This observation is consistent with the known oxidationstates for copper in the bulk oxides that can have a rangeof compositions due to the variable oxidation states ofcopper, 7 and suggests that the cluster studies can providerelevant information to the understanding of the bulk.The Cu 2 O x species are produced using a laser vaporizationcluster beam apparatus, equipped with a magnetic bottletime-of-flight TOF photoelectron analyzer. 8 The details ofthe apparatus have been published. 9,10 Briefly, a copper targetis vaporized into a helium carrier gas containing a smallamount of O 2 0.1%. The oxide clusters produced undergo asupersonic expansion to form a collimated cluster beam,from which the negative clusters are extracted perpendicularlyinto a TOF mass analyzer. The clusters of interest areselected by a mass gate and then decelerated before interactionwith a detachment laser beam. Several detachment energies532, 355, and 266 nm are used to allow good energyresolution for the low-lying excited states since the resolutionof the TOF electron analyzer is better with lower-energyelectrons. All PES spectra are calibrated with the knownspectrum of Cu and smoothed with either a 3- or 5-meVfor the 266-nm spectra window function. We obtain thepresented binding-energy spectra by subtracting the measuredelectron kinetic-energy distributions from the respectivedetachment photon energies.Figure 1 shows the PES spectra of Cu 2 O x x1–4 withwell-resolved ground states labeled X and low-lyingexcited-state features labeled A, B, C, and so on in ascendingorder. The weak signals seen at the low binding-energyside in the spectra of Cu 2 O 2–4 are most likely due to thermalexcitations in the anions and isomers with weakly bound O 2as observed for CuO 2 . 10 The measured energies of all thestates are listed in Table I. The adiabatic electron affinityEA of the neutral clusters, derived from the ground-statefeature, clearly shows a stepwise increase with x up to x3and levels off at x4. Extensive vibrational structures areresolved for the X and A bands of Cu 2 O 2 . However, thespectra of all other clusters show relatively sharp electronic0163-1829/96/5312/80284/$10.00 53 8028 © 1996 The American Physical Society
53 ELECTRONIC STRUCTURE OF SMALL COPPER OXIDE ...8029TABLE I. Observed electronic states and vibrational frequenciesof Cu 2 O x x1–4 clusters and predicted electron affinities andground-state vibrational frequencies.BE aeV exp bcm 1 EA ceV theor dcm 1 Cu 2 O eX 1.10 200 1.10 1 681 fA 2.53 2 156B 2.66 3 586C 2.85D 2.95Cu 2 O 2X 2.46 630 30 2.12 182 302 466A 2.91 650 30 493 653 718 fB 3.12C 3.30Cu 2 O 3X 3.54 640 3.03 259 259 318A 4.02 321 321 351B 4.32 608 608 678 feCu 2 O 4X 3.50 2.94 119 222 244A 3.66 267 277 354B 3.80 533 612 612C 3.95 647 912 985 fFIG. 1. Photoelectron spectra of Cu 2 O x x1–4. The groundstates of the neutral clusters are labeled ‘‘X,’’ and their low-lyingelectronic states are labeled with the alphabet. The vibrational structuresfor the X and A bands of Cu 2 O 2 and the X band of Cu 2 O 3 arealso indicated.transitions with little vibrational excitation, indicating thereis little geometry change from the anions to the neutrals.Discernible vibrational structures can be seen for the X bandof Cu 2 O 3 and the E band of Cu 2 O. The peak width of the Xband of Cu 2 O indicates that there is vibrational excitation.But it could not be resolved even with a 25-meV 200-cm 1 resolution when the 532-nm detachment light was used. Theobtained vibrational frequencies are also listed in Table I.The PES spectra Fig. 1 contain a wealth of electronicstructure information for the clusters. The Cu 2 O spectrumshows a large gap between the X and A bands, representingthe energy gap between the lowest unoccupied molecularorbital LUMO and the highest occupied molecular orbitalHOMO of Cu 2 O. The presence of the large HOMO-LUMOgap suggests neutral Cu 2 O is an electronically closed shell.Similarities in both spectral features and intensity ratio areseen between the A and C bands, and between the B and Dbands. These suggest that the origins of these bands shouldbe due to two triplet-singlet pair states, arising from removingeither a spin-down or spin-up electron from the innerfilled orbitals just below the highest singly occupied orbitalof Cu 2 O . The details of the electronic structures and chemicalbonding of the cluster series are better understoodthrough the DFT calculations.The fully optimized equilibrium structures of the Cu 2 O xx1–4 clusters are shown in Fig. 2, including geometrica Measured electron binding energy uncertainty: 0.03 eV. Thebinding energy BE of the X ground state yields the measuredadiabatic electron affinity.b Measured symmetric stretching vibrational frequencies for thegiven states see text. Relative peak positions can be determinedmore accurately.c Calculated adiabatic electron affinities in eV.d Calculated vibrational frequencies for the ground-state clusterstructures shown in Fig. 2.e More highly excited states are not listed due to their broad andoverlapping nature.f Totally symmetric vibrational modes.parameters and atomic charges from Mulliken populationanalyses. The local-spin-density LSD correlation potentialof Vocko, Wilk, and Nusair is used in determining the clustergeometries. 