3706 J. Phys. Chem.

A 1999, 103, 3706-3720

Reaction Dynamics of Zr and Nb with Ethylene

Peter A. Willis, Hans U. Stauffer, Ryan Z. Hinrichs, and H. Floyd Davis*

Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell UniVersity,
Ithaca, New York 14853-1301
ReceiVed: December 8, 1998; In Final Form: March 11, 1999

The reactions of transition metal (M) atoms Zr and Nb with ethylene (C2H4) were studied using the technique
of crossed molecular beams. Angular and velocity distributions of MC2H2 products following H2 elimination
were measured at collision energies between 5 and 23 kcal/mol using electron impact and 157 nm
photoionization mass spectrometry. Photodepletion studies identify that the atomic reactants are predominantly
in their ground electronic states and that the observed MC2H2 products result primarily from reactions of
these ground-state atoms. Center-of-mass product angular distributions derived from the data indicate that
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reactions involve the formation of intermediate complexes having lifetimes longer than their rotational periods.
Product translational energy distributions demonstrate that a large fraction of excess available energy is
channeled into product internal excitation. Wide-angle nonreactive scattering of metal atom reactants following
decay of long-lived MC2H4 association complexes was also observed for both transition metal reactants at
collision energies g 9 kcal/mol, with approximately 36% of the initial translational energy converted into
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

C2H4 internal excitation. At collision energies of e 6 kcal/mol, nonreactive scattering of Zr from ZrC2H4
decay was found to be negligible, whereas this channel was clearly observed for Nb. RRKM modeling of the
competition between decay of MC2H4 complexes back to M + C2H4 and C-H insertion forming HMC2H3
indicates that there exists an adiabatic potential energy barrier for M + C2H4 association in the case of Zr and
that the transition state for this process is tighter than for the analogous process in Nb + C2H4. The barrier
for Zr + C2H4 association is attributed to the repulsive s2 ground state configuration of Zr, whereas for Nb
the s1 ground state configuration results in no barrier for association. The absence of decay of ZrC2H4 back
to Zr + C2H4 at low collision energies indicates that the barrier for C-H insertion forming HZrC2H3 lies
below the barrier for Zr + C2H4 association. This opens up the possibility that direct C-H insertion without
initial ZrC2H4 formation may play an important role.

I. Introduction sections for competing channels are determined as a function

The interaction of transition metal centers with alkenes plays of collision energy. An analysis of resulting data yields a wealth
an important role in a variety of homogeneous and heteroge- of mechanistic information, as well as barrier heights for reaction
neous catalytic processes, such as hydrogenation of unsaturated and bond dissociation energies.
hydrocarbons and polymerization of olefins.1-3 For example, Because of long-range ion-induced dipole forces, potential
Ziegler-Natta catalysis is used to produce more polyethylene energy surfaces (PES) for transition metal ion reactions are
annually than any other organic chemical.1 However, at present, highly attractive.8,11 In the case of neutral transition metal atoms,
the mechanisms governing these processes are still not well interactions occur at a much shorter range and potential energy
understood. One approach toward a greater understanding of barriers are comparable to the available energy. The reaction
these systems is to study model chemical reactions lacking the dynamics and product branching ratios are expected to be very
complicating effects of ligands and solvent.4,5 Ab initio and
sensitive to the topography of the PES.11 Therefore, the
density functional calculations facilitate systematic studies of
interactions of neutral transition metal atoms with hydrocarbon
reactivities across entire rows of bare transition metal atoms,4
as well as the effects of covalent ligands on these reactivities.5 molecules are expected to more closely resemble those in
By studying trends in barrier heights and reaction energetics in transition metal complexes important in homogeneous cataly-
such model systems, theory has begun to provide fundamental sis.11
insight into how electronic configuration and orbital occupancy Neutral transition metal atom reactions with small hydrocar-
control transition metal-hydrocarbon reactivity.4-7 bons have been studied in the gas phase using both flow tube
Extensive studies have been performed on reactions involving techniques11-14 andlaserphotolysis-laserfluorescencemethods.15-17
transition metal cations with small hydrocarbons and other In the flow tube experiments, the metal (M) + hydrocarbon
molecules,8-10 particularly by Armentrout and co-workers, using reactivity was measured at 300 K in 0.5-1.1 Torr of He.11-14
guided ion beam tandem mass spectrometry.9,10 The mass- Metal atoms were created by sputtering from a solid metal
selected transition metal cations are accelerated into a collision
sample or by laser ablation and were thermalized by collisions
cell containing a neutral target gas, and the reaction cross-
with He carrier gas before mixing downstream with hydrocarbon
* To whom correspondence should be addressed: e-mail, hfd1@cornell. gas. By monitoring the depletion of metal atom number density
edu. using laser induced fluorescence (LIF) as a function of
10.1021/jp9846633 CCC: $18.00 © 1999 American Chemical Society
Published on Web 04/24/1999
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3707

hydrocarbon pressure, pseudo-first-order rate constants for M

+ hydrocarbon reactions have been determined.11-13 These rate
constants include contributions from bimolecular elimination
reactions as well as termolecular processes. In nearly all
experiments carried out to date, the chemical reaction products
were not detected, but were inferred by comparison to theoretical
models. Studies of this sort have shown that under low-pressure
conditions in which termolecular processes do not play a major
role, a number of second row transition metal atoms undergo
C-H insertion reactions with ethylene and other hydrocarbons,
ultimately leading to H2 elimination.11-14 Recently, the ZrC2H2
product from the Zr + C2H4 reaction was detected directly using
157 nm photoionization by Wen and co-workers.14 These Figure 1. Reaction coordinate for Zr + ethylene system. Note that
experimental studies have facilitated direct comparison with the barrier for metallacyclopropane formation is inferred from the
theoretical predictions.4,5,12,13,18,19 present work. All other stationary points from ref. 13.
In the laser photolysis-laser fluorescence technique, metal
atoms are produced via multiphoton dissociation (MPD) of an a π-bond, involving back-donation from a metal d orbital to
the empty alkene CdC π* antibonding orbital. This bonding
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appropriate volatile metal complex precursor such as Fe(CO)5.15-17

