12 886 BRIEF REPORTS55A vibrationally resolved PES spectrum of Cr 2 has beenobtained previously for the X and A states. 9 The currentspectrum taken at 3.49 eV allows the observation of the Bstate, which is produced by removing a spin-up electronfrom the 4s orbital, similar to the A state formed by removinga spin-down 4s electron.The Cr 3 trimer is basically composed of a dimer plus aloosely bonded atom with an overall C 2v symmetry. Theelectronic configuration of Cr 3 obtained from the DFTcalculations can be approximately described as( 2 3d 4 3d 4 3d 2 4s )3d 5 4s 1 , with the third atom maintainingall its six unpaired electrons. The orbitals in the parenthesesare from the dimer. Of course, all the orbital degeneracy willbe lifted under the C 2v symmetry and, in particular, the 3dorbitals of the odd atom are split into five nondegenerateorbitals. The energy gaps between the adjacent electronicstates are small, reflecting the weak interactions between thedimer and the odd atom. This is clearly shown in the PESspectrum of Cr 3 in Fig. 1. The 4s orbital of the odd atomhas some mixing with the 4s orbital of the dimer, and becomesthe HOMO of Cr 3 . The extra electron in the anionresides in the 4s orbital of the odd atom. The first feature ofthe Cr 3 PES spectrum at 1.4 eV is mainly due to the removalof a 4s electron from the odd atom. The sharp peaknear 2.9 eV is actually due to the removal of a 4s electron,and is of the same orbital origin as the A state in the dimerspectrum. This state is shifted slightly to a higher BE valuein Cr 3 due to the interaction between the 4s orbital on thedimer and the 4s orbital on the third atom. All the features inbetween the first peak and the 2.9-eV peak are due to the3d electrons of the odd room. It is important to point out thatall the states arising from the odd atom in Cr 3 are in factfalling in between the HOMO-LUMO gap of the Cr 2 dimer.This is essential in understanding the larger odd clusters,where similar electronic characters arise, leading to the morecomplicated features in their PES spectra.The PES spectra of Cr 4 and Cr 8 suggest that the neutralsare closed shell, each with a HOMO-LUMO gap ofabout 0.48 and 0.41 eV, respectively. The spectrum ofCr 6 is unusual with an intense threshold peak and an abnormallyhigh EA Figs. 1 and 2. These can all be accountedfor by the DFT calculations, which show that both Cr 4(D 4h ) and Cr 8 (D 4h ) are indeed closed shell. However, Cr 6(D 3h ) is found to be open shell with two electrons in a doublydegenerate HOMO. The d electrons in Cr 6 are all pairedin the three dimers, and the six 4s orbitals combine to formfour MOs: two nondegenerate orbitals with lower energiesand two doublet degenerate orbitals with higher energies.The two nondegenerate MOs are filled with two electronseach. The remaining two electrons fill one of the degenerateMOs, resulting in the open-shell configuration for Cr 6 with atriplet ground state. The extra electron in the anion entersinto the partially filled HOMO, in contrast to Cr 4 andCr 8 , where the extra electron occupies the empty LUMO ofthe neutral clusters. 20 This results in a very high EA forCr 6 , compared to Cr 4 and Cr 8 , in excellent agreement withthe experimental observation.For the odd clusters from Cr 5 to Cr 9 , their electronic configurationcan be described as due to the coupling betweenthe electronic structure of the even cluster and that of the oddatom. As expected, the energy levels of the odd atom are allcongested near the HOMO and in between the HOMO-LUMO gap of the corresponding even cluster, similar to thesituation in Cr 3 . These lead to the complicated features in thePES spectra and higher EA’s for the odd clusters comparedto their even neighbors except Cr 6 , since the extra electronenters into the open-shell HOMO in the odd clusters. Theinteractions between the odd atom and the correspondingeven cluster increase from Cr 5 to Cr 9 , resulting in a systematicshift of some 3d levels of the odd atom to higher BE.This is evident in the well-resolved spectrum of Cr 9 , wherethe 3d level shifts lead to less density of states near theHOMO, compared to Cr 5 and Cr 7 .Cr 10 and Cr 11 deviate slightly from the expected dimergrowth structures, 15 each with only four dimers instead offive. In Cr 10 the four dimers form a cubic framework withtwo capping atoms, giving an overall D 4h symmetry. Cr 11(D 4h ) is similar to Cr 10 , except that the eleventh atom sits inthe center of the cube, forming a structure resembling a bccfragment. The interpretations of their PES spectra are lessstraightforward compared to the smaller ones. Nevertheless,they each seem to resemble the smaller ones, fitting nicely inthe even-odd pattern both in their EA’s Fig. 3 and theirPES spectral patterns Fig. 1.From Cr 12 to Cr 15 , the DFT results suggest that a significantstructural change takes place and the cluster structuresbegin to resemble the bulk bcc structure Fig. 2. Thus thedimer growth pattern disappears. Experimentally, we observethat the even-odd alternations in the PES spectra andthe EA’s also disappear abruptly at the same size, in excellentagreement with the theoretical predictions. The PESspectra of the larger clusters begin to exhibit similarities, allwith a sharp feature near the threshold. This feature slowlymerges with the higher BE features from Cr 12 to Cr 15 ,asseen in Fig. 2. The well-resolved features at the higher BE’sas observed in Cr 12 and Cr 13 become hard to resolve in thelarger clusters due to increasing electronic density of states.Discrete spectral features still can be resolved up to Cr 24 ,beyond which only one broad band is observed near thethreshold at the 3.49- and 4.66-eV photon energies. 