11 The computational method utilizes threedimensionalnumerical integration and a multiple expansionfor the electrostatic potentials. The basis functions used arenumerical solutions of the involved atoms and their properionic states. For Cu, a double-zeta plus single-polarizationbasis is used, while for oxygen a similar type of basis augmentedwith a pair of s and p functions is used. 12 Test calculationson Cu 2 and CuO diatomics are summarized inTable II, showing very good agreement withexperiments. 13,14 The gradient correction, appliedperturbatively, 12,15 significantly reduces the atomization energyvalues overestimated by the LSD, but does not changethe calculated electron affinity as much because it affectsboth the anion and the neutral similarly. The overestimate ofthe vibrational frequency for CuO is largely due to the anharmonicityin the CuO potential well.The ground states of Cu 2 O and Cu 2 O 2 are found to be aC 2v triangle and a D 2h rhombus, respectively. For Cu 2 O 3 ,
8030 WANG, WU, DESAI, AND LOU53FIG. 2. The optimized structures and Mulliken charge distributionsfrom density-functional theory calculations for Cu 2 O x x1–4.TABLE II. Density-functional calculations for Cu 2 and CuO andtheir anions compared to experimental measurements in parentheses.The experimental spectroscopic values are from Refs. 13 and14 for the copper dimer and monoxide, respectively.Cu 2Cu 2CuOCuO ELSD a2.46 3.16 4.01 5.73eVEPB86 b 1.89 2.57 3.21 4.82eV 2.03 2.75EA 0.74 1.68eV 0.84 1.78bond length 2.19 2.31 1.69 1.67Å 2.22 2.34 1.73 1.67 cm 1 285 216 735 773265 210 631 739a Atomization energy at the local-spin-density approximation level.b Atomization energy after gradient correction is applied. The experimentaldissociation energy of the neutral is in the parentheses.FIG. 3. Comparison of the calculated adiabatic electron affinitiesto that from the experiments. The experimental value for Cu 2 isfrom Ref. 13.two isomers with close energies are found: a D 3h bipyramidFig. 2 and a C 2v bent structure with an O-Cu-O-Cu-Oatomic arrangement. The C 2v structure is slightly favored byabout 0.5 eV, but it yields an EA about 1 eV higher than theexperimental value. As will be seen below, the D 3h structuregives an EA that is in better agreement with the experimentand is responsible for the observed PES spectrum. A D 2hhexagonal ring with two O-O bonds is found to be the moststable structure for Cu 2 O 4 .The calculated EA values Table I increase stepwise withx and level off at x4, following closely the trend of theexperimental values Fig. 3. Note that for Cu 2 O 3 , the D 3hisomer is chosen for comparison. The calculated EA for theC 2v bent isomer of Cu 2 O 3 4.4 eV is out of the scale of Fig.3. From the overall accuracy of the calculated EA, we suspectthat the C 2v isomer may have a real EA value largerthan the photon energy 4.66 eV used in the experiment, andcould not have been observed even if it was present in thecluster beam. This atomic arrangement is optimal for thelocalization of charges around the O centers, leading to theextremely high EA. The four clusters Fig. 2 are all found tohave closed-shell electronic structure in the neutral groundstates. The calculated HOMO-LUMO gap for Cu 2 Ois1.2eV, and in the range of 0.2–0.6 eV for Cu 2 O 2–4 , in goodagreement with the experiments. The smaller gaps for thelarger clusters imply that stronger correlation effects may bepresent, leading to the deteriorated agreement between thecalculated EA values and the experiments for the larger clusters.On the other hand, the large HOMO-LUMO gap inCu 2 O is responsible for the nearly perfect agreement betweenits calculated EA and the measured value. The same istrue for Cu 2 , for which excellent agreement is obtained betweenthe current calculation and the measured value. 13Vibrational structures resolved in the PES experimentsprovide important information about the cluster structures.The calculated vibrational frequencies Table I for theCu 2 O x clusters agree well with the observed ones for x1–3, where vibrational information is available. The unresolvedvibrational structure in the X band of Cu 2 O largely involvesthe Cu-Cu stretching vibration, since the LUMO of Cu 2 Oismainly of Cu 4s bonding character. The experimental estimateof the upper bound of this mode is 200 cm 1 , which isconsistent with the calculation. The 630-cm 1 vibrationalfrequency resolved for the ground state of Cu 2 O 2 is due tothe totally symmetric mode because only totally symmetricvibrational modes are expected to be active in PES experiments.The calculated frequency for this mode is 724 cm 1 ,in reasonable agreement with the experiment. The estimated640-cm 1 frequency for the ground state of Cu 2 O 3 also comparesfavorably to the totally symmetric mode of 678 cm 1from the calculation. As mentioned above, highly accuratevibrational frequencies are difficult to obtain due to the neglectof the anharmonicity in the calculations.Several interesting trends can be observed in the evolution