A tunable laser probes the population of metal atoms by LIF as interaction is optimized for doubly occupied d orbitals.
a function of delay time after the MPD laser. Using this Ab initio calculations indicate that sd hybridization of the
technique, the binding energy of the π-bonded NiC2H4 complex, transition metal center promotes bond formation in the DCD
a theoretical benchmark,20-22 was found to be 35.5 ( 5 kcal/ mechanism.21 However, only certain electron configurations on
the metal allow for sd hybridization, namely, s1dn-1 configura-
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

mol.15b Although thermodynamic quantities are now fairly well-

known for many M-H and M-CH3 systems,9 relatively few tions in which the s and d electrons to be hybridized haVe
other bare transition metal-ligand binding energies have been opposite spins.21a This state, which correlates diabatically to the
determined experimentally. ground state of the complex, is not in general the ground state
of the metal atom, but rather a low-lying, electronically excited,
We have recently begun an experimental program to study
low-spin state. In most cases, the ground state of the metal atom
the reactivity of neutral transition metal atoms with hydrocarbons
(s2dn-2 or high-spin s1dn-1) correlates diabatically to an excited-
under single-collision conditions using the technique of crossed
state MC2H4 complex that may be either attractive or repulsive.
molecular beams.23-25 Mass spectrometry facilitates the unam-
The avoided crossing of these two diabatic curves may lead to
biguous detection of the neutral chemical products from a small adiabatic barrier for association.11
bimolecular reactions at well-defined collision energies. Using B. Zr + C2H4. Ab initio calculations for various stationary
the seeding technique, we are able to study these neutral points along the reaction pathway of Zr + C2H4 f ZrC2H2 +
reactions over a relatively wide range of collision energies. Thus, H2 yield the energetics depicted in Figure 1.13 For transition
even reactions with substantial endoergicity or potential energy metal atoms on the left-hand side of the periodic table, such as
barriers may be studied for direct comparison to theoretical Nb and Zr, the low-spin ground-state MC2H4 complexes have
predictions. Measurements of product velocity and angular been described as “metallacyclopropanes” having a C-C single
distributions are also carried out, providing insight into the bond and two covalent M-C bonds.18 In the case of Zr,
reaction mechanism. This experimental technique also facilitates calculations indicate that the triplet ground-state metallacyclo-
studies of nonreactive scattering events, which provide important propane has a Zr-C2H4 distance of 2.07 Å and a C-C bond
complementary insight into the nature of the bimolecular process length of 1.52 Å.18 This C-C bond length is comparable to
that cannot be obtained using other methods. Here we describe that in ethane (1.54 Å), which is considerably longer than in
a study of the interactions of two early second-row ground- free ethylene (1.34 Å). The ZrC2H4 metallacyclopropane species
state transition metal atoms (Zr and Nb) with the simplest lies at a subtantially lower energy than the high-spin excited-
unsaturated hydrocarbon, ethylene (C2H4). state complex, which is better described as a π-complex with a
A. Formation of M-C2H4 Complexes. Previous experi- shorter C-C bond (1.42 Å) and a relatively long Zr-C2H4
mental studies have established that the second-row transition equilibrium distance (2.39 Å).18 For the purposes of this paper,
metal atoms are more reactive than the first row.11-13 Because when the distinction between the ground-state metallacyclo-
most first-row transition metal atoms have filled 4s orbitals that propane and excited state π-complex is not important to the
are larger than the 3d orbitals, the ground-state dn-2s2 configura- discussion, any intermediate species having four intact C-H
tions of most first-row atoms somewhat resemble noble gas bonds will be denoted by the molecular formula MC2H4.
atoms. When these atoms approach ethylene, large potential Intermediate species resulting from C-H insertion, on the other
barriers give rise to net repulsive interactions. hand, will be denoted HMC2H3 or H2MC2H2.
The interaction of second-row transition metal atoms with A key step in the reaction of transition metal atoms with
ethylene proves more interesting. Here, the 5s and 4d orbitals hydrocarbons involves insertion of the metal into a C-H bond
are comparable in both size and energy, leading to a variety of (shown for the case of Zr in Figure 1).13,19 In reactions of
ground-state orbital occupancies (dn-2s2 for Y, Zr, Tc, and Cd, transition metal atoms with saturated hydrocarbons, such as
dn-1s1 for Nb, Mo, Ru, Rh, and Ag, and dns0 for Pd). The methane (CH4) or ethane (C2H6), insertion is expected to be a
simplest model for metal-ethylene bonding is the Dewar- direct process without significant participation of the very
Chatt-Duncanson (DCD) model,26 involving two simultaneous weakly bound M-CH4 or M-C2H6 σ-complexes.13 In reactions
bonding interactions. The first bond, a σ-bond, involves transfer with unsaturated hydrocarbons such as ethylene, on the other
of electron density from the alkene CdC π-orbital to symmetry- hand, the MC2H4 complex represents a deep minimum on the
allowed unoccupied orbitals of the metal. This is favored by s1 potential energy surface. Insertion of a transition metal center
or s0 orbital occupancy on the metal atom. The second bond is into the C-H bond of a hydrocarbon molecule is favorable for
 3708 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.

Figure 2. Reaction coordinate for Nb + ethylene system, adapted from

ref 13.

low-spin electronic configurations of the metal. This is because

formation of two covalent bonds in the insertion intermediate
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requires participation of two electrons from the metal atom

Figure 3. Cross-section of experimental apparatus in the plane of the
(often involving sd hybridization) which are spin paired. This
atomic and molecular beams.
low-spin requirement is ubiquitous in insertion reactions, and
explains, for instance, why O(1D) but not O(3P) readily inserts dehydrogenation products is low-spin, which in this case is of
into H2 or CH4.27 Thus for Zr, the reaction coordinate leading quartet multiplicity.13,19 However, unlike the Zr case, because
to C-H insertion has triplet multiplicity, as does the metalla- the ground state of Nb is high-spin, intersystem crossing is
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

