ZEKE spectroscopy of free transition metal clusters

Journal of Electron Spectroscopy and Related Phenomena 106 (2000) 153–169www.elsevier.nl / locate /elspec

ZEKE spectroscopy of free transition metal clustersa , b*Dong-Sheng Yang , Peter A. Hackett

aDepartment of Chemistry, University of Kentucky, Lexington, KY 40506-0055, USAbNational Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, Canada K1A 0R6

Abstract

Transition metal clusters are produced in molecular beams with laser vaporization of metal targets. Vibrationally androtationally resolved electronic spectra of the metal clusters are obtained with zero electron kinetic energy (ZEKE)photoelectron spectroscopy. The resolution of the spectra is of the order of sub-millielectron volts. Experiments on barevanadium and yttrium clusters and ligated yttrium, zirconium, and niobium clusters are presented. The bond length ofvanadium dimer is determined from the rotationally resolved spectra. Electronic states and molecular geometries of largerclusters are determined by combining the vibrationally resolved spectra with density functional theory and Franck–Condonfactor calculations. 2000 Elsevier Science B.V. All rights reserved.

Keywords: Metal cluster; ZEKE spectroscopy; Density functional calculation

1. Introduction theoretical predictions. However, the validity ofdifferent theoretical approaches is still under debate.

Many transition metals form important heteroge- Zero electron kinetic energy (ZEKE) photoelec-neous catalysts. To help understand chemistry occur- tron spectroscopy [2] has emerged as a most promis-ring at the surface of heterogeneous catalysts, an ing means to provide quantum state-specific infor-approach termed molecular surface science has been mation and to probe the structure of electronicallyproposed [1]. This approach recognizes the possi- complex transition metal clusters in the gas phase.bility of learning much about the metal-centered The technique offers superb spectral resolution with-chemistry from studies of small metal clusters, both out the need for the knowledge of excited electronicin the absence and presence of ligands. Indeed, the states. Fig. 1 demonstrates the superior resolution ofpotential of this approach has been evidenced by the the ZEKE technique by comparing the spectra of adiscovery of interesting size-dependent properties of niobium cluster obtained from three techniques:metal cluster systems. It would be desirable if we photoionization efficiency (PIE), conventional photo-could correlate the cluster size-dependent properties electron spectroscopy (PES), and ZEKE spectros-with their structures. However, there is a severe lack copy. A single-photon process is employed in allof reliable structural information even for clusters three techniques. The PIE curve is obtained bycontaining a few transition metal atoms. Our current collecting the ion signals as laser scans. The spec-knowledge about structures of small clusters is from trum displays an onset of ionization that can be used

to estimate the ionization potential (IP) of thecluster. The conventional PES spectrum is obtained

*Corresponding author. by collecting the signals of kinetic electrons with

0368-2048/00/$ – see front matter 2000 Elsevier Science B.V. All rights reserved.PI I : S0368-2048( 99 )00073-0

154 D.-S. Yang, P.A. Hackett / Journal of Electron Spectroscopy and Related Phenomena 106 (2000) 153 –169

lasers, making the application of ZEKE techniquefairly routine. Third, vibrational normal modes oftransition metal clusters are small enough to bepopulated at the room temperature, making it pos-sible to measure vibrational frequencies of neutralclusters, in addition to that of their cations. Finally,the ZEKE signals are recorded against the nullbackground, thus the technique is extremely sensi-tive.

ZEKE technique has been implemented in twoways. In the first, electrons with zero kinetic energyare produced directly via threshold photoionizationof neutral molecules or photodetachment of anions.The ZEKE electrons are then collected by an electricpulsed extraction field that is delayed from theionization time to discriminate against kinetic elec-trons. This approach has been used to study metalcluster anions constituted of the atoms with com-pletely filled d-subshells [3–5] and has proved to berather difficult to implement experimentally. In thesecond approach, neutral molecules are photoexcitedto high lying Rydberg states (n.100) that convergeto various eigenstates of the cations. A few mi-croseconds after photoexcitation, a small voltage

21Fig. 1. Spectra of triniobium monoxide obtained from photoioni- pulse (|1 V cm ) is switched on to remove thezation efficiency (a), anion photoelectron (b), and PFI-ZEKE (c)

Rydberg electrons from the ionic cores, and mole-spectroscopic measurements.cules are ionized. This approach, known as pulsed-field-ionization-ZEKE (PFI-ZEKE), has proved to berelatively easy to implement.

fixed photon energy. The spectrum shows a broad With the PFI-ZEKE technique, we have studiedband with a full width at the half maximum small vanadium and yttrium bare clusters and

21(FWHM) of |40 meV, or 300 cm . In contrast, the yttrium, zirconium, and niobium cluster carbides,fully resolved vibrational structure with the FWHM nitrides, and oxides (Table 1). For the first time, we

21of |5 cm is revealed in the ZEKE spectrum, have been able to obtain rotationally resolved spectrawhich is obtained by detecting the ZEKE electrons and measure the bond length of an open d-subshellthat are produced when laser wavelengths are cationic dimer [6], and to obtain vibrationally re-scanned across each ionization threshold. Because solved spectra and determine electronic and geomet-there is a severe lack of knowledge of the inter- ric structures of some larger clusters [7–10]. We usemediate states for transition metal clusters other than one-photon and two-photon excitation schemes priorsome dimers, the high ZEKE spectral resolution to field ionization, depending on the availability ofachieved without a resonance state selection is an the information about the intermediate states of theimportant advantage over other high resolution tech- clusters. The rotationally resolved PFI-ZEKE spectraniques, such as resonant two-photon ionization of vanadium dimer are obtained through two-photon(R2PI) and laser-induced fluorescence (LIF) that excitation processes, while the vibrationally resolvedrequire a long-lived excited state. Second, the IPs of spectra of other clusters are obtained through single-many transition metal clusters are in a spectral region photon excitation. The assignment of the carrier ofeasily accessible to frequency-doubled tunable dye the PFI-ZEKE spectra from single-photon processes

