Competition between linear and cyclic structures in ... - ResearchGate

Competition between linear and cyclic structures in ... - ResearchGate

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters8997We have used photoelectron spectroscopy PES to studyTiC n (n2–5) Ref. 26 and interpreted the vibrationallyresolved PES spectra in terms of the cyclic configurations ofthe anions, which were confirmed by subsequent theoreticalcalculations. 12,13 A recent PES study of NbC n (n2–7)revealed experimental evidence for a cyclic-to-linear structuraltransition from NbC 3 to NbC 4 Ref. 27. Interestingly,the PES data suggest that the Nb atom may substitutea carbon atom in the carbon chain, giving rise to linear NbC nclusters with similar electronic properties as pure C n1 clusters.For late TM systems, ion mobility experiment was carriedout for FeC n (n48), 28 in which a linear isomerwas observed for FeC 4 and a two-dimensional isomer wasobserved for FeC 7 , whereas both linear and twodimensionalisomers were observed for FeC 5 , FeC 6 , andFeC 8 . A subsequent PES study of FeC n (n2–5) Ref.29 suggested a possible linear-to-cyclic transition fromFeC 3 to FeC 4 , consistent with the ion mobility measurements.In this article, we report the results of a combined PESand DFT study on a series of monochromium carbidesCrC n and CrC n (n2 – 8). The combination of theory andexperiment has proved successful in obtaining electronic andstructural information about TM compound clusters. 30–33 Tothe best of our knowledge, previous calculations were reportedonly for CrC, 34–36 CrC , 36 and CrC , 37 whereas wehave reported previously PES spectra for CrC 2 and CrC 3in studies of the 3d TM MC 2 and MC 3 species. 38,39 Thecurrent work presents a comprehensive study on the CrC nseries for n2 – 8, including CrC 2 and CrC 3 for completeness.Well-resolved PES spectra were obtained, providinga wealth of structural, electronic, vibrational, and isomericinformation. Extensive DFT calculations usinggeneralized gradient approximation for the exchangecorrelationfunctional were carried out for both CrC n andCrC n . The experimental and theoretical data were combinedto elucidate the electronic and structural evolution inthe series.the known spectrum of Rh , and the energy resolution of theapparatus was Ek/Ek2.5%—that is, 25 meV for 1-eVelectrons.B. Theoretical methodsThe GAUSSIAN 98 program 42 and the basis set denoted as6-311G*—namely, (15s11p6d1 f )/10s7p4d1 f for CrRefs. 43–45 and (12s6p1d)/5s4p1d for C Ref. 46—were used. Seven exchange-correlation functionals weretested on CrC 2 and CrC 2 :BLYPBecke’s exchange 47 andLee–Yang–Parr correlation 48 , BP86 Becke’s exchange 47and Perdew’s correlation 49 , BPW91 Becke’s exchange 47and Perdew–Wang correlation 50 , PW91PW91 both exchangeand correlation are due to Perdew and Wang 50 ,BPBE Becke’s exchange 47 and Perdew–Burke–Ernzerhofcorrelation 51 , PBEPBE Perdew–Burke–Ezerhoff exchangeand correlation 51 , and hybrid B3LYP. 52,53 Since two contendersfor the ground state of CrC 2 are close in energy atthe DFT level, we also investigated the anion using thecoupled-cluster singles and doubles approach 54 including theeffect of connected triples determined using perturbationtheory, 55 which is denoted UCCSDT in theMOLPRO program 56 used in this work. TheCr (20s15p10d6 f 4g)/7s6p4d3 f 2g averaged atomicnatural orbital set 57 and carbon-augmented correlationconsistentpolarized valence triple-zeta aug-cc-pVTZset 58,59 were used.Only the BPW91 functional was used in the calculationsfor n3. Our assignment of the spectroscopic states wasbased on the symmetry of the Slater determinants built usingthe one-electron DFT orbitals. After the geometry of a specieswas optimized, subsequent harmonic frequency calculationswere performed using analytical second derivatives inorder to confirm that the optimized geometry correspondedto a minimum. Theoretical electron affinities EAs were obtainedby the differences in total energies of a neutral and itsanion at their respective equilibrium geometries correspondingto adiabatic values:II. EXPERIMENTAL AND COMPUTATIONAL DETAILSA. Experimental methodsThe experiments were carried out using a magneticbottle-typePES apparatus equipped with a laser vaporizationsupersonic cluster source. A detailed description of the experimentaltechniques can be found elsewhere. 