cyclopropane complex. Consequently, C-H bond insertion may required to access the insertion intermediate. Although diabatic
be preceded by formation of the metallacyclopropane complex. curves of different spin multiplicities are more weakly coupled
However, according to calculations,19 the optimized transition than those of the same multiplicity, for 4d series atoms, spin-
state for C-H insertion has an M-C-C bond angle greater orbit interactions can effectively couple the two states. Calcula-
than 120°. This transition state, calculated to lie 1.8 kcal/mol tions suggest that when the system accesses the quartet reaction
above the ground-state reactants, lies quite far from the coordinate via a curve crossing, there are no potential energy
equilibrium geometry of the MC2H4 complex which has an barriers to dehydrogenation above the Nb(a6D) + C2H4 asymp-
M-C-C angle considerably smaller than 90° (Figure 1).13,18,19 tote (Figure 2). Carroll and co-workers observed that at room
Thus the C-H bond insertion step in the Zr + C2H4 reaction temperature, ground-state Nb (a6D1/2) reactant is depleted by
may also occur directly, without first accessing the deep well ethylene at approximately the gas kinetic limit under low-
associated with the M-C2H4 complex. pressure conditions where termolecular processes should be
Following C-H bond insertion, a second intramolecular negligible.11,13 Thus, Nb is five times more reactive than Zr at
rearrangement may lead to formation of an H2MC2H2 interme- an average collision energy of 0.9 kcal/mol.
diate.13 This species may be either a metal-acetylene type
II. Experiment
complex (Figure 1) or a metal-vinylidene complex (H2Md
CdCH2). To date, ab initio calculations have focused only on All of the experiments described in this paper were performed
the metal-acetylene structure.13 Either intermediate can elimi- using a newly constructed universal crossed molecular beams
nate molecular hydrogen. Because potential energy barriers for apparatus (Figure 3).23-25 The apparatus facilitates production
the reverse process (insertion of transition metal centers into of two supersonic molecular beams that intersect at 90 degrees
H2) are generally small or nonexistent,4a,22 no barrier in excess in the main vacuum chamber. The transition metal atomic beam
of the reaction endoergicity for H2 elimination is indicated in is produced by laser ablation30 from a 0.25 in. diameter rod
Figure 1. The reaction Zr + C2H4 f ZrC2 + 2H2 is endothermic (Alfa 99.9%) that is rotated and translated in front of a
by 47 kcal/mol and thus cannot occur at the collision energies piezoelectric pulsed valve31 delivering an inert carrier gas. The
used in our experiments.28,29 532 nm output (15 mJ, 7 ns, 30 Hz) from a Nd:YAG laser
Using a fast-flow reactor, Carroll and co-workers observed (Continuum Surelite 2) is focused to a 1 mm diameter spot on
that ground-state Zr (a3F2) reactant was depleted by ethylene at the surface of the metal rod. The ablated metal beam, entrained
room temperature on one in every five hard-sphere collisions in carrier gas, passes through a skimmer and then through a
under low-pressure conditions where collisional stabilization of second defining aperture into the main chamber. A mechanical
ZrC2H4 complexes should be negligible.11,13 More recently, the chopper wheel (9 in. diameter, 0.5 mm slot) is spun synchro-
ZrC2H2 reaction product was observed via 157 nm photoion- nously at 210 Hz with the vaporization laser and pulsed valve
ization, mass-selection, and ion detection.14 for additional temporal resolution of the metal atom beam pulse.
C. Nb + C2H4. Calculations show that for the Nb/ethylene The secondary molecular beam source consists of a second
system (Figure 2), the two most stable complexes are a low- piezoelectrically actuated pulsed nozzle which delivers C2H4
spin 4B1 ground-state metallacyclopropane (which correlates to (Matheson, polymer grade, 99.9%), either neat or 20% in
excited quartet atomic states) and a high-spin 6A1 excited state helium.
π-complex (which correlates to the ground sextet atomic states). The entire source assembly can be rotated in a vertical plane
Unlike the case for Zr, these two complexes are very similar in with respect to a fixed detector (Figure 3).25 This is ac-
energy, both being bound by approximately 36 kcal/mol with complished by supporting the source assembly on two rotatable
respect to ground-state reactants.13,18 The equilibrium Nb- bearings with associated differentially pumped 30 in. diameter
ethylene distances are calculated to be 2.07 Å for the 4B1 ground Teflon spring-loaded dynamic seals. In this configuration, a
state and 2.34 Å for the excited 6A1 state.18 pressure (P) of < 2 × 10-6 Torr is maintained in the main
As in the case of Zr, the reaction coordinate leading to chamber of the apparatus with both beams running. Because
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3709

the source is rotatable, it is necessary to continually maintain

alignment of the vaporization laser on the metallic sample rod.
This is accomplished by propagating the ablation laser beam
along the axis of rotation of the source and then periscoping
this beam into the source region using a pair of mirrors mounted
on the rotating flange. In some cases, optical pumping of the
resulting metal atom beam is also performed upstream of the
collision region using a second rotatable periscope assembly.23
The fixed detector unit is triply differentially pumped and
equipped with electron impact ionizer, mass filter, and ion-
counting electronics.25,32 For all experiments reported here, the
mass spectrometer was operated at unit mass resolution. Because
the detector is fixed in space, it is possible to introduce laser
light into the ionization region of the mass spectrometer, which
is held at P e 2 × 10-10 Torr during the experiment. This allows
for ionization of neutral atomic species via resonance enhanced
multiphoton ionization (REMPI), as well as ionization of most Figure 4. Cross-section of the experimental apparatus (with source at
zero degree angular position) in plane of detection axis, perpendicular
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transition metal-containing species using 157 nm VUV excimer

to molecular beam source.
radiation. Product detection using photoionization methods
proves especially useful, leading to greatly increased sensitivity
levels over conventional electron-impact detection. A detailed
account of this detection method is described elsewhere.25
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

Briefly, the ionization laser delay is scanned relative to a time

zero for reaction, defined by the chopper wheel, and total ionized
products are mass-selected and counted as a function of
ionization laser delay to obtain a time-of-flight (TOF) spectrum
at a given angle. Both photoionization and conventional electron
impact ionization methods were employed in these experiments.
The data analysis was performed using a Windows-based
analysis program written at Cornell for use on a PC.33 Velocity
distributions of reactant beams were first measured by sampling
the beams directly on-axis through a pinhole aperture in the
front of the mass spectrometer. Using these distributions, as
well as the relevant instrumental parameters for the apparatus,
the beam velocities and speed ratios of the reactant beams were
determined. To determine the product translational energy and
angular distributions in the center-of-mass (CM) reference frame,
a forward convolution technique was employed.33,34 This
forward convolution assumes a separable CM translational
energy distribution, P(E), and CM angular distribution, T(Θ),
in calculating the center-of-mass product flux distribution, ICM-
(Θ,E) ) P(E) × T(Θ). The program accepts as inputs trial
distributions for P(E) and T(Θ), measured beam velocities and
speed ratios, known collision geometry, detector aperture sizes,
etc., and then calculates laboratory angular distributions and Figure 5. Fluorescence excitation spectrum of Zr beam. Peaks are
TOF spectra based on calculated differential cross-sections in labeled by the lower spin-orbit electronic state.35,36
the laboratory frame of reference, ILAB(θ,V), where V is the
(i.e., laser “A” in Figure 4; Scanmate 2 circulating Pyridine-1
magnitude of the detected particle velocity in the laboratory
dye) at the interaction region. The fluorescence from the laser
frame. These laboratory-based quantities are determined from
beam interaction region was imaged onto a photomultiplier tube
the calculated center-of-mass differential cross-sections ICM(Θ,u)
(PMT) via a telescope, while the excitation laser wavelength
using the Jacobian relation ILAB(θ,V) ) V2/u2 × ICM(Θ,u), where
was scanned. The resulting fluorescence excitation spectrum of
u is the magnitude of the velocity in the center-of-mass frame
the Zr beam is shown in Figure 5. The atomic symbols shown
of reference. The calculated TOF and angular distributions are
in Figure 5 correspond to the lower electronic state assigned to
compared to the experimental ones, and the input P(E) and T(Θ)
each transition. Clearly, most peaks originate from excitation
are then varied until optimal agreement between the simulated
out of spin-orbit levels of the ground Zr a3F electronic state.
and experimental data is observed.
It is notable that no peaks corresponding to well-known atomic
transitions from higher metastable states, such as the a3P or a1D
III. Results and Analysis
states,35,36 were present. For example, the 345.69 nm (x3S01 r
A. Characterization of Zr Atomic Beam. The first stage in a3P2), 356.99 nm (x3S01 r a1D2), and 348.40 nm (w1F04 r
our investigation of the Zr + C2H4 system involved the a1G4) transitions, with gf ) 0.33, 0.39, and 0.89, respectively,
characterization of electronic state populations present in the where f is the transition oscillator strength and g is the measured
atomic Zr beam. Figure 4 schematically displays the experi- degeneracy of the excited state,36 were not observed. Yet, the
mental configuration used. The Zr beam (in He carrier gas) was weaker 359.27 nm (x3G03 r a3F3) transition (gf ) 0.034) was
crossed by the frequency-doubled output of a tunable dye laser clearly observed.
 3710 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.