D.-S. Yang, P.A. Hackett / Journal of Electron Spectroscopy and Related Phenomena 106 (2000) 153 –169 155

Table 121 21 aIPs (cm ) and vibrational frequencies (cm ) of transition metal clusters

b b bCluster IP d (M ) n (M–M) n (M–L) Referencesn s s

c d dNb 46 858 227 335 [50,53]3

Nb C 40 639 (42 800) 237 (250) 327 (378) (817) [8]3 21Nb C 258 (278) 339 (385) (828) [8]3 2

Nb N 43 902 (47 200) (261) (391) (757) [10]3 21Nb N 257 (277) (395) (787) [10]3 2

eNb O 44 578 (49 600) 320 (322) (366) 720 (743) [7,54]31Nb O 312 (326) (386) (777) [7]3

cNb 43 950 [53]5

Nb C 37 104 [46]5 2

Nb N 37 563 [46]5 2

Y 40 129 (41 450) 185 (183) [37]21Y 197 (202) [37]2

cY 40 325 [38]3

Y C 34 065 (38 490) 82 (92) (232) (594) [9]3 21Y C 86 (87) 228 (245) (604) [9]3 2

c d dZr 42 105 177 258 [51,55]3

Zr O 41 838 (46 560) (236) (281) (651) [44]31Zr O (239) 272 (288) (678) [44]3

V 51 271 [6]2

V 44 342 [12]31V 172 [12]3

V 45 644 [33]4

a 21Except where noted, values are from the PFI-ZEKE measurements. The uncertainty of the measurements is typically |3 cm . Thevalues in parentheses are from the DFT calculations and are averaged if results are available from more than one computational codes.

bd (M ), symmetric metal bending; n (M–M), symmetric metal stretching; n (M–L), symmetric metal–ligand stretching.n s s

c 21From photoionization efficiency measurements with the uncertainty of 6400 cm .d From resonant Raman spectroscopic measurements in argon matrix.e From anion photoelectron spectroscopic measurements.

is aided by the velocity slip of the seeded cluster 2. Experimental and computational methodsbeam that provides a degree of mass separation tothe neutral clusters and thus the ability to cross- 2.1. Experimentcorrelate the PFI-ZEKE spectra with particular clus-ter species [11,12]. The interpretation of the vi- Fig. 2 shows a schematic of the cluster beambrationally resolved spectra and the determination of PFI-ZEKE photoelectron spectrometer system. Thethe cluster structures are facilitated by density func- system consists of two vacuum chambers. The firsttional theory (DFT) calculations and spectral simula- chamber houses a Smalley-type cluster source [14]

21tions based on the Franck–Condon (FC) principle. and is pumped by a 2200 l s diffusion pump. TheThe combination of the PFI-ZEKE spectra and second chamber houses the PFI-ZEKE spectrometer

21theoretical calculations has allowed us to obtain and is pumped by two 400 l s turbomolecularreliable structures for some of the most electronically pumps. The PFI-ZEKE spectrometer consists of acomplex transition metal clusters studied to date. In two-stage extraction assembly, a 34-cm long tube,

´addition to our work, Nemeth et al. have reported the and a dual microchannel plate detector. The ioniza-vibrationally resolved PFI-ZEKE spectra of silver tion region is well shielded from the high voltagesdimer through resonant two-photon excitation [13]. applied in the acceleration region and to the mi-


Fig. 2. Schematic of the metal cluster beam PFI-ZEKE photoelectron spectrometer system. DP, diffusion pump; TP, turbomolecular pump;TOF, time-of-flight tube; MCP, microchannel plate detector.

crochannel plate detector. It is also magnetically taken via a single-photon excitation, except forshielded by a cylindrical, double layer of m-metal. vanadium dimer for which a resonant two-photonThe spectrometer could also be operated as a two- scheme was employed. Prior to single-photon PFI-field, space-focused, Wiley–McLaren time-of-flight ZEKE experiments on a cluster, PIE curves weremass spectrometer by supplying the appropriate recorded to locate approximate IP of the cluster.voltages. Then, with laser energy set above the IP, experimen-

Bare metal clusters were produced by laser vapor- tal conditions, such as the timing and the fluence ofization (Nd-YAG laser, 355 nm) of a metal rod both the vaporization and ionization lasers, the(.99.5%) in the presence of a pulse of helium gas backing pressure of the helium gas, and the reactantfrom a home-built pulsed valve [15]. A trace amount concentration, were carefully optimized in order to

25of an appropriate reactant (e.g. |10 of ethylene, maximize the ratio of the mass peak of the cluster ofnitrogen, oxygen) was doped in helium gas to interest in the time-of-flight mass spectrum to that ofproduce metal cluster carbides, nitrides, and oxides. all other peaks. This step was crucial for identifyingThe resulting clusters passed down a clustering tube the carrier of the PFI-ZEKE electrons. With the(2 mm inner diameter, 2 cm length) and were optimized experimental conditions, the cluster wassupersonically expanded into the first vacuum excited to high-lying Rydberg states by a single-chamber. The clustering tube was maintained at photon excitation. After a suitable delay, the high-room temperature or cooled by liquid nitrogen. The lying Rydberg states were field ionized by a voltagesupersonic jet was skimmed (2 mm diameter) |5 cm pulse from a digital delay generator applied to the