18 Thespectra in this size range resemble the first bulk feature to asignificant degree where a sharp feature near the Fermi levelis followed by a broad surface feature. 21 At 6.42 eV, a secondband is further revealed at a much higher BE 5 eVand the overall spectral features begin to resemble the fullbulk valence photoemission spectrum. 21Finally, it is noteworthy that even-odd alternations havebeen observed for alkali- and coinage-metal clusters, wherethey are explained by the ellipsoidal jellium model due to theitinerary nature of the valence s electrons of these elements. 1However, we show that the even-odd alternation found in Crclusters is completely different in nature. Here it is due to thespecial dimer growth of the small Cr clusters and the evenoddalternations disappear as the cluster structure changesfrom dimer growth to bulklike bcc structures.In conclusion, even-odd alternations in photoelectronspectroscopy and electron affinity are observed for clustersof a TM element. These reflect the even-odd nature of theunderlying electronic structures of the Cr clusters and aresatisfactorily interpreted based on a dimer growth routefound in a previous density-functional theory study. The cur-
55 BRIEF REPORTS12 887rent work presents a rather complete picture of the structureand bonding of the small chromium clusters, and shows thatphotoelectron spectroscopy coupled with appropriate theoreticalcalculations opens the possibility to completely understandthe complicated structure and bonding of transitionmetal clusters.Support for this research by the National Science FoundationCHE-9404428 is gratefully acknowledged. H.S.C.gratefully acknowledges Dr. P. M. Mathias for his support.The work was performed at Pacific Northwest NationalLaboratory, operated for the U. S. Department of Energy byBattelle under Contract No. DE-AC06-76RLO 1830.1 W. A. de Heer, Rev. Mod. Phys. 65, 611 1993.2 Physics and Chemistry of Finite Systems: From Clusters to Crystals,edited by P. Jena, S. N. Khanna, and B. K. Rao KluwerAcademic, Boston, 1992, Vols. I and II.3 C. Massobrio, A. Pasquarello, and R. Car, Phys. Rev. Lett. 75,2104 1995; N. Bingggeli and J. R. Chelikowsky, ibid. 75, 4931995.4 D. R. Salahub, in Ab Initio Methods in Quantum Chemistry, editedby K. P. Lawley Wiley, New York, 1987, Vol. 2.5 D. P. Pappas et al., Phys. Rev. Lett. 76, 4332 1996; S. K. Nayaket al., Chem. Phys. Lett. 253, 390 1996; F. A. Reuse and S. N.Khanna, ibid. 234, 771995.6 K. Lee, J. Callaway, and S. Dhar, Phys. Rev. B 30, 1724 1984;K. Lee et al., ibid. 31, 1796 1985; M. Castro and D. R.Salahub, ibid. 49, 11 842 1994.7 M. D. Morse, Chem. Rev. 86, 1049 1986.8 K. M. Ervin, J. Ho, and W. C. Lineberger, J. Chem. Phys. 89,4514 1988; L. S. Wang, H. S. Cheng, and J. Fan, Chem. Phys.Lett. 236, 571995; H. Wu, S. R. Desai, and L. S. Wang, Phys.Rev. Lett. 76, 212 1996.9 S. M. Casey and D. G. Leopold, J. Phys. Chem. 97, 816 1993,and references therein.10 M. M. Goodgame and W. A. Goddard, Phys. Rev. Lett. 54, 6611985.11 K. Andersson, Chem. Phys. Lett. 237, 212 1995; B. O. Roosand K. Andersson, ibid. 245, 215 1995; K. E. Edgecombe andA. D. Becke, ibid. 244, 427 1995; C. W. Bauschlicher and H.Partridge, ibid. 231, 277 1994.12 D. R. Salahub and R. P. Messmer, Surf. Sci. 106, 415 1981; G.M. Pastor, J. Dorantes-Davila, and K. H. Bennemann, Phys.Rev. B 40, 7642 1989; K. Lee and J. Callaway, ibid. 48,15 358 1993; 49, 13 906 1994; B. V. Reddy and S. N.Khanna, ibid. 45, 10 103 1992.13 C.-X. Su and P. B. Armentrout, J. Chem. Phys. 99, 6506 1993.14 D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, Phys. Rev. B45, 6341 1992.15 H. S. Cheng and L. S. Wang, Phys. Rev. Lett. 77, 511996.16 L. S. Wang, H. S. Cheng, and J. Fan, J. Chem. Phys. 102, 94801995.17 P. Kruit and F. H. Read, J. Phys. E 16, 313 1983; O. Cheshnovskyet al., Rev. Sci. Instrum. 58, 2131 1987.18 We have obtained PES spectra for Cr n up to n70. The PESspectra above n25 exhibit no sharp features. At 3.49 and 4.66eV, one broadband similar to that of Cr 25 is observed for all thehigher clusters, while at 6.42-eV photon energy a second band athigher BE is also observed.19 The EA is systematically estimated by drawing a straight linealong the leading edge of each spectrum. The intercept with theBe axis plus a constant of 0.06–0.10 eV for compensation offinite resolution and thermal broadening is taken as the adiabaticEA. The uncertainty for the EA values is 0.06 eV orbetter depending on the sharpness of the leading edge.20 A Jahn-Teller effect is anticipated for the Cr 6 anion. The PESspectrum suggests that this effect is rather small and gives rise toa slight broadening of the PES feature in Cr 6 . A similar effectis expected to occur in Cr 8 because the LUMO of neutralCr 8 , where the extra electron enters, is doubly degenerate. Theslight broadening in the first feature of the Cr 8 spectrum isconsistent with a weak Jahn-Teller effect in Cr 8 .21 L. E. Klebanoff, R. H. Victora, L. M. Falicov, and D. A. Shirley,Phys. Rev. B 32, 1997 1985; L. E. Klebanoff, S. W. Robey, G.Liu, and D. A. Shirley, ibid. 30, 1048 1984.