TABLE 1. Experimental Conditions for Zr + C2H4 Studies

Zr beam carrier gas C2H4 gas mixture mean collision
mixture composition composition energy (kcal/mol)
pure Ne pure C2H4 5.9
70% Ne/30% He 20% C2H4/80% He 9.1
13% Ne/87% He 20% C2H4/80% He 14.0
50% H2/50%He 20% C2H4/80% He 23.1
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Figure 6. Zr TOF spectra at 0° recorded using electron impact

ionization and 1+1 REMPI (laser “B” in Figure 4). Closed circles
denote TOF when 1+1 REMPI depletion laser (laser “A” in Figure 4)
is off; open circles correspond to spectra when depletion laser is on.
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

Temporal shift between electron impact and REMPI TOF is due to

slightly different flight distances in each case.

To provide quantitative insight into the composition of the

Zr atomic beam, a number of photodepletion studies were
carried out. The experimental arrangement is also shown in
Figure 4. In these experiments, 1+1 REMPI was used to ionize Figure 7. Newton diagram in velocity space for Zr + ethylene at 14.0
kcal/mol. Lab angle θ ) 0° defined as axis of Zr beam. Velocity of
a selected spin-orbit level of Zr slightly upstream of the
the center of mass of the system (at θcm ) 11°) is indicated by a vector.
interaction region (laser “A”). For ionization of the ground Angles in the center-of-mass frame of reference, Θ ) 0°, 90°, and
atomic 3FJ spin-orbit states, the following wavelengths were 180°, are also indicated.
used: 352.06 nm (x3G03 r a3F2), 354.87 nm (x3G04 r a3F3),
and 360.22 nm (x3G05 r a3F4).35,36 Ionization leads to deple- B. Zr + C2H4 Reaction at 14.0 kcal/mol. We have studied
tion of the measured neutral beam intensity because positive the Zr + C2H4 reaction at several collision energies, as
ions are unable to enter the detector because of a large positive summarized in Table 1. For each collision energy, data sets were
bias (+100 V) applied to the front ion lens. The fractional recorded utilizing electron impact ionization as well as VUV
depletion of a given spin-orbit level due to ionization by laser photoionization for product detection. Naturally occurring Zr
“A” was determined by measuring the depletion of Zr beam exists as 51.5% 90Zr, 11.2% 91Zr, 17.2% 92Zr, 17.4% 94Zr, and
intensity at the detector, again by 1+1 REMPI using a second 2.8% 96Zr.37 For all experiments, the lightest and most abundant
laser in the ionization region of the mass spectrometer (laser Zr isotope was monitored at m/e ) 90. Our observation of
“B” of Figure 4). By comparing the fractional depletion of a 90ZrC H (m/e ) 116) is in agreement with the recent observa-
2 2
given spin-orbit state (measured by 1+1 REMPI at the detector) tions of this channel by Wen and co-workers at an average
to the fractional depletion of the entire beam (measured by collision energy of 0.9 kcal/mol.14
electron impact ionization at the detector), we are able to The results from an intermediate collision energy (Ecoll), of
determine the absolute beam composition. For example, using 14.0 kcal/mol will first be presented in detail, the lower and
relatively high laser “A” pulse energies (4 mJ), we were able higher collision energy data being discussed later. The measured
to photodeplete a large fraction (63%) of the ground spin-orbit peak beam velocities (Vpk) and full width at half-maximum
state, 3F2, present in the beam (Figure 6). While maintaining (fwhm) values were, respectively, 1876 and 263 m/s for the Zr
the same photodepletion laser intensity, we also measured the beam, and 1208 and 138 m/s for the C2H4 beam. These
total Zr beam photodepletion using electron impact mass measured peak beam velocities and the calculated exothermic-
spectrometry, and obtained a depletion of 34%. Because ity13 of the reactive channel Zr + C2H4 f ZrC2H2 + H2 (∆E
depletion of 63% of the ground spin-orbit level led to 34% ) -18.5 kcal/mol) yield the Newton diagram38 in velocity space
depletion of the total beam intensity, we conclude that 53% of shown in Figure 7. The Newton diagram facilitates the
the beam is in the ground spin-orbit (a3F2) level of the ground transformation between the laboratory and center-of-mass frames
electronic state. Depletion TOFs for this state utilizing both of reference.38 The two circles in the figure denote the maximum
electron impact ionization and 1+1 REMPI (via laser “B”) are velocities of ZrC2H2 and Zr in the CM frame based on energy
shown in Figure 6. Using this photodepletion technique for the and momentum conservation. As indicated by the circles, the
other spin-orbit states of the ground electronic state, the Zr ZrC2H2 products are constrained to appear at laboratory angles
beam was found to be comprised of 53((10)% 3F2, 27((2)% (θ) ranging from 4° to 19°, where θ ) 0° is defined as the axis
3F , and 5((4)% 3F . (Uncertainties quoted refer to a 1σ of the Zr beam. The nonreactively scattered Zr atoms, on the
3 4
deviation in a set of 3 replicate measurements.) These measure- other hand, may appear over a wider range of laboratory angles,
ments account for 85((11)% of the total Zr population. The ranging from θ ) -10° to θ ) 34°.
results of these studies did not change significantly when Product 90ZrC2H2 TOF spectra recorded at m/e ) 116 using
different carrier gases were used. electron impact ionization over the angular range of 9° to 15°
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3711

Figure 8. ZrC2H2 product TOF spectra (Ecoll ) 13.7 kcal/mol) recorded Figure 10. ZrC2H2 laboratory angular distribution at Ecoll ) 14.0 kcal/
at several laboratory angles using electron impact ionization detection. mol. Lines represent simulation of distribution using T(θ) and P(E) in
Each TOF corresponds to 24 000 laser shots. Figure 11. Solid line corresponds to best simulation of data. Dashed
lines represent a range of acceptable fits.
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Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

Figure 9. ZrC2H2 product TOF spectra (Ecoll ) 14.0 kcal/mol) recorded

at several laboratory angles using 157 nm photoionization detection.