21downstream from the exit end of the clustering tube. repeller plate. Typically, a field of 1 V cm wasA pair of deflection plates located after the skimmer applied for 100 ns after a delay of |3 ms. A DC

21removed residual charged species from the molecular field, smaller than 0.1 V cm , was used to rejectbeam before it entered the second chamber. electrons from prompt photoionization. The PFI-

The PFI-ZEKE measurements on all clusters were ZEKE electron signals were capacitively coupled


from the microchannel plate detector anode and were andamplified by a preamplifier, averaged by a gated TQ 5 (L9) D. (5)integrator, and collected in a laboratory computer.

D being the vector of the differences of the mass-weighted Cartesian coordinates at equilibrium for the2.2. Computationneutral and ion. The fact that S is not an identitymatrix, because the normal coordinates of the ion areDFT methods were carried out to calculate mini-rotated with respect to those of the neutral, was firstmum energy structures and harmonic vibrationalpointed out by Duschinsky [21].frequencies of the neutral and cationic metal trimer

Assuming that the potentials of the neutral and ionoxides, carbides, and nitrides, as well as yttriumare adequately described by a harmonic approxi-dimer. Three computational codes, deMon-KS [16],mation makes it possible to calculate the FC overlapsGaussian 94 [17] and Amsterdam Density Functionalin closed form (without setting S51 or neglecting(ADE) [18,19], were used in some cases, such asdifferences between the neutral and ion frequencies)triniobium dicarbide and dinitride, to test the sen-using recursion relations given by Doktorov et al.sitivity of the results to the choices of functional,[22,23]. In the case of Nb O, using the L matricesbasis set, and implementation. It has been found that 3

computed from DET we find an S matrix that is verythese computational codes all yield similar generalclose to the identity and a Q vector whose com-features for the geometries and vibrational frequen-ponents are substantial. In such a case, a goodcies. Thus, only the representative results are pre-approximation to the FC structure of a cold spectrumsented. The computational details for individualis obtained for a transition by using displacementcluster were described previously [7–10].parameters expressed in terms of the final stateFC factors were calculated assuming that the(cation) [24,25]. In this case, the intensity of transi-neutral and ionic potentials are both harmonic.tions between two vibrational states is due to theNormal coordinates for the neutral and ion are lineardisplacement of the two electronic surfaces. Thecombinations of Cartesian displacements of theintensity of the ith totally symmetric mode is de-atoms from the neutral or ionic equilibrium geome-termined by B , the displacement of the ith normaltry. The normal coordinates of the neutral and ion i

coordinate,differ because the equilibrium geometries are differ-ent and the linear combinations of the atomic

1 / 2B 5 (v /h) Q . (6)i i idisplacements are different. Normal coordinates forthe neutral and ion are denoted by q and q9, Here Q is a component of the vector Q definedirespectively, and are defined in terms of the Car- above. This treatment reduces the FC integral to thetesian displacements of the atoms by: product of one-dimensional integrals.

T Spectral broadening was simulated by giving eachq9 5 (L9) d, (1)line a Lorenztian lineshape with the FWHM of theexperimental spectra.and

Tq 5 (L) d. (2)

3. Results and discussionThe L and L9 matrices are determined by diagonaliz-ing mass-weighted Cartesian force constant matrices

3.1. Bare metal clustersfor the neutral and ion. The two sets of normalcoordinates are related [20],

3.1.1. Vanadium dimer, V [6]2q9 5 Sq 1 Q, (3) Langridge-Smith et al. first studied the neutral V2

molecule in the gas phase using R2PI spectroscopywhereand reported a rotationally resolved band system

TS 5 (L9) L, (4) with the origin near 700 nm [26]. The band system


3 3 2 4 2was assigned to the transition A P ←X S . Also ponent show only transitions to the S (Fig. 3au g 1 / 2g3using R2PI, Spain et al. obtained an additional band and b), while the spectra through the P com-2u

4 2 4 2system in the infrared spectral region [27,28]. By ponent show transitions to both the S and S1 / 2g 3 / 2grecording two-photon PIE curves, James et al. ob- (Fig. 3c and d). This observation is consistent withserved two ionization thresholds and attributed them the DS561/2 selection rules of photoionization ofto the two spin-orbit components of the cation a diatomic molecule derived by Xie and Zare [31]

4 2 4 2ground state X S [29,30]. With the available and confirms the S symmetry of the cation groundg ginformation on the intermediate states and IP, we state, suggested by previous studies [29,30]. Themeasured PFI-ZEKE spectra of V using two-photon second major difference is that when probing from2

3 3 2 3 1excitation through the 700 nm A P ←X S the P component, only two J values are ac-u g 2u21 3system. The spectra have a FWHM of 1.5 cm , cessed, while probing from the P component, a2u

1which is sufficient to resolve the rotational levels of wide range of J values are observed. Detailedthe ground state of the vanadium dimer cation. Fig. 3 analysis of the rotational spectra was based on thepresents representative PFI-ZEKE spectra obtained selection rules for photoionization of a diatomicby the prior excitation of transitions in the A molecule [31] and the rotational Hamiltonian matrix3 3 2 3 3 2 4 2P ←X S (0,0) and A P ←X S (0,0). for a S state in a Hund case (a) [32]. The analysis1u 0g 2u 1g