40,41 Briefly,the CrC n anions were produced by laser vaporization of achromium carbide (Cr 3 C 2 ) target in the presence of a heliumcarrier gas. Various Cr x C y clusters were generated andmass analyzed using a time-of-flight mass spectrometer. TheCrC n (n2 – 8) species of interest were each mass selectedand decelerated before being photodetached. Three detachmentphoton energies were used in the current study: 532 nm2.331 eV, 355 nm 3.496 eV, and 266 nm 4.661 eV.Photoelectrons were collected at nearly 100% efficiency bythe magnetic bottle and analyzed in a 3.5-m-long electronflight tube. The photoelectron spectra were calibrated usingEA ad E tot N,R N Z N E tot A,R A Z AE el E nuc ,where R N and R A denote ground-state equilibrium geometriesof a neutral species N and its anion A, respectively.Zero-point energies Z are computed within the harmonicapproximation.Vertical detachment energies VDEs were computed asthe difference in energies between the anion ground state andthe neutral state at the anion geometry:VDE k E tot N k ,R A E tot A,R A .With the present approach, two VDEs corresponding to removalof an electron from the - and -spin orbitals can becomputed—i.e., transitions to the neutral states with spinmultiplicities of 2S1M1 M stands for the spin multiplicityof an anion state were computed.12Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

8998 J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Zhai et al.TABLE I. Observed adiabatic ADE and vertical VDE detachment energies and vibrational frequencies forCrC n (n2 – 8). The numbers in parentheses are uncertainties in the last digits.Obs. feature ADE eV VDE eV Vib. Freq. cm 1 CrC 2 X 1.61715 1.680 15 510 20A 2.01110 2.076 10 520 20B 2.30 5 2.36 5C 2.466 15 480 30D 2.68 3E 2.88820 2.888 20 515 20F 3.160 10 440 20G 3.41410 3.414 10 620 20CrC 3 X 1.47415 1.474 15 700 30A 1.64015 1.640 15 720 30B 1.79720 1.797 20 400 30C 1.93610 1.936 10 540 20D 2.25E 2.46120 2.461 20 720 20, 116040F 2.82620 2.826 20 480 40G 3.00–3.35CrC 4 X 2.78115 2.781 15A a 3.02715 3.027 15b3.063 15c3.102 15d3.144 20e3.186 15B 3.35 3C 3.55 2D 3.88 2 3.94 2 480 30E 4.37 2X 1.85 2.05CrC 5 X 2.20 8 2.43 8A 2.76 6B 3.34 6C 3.53 6D 4.37 8CrC 6 X 3.15610 3.156 10 680 20A 3.33310 3.38 2 390 30, 65020B 3.61 5C 3.69 3D 3.92 2X 2.60 2.73CrC 7 X 2.96 3 3.01 3A 3.20 3B 3.6C 3.9CrC 8 X 3.45010 3.450 10A 3.57 2 3.57 2 970 40B 3.81 2C 3.94 2D 4.19 2III. EXPERIMENTAL RESULTSThe photoelectron spectra of CrC n (n2 – 8) are presentedin Figs. 1–9. Figures 3 and 5 provide evidence for theexistence of low-lying isomers for CrC 3 and CrC 4 . Theadiabatic detachment energies ADEs, VDEs, and vibrationalfrequencies for the resolved spectral features are givenin Table I for all seven species.A. PES spectra of CrC 2ÀFigure 1 shows the PES spectra of CrC 2 at 532 and 355nm. The spectra were slightly better resolved compared tothose reported in our previous study. 38 In particular, hot bandtransitions were significantly suppressed due to our improvedability to control cluster temperatures. 60–63 Two vibrationallyresolved bands X and A were observed in the 532-nm spectrumFig. 1a. The 0–0 transition of band X at 1.617 eVdefines the ground-state ADE—i.e., EA of CrC 2 . This valueis more accurately measured than in our previous study,which yielded an EA of 1.630.01 eV for CrC 2 . The VDEof band X is defined by the 1←0 transition at 1.680 eV. Thewell-resolved vibrational progression yielded a vibrationalfrequency of 51020 cm 1 for the ground state of CrC 2 .Asimilar vibrational frequency of 52020 cm 1 was observedfor band A. These values agree with our previous studywithin the experimental uncertainties.A congested spectral pattern was revealed at higher bind-Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters8999FIG. 1. Photoelectron spectra of CrC 2 at a 532 nm 2.331 eV and b355 nm 3.496 eV. The vertical bars indicate resolved vibrational energies at 355 nm Fig. 1b, where numerous vibronicfeatures were observed in the higher-binding-energy rangeand were tentatively labeled from B to G. Compared to ourprevious spectrum reported in Ref. 38, the intensity of the Bband was reduced in the current colder source conditions,suggesting that this band might be due to a low-lying isomer.As will be shown later, this observation was borne out fromthe theoretical calculations.B. PES spectra of CrC 3ÀFIG. 2. Photoelectron spectra of CrC 3 at a 532 nm and b 355 nm.The spectra of CrC 3 are shown in Fig. 2 at 532 and 355nm. The 532-nm spectrum Fig. 2a, though better resolved,is similar to our previous report. 