are shown in Figure 8. Each TOF shown represents 24 000 laser

shots, corresponding to 13.3 min data acquisition time. Product Figure 11. Center of mass distributions used for simulation of ZrC2H2
TOF spectra recorded using 157 nm photoionization are shown reactive signal at Ecoll )14.0 kcal/mol. Solid line represents “best fit”
with uncertainties shown by dashed lines.
in Figure 9. Note that the arrival times are slightly earlier than
in Figure 8. This is due to the somewhat shorter flight distance this laboratory distribution from varying how far the P(E) peaks
to the photoionization region as well as slightly greater beam away from zero is demonstrated in Figure 12. Note that the
velocities used to record the data shown in Figure 9. The best agreement between the experimental data and experimental
photoionization TOFs have a much better signal-to-noise ratio fit is obtained using the P(E) shown as a solid line in Figures
with essentially zero background, although each TOF was 11 and 12. As indicated in Figure 13, the laboratory angular
acquired in only 2550 laser shots (85 s of real time). The distribution is not properly simulated using P(E)s having
laboratory angular distribution of ZrC2H2 products, obtained by substantially different shapes from the optimum P(E), shown
integrating the TOFs recorded via photoionization in one-degree again in the upper panel. Most of the available energy is
laboratory angle increments, is shown in Figure 10. therefore channeled into the internal energies of the product
The solid lines shown in Figures 8-10 are the simulated ZrC2H2 and H2 molecules. The forward-backward symmetric
TOFs (Figures 8 and 9) and laboratory angular distribution nature of the CM angular distribution suggests that the reaction
(Figure 10) resulting from the input P(E) and T(Θ) shown in proceeds via one or more intermediates having lifetimes
Figure 11. The best match of the simulation to the data indicates exceeding their rotational periods.34,38
a P(E) that peaks slightly away from zero, extending out to the C. Identity of the Reactive Zr State. To identify the reactive
calculated maximum available energy of approximately 30 kcal/ state(s) of Zr, a series of photodepletion studies were carried
mol. The calculated laboratory angular distributions are more out. In these experiments, the ZrC2H2 products were monitored
sensitive to the form of the P(E) than the simulations of at the CM angle while the Zr reactant beam was state-selectively
individual TOF spectra. photodepleted by 1+1 REMPI, slightly upstream (8 mm) of
The dashed lines in the P(E) of Figure 11 indicate the range the reaction volume (laser “A” in Figure 4). If the photodepleted
of distributions that give satisfactory simulation of the data. The state is reactive, a decrease in ZrC2H2 product intensity should
corresponding laboratory angular distributions are indicated as be observed. The fractional depletion of the product intensity
dashed lines in Figure 10. The laboratory angular distribution provides information about the relative contribution of a given
(Figure 10) drops off sharply and in a symmetric fashion away state to the total reactive signal. In some experiments, a strong
from the center of mass of the system (θcm ∼ 11°) which is electric field was used to extract the resulting ions before they
consistent with a P(E) that peaks close to zero. The effect upon crossed the molecular beam. No difference was seen in the
 3712 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.
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Figure 14. Photodepletion spectra of reactant Zr beam (top panel)

and resulting ZrC2H2 signal at θ ) 13° (bottom panel). Open circles
correspond to 1+1 REMPI depletion laser on (laser “A” in Figure 6);
closed circles are for depletion laser off.
Figure 12. The upper panel shows the “best fit” P(E) and two alternate
P(E)s having peaks at higher and lower energies. Laboratory angular
distributions resulting from these P(E)s are shown in bottom panel.
of VUV photoionization, the results presented here were carried
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

out using this method (i.e., using laser “C” in Figure 4).
However, photodepletion of reactive signal was also detected
using electron impact ionization.
The depletion of reactive signal (m/e ) 116) resulting from
crossed beams experiments in which one of the ground spin-
orbit states was depleted was found to be comparable in
magnitude to the total depletion of the corresponding reactant
Zr beam (measured by electron impact ionization). TOF spectra
displaying depletion of reactive signal resulting from the 3F2
ground spin-orbit state are given in the bottom panel of Figure
14. This verifies that the observed reactive signal results
predominantly from reactions of ground state Zr atoms.
D. Nonreactive Zr + C2H4 Scattering at 14.0 kcal/mol.
The nonreactive channel, Zr + C2H4 f Zr + C2H4, in which
Zr reactants are reformed after collision and possible association
with ethylene, was also examined. Collisions that result in the
formation of ZrC2H4 complexes having lifetimes longer than a
rotational period before subsequent reformation of reactants are
expected to produce Zr signal at large laboratory angles,
corresponding to CM angles, Θ, near 180° (Figure 7).34 Zr atom
(m/e ) 90) TOF spectra at laboratory angles of 15°, 20°, and
25° (recorded using 157 nm photoionization) are shown in
Figure 15. The large, slow peak in the TOF at θ ) 15°,
occurring at t ) 175 µs, is due primarily to fragmentation of
product ZrC2H2 in the mass spectrometer. This contribution to
the TOF is simulated using the reactive P(E) and T(Θ) discussed
above (Figure 11). Fragmentation of ZrC2H2 to form Zr is also
observed at θ ) 20°, although only very weakly, because at
this angle, the extreme edge of the reactive Newton circle
(Figure 7) is being sampled. The solid lines in Figure 15 are
thus comprised of two components (shown as dashed lines):
fragmentation of the reactive channel and the nonreactive
channel, which was best simulated using the P(E) and T(Θ)
Figure 13. Simulation of ZrC2H2 laboratory angular distribution. Top shown in Figure 16. The dashed lines in Figure 16 represent
panel shows simulation using optimum P(E). Lower panels show the range of P(E)s that are deemed to adequately model the
simulations using different P(E) distributions which lead to poorer nonreactive signal.
simulation of angular distribution. As expected from the Newton diagram (Figure 7), the Zr TOF
observed TOF data when this field was applied. This was recorded at θ ) 25° has no contribution from fragmentation of
expected because metal cations or positively charged reaction ZrC2H4 reaction products. Two distinct peaks are observed,
products are unable to enter the mass spectrometer because of which correspond to the fast and slow edges of the nonreactive
a large applied positive DC field at the entrance to the mass Zr Newton circle. The slower peak, which corresponds to very
spectrometer ion lenses. Owing to the much greater sensitivity large CM angles, Θ, is more intense than the faster peak. This
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3713
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Figure 15. Nonreactively scattered Zr atom TOF spectra (Ecoll ) 14.0

kcal/mol).
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

Figure 17. Fluorescence excitation spectrum of Nb atomic beam

seeded in 87% He/13% Ne. Peaks are labeled by the lower spin-orbit
electronic state.35,36