There are striking differences between the PFI-ZEKE of the rotationally resolved spectra has allowed us to3 3 ˚spectra recorded through the P and P com- determine the bond length, r 51.7347 A, of the X1u 2u 0

3 4 2 1ponents. First, the spectra through the P com- S state of V . To our knowledge, this is the only1u g 2

3 3Fig. 3. PFI-ZEKE spectra of V recorded with the excitation laser tuned to the lines Q(1) (a) and R(7) (b) in the A P ←X S (0,0); to2 1u 0g3 3Q(2) (c) and R(6) (d) in the A P ←X S (0,0) band.2u 1g


experimental determination to date of the bond accuracy than the previous measured values [34].length for an open d-subshell transition metal The PFI-ZEKE spectrum of V in Fig. 4 also3

1diatomic cation. The experimental bond length of V displays some fine structures. The band at 44 514221 21is in a remarkable agreement with that predicted by cm is 172 cm apart from the band origin, the

˚prior DFT calculations, 1.741 A [30]. The bond lowest energy band. By comparing the energy spac-1 ˚length of V is shorter than that of V , 1.77 A [26], ing and theoretical vibrational frequencies, this band2 2

1providing a further evidence for the fact that V may be attributed to the transition from the ground20(D 53.140 eV) is more strongly bound than V electronic state of V to the first excited level of a0 2 30 totally symmetric vibration mode of the ground(D 52.753 eV) [29,30]. Other spectroscopic param-0

1electronic state of V . An alternate explanationeters from the PFI-ZEKE spectra are adiabatic IP, 321 involving low-lying (spin-orbit) excited electronic51 271.14 cm ; electronic term value, 51 282.20

21 state may also be considered. For V , there is nocm ; second-order spin-orbit splitting parameter, 421 21 additional structure appearing in the PFI-ZEKE5.248 cm ; rotational constant, 0.21993 cm ; and

21 ¨spectrum, other than the 0–0 transition. Gronbeckspin-rotation constant 0.0097 cm .´and Rosen [35] and Wu and Ray [36] have recently

calculated geometries and IPs of small vanadium¨ ´3.1.2. Vanadium trimer and tetramer, V and V clusters using DET methods. Gronbeck and Rosen3 4

[12,33] found that the lowest energy geometry of both V and41Cox et al. measured the IPs of V and V from PIE V was a planar and that the adiabatic IP of the3 4 4

measurements [34]. Their values are 44 300 (400) cluster was |5.5 eV, which is close to our ex-21 21cm for V and 45 400 (400) cm for V . Our perimental value, 5.6596 (4) eV. In contrast, Wu and3 4

single-photon PFI-ZEKE measurements on V and V Ray found that the lowest energy isomer of V and3 4 421 1determined the IP of 44 342 (3) cm for V and V was a tetrahedron and that the adiabatic IP of V3 4 4

2145 644 (3) cm for V that has 100 times better was |5.1 eV. Although they did not report the4

Fig. 4. PFI-ZEKE spectrum of V , together with DET results for the vibrational frequencies of the cation.3


1detailed structural parameters for V and V , The whole profile of the doublet spans about 224 421¨ ´Gronbeck and Rosen and Wu and Ray did show that cm . Based on previous experiments in which

the adiabatic and vertical IPs of V were almost rotational temperatures of 25–30 K were observed,4

identical, implying the geometries of the neutral and and on the DET calculations from which the rota-ion are very similar. Thus, the similar geometries tional constants of Y were predicted to be of the2

1 21between V and V may be the reason for the lack of order of 0.05 cm , we estimate that the rotational4 4

vibrational progressions in the PFI-ZEKE spectra, envelope of single vibronic band should span no21although the autoionization of the excited vibrational more than 12 cm . Thus, we believe that the

1levels of V may also be possible. doublet is due to two overlapping vibronic transi-4

The 0–0 bands in the V and V spectra have a tions, each consisting of unresolved rotational struc-3 421FWHM of 8 cm , which is five times that of the V tures. In the analysis of the spectrum, we assume that2

spectrum. The line broadening is attributed to rota- the PFI-ZEKE spectrum originates from only one oftional band envelopes that cannot be resolved with the two possible ionization processes:

21 1 4 2 5 2 1 2 1 1the resolution, 1.5 cm , of our PFI-ZEKE spec- Y ( S )←Y ( S ) and Y ( P )←Y ( S ). If the2 g 2 u 2 u 2 g1 2 1 1trometer. Similar rotational envelopes have also been spectrum was assigned to the Y ( P )←Y ( S )2 u 2 g

observed for the metal cluster oxides, carbides, and process, the doublet structures of the two strong21nitrides [7–10]. bands at 40 129 and 40 326 cm , as well as the

21weak feature at 39 946 cm , would be left un-3.1.3. Yttrium dimer, Y [37] explained. Also, the spectral intensity profile would2

Knickelbein measured IP of Y as 40 000 (400) be in a very poor agreement with the calculated FC221 1 2 1 1cm from PIE measurements [38]. Morse at the factors. Thus, the Y ( P )←Y ( S ) process could2 u 2 g

University of Utah and Simard at NRC Canada not be responsible for the observed spectrum. On theperformed R2PI measurements in the 10 000–20 000 other hand, the assignment present in Fig. 5 explains