39 The X, A, B, and Cbands are consistent with the previous spectrum, but eachwith a better-resolved vibrational progression.A congested spectrum with numerous transitions at thehigher-binding-energy range was observed in the 355 nmFig. 2b, which was dominated by an extremely intenseband E at 2.461 eV. Surprisingly, the 355-nm spectrumshown in Fig. 2b was quite different from the spectrumreported previously due to the colder source condition in thecurrent experiment. 60–63 Figure 3 compares the 355-nm spectraof CrC 3 taken at two different source conditions. Thedata in Fig. 3a are the same as in Fig. 2b. The spectrumshown in Fig. 3b was taken at a relatively hot source condition,and this spectrum was similar to that reported previouslyin Ref. 39. In addition to the deterioration of spectralresolution, dramatic intensity changes were observed. It appearedthat the intensities of the lower- (X,A,B) and higher-(F,G) binding-energy regions were significantly enhancedrelative to the central part of the spectrum (C,D,E). Thisobservation indicates that there existed at least two low-lyingisomers for CrC 3 : one gave rise to the spectral features inthe low- and high-binding-energy ranges and the other gaverise to the spectral features C, D, and E in the middle part ofthe 355-nm spectra Fig. 3. The coexistence of both isomersat the colder conditions suggested that they are close in stability,similar to our recent observation for B 7 Ref. 64.C. PES spectra of CrC 4ÀFigure 4 shows the spectra of CrC 4 at 355 and 266 nm.The spectra shifted significantly to higher binding energiesrelative to those of CrC 2 and CrC 3 and became muchsharper and less congested. The 355-nm spectrum Fig. 4arevealed three main bands X, A, and B. Band X is sharp withlittle vibrational excitation, indicative of little geometrychange upon photodetachment. The sharp feature X yieldedan EA of 2.781 eV for CrC 4 . Band A contains several resolvedfine features a, b, c, d, and e as shown in the inset ofFig. 4a. The binding energies of these features are given inTable I, and they are likely due to vibrational structures formore than one electronic transition. Four more bands wereobserved at 266 nm, B, C, D, and E Fig. 4b. The D bandconsisted of a vibrational progression with a frequency of480 cm 1 .A very weak band (X) was observed at the lowbinding-energyside of the main features Fig. 4. Figure 5Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

9000 J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Zhai et al.FIG. 3. Photoelectron spectra of CrC 3 at 355 nm under two source conditions:a cold and b hot. Note the relative intensity changes of spectralfeatures, indicating the coexistence of isomers in the CrC 3 beam.FIG. 4. Photoelectron spectra of CrC 4 at a 355 nm and b 266 nm 4.661eV. The inset shows fine features in band A in the 355-nm spectrum.shows that the relative intensity of the feature X was enhancedunder hot source conditions, suggesting that it camefrom a higher-energy isomer. We estimated an ADE andVDE of 1.85 and 2.05 eV, respectively, for this low-lyingisomer of CrC 4 .to a low-lying isomer was observed at the lower-bindingenergyside of the main features with an ADE and VDE of2.60 and 2.73 eV, respectively Fig. 7.D. PES spectra of CrC 5 À and CrC 6ÀThe spectra of CrC 5 at 355 and 266 nm are shown inFig. 6. These spectra represent a complete departure fromthose of CrC 4 , showing extremely broad and congestedfeatures. Five bands X, A, B, C, and D were tentativelylabeled. The ground-state VDE was estimated to be 2.43 eV,and the ADE was evaluated from the onset of feature X to be2.2 eV. The broad spectral features suggested that there arelikely large geometry changes between the anion and neutralof CrC 5 .The spectra of CrC 6 are shown in Fig. 7 at 355 and 266nm. These spectra are quite similar to those of CrC 4 Fig.4. Analogous to that of CrC 4 , the 355-nm spectrum ofCrC 6 Fig. 7a also exhibits two bands. The X band wassharp and intense with a short vibrational progression. The Xband yielded an EA of 3.156 eV for CrC 6 and vibrationalfrequency of 680 cm 1 . The A band again consisted of severalfeatures likely due to vibrational features of more thanone electronic transition. The intensity of band A increasedsubstantially at 266 nm Fig. 7b. Three more