53 ELECTRONIC STRUCTURE OF SMALL COPPER OXIDE ...8031of the atomic structures and chemical bonding in these clusters.First, the Cu-O bond length steadily increases as moreoxygens x1–3 are added to the Cu 2 dimer, all occupyingbridge positions. The increase in Cu-O bond length is accompaniedby a decrease of atomic charges at the respective Osites. The atomic charge distribution suggests significantionic bonding between Cu-O. Second, the Cu-O-Cu bondangle decreases from near 90° in Cu 2 O to about 70° inCu 2 O 3 . The smaller bond angle allows the bridge-bondedoxygens to separate further away from each other, and inducesa shortening of the Cu-Cu distance. Third, the oxidationstate of the copper atoms in the clusters, as formallyindicated by the number of directly connected oxygens,raises from 1 inCu 2 Oto3inCu 2 O 3 , and then drops to2 inCu 2 O 4 . The lowering of the oxidation state for Cu 2 O 4is caused by the formation of two O-O bonds.Therefore, we are seeing an interesting trend of sequentialoxidation and oxidation saturation. The Cu atoms are oxidizedformally from 1 to3 from Cu 2 OtoCu 2 O 3 saturatingat Cu 2 O 4 , where the further increase in the oxygen contentdoes not lead to further oxidation, and the coordinationof copper is reduced to 2. This agrees with the known chemistryof copper, whose common oxidation states are 1 and2. The 3 oxidation state is rare, and is known to occur inthe copper oxide superconductors and other materials. 16 The4 oxidation state is extremely rare, and occurs only in certaincompounds of fluorine, 16 the most oxidizing chemicalelement. Therefore, it is not surprising that the 4 oxidationstate is not realized in Cu 2 O 4 , which is close to a peroxide.The sequential oxidation has a strong effect on the stabilityof the extra charge as manifested by the large stepwise EAincrease from Cu 2 O to Cu 2 O 3 , caused by the increasingcharge depletion on the Cu sites.The Cu-O bond in the Cu 2 O x clusters is complicated, involvingboth ionic and covalent characters. The best case forillustrating the polarized covalent bonding nature betweenCu-O is the Cu 2 O triatomic, that has a triangular structurewith a nearly perfect Cu-O-Cu bond angle for the O 2pbonding. It is seen clearly from Fig. 2 that there is a largecharge transfer from Cu to O. Further analysis, based on thesingle-particle density matrix and in terms of molecular orbitals,shows that the charge transfer is mainly from the Cu4s shell to the O 2p shell. The occupation of the O 2s shellchanges very little 0.1e. On the Cu atoms, the 4s electronis partially promoted to the 4p orbitals; the sp hybridsthus formed are spatially more oriented than the spherical 4sorbitals for optimal overlaps with the O 2p. The Cu 3dorbitals also interact with the O 2p, but the net contributionto the Cu-O bonding is negligible because of the almost exactcancellation between the bonding and antibonding components.The Cu-Cu interactions in the Cu 2 O x x1–4 clustersare essentially electrostatic. The covalent interaction isfound to be negligible due to the cancellation between thebonding and antibonding overlap contributions. Therefore,the bonding in the Cu 2 O x clusters is dominated by the strongpolarized covalent interactions between Cu-O and the intramolecularO O 2 Coulomb repulsion.Support for this research from the National Science Foundationis gratefully acknowledged. The computation was partiallyperformed on the Intel Touchstone Delta supercomputersystem. The experimental work was performed atPacific Northwest Laboratory, a multiprogram national laboratoryoperated for the U.S. Department of Energy by BattelleMemorial Institute under Contract No. DE-AC06-76RLO 1830.* Author to whom correspondence should be addressed.1 See, for example, Physics and Chemistry of Finite Systems: FromClusters to Crystals, edited by P. Jena, S. N. Khanna, and B. K.Rao Kluwer Academic, Boston, 1992, Vols. I and II.2 D. M. Rayner et al., Phys. Rev. Lett. 74, 2070 1995.3 P. Dugourd et al., Phys. Rev. Lett. 67, 2638 1991; E. C. Honeaet al., Nature 366, 421993.4 J. Fan, L. Lou, and L. S. Wang, J. Chem. Phys. 102, 2701 1995;J. B. Nicholas et al., ibid. 102, 8277 1995; J.Fanet al., J. Am.Chem. Soc. 117, 5417 1995.5 N. Bingggeli and J. R. Chelikowsky, Phys. Rev. Lett. 75, 4931995; C. Massobrio, A. Pasquarello, and R. Car, ibid. 75, 21041995.6 G. C. Nieman et al., High Temp. Sci. 22, 1151986; J. R. Gord,R. J. Bemish, and B. S. Freiser, Int. J. Mass Spectrom. 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