21cm region, but failed to record any signal. Knight every experimental feature both in terms of theet al. failed to obtain an electron spin resonance energy positions and intensity distributions, and(ESR) spectrum of Y , whereas the same experimen- agrees with the predictions of our DFT and other ab2

tal conditions gave a spectrum for Sc [39,40]. Based initio calculations. Thus, we attribute the PFI-ZEKE21 4 2 5 2on the ESR experiments, Knight et al. suggested that spectrum to the Y ( S )←Y ( S ) transition.2 g 2 u

5 2 5 2Sc has a S ground state, while the ground state of From the spectral assignment, both the S (Y ) and2 u u 21 3 5 4 2 1Y might be S or D, but not S. However, Walch S (Y ) states suffer from extensive second-order2 g 2

21and Bauschlicher [41] and Dai and Balasubramanian spin-orbit interactions. The splitting is 210 cm4 2 4 2[42] found using high level ab initio methods that the between the S (V 5 3/2) and S (V 5 1/3 / 2,g 1 / 2,g

5 2 1 1 21 5 2lowest energy state of Y is S rather than S . 2) components, 64 cm between S (V 5 2) and2 u g 2,u5 2 21 5 2Dai and Balasubramanian also calculated the IPs for S (V 5 1), and 4 cm between S (V 5 1)1,u 1,u1 4 2 5 2 5 2the ionization processes of Y ( S )←Y ( S ) and and S (V 5 0). These splittings are explained2 g 2 u 0,u1 2 1 1Y ( P )←Y ( S ) [43]. They predicted the IP of schematically in Fig. 6. The IP of2 u 2 g

21 1 4 2 5 2the former process to be 39 680 cm and the IP of Y ( S )←Y ( S ) is determined as 40 1312 1 / 2,g 2 0,u21 21the latter process to be 35 080 cm . The calculated cm . The vibrational frequencies are measured as1 4 2 5 2 21 4 2 1 21IP of the Y ( S )←Y ( S ) is much closer to the2 g 2 u 197 cm for the X S state of Y and 185 cmg 221 5 2experimental value, 40 000 cm [38]. for the X S state of Y .u 2

Our PFI-ZEKE measurements were to establish1the ground states of Y and Y . A representative2 2

PFI-ZEKE spectrum is shown in Fig. 5. The spec- 3.2. Metal cluster oxides, carbides, and nitridestrum consists of two strong bands at 40 129 and

2140 326 cm and a number of weak ones. Each of 3.2.1. Triniobium and trizirconium monoxides,the two strong bands is a doublet separated by 4 Nb O and Zr O [7,44]3 3

21cm . The doublet structure is shown from the Fig. 7a and b show the PFI-ZEKE spectra ofexpansion of the first strong band, band A, in Fig. 5. Nb O at 300 and 100 K. The spectrum in Fig. 7a3


Fig. 5. PFI-ZEKE spectrum of Y , together with the spectral assignment. The first band, band A, is expanded to show the doublet structure.2

21shows a short progression formed by the bands K. The FWHM narrows down to 4 cm at 100 K.labeled 0, 1, and 2, with the energy spacing of 312 The reduction of the FWHM at the lower tempera-

21 21cm . These bands have a FWHM of 5 cm at 300 ture indicates that the line broadening is due tounresolved rotational structure. There are less-intensebands located at each side of the main bands. There

21is also a band, band a, 320 cm to the red of theband 0. The intensity of the weak bands decreaseswhen the molecular beam source is cooled to 100 K,as shown in Fig. 7b, indicating they are hot bandsand sequence structures originating from the excitedvibrational levels of the neutral ground electronicstate.

The PFI-ZEKE spectra shown in Fig. 7a and byield the following preliminary spectroscopic andstructural information for the cluster. First, thecluster ion has a totally symmetric vibrational mode

21of 312 cm . This mode is most likely a symmetricvibration of the niobium atoms because a symmetricNb–O vibration would have much higher frequency[45]. Second, the vibrational modes of the neutralthat are associated with the hot bands and sequence

4 2 1 structure should have frequencies lower than |500Fig. 6. Spin-orbit splittings in the X S state of Y and the Xg 2215 2

S state of Y . cm , an estimate based on the thermal populationsu 2


Fig. 7. PFI-ZEKE spectra of Nb O at 300 K (a) and 100 K (b) and the spectrum of Zr O at 300 K (c).3 3

at 300 K. Third, the geometries of the neutral and ion sional one with the oxygen bound to three Nb atomsare rather similar because only a short progression (see the insertion in Fig. 8c). This structure lies 1.03appears in the spectrum. eV higher in energy than the planar one for both the

To assign the spectrum in detail and determine the neutral and ion, implying that the IP of the threegeometry of the cluster, DFT calculations and spec- dimensional structure is the same as that of thetral simulations were carried out. Two minimum planar structure. The geometric symmetry of theenergy structures were obtained from many-trial three dimensional structure is C for the neutral ands

geometries. The most stable structure for both Nb O C for the ion. The reduced symmetry of the neutral3 3v1and Nb O has a planar C symmetry (see the structure is largely due to a Jahn–Teller distortion.3 2v

insertion in Fig. 8b). The oxygen atom is bound with Spectral simulations were carried out by calculat-an equal bond length to two Nb atoms. Two distinct ing multidimensional FC factors using the geomet-Nb–Nb bond distances are present in the cluster with ries, harmonic vibrational frequencies, and normal

1the Nb–Nb bond bridged by oxygen being longer mode coordinates obtained for Nb O and Nb O3 3

than the other two. The ground electronic symmetry from the DFT calculations. The simulated spectra are2 1of the C structure is B for the neutral and A for compared with the experimental spectrum in Fig. 8.2v 1 1

the ion. A second stable structure is a three dimen- The theoretical transition energies are plotted relative


the neutral to the ground state of the ion. The neutral21bending mode has a frequency of 320 cm . On the

blue side of the main progression is the sequencebands due to the asymmetric niobium–niobiumstretching vibration. The frequency difference of theasymmetric stretching mode in the ion and neutral is

2123 cm . On the red side of the main progression arethe sequence bands associated with the out-of-plane

21deformation of the cluster. This mode is 11 cmsmaller in the ion than in the neutral.