bands werealso observed at 266 nm in the higher-binding-energy range:B, C, and D. Similar to CrC 4 , a very weak feature X dueE. PES spectra of CrC 7 À and CrC 8ÀThe PES spectra of CrC 7 are shown in Fig. 8 at 355and 266 nm. These spectra display broad and congested featuressimilar to those of CrC 5 . The ground-state transitionX was fairly well defined, yielding an EA of 2.96 eV forCrC 7 . The higher-binding-energy bands (A,B,C) were tentativelyidentified.The spectra of CrC 8 are shown in Fig. 9, and they aresimilar to those of CrC 4 and CrC 6 with sharp and wellresolvedPES features. The 355-nm spectrum Fig. 9a revealedonly a single sharp feature X at 3.450 eV, whichyielded an accurate EA of 3.450 eV for CrC 8 . At 266 nmFig. 9b, four well-resolved bands A, B, C, and D wereobserved. Band A was intense and appeared to possess apartially resolved vibrational progression with a spacing of970 cm 1 . The 0–0 transition of band A was broad and likelycontained unresolved vibrational features corresponding to alower-frequency mode.The ADEs, VDEs, and vibrational frequencies for all theobserved spectral features are given in Table I.Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters9001FIG. 5. Photoelectron spectra of CrC 4 at 355 nm under two source conditions:a cold and b hot. Note the relative intensity change of feature X,indicating that this feature was due to a minor isomer of CrC 4 .IV. THEORETICAL RESULTSTheoretical results at the BPW91/6-311G* level forthe neutral and negatively charged CrC n species (n2–8)are presented in Figs. 10–16. In general, two types of structureswere found: linear and cyclic fan like. For n2–4,the local magnetic moments are also presented in order toassess changes in the spin density due to electron detachment.The local magnetic moment is defined by the differencesin populations of the - and -spin representations.The spin densities reported in Figs. 10–12 were obtainedusing the conventional Mulliken analysis. 65 The differencescomputed using the atomic natural orbital populations 66,67NAOs are essentially the same, as was noted for othersystems. 68 Positive and negative values of local spin densitieson carbon atoms correspond to larger populations in the- and -spin representations, respectively. Generally, theasymmetry in the and populations is small in fanlikestructures, while it can reach one electron in the linear structuresFig. 11.A. CrC 2 À and CrC 2We have performed an extensive search for the n2system, including linear and nonlinear configurations. Thelinear CrCC structure was found to be the lowest for theCrC 2 anion at the DFT level Fig. 10. We paid particularattention to the nonlinear structures, including states of allpossible C 2v symmetries, A 1 , B 1 , A 2 , and B 2 , as well asFIG. 6. Photoelectron spectra of CrC 5 at a 355 nm and b 266 nm.states corresponding to asymmetric angular CCrC and CrCCconfigurations for spin multiplicities of 4 and 6. At theBPW91 level, the lowest state found is 6 A 1 , which is abovethe 6 linear state by 0.13 eV Fig. 10. In order to makesure that this result was not an artifact of the BPW91 approach,we performed computations using six otherexchange-correlation functionals, including the hybridB3LYP functional, on the 6 and 6 A 1 states of CrC 2Table II. We also calculated the lowest 5 A 1 state for neutralCrC 2 at the same levels of theory, which allowed us to estimatethe EA ad of the C 2v CrC 2 at the different levels oftheory. However, we found that the linear neutral CrCC wasnot a minimum with one imaginary frequency. In addition,calculations with the basis set extended to 6-311G3df atthe carbon atoms were performed. As shown in Table II,neither functional nor the basis extension influence the orderof the anion states. The maximum variation in the EA ad withrespect to that computed at the BPW91 level was about 0.1eV. All the approaches produced rather similar geometricalparameters and vibrational frequencies.We also carried out CCSDT computations, which favoredthe C 6 2v A 1 state over the linear 6 state by 0.06 eV.According to Table II, the geometrical parameters andvibrational frequencies obtained at the CCSDT levelwere in good agreement with those obtained at the DFTlevels. According to the NAO analysis, the electronicconfiguration of Cr in the ground 5 A 1 state ofCrC 2 is (3d 4.34 4s 0.33 ) (3d 0.35 4s 0.10 ) . Attachment of anextra electron leads to the lowest-energy states 6 and 6 A 1 of CrC 2 . The corresponding electronicDownloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