reactive scattering data at these three collision energies were

nearly identical to the best fit T(Θ) for Ecoll ) 14.0 kcal/mol,
shown in Figure 11. The P(E)s found to best simulate the data
were of similar shape to the P(E) found to best simulate the
14.0 kcal/mol data, although they were stretched (higher
Figure 16. CM distributions for simulation of nonreactive signal (Ecoll collision energy) or compressed (lower collision energy) because
) 14.0 kcal/mol). Dashed lines in P(E) represent uncertainty in of the differing amounts of total energy available at the different
simulation. collision energies.
indicates that T(Θ) is sharply peaked at Θ ) 180°, i.e., backward For the two highest collision energies, a single T(Θ) was used
scattered in the CM frame relative to the incoming Zr atom for simulation of both nonreactive scattering data sets. At all
(Figure 7). The T(Θ) which was found to best simulate the collision energies, the P(E)s used for best simulation of the data
nonreactive Zr scattering (Figure 16) exhibits this feature. Such were the same shape, although stretched or compressed ap-
sharply peaked wide angle nonreactive scattering indicates the propriately. However, as discussed in detail in section III. H.,
formation of a long-lived collision complex that subsequently the second (slower) Zr peak corresponding to sharp backscat-
falls apart to reform reactants.34,38 Although near-zero impact tering at Θ ) 180°was not observed at the two lowest collision
parameter collisions (b ≈ 0) can also produce signal at Θ ) energies studied, i.e., at Ecoll e 9.1 kcal/mol.
180°, such events are relatively improbable (πb2 f 0 as bf 0) F. LIF Study of Nb Beam and Identity of Reactive State.
and would not lead to a sharp peak at Θ ) 180°. A The sextet spin multiplicity of the Nb ground state makes an
corresponding peak at Θ ) 0° is also expected from this exhaustive population analysis of the Nb beam more difficult
nonreactive collision complex channel; however, this peak than for the case of Zr (which has a triplet ground state). A
cannot be experimentally distinguished from the directly forward fluorescence excitation spectrum (Figure 17) of the Nb beam
scattered Zr atoms that result from large impact parameter (He carrier gas seeded with 13% Ne) was acquired in the same
collisions. The recoil translational energy distribution, P(E), has way as described for the Zr spectrum (Figure 5), although for
an average value, E′trans, of 8.9 ((1.1) kcal/mole. Thus, reactants the longest wavelengths in the spectrum, Pyridine-2 dye was
are reformed with approximately 36% of the initial translational used in the Scanmate 2 dye laser. Although it is possible to
energy appearing as internal excitation of ethylene. assign certain peaks in the spectrum to metastable electronic
E. Effect of Collision Energy on Zr + C2H4. The Zr + states, such as a4F, a4P, or a2D,35,36 the total population of these
C2H4 system was studied at three other collision energies: 5.9, states was very small.
9.1, and 23.1 kcal/mol. Product ZrC2H2 was clearly observed To determine the identity of the reactive state, a photodeple-
at all collision energies. The T(Θ)s found to best simulate the tion study similar to that described for the Zr system was
 3714 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.
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Figure 18. (a) The peak Nb atomic beam intensity at 0° as a function

of 1+1 REMPI depletion laser (laser “A” in Figure 4) delay. At optimal Figure 19. NbC2H2 product TOF spectra (13.5 kcal/mol) recorded at
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

delay, 21% of the Nb beam is depleted. (b) NbC2H2 reactive signal at several laboratory angles using 157 nm photoionization detection. Solid
12° with the depletion laser on (open circles) and off (closed circles). lines are simulations using CM functions given in Figure 21.
With depletion laser set at optimal delay, 22% of the reactive signal is
depleted.

TABLE 2. Experiment Conditions for Nb + C2H4 Studies

Nb beam carrier gas C2H4 gas mixture mean collision
mixture composition composition energy (kcal/mol)
pure Ar pure C2H4 4.8
pure Ne pure C2H4 6.2
70% Ne/30% He 20% C2H4/80% He 9.1
13% Ne/87% He 20% C2H4/80% He 13.5
50% H2/50% He 20% C2H4/80% He 23.2

performed in which two atomic ground spin-orbit states were

ionized via 1+1 REMPI using a single laser. The transitions Figure 20. NbC2H2 laboratory angular distribution (13.5 kcal/mol data
used were 356.35 nm (zS03/2 r a6D3/2) and 356.36 nm (y4P05/2 set). Solid line represents “best fit” simulation using solid line P(E)
r a6D5/2),35 both of which could be accessed simultaneously shown in Figure 21. Dashed lines correspond to alternate P(E)
by a single dye laser. These transitions were chosen because distributions also shown in Figure 21.
1+1 REMPI of Nb was found to be much less efficient than
The solid lines shown in Figures 19 and 20 are the simulated
for Zr, presumably because of a smaller cross-section for the
TOFs and laboratory angular distribution resulting from the input
ionization step. The results are illustrated in Figure 18. The upper
P(E) and T(Θ) of Figure 21. The dashed lines shown in the
panel illustrates the peak Nb beam intensity as a function of
figure represent the range of acceptable P(E)s that simulate the
depletion laser delay. At the optimal depletion laser delay, it
observed data, giving rise to the dashed angular distributions
was possible to deplete a total of 21((3)% of the total beam
of Figure 20. The similarity between these input functions and
population by ionizing these two spin-orbit states. The lower
those used to simulate the Zr reactive signal suggests that, again,
panel indicates a 22((3)% depletion of NbC2H2 product signal
most of the available energy is channeled into internal energy
at θ ) 11° resulting from this optimal delay. This result of the NbC2H2 + H2 products which are formed from decay of
demonstrates that the predominant reactive state is the ground one or more long-lived intermediates.
a6D state. Nonreactively scattered Nb atom TOFs for the intermediate
G. Nb + C2H4 at 13.5 kcal/mol. As was seen for the Zr collision energy of 13.5 kcal/mol (detected via 157 nm photo-
reactions studied, dehydrogenation products (i.e., NbC2H2, m/e ionization) at laboratory angles of 15°, 20°, 25°, and 30° are
) 119) were observed at all collision energies (Table 2). For shown in Figure 22. The P(E) and T(Θ) used to simulate the
the intermediate collision energy of 13.5 kcal/mol, the measured data (Figure 23) are qualitatively quite similar to those found
peak beam velocities (Vpk) and fwhm values were, respectively, for Zr at Ecoll ) 14.0 kcal/mol. The T(Θ) indicates that a
1890 and 228 m/s for the Nb beam and 1208 and 138 m/s for substantial fraction of Nb atoms are strongly backward scattered
the C2H4 beam. The Newton diagram for this system is very in the CM frame relative to the incoming Nb reactant.
similar to that of the corresponding Zr system (Figure 7), H. Effect of Translational Energy on Nb and Zr Collisions
although the exothermicity has been calculated13 to be slightly with C2H4. As displayed in Table 2, the Nb + C2H4 reaction
less (14.4 kcal/mol), giving rise to a slightly smaller NbC2H2 was also studied at a range of collision energies. As was the
Newton circle. Recorded NbC2H2 product data (using 157 nm case in the Zr system, reactive dehydrogenation products are
photoionization) are displayed as TOF spectra (Figure 19) and clearly observed at all collision energies. For all data sets, the
in the lab angular distribution (Figure 20). T(Θ) resulting in the best simulation of reactive signal does
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3715
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Figure 21. CM distributions used for simulation of NbC2H2 reactive Figure 23. P(E) and T(Θ) for simulation of Nb nonreactive signal
signal from 13.5 kcal/mol data set. Solid line P(E) represents “best (13.5 kcal/mol). Dashed lines in P(E) represent uncertainty in simula-
tion.
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

fit” and dashed lines indicate uncertainties.