The general feature of the PFI-ZEKE spectrum ofZr O is similar to that of Nb O, as shown in Fig. 7c,3 3

although the satellite bands are not well resolved asthat in the spectrum of Nb O. The frequency of the3

symmetric zirconium bending vibration is measured21 21as 272 cm , 40 cm less than that of Nb O. The3

21 21IP of Zr O is 41 838 cm , 2740 cm lower that of35Nb O. Preliminary DFT calculations suggest a A3 2

3 4(or A ) ground state for Zr O and B state for2 3 11Zr O .3

3.2.2. Triniobium and triyttrium dicarbides, Nb C3 2

and Y C [8,10]3 2

PFI-ZEKE spectra of the metal cluster carbidesshow much richer structures than that of their oxides.

12Fig. 9a presents the spectrum of Nb C at the room3 2Fig. 8. Experimental (a) and simulated (b–c) PFI-ZEKE spectratemperature. The spectrum has the following fea-of Nb O at 300 K. The simulations were calculated using the3

tures: it consists of a strong vibrational progressionplanar geometry (b) and the three dimensional geometry (c) fromthe DFT calculations. (a ) and six weak ones (b , c , d , e , f , and g ).n n n n n n n

All seven progressions have the same energy spacing21of 258 cm . Six of the seven progressions can beto the position of the band 0 in the experimental

grouped into three pairs, a and b , c and d , and fspectrum. A remarkable agreement exists between n n n n n21and g , with the same energy separation of 20 cm .the experiment and theory for the planar structure. n

21The separation of d and e is 13 cm . The fHowever, the experimental spectrum is very different n n n21progression is 339 cm from the progression a .from the simulation of the three dimensional struc- n

21ture. Thus, the comparison establishes that both The main bands, a , have a FWHM of 7 cm ,n1 21Nb O and Nb O have the planar C structure, which decreases to 5 cm at 100 K, due to the3 3 2v

rather than the three dimensional one. The excellent narrowing of rotational envelope. The intensities ofagreement between the experiment and the simula- most small bands depend on the cluster source

13tion of the planar structure makes the spectral conditions. Fig. 9b presents the spectrum of Nb C .3 2

assignment trivial. The main progression consisting The spectrum has the same energy spacing and12of the bands 0, 1, and 2 in Fig. 7a, is due to the intensity profile as that of Nb C , but shifts to the3 2

21transitions from the ground state of the neutral to the red by 3 cm . From these two spectra, we concludeexcited levels of the symmetric niobium bending in that the geometries of the neutral and ion are rather

21the ion. The frequency of this vibration is 312 cm . different because relatively long progressions appearThe hot band, band a, is the transition from the first in the spectra. All observed transitions are associatedexcited level of the symmetric niobium bending in with the vibrations of the niobium atoms because the


1 2bridged structure is A for the ion and A for the1 1

neutral. Like triniobium monoxide, triniobium di-carbide also prefers the state with low electron spinmultiplicity.

Fig. 10 compares the spectral simulations fromboth the trigonal bipyramid and doubly bridgedstructures with the experimental spectrum. The com-parison indicates that the cluster has the trigonalbipyramid structure, rather than the doubly bridgedone. The overall good agreement between the simu-lation from the trigonal bipyramid structure makesdetailed spectral assignments possible. These assign-ments are summarized as follows: the main pro-gression a is due to the transitions from the groundn

state of the neutral to the vibrational levels of thedegenerate mode (e9) in the ion. The e9 mode is

12 13 12Fig. 9. PFI-ZEKE spectra of Nb C (a), Nb C (b), and Y C3 2 3 2 3 2

(c).

energy spacing of the progressions is independent ofthe carbon isotopes. One of the symmetric normalmodes of the niobium vibrations in the ion has a

21frequency of 258 cm .The DFT calculations predicted that triniobium

dicarbide has two stable geometries: trigonalbipyramid and doubly bridged structures. The energydifferences of the two structures are calculated to beless than a few hundredths of eV, implying that thetwo theoretical structures are indistinguishable interms of their energies. For the trigonal bipyramid

1 1 9structure, Nb C has a D geometry and a A3 2 3h 1

ground electronic state. Adding an electron to1Nb C to form Nb C populates a degenerate3 2 3 2

orbital (e0), leading to a Jahn–Teller distorted struc-ture of lower symmetry, that is C or C depending2v s

on the computational methods. The electronic stateFig. 10. Experimental (a) and simulated (b, c) PFI-ZEKE spectra2 2of Nb C is A (in C ) or A9 (in C ). For the 123 2 1 2v s of Nb C . The simulations were calculated using the trigonal3 21doubly bridged structure, both Nb C and Nb C bipyramid geometry (b) and the doubly bridged geometry (c) from3 2 3 2

have a C symmetry. The ground state of the doubly the DFT calculations.2v


identified as the symmetric bending of the niobium electronic states with multiplicities of 2 and 4 are21atoms with a frequency of 258 cm . Because of the calculated to be the most stable. The doublet gives a

2low symmetry of the neutral cluster, the degenerate C geometry with a B ground state, while the2v 14e9 mode splits into two non-degenerate bending quartet gives a D geometry with a degenerate E93h

2modes (a and b in C and a9 and a0 in C ). In the state. The B state is 0.3 eV lower in energy than1 2 2v s 14rigid molecular limit, this symmetry transformation E9. The removal of an electron from the neutral

would have a one-to-one correspondence. That is, states forms ionic states with multiplicities of 1, 3,1 39only transitions from the neutral ground state to the and 5. These ionic states are calculated as A , B ,1 1

5vibrational levels involving an arbitrary number of and A , with the singlet being the lowest in energy1

quanta of one component of the e9 and an even and the highest in geometric symmetry (D ). From3h

number of quanta of the other component of the e9 the calculated electronic states of the neutral and ion,mode are allowed. However, our calculations indi- there are four electronically allowed ionization pro-

1 2 3 2 3 49cate a rotation of the normal coordinates of the e9 cesses: A ← B , B ← B , B ← E9, and1 1 1 1 15 4mode of the ion with respect to the corresponding A ← E9. However, the comparisons between the2

modes of the neutral. This rotation results in the e9 experimental and simulated spectra indicate that the1 29mode being a 30–50% mixture of the neutral a with most likely process is A ← B [10].1 1 1

b , or a9 with a0. The progressions b , c , and d are2 n n n

associated with the transitions, respectively, from the 3.2.3. Triniobium dinitride, Nb N [9]3 2

first excited levels of the a (or a9), b (a0), and Fig. 11a presents the spectrum of Nb N . The1 2 3 2

a 1b (a91a0) modes to the vibrational levels of the spectrum is characterized by a short progression with1 221e9 mode in the ion. The frequencies are measured as the energy spacing of 257 cm and small bands on

21 21237.6 cm for the a (or a9) mode and 82.7 cm the blue side of the main progression, which are 17121for the b (a0) mode. The remaining progressions, e , cm apart. The spectral intensity profile appears2 n

f , and g , are the combination bands due to then n

transitions involving the bending and stretchingmodes. The frequency of the symmetric stretching is

21 21326.3 cm in the neutral and 339 cm in the ion.The PFI-ZEKE spectrum of Y C , as shown in3 2

Fig. 9c, has a similar structure with that of Nb C ,3 2

although the IP and vibrational frequencies of Y C3 2

are much lower. The IP of Y C is measured to be3 221 2134 065 cm , while the IP of Nb C is 40 639 cm .3 2

The yttrium symmetric stretching mode has a fre-21quency of 228 cm in the ion. Two yttrium bending

21modes have the frequencies of 82 and 24 cm in the21neutral and a degenerate frequency of 86 cm in the

ion. It was noted that unlike Nb C the excitation of3 2

the yttrium stretching mode in the neutral was notobserved in the spectrum of Y C although the3 2

yttrium mode should be thermally populated at theroom temperature. One of the reasons is that thePFI-ZEKE spectrum of Y C is noisier than that of3 2

Nb C , making hot bands more difficult to identify.3 2

The DFT geometry optimization has found only astable trigonal bipyramid structure for the triyttriumdicarbide. The trigonal bipyramid geometry has Fig. 11. Experimental (a) and simulated (b) PFI-ZEKE spectra ofeither a C or D symmetry, depending on the Nb N . The simulation was calculated using the doubly bridged2v 3h 3 2

electron spin multiplicity. For the neutral cluster, geometry from the DFT calculations.


much different from that of Nb C , but rather similar3 221with that of Nb O. The energy spacing, 257 cm , of3

the progression is close to that of the main pro-gression in the spectrum of Nb C . These observa-3 2

tions indicate that the structure of triniobium di-nitride does not change significantly upon ionization,as in the case of triniobium monoxide, and one of theniobium vibrations has a frequency close to that oftriniobium dicarbide.

Unlike triniobium dicarbide for which trigonalbipyramid and doubly bridged structures were calcu-lated to be stable, triniobium dinitride was calculatedto adopt only the doubly bridged geometry (see theinsertion in Fig. 11b). For this doubly bridged

1structure, both Nb N and Nb N have a C3 2 3 2 2v2symmetry with B ground state for the neutral and a1

1A ground state for the ion. The simulation from the11 2transition A ← B is shown in Fig. 11b. The1 1

comparison of the experiment and theory indicates21that the 257 cm progression is due to the symmet-

1ric bending of the niobium atoms in Nb N . This3 2 Fig. 12. PFI-ZEKE spectra of Nb C (a) and Nb N (b).5 2 5 2bending vibration has a very similar frequency to

1 21that of the bending in Nb C , which is 258 cm .3 2

The small bands on the blue side of the main 3.3. Chemical bonding and ionization effectsprogression are sequence bands associated with theniobium asymmetric bending vibrations. The Table 1 summarizes IPs and vibrational frequen-

21asymmetric bending mode is 17 cm smaller in the cies of the transition metal clusters. The IPs of theneutral than in the ion. ligated clusters are lower than that of the bare ones.