9002 J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Zhai et al.FIG. 7. Photoelectron spectra of CrC 6 at a 355 nm and b 266 nm. Theweak feature labeled X is due to a minor isomer in CrC 6 .FIG. 8. Photoelectron spectra of CrC 7 at a 355 nm and b 266 nm.configurations are (3d 4.44 4s 0.67 ) (3d 0.28 4s 0.15 ) and(3d 4.56 4s 0.78 ) (3d 0.25 4s 0.08 ) , respectively. Thus there is nosubstantial differences between the 6 and 6 A 1 NAO populations.Attachment of the extra electron substantially increasesthe population of the Cr 4s orbitals.B. CrC n À and CrC n „nÄ3,4…As shown in Fig. 11, the fanlike ( 4 B 1 ) and the linear( 4 ) structures of CrC 3 were found to be nearly degenerate,with the former slightly more stable at the BPW91level of theory. For neutral CrC 3 , the low-spin ( 3 B 1 ) fanlikestructure was the ground state with the high-spin one ( 5 B 2 )being 0.15 eV higher in energy. The linear CrC 3 was higherthan the 3 B 1 structure by 0.30 eV. The electronic configurationof Cr in the ground 3 B 1 state of CrC 3 is(3d 3.68 4s 0.16 ) (3d 1.31 4s 0.06 ) . Attachment of an extra electronto CrC 3 led to 4 B 1 of CrC 3 with a Cr occupation of(3d 4.27 4s 0.78 ) (3d 0.71 4s 0.06 ) . The electron attachment substantiallyincreased the population of the Cr 4s orbitals similarto CrC 2 . Note that FeC 2 and FeC 3 also possess similarcyclic structures, 23,69 although the binding patterns should bequite different since the effective configuration of an ironatom is close to 3d 7 4s 1 .The ground state of CrC 4 was found to be the linear6 , which is well separated from the fanlike configurationsFig. 12. However, for neutral CrC 4 , the linear structure ishigher than the ground-state fan structure ( 5 B 2 ) by 0.34 eV.C. CrC n À and CrC n „nÄ5,6…Our BPW91 optimizations yielded a linear 4 groundstate for CrC 5 Fig. 13. A nonplanar fanlike structure( 4 A), which is 0.29 eV higher, is the lowest nonlinear structure.There are also two high-spin bent structures ( 6 A and8 A), but they are significantly higher in energy. NeutralCrC 5 was also predicted to have a linear ground state, whichis 0.16 eV below the nonplanar fanlike structure. Again, ahigh-spin bent CrC 7 ( 7 A) was predicted to be 0.32 eVhigher than the linear ground state. It seemed that the highspinstates prefer quasilinear configurations. We tried severalstarting geometries comprised of Cr on the top of or added tothe side of a pentagon C 5 ring. In the first case, optimizationsresulted in transition states, which finally led to the cyclicconfigurations found previously, while the latter convergedto a cyclic 4 A configuration, which is above the 4 stateby as much as 1.85 eV Fig. 13.Like CrC 4 , the ground state of the CrC 6 anion wasfound to be linear ( 6 ), which is well separated from thefan structures Fig. 14. The closest-lying fan structure ( 4 A)is 0.82 eV higher in energy. The neutral ground state of CrC 6is also linear, but the fan structure ( 5 A) is almost degeneratewith the linear structure, only 0.04 eV higher. Optimizationsof a configuration consisting of a Cr atom on the top of a C 6ring led to the 3 A and 2 A states for the neutral and anion,respectively, as shown in Fig. 14. Both states are significantlyabove the ground states.Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters9003FIG. 10. Optimized structures of CrC 2 and CrC 2 at BPW91/6-311G*.Bond lengths are in Å and the local magnetic moments are in Bohr magnetons.D 0 CrC n 0, E tot CrE tot C n 0, ZC n 0, E tot CrC n 0, ZCrC n 0, ,3D 0 CrC n 0, E tot CrC n1 0, E tot C 0, FIG. 9. Photoelectron spectra of CrC 8 at a 355 nm and b 266 nm.D. CrC n À and CrC n „nÄ7,8…As shown in Fig. 15, both CrC 7 and CrC 7 were foundto possess cyclic ground-state configurations correspondingto the 3 B 1 and 4 B 1 states, respectively. The linear structuresare low-lying isomers corresponding to the 5 state for CrC 7and 4 state for CrC 7 . The linear anion is 0.33 eV higherin energy than the cyclic ground state, but the neutral linearstructure is almost degenerate with the ground state, only0.08 eV higher. The fanlike structures are much higher inenergy for both CrC 7 and CrC 7 .The CrC 8 anion continues the trend of the series withan even number of carbon atoms: its ground state is linearand corresponds again to a 6 state, while the neutralground state is 5 Fig. 16. These states are significantlymore stable than the lowest cyclic states by 0.75 and 0.93 eV,respectively.E. Theoretical EAs and VDEsWe computed the EAs for the two lowest-lying isomersfor each species and the VDEs for two detachment channelsa low- and a high-spin channel. These theoretical data aregiven in Table III and compared with experimental data, aswill be discussed below.F. Thermodynamic stability of CrC n and CrC nÀclustersIn order to assess the thermodynamic stability of themonochromium carbide clusters, we evaluated the fragmentationenergies of two decay channels, the loss of aCorCratom, as follows:ZCrC n1 0, E tot CrC n 0, ZCrC 0, n .4The geometries of C n and C n were reoptimized at theBPW91/6-311G* level beginning with the bond lengthstaken from the B3LYP/6-311G* calculations. 70 As is wellknown, pure DFT approaches are biased towards overestimatingthe dissociation energies, by as much as 1 eV in thecase of homonuclear 3d-metal dimers. 71 If one assumes theoverestimation to be nearly the same for the series of neutraland anionic species, one may compare the trends along theseries.The C n chains possess triplet ground states for even n,which are less stable than the odd-n singlet ground-statestates see Ref. 70 and references therein. C 2 presents anexception since its singlet 1 g state is slightly below 72 thetriplet 3 u state by 0.09 eV. The BPW91 level places thetriplet state of C 2 somewhat below the singlet state because itis well known 73 that it is difficult to obtain a singlet groundstate of C 2 without using a multireference approach. As seenfrom Table IV, the even-n CrC n species are more stable withrespect to both Cr–C n and CrC n1 – C decay channels, althoughthey possess higher-spin-multiplicity quintet states.The CrC n anions are less stable than the correspondingneutrals with respect to the Cr–C n decay channel, while thelarge-n CrC 6 , CrC 7 , and CrC 8 anions are the moststable with respect to the CrC n1 –C channel.V. DISCUSSIONChromium is challenging both experimentally and theoreticallydue to its unique half-filled 3d 5 4s 1 electronicconfiguration. 74,75 The existence of structural isomers re-Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters9005FIG. 14. Optimized structures of CrC 6 and CrC 6 at BPW91/6-311G*.Bond lengths are in Å.FIG. 12. Optimized structures of CrC 4 and CrC 4 at BPW91/6-311G*.Bond lengths are in Å and the local magnetic moments are in Bohr magnetons.ues Table III. A high-spin excited state was also calculatedfor each isomer. Because of the low abundance of the linearisomer, no other spectral transitions could be identified forthis isomer other than the ground-state transition. For thecyclic isomer, the C band with a VDE of 2.47 eV was ingood agreement with calculated VDE for the high-spin finalstate Table III. Thus we conclude that the cyclic CrC 2 wasthe dominant isomer experimentally and should be theground state, in agreement with the CCSDT results TableII.B. CrC 3 À and CrC 3Our DFT results predicted that the quartet cyclic CrC 3and the linear isomer are nearly degenerate Fig. 11. Thusthey both should be populated experimentally. Figure 3 displaysunambiguously the existence of two isomers in thePES spectra, as described in the Sec. III B. The calculatedEA for the cyclic isomer was 1.69 eV, in reasonable agree-FIG. 13. Optimized structures of CrC 5 and CrC 5 at BPW91/6-311G*.Bond lengths are in Å.FIG. 15. Optimized structures of CrC 7 and CrC 7 at BPW91/6-311G*.Bond lengths are in Å.Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

9006 J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Zhai et al.D, and E were due to the linear isomer and the rest were dueto the cyclic isomer. Since the abundance of the cyclic isomerincreased at hotter source conditions, we conclude thatthe linear isomer is probably more stable than the cyclic one,although the DFT results showed that the cyclic isomer isslightly more stable Fig. 11. We note that the agreementbetween the DFT results of the cyclic isomer and the experimentaldata is not as good as that between the DFT results ofthe linear isomer and the experimental data.FIG. 16. Optimized structures of CrC 8 and CrC 8 at BPW91/6-311G*.Bond lengths are in Å.ment with the value of 1.474 eV derived from the X bandFig. 2. The calculated EA for the linear isomer 1.94 eVwas in excellent agreement with the value of 1.936 eV measuredfrom the C band. Therefore, spectral features can beunambiguously identified for the two isomers on the basis ofthe temperature-dependent spectra shown in Fig. 3. Bands C,C. CrC n À and CrC n „nÄ4,6,8…The PES spectra for these larger even-carbon systemsexhibited sharp and well-resolved data, which were differentfrom the other spectra. Our DFT calculations predicted thatall these species possess linear ground states, which aremuch more stable than the closest cyclic structures. Indeed,these theoretical results are in excellent agreement with ourexperimental observations, as shown in Table III, where thecalculated EAs for the linear structures of the three speciesare compared with the experimental values. The sharp peakfor the ground-state transitions in each case is consistent withthe theoretical results that showed very little geometricalchange between the anion and neutral linear structures. Eventhe calculated VDEs for the first excited state are in goodagreement with the experimental data. Weak populations ofminor isomers in the PES spectra of CrC 4 and CrC 6 wereobserved, which were in good agreement with the lowestcyclic isomers in each case. The large difference in stabilitybetween linear isomers and the cyclic ones was consistentwith the extremely weak populations of the cyclic isomers ineach case.TABLE III. Comparison of experimental data with the BPW91 adiabatic electron affinities EAs of CrC n and BPW91 vertical detachment energies VDEsfrom the CrC n . a EA (L →L) b EA (C →C) c VDE (L ) d VDE (C ) eTheor. Expt. f Theor. Expt. f Finalstate Theor. Expt. f Finalstate Theor. Expt. fCrC 2 6 → 5 g 2.35 2.30 (B) 6 A 1 → 5 A 1 1.66 1.617 (X) 5 2.39 2.36 (B) 5 A 1 1.71 1.680 (X)7 2.72 7 A 1 2.56 2.466 (C)CrC 3 4 → 5 1.94 1.936 (C) 4 B 1 → 3 B 1 1.69 1.474 (X) 5 2.04 1.936 (C) 3 B 1 1.80 1.474 (X)3 2.85 2.461 (E) 5 B 2 2.04 1.640 (A)CrC 4 6 → 5 2.65 2.781 (X) 6 A 1 → 5 B 2 1.68 1.8 (X) 5 2.69 2.781 (X) 5 B 2 2.07 2.05 (X)7 3.24 3.027 (A) 7 A 2 3.57CrC 5 4 → 5 2.37 4 A → 3 A 2.23 2.20 (X) 5 2.46 3 A 2.43 2.43 (X)3 3.35 5 A 2.85 2.76 (A)CrC 6 6 → 5 2.96 3.156 (X) 4 A → 5 A 2.18 2.6 (X) 5 3.00 3.156 (X) 5 A 2.82 2.737 3.40 3.38 (A) 7 A 3.79CrC 7 4 → 5 2.70 4 B 1 → 3 B 1 2.96 2.96 (X) 5 2.79 5 B 2 2.97 3.01 (X)3 3.63 3 B 1 3.22 3.20 (A)CrC 8 6 → 5 3.20 3.450 (X) 5 3.23 3.450 (X)7 3.54 3.57 (A)a All energies are in eV.b EA for linear anion to linear neutral.c EA for cyclic anion to cyclic neutral.d VDE for the linear anion leading to a low and high spin final state.e VDE for the cyclic anion leading to a low and high spin final state.f See Table I for spectral feature assignments and uncertainties.g The 5 state of CrC 2 has one imaginary 287i cm 1 and corresponds to a transition state.Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

J. Chem. Phys., Vol. 120, No. 19, 15 May 2004 Linear and cyclic chromium carbide clusters9007TABLE IV. Fragmentation energies FEs of CrC n and CrC n (n1–8)computed at the BPW91/6-311G* level of theory.NeutralD. CrC n À and CrC n „nÄ5,7…AnionChannel FE eV Channel FE eVCrC ( 3 )→Cr( 7 S)C( 3 P) 3.50 CrC ( 2 )→CrC ( 4 S) 3.43CrC 2 ( 5 A 1 )→CrCC 7.30 CrC 2 ( 6 )→CrCC 6.08→CrC 2 ( 3 u ) 4.30 →CrC 2 ( 2 g ) 2.75CrC 3 ( 3 B 1 )→CrC 2 C 6.05 CrC 3 ( 4 B 1 )→CrC 2 C 6.37→CrC 3 ( 1 g ) 2.68 →CrC 3 ( 2 g ) 2.28CrC 4 ( 5 B 2 )→CrC 3 C 6.83 CrC 4 ( 6 )→CrC 3 C 7.63→CrC 4 ( 3 g ) 3.94 →CrC 4 ( 2 g ) 2.61CrC 5 ( 5 )→CrC 4 C 6.13 CrC 5 ( 4 )→CrC 4 C 6.91→CrC 5 ( 1 g ) 2.58 →CrC 5 ( 2 u ) 2.14CrC 6 ( 5 )→CrC 5 C 6.65 CrC 6 ( 6 )→CrC 5 C 8.06→CrC 6 ( 3 g ) 3.46 →CrC 6 ( 2 u ) 2.51CrC 7 ( 3 B 1 )→CrC 6 C 6.49 CrC 7 ( 4 B 1 )→CrC 6 C 7.92→CrC 7 ( 1 g ) 2.78 →CrC 7 ( 2 g ) 2.47CrC 8 ( 5 )→CrC 7 C 6.52 CrC 8 ( 6 )→CrC 7 C 8.16→CrC 8 ( 3 g ) 3.34 →CrC 8 ( 2 g ) 2.46In contrast to the well-resolved spectra of the evencarbonclusters, these two odd-carbon cluster species yieldedvery broad PES spectra, signaling that they may have verydifferent structures or large geometry changes between theiranions and neutrals. Indeed, for CrC 7 our DFT results predicteda cyclic structure Fig. 15 which is more stable thanthe linear isomer by 0.33 eV. The calculated EA and VDE forthe cyclic structure are almost in perfect agreement with theexperimental value Table III. The linear isomer has a computedEA of 2.70 eV, slightly lower than the cyclic isomer.But there was no experimental evidence that this isomer waspopulated in any measurable amount Fig. 8. The lowbinding-energytail in the 355-nm spectrum of CrC 7 Fig.8a could be due to this isomer, but this part of the spectrumwas not well resolved.The CrC 5 and CrC 5 turned out to be the most difficultspecies in the series. The situation of CrC 5 was quite unusual.Its PES spectra represented the worst resolved dataamong the whole CrC n series. Surprisingly, our extensiveDFT calculations predicted a linear ground state for CrC 5 ,which is lower in energy than the closest nonplanar cyclicstructure by 0.29 eV Fig. 13. However, the calculated EAand VDEs for the nonplanar cyclic structure are in goodagreement with the experimental data Table III, whereasthe calculated EA for the linear isomer appeared to be highcompared to the EA measured from the X band Fig. 6. Thuswe conclude that the main spectral features of the CrC 5spectra were due to the nonplanar cyclic isomer. The broadspectral transitions were consistent with the anticipated floppinessof this structure. Significant geometry changes wereseen between the anion and neutral of this isomer Fig. 13,consistent with broad PES spectral features. However, sincethe EA of the linear CrC 5 isomer was calculated to behigher than the cyclic isomer, all its PES features wouldappear in the higher-binding-energy part of the spectra completelyoverlapping with those form the nonplanar cyclic isomer.Thus we could not rule out a small population of thelinear isomer experimentally. But this population had to bevery small, because we would expect the linear isomer togive rise to more intense and sharper features dominating thePES spectra if it had a significant population, such as thatobserved in the spectra of CrC 3 Fig. 2. Thus our experimentalobservation suggested that CrC 5 most likely possessesa nonlinear structure and the nonplanar cyclic one is agood candidate. In light of this apparent discrepancy, furthertheoretical calculations are warranted for CrC 5 and CrC 5 .E. General remarksThe conclusions on the geometrical structures deducedfrom experimental observations are supported by the resultsof our extensive DFT calculations in terms of the relativeenergetics of different isomers, as well as by comparison ofthe ADE and VDE values presented in Table III. Discrepanciesbetween theory and experiments were observed forCrC 5 . We should point out that the CCSDT result forCrC 2 predicted an ordering of stability for the linear andcyclic isomer different from the DFT results Table II. Asimilar discrepancy between results of DFT and CCSDTcomputations was previously found for the 4 and 6 states of CrO as well. 76 It is thus possible that a highlycorrelated level of theory would be needed for CrC 5 .Finally, it is interesting to note that the structural evolutionin the CrC n series is nearly identical to that found forthe FeC n (n4 – 8) series 23,28 and is similar to that observedin the NbC n (n2 – 7) series. 27 We note that thelinear CrC n clusters all possess higher electron binding energies,similar to C n and NbC n in which linear isomerswere also found to possess higher binding energies than thecyclic isomers. 27,77–79VI. SUMMARYA combined anion photoelectron spectroscopy and densityfunctional theory study on a series of monochromiumcarbide clusters CrC n and CrC n (n2 – 8) is reported.Well-resolved photoelectron spectra for CrC n yielded awealth of structural, electronic, and vibronic information.Extensive DFT calculations using the generalized gradientapproximation were performed for both CrC n and CrC nseries. Optimized geometries of the ground and low-lyingexcited states of both series were reported and comparedwith the experimental data. We found that the small clustersCrC 2 and CrC 3 possess both fanlike and linear structureswith similar stability. For larger CrC n clusters, the even-nspecies (CrC 4 ,CrC 6 ,CrC 8 ) exhibited sharp PES featuresand high binding energies and were found to possess linearstructures. On the other hand, the odd-n species(CrC 5 ,CrC 7 ) displayed low binding energies and broadPES patterns and were suggested to be due to nonlinearstructures. In addition to CrC 2 and CrC 3 , direct experimentalevidence was observed for the coexistence of minornonlinear isomers for CrC 4 and CrC 6 .Downloaded 23 Mar 2007 to Redistribution subject to AIP license or copyright, see

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