signal-to-noise ratio and to remove any contribution from

fragmentation of ZrC2H2 products, the wide-angle Zr TOF
spectra were also taken using 1+1 REMPI (λ ) 352.06 nm) to
detect the ground-state Zr a3F2 atoms at the detector. The
Newton diagram shown in velocity space schematically repre-
sents the nonreactive scattering of Zr and Nb at Ecoll ≈ 14 kcal/
mol. Note that the fast peak corresponds to Θ ≈ 100°, while
the slow peak corresponds to Θ ≈ 180°. Experimental Nb and
Zr TOF spectra at Ecoll ≈ 14 kcal/mol, taken at θ ) 25°, are
shown in the top panel. At 14 kcal/mol, the Nb and Zr TOF
spectra are similar, with two peaks clearly evident. The lower
panels show Zr and Nb TOF spectra taken at analogous angles
for Ecoll ≈ 9 and 6 kcal/mol. For Nb, the two peaks are observed
down to the lowest collision energy studied. However, for Zr,
at Ecoll ) 9.1 kcal/mol the slower peak is very weak and at 5.8
kcal/mol it is absent. We conclude that at low collision energies,
the sharp backscattering (Θ ) 180°) of Zr atoms resulting from
decay of long-lived complexes is absent.
We have also compared the absolute reactivities of the two
atoms with ethylene. For each atom, the total MC2H2 product
flux was normalized to the reactant atomic beam intensity at
each collision energy studied. In this way, the ratio of the
reactivity of Zr to Nb as a function of collision energy was
Figure 22. Nonreactively scattered Nb atom TOF spectra at 13.5 kcal/
mol. Solid line represents simulation of data using the CM distributions
determined. As displayed in Figure 25, the reactivity of Zr
shown in Figure 23. Contribution to 15° TOF at t ) 175 µs is due to increases relative to that of Nb as the collision energy is
fragmentation of NbC2H2 upon 157 nm photoionization. increased.

not change as a function of collision energy. The T(Θ)s for IV. Discussion
best simulation of nonreactively scattered Nb atoms are also A. Angular Momentum in Nonreactive Scattering. Con-
found to be quite similar for all data sets, sharply peaking at Θ servation of angular momentum through the nonreactive inelastic
) 180° at all collision energies studied. The resulting P(E)s collision is represented by eq 1:
for best simulations of data (reactive and nonreactive) are found
to be stretched or compressed proportionately with increasing L + J ) J* ) L′ + J′ (1)
or decreasing collision energy supplied.
Figure 24 shows the effect of collision energy on the wide- where J and J′ represent the rotational angular momenta of the
angle scattering of Zr and Nb atoms off of C2H4. At all three initial reactant and reformed reactant molecules, respectively.
collision energies shown, TOFs were recorded at laboratory L and L′ are the relative orbital angular momenta of the colliding
angles (θ ) 25° or 30°) where significant backward scattering and recoiling bodies, and J* is the angular momentum of the
in the CM frame (Θ ) 180°) relative to the incoming metal intermediate complex. The efficient rotational cooling of the
atom from decay of long-lived complexes should be evidenced supersonic expansion will leave ethylene with very little average
by an intense slower peak in the TOF spectra. To improve the rotational angular momentum (J < 5p).39 For a colliding pair,
 3716 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.

Figure 25. Ratio of absolute reactivities of Zr to Nb with ethylene as

a function of collision energy. Error bars represent 1σ deviation in a
set of three replicate measurements.

The radial distance between the Nb + C2H4 pair is governed

by motion under the influence of an effective potential given
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by eq 4:

L2
Veff ) V(r) + (4)
2µr2
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

Thus, at increasing impact parameters, the magnitude of the

repulsive centrifugal potential (L2/2µr2) begins to exceed the
attractive dispersive potential V(r), leading to a barrier in Veff.
Using this model, the maximum impact parameter bmax capable
of surmounting the resulting centrifugal barrier to association
is given40 by eq 5:

[ ]( ) C6
( ) C6
1/2 1/6 1/6
3
bmax ) ) 1.375 (5)
22/3 Ecoll Ecoll

Hence bmax ) 4.2 Å for the collision energy of Ecoll ) 13.5

kcal/mol. Furthermore, using the measured most probable
relative velocity |v| ) 2243 m/s, eq 2 gives |Lmax| ) |µvbmax|
) 319p.
For long-lived complexes, the shape of the T(Θ) is determined
only by the disposal of angular momentum into the reformed
reactants.34 For systems such as this where Lmax . J, the
statistical complex model34 reveals that the shape of the T(Θ)
is related to a single parameter, X, given by the ratio

|Lmax|
X) (6)
〈M′〉rms
Figure 24. Top: Newton diagram for nonreactive collisions at Ecoll
≈ 14 kcal/mol. Bottom: TOF spectra for Zr and Nb + C2H4 at 14, 9,
and 6 kcal/mol. Note that at 6 kcal/mol, the slower peak disappears in Here, M′ is defined as the projection of J* onto the relative
the Zr system. recoil velocity vector v′ and 〈M′〉rms refers to the root-mean-
the magnitude of the orbital angular momentum (L) is square (rms) average value of M′. For prolate rotors (i.e., Ix )
Iy > Iz) in which the decomposition occurs directly along the
L ) µWb (2) principal axis Iz (v′ || Iz), the rms value of M′ is zero and Xf∞.
where µ is the reduced mass, W is the relative velocity, and b Classically, this results in a T(Θ) with a 1/sin(Θ) form,
the collision impact parameter. To estimate the maximum impact extending to infinity at Θ ) 0° and 180°.34 Decomposition with
parameter that leads to complex formation, we assume a greater rms values of M′ (i.e., smaller values of X), results in a
standard “capture model”.40 Let us examine one particular less sharply peaked T(Θ). A comparison of the T(Θ) used for
system in detail: Nb + C2H4 at 13.5 kcal/mol. The attractive best simulation of our data (Figure 16) to the T(Θ) calculated
long-range interaction potential between the Nb and ethylene from the statistical complex model34 suggests that the Nb +
is approximated by a C6 potential, i.e., C2H4 system decomposes along the principal axis of a prolate
rotor complex with X ) 8((1). Using |Lmax| ) 319p, this yields
C6 〈M′〉rms ) 40 ((5)p. This is consistent with the calculated nearly-
V(r) ) - 6 (3)
r prolate geometry18 of the ground-state NbC2H4 complex, having
with C6 ) 10.6 × 103 Å6 kcal/mole for the Nb/ethylene moments of inertia Ix ) 113 amu‚Å2, Iy ) 95.7 amu‚Å2, and Iz
system.41,42 ) 24.3 amu‚Å2 decomposing to reactant Nb + C2H4 along its
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3717

principal moment of inertia Iz, i.e., along the Nb/CdC bond

axis. Hence a large fraction of the total angular momentum (J*)
in the complex appears as relative orbital angular momentum
of the reformed reactants, L′.
B. The Absence of Zr Nonreactive Scattering at E e 9.1
kcal/mol. As indicated in Figure 24, the difference between
the Nb and Zr nonreactive scattering signal at low collision
energies is quite striking. In the case of Zr at collision energies
of 9.1 and 5.8 kcal/mol, the faster peak in each TOF corresponds
to those scattering events leading to smaller-angle deflection
(Θ ≈ 100°) of Zr atoms in the CM frame of reference. A small
broad tail is also observed at longer times, indicating that some
“direct rebound” collisions of Zr off of C2H4 at small impact
parameters can also be detected at these wider angles. The
important observation is that the sharply backward-scattered
component (Θ ≈ 180°) indicative of long-lived complexes is
relatively weak at 9.1 kcal/mol and is absent at 6.0 kcal/mol.
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This contrasts the observed nonreactive scattering of Nb, which