For the same metal, the carbon coordination has thelargest effects on the IPs of the bare clusters. The

3.2.4. Pentaniobium dicarbide and dinitride, Nb C oxygen atom, on the other hand, has the least effects.5 2

and Nb N [46] Furthermore, the IP reduction upon the carbon5 2

PFI-ZEKE spectra of the two clusters are shown in coordination is very similar for the clusters of theFig. 12. Each spectrum consists of several bands. same sizes. For example, the IPs of both triniobium

21 21The band separation is 9 cm in the case of Nb C and triyttrium are about 6200 cm (or 0.8 eV) lower5 221and 13 cm in Nb N . The first band is attributed to than that of the bare clusters. However, the IP5 2

the 0–0 transition with the transition energies of reduction upon the oxygen coordination is quite21 2137 104 cm in Nb C and 37 563 cm in Nb N . different for different metals. For instance, the IP of5 2 5 2

21Other bands are assigned to the transitions from the Nb O is about 2300 cm lower than that of Nb ,3 321excited vibrational levels of the neutral clusters to while the IP of Zr O is only about 300 cm less3

the ground states of the ions because the band than that of Zr . The IP reduction of the metal3

intensities depend on the cluster source temperatures. clusters upon ligation is in contrast to the ligation ofThe lack of the vibrational progressions may indicate the metal atoms for which the ligated atoms aresimilar geometries between the neutral and ionic found to have higher IPs than the bare metal atoms.clusters or the autoionization of the excited vibra- For example, the diatomic molecules, ML, wheretional levels of the ionic clusters. However, there M5Y, Zr, Nb and L5C and O, have been reportedhave not been high level theoretical calculations on to have higher IPs than the metal atoms [47].the structures of these clusters. The IP decreases upon ligation of the metal


clusters implies that the M–L bonds are stronger in orbitals. The energy for promoting the s-electron is2 1 1 2the ions than in the neutrals, on the bases of the 1.36 eV from the 5s 4d to 5s 4d configuration. For

1thermodynamic cycle, D (M –L)2D (M –L)5 zirconium, the promotion energy for the s-electron is0 n 0 n

IP(M )2IP(M L), where L52C or 2N or O. The 0.59 eV, while for niobium no promotion is necessaryn n4 1stronger M–L bonding upon ionization is also evi- since the ground state configuration is 4d 5s . Thus,

denced from the higher vibrational frequencies in the the bonding difference in these metal clusters isions, as shown in Table 1. To help understand the largely due to the difference in promotion energiesionization effect on the M–L bonding in these required to prepare the metal atoms into appropriateclusters, we performed Mulliken population analysis electron configurations.for some of the clusters and found that in addition to The M–M bonds in the cations are slightlythe covalent contributions, the M–L bonding has stronger than that in the neutrals. This is indicated byconsiderable ionic character due to the combination the frequencies of the M–M stretching vibrationsof the electropositive metals and electronegative (Table 1). For example, for triniobium dicarbide the

21ligands. For example, the calculated orbital overlaps Nb–Nb stretching frequency is 327 cm in Nb C3 221 1between the yttrium and carbon are the same in Y C and 339 cm in Nb C . For yttrium dimer, the3 2 3 2

1 21 21and Y C , indicating that the covalent contributions Y–Y frequency is 185 cm in Y and 197 cm in3 2 21to the Y–C bonds are similar in the neutral and ion. Y . For the other clusters, although experimental2

In contrast, the net charges on the yttrium atom frequencies are not available for comparisons, theincrease from an average of 0.46 to 0.77, while the theoretical results show a similar increase of thenegative charges on the carbon atoms, 20.66, re- M–M stretching frequencies upon ionization.main unchanged. Thus, the stronger M–L bonds inthe ionic clusters are largely due to the enhancementof electrostatic attractions. Similar results were also

4. Conclusionsobtained for triniobium dinitride.

Examination of the metal vibrational frequenciesPFI-ZEKE spectroscopy has been successfully

in Table 1 shows that the niobium vibrations haveapplied to small transition metal clusters in the

the highest frequencies and that the yttrium vibra-absence and presence of simple ligands. The tech-

tions have the lowest. Because the atomic masses ofnique offers the capability to resolve vibrational

Nb, Zr, and Y are very similar, the higher fre-structures in general and rotational structures in

quencies mean stronger metal–metal bonds. Thus,special cases, such as vanadium dimer. Geometries

the strengths of the metal–metal bonding can beand ground electronic states of the neutral and ionic

arranged in the order of Nb–Nb.Zr–Zr.Y–Y inclusters can be determined by combining the PFI-

these ligated clusters. Different bonding strengthsZEKE technique with density functional theory and

among these metals were also found for metal dimersFranck-Condon factor calculations. This synergic

and trimers. For example, the bond dissociationapproach is rather important because currently it is

energies of Nb , Zr , and Y were measured as 5.48,2 2 2 still very difficult to establish reliable structures of3.05, and 1.62 eV, respectively [29,48,49]. The M–M

free transition metal clusters by either experimentalstretching frequency of Nb was measured as 3353 or theoretical technique alone.21 21cm , while that of Zr was measured as 258 cm3

from resonant Raman spectra in argon matrix[50,51]. Morse has discussed the causes for thebonding differences in the metal dimers [48,52]. The Acknowledgementsmain reason for the weak Y–Y bonding is the strong

2 1s-electron repulsion between the 5s 4d ground We thank our collaborators whose names appearstates of the yttrium atoms. To form chemical bonds, on the papers quoted herein. Partial funding of this

2 1at least one of the 5s 4d yttrium atoms must be work was provided by the Network of Centers of1 2promoted to a configuration, such as 5s 4d , to Excellence in Molecular and Interfacial Dynamics,

reduce the Pauli repulsion between the filled-s once one of the 15 Networks of Centers of Ex-


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ZEKE spectroscopy of free transition metal clusters