exhibits sharply backward scattered signal at all collision
energies studied (Figure 24).
The calculated potential energy barriers for C-H insertion
are higher than all subsequent calculated barriers along the
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

reaction coordinate for both the Zr + C2H4 and Nb + C2H4

(Figures 1 and 2). Following C-H insertion, rearrangement and
H2 elimination is very favorable, whereas decay back to M +
C2H4 requires passage back over a relatively tight transition state.
Therefore, the sharply backward-scattered signal observed for
Nb at all collision energies and for Zr at higher collision energies Figure 26. Simplified energy diagram for unimolecular decomposition
is attributed primarily to decay of MC2H4 complexes back to of ZrC2H4 complexes at Ecoll ) 6.0 kcal/mol. Complexes may dissociate
reactants, rather than from decay of HMC2H3 insertion inter- back to reactants (kdiss) or undergo C-H insertion (kinsert). Lower panel
mediates. shows ratio of reaction rate constants for competing channels as function
At Ecoll ) 6.0 kcal/mol, although the reaction M + C2H4 f of Ebarr, defined as the height of the C-H insertion barrier relative to
separated Zr + C2H4 reactants.
MC2H2 + H2 proceeds readily for both Nb and Zr with similar
cross-sections, no significant wide-angle contribution from decay asymptote. The rate constant for C-H bond insertion (kinsert)
of ZrC2H4 complexes back to Zr + C2H4 is observed. Note that was also calculated as a function of the barrier height for
the hard sphere collision cross-sections with ethylene should insertion (Ebarr; see Figure 26). The ratio of the reaction rate
be comparable for both atoms. Our finding that Zr + C2H4 f constants (kdiss/kinsert) was then computed. The geometry and
ZrC2H2 + H2 proceeds readily at low collision energies without 15 vibrational frequencies used for modeling the ZrC2H4
reformation of Zr from ZrC2H4 complexes implies either (1) metallacyclopropane complex were those calculated by Siegbahn
all ZrC2H4 complexes formed at low collision energies proceed and have been reported elsewhere.41 Decay back to reactants
to dehydrogenation products, or (2) ZrC2H4 complexes are not proceeds via a loose transition state, with the Zr atom located
formed at low collision energies and all reactions proceed via at a distance R†(J) from the ethylene molecule. R†(J) was
direct C-H bond insertion. We now explore these two pos- calculated as the position of the maximum in the long-range
sibilities in some detail. effective potential (eq 4) for each orbital angular momentum J
According to the recent electronic structure calculations, the considered. Two of the rotations of the ethylene molecule,
barrier for Zr insertion forming HZrC2H3 lies 1.8 kcal/mol aboVe corresponding to “rocks”, were treated as active rotations, and
the Zr + C2H4 asymptote, whereas the analogous barrier for angular momentum was conserved during dissociation. The
Nb insertion lies 1.3 kcal/mol lower than Nb + C2H4.13 On the vibrations used for the loose transition state were the 12 highest
basis of these C-H insertion barrier heights, it would be frequency vibrations of the complex (which are very similar,
expected that ZrC2H4 complexes should be less likely to undergo but slightly perturbed in comparison to the 12 vibrations of the
C-H insertion than NbC2H4 at low collision energies. Indeed, ethylene molecule), as suggested by Carroll.41 The geometry
Carroll and co-workers find that Zr is considerably less reactive of the tight transition state leading to insertion products has also
than Nb at room temperature.13 Although the Nb reaction been calculated by Seigbahn, although the vibrational frequen-
ultimately requires a spin flip, Carroll’s observation that Nb + cies have not been reported.19 As an estimate of these, the
C2H4 reacts on nearly every gas kinetic collision indicates that vibrational modes of the metallacyclopropane complex were
the crossing to the quartet surface is facile at low collision used, with one of the low-frequency vibrations (corresponding
energies. Therefore, the observation that decay back to reactants to the reaction coordinate) removed. Angular momentum
is seen for Nb but not for Zr at low collision energies is not conservation was also obeyed for the insertion process.
likely to be attributable to a bottleneck for intersystem crossing The results of the RRKM modeling at an energy of 6 kcal/
in the Nb case. mol above the separated Zr + C2H4 reactants are summarized
RRKM calculations43 were undertaken to determine the in Figure 26. Using the ab initio insertion barrier height (Ebarr)
unimolecular reaction rate constant for dissociation of the of +1.8 kcal/mol, the rate constant for dissociation is 2-4 orders
ZrC2H4 metallacyclopropane complex back to reactants (kdiss) of magnitude greater than that for insertion. Clearly, by lowering
assuming no barrier to decay in excess of the Zr + C2H4 the barrier for insertion (i.e., more negative values of Ebarr), the
 3718 J. Phys. Chem. A, Vol. 103, No. 19, 1999 Willis et al.

ratio of dissociation to insertion (kdiss/kinsert) decreases. However,

to reproduce the experimental observations (Figure 24), this ratio
must become smaller than 0.05, requiring the barrier for insertion
to be below -20 kcal/mol. It seems very unlikely that the
calculated value of +1.8 kcal/mol13 could be so grossly in error.
Furthermore, if the barrier for C-H insertion was so low, it
would be difficult to rationalize the abrupt onset of strong wide-
angle Zr nonreactive scattering from decay of complexes back
to reactants at Ecoll g 9 kcal/mol. Hence, it is not possible to
explain the observed lack of backward scattered Zr atoms at
low collision energies using a model involving barrierless
association through a loose transition state for Zr + C2H4. Thus,
we conclude that there exists a barrier leading to ZrC2H4
formation that is not present in the analogous case of NbC2H4
complex formation.
Figure 27. Effective potential for ZrC2H4 association and C-H
Clearly, the inert gaslike s2 ground state electronic configu- insertion as a function of total angular momentum quantum number J,
ration of Zr may lead to a barrier for complex formation that is assuming a 2 kcal/mol association barrier and a C-H insertion transition
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not likely to be present for Nb, having an s1 configuration.11 state at -5 kcal/mol.

As noted by Carroll et al., the height of the barrier for complex
+ C2H4 becomes significant because of the smaller effective
formation (Figure 1) is related to the magnitude of the energy
barrier for this process relative to that for C-H insertion. Similar
spacing between the metal atom ground-state s2 configuration
behavior has been implicated in recent studies of Ni+ + C3H844.
(correlating to an excited state of the complex) and the low-
At large values of J, reaction rate constants for decay back to
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

spin excited state of the metal atom (correlating to the ground-

Ni+ + C3H8 were calculated to greatly exceed those for C-H
state complex).11 Furthermore, as noted in the Introduction, the
or C-C bond insertion.44
ground-state ZrC2H4 complex is actually best described as a
Our RRKM modeling of the Zr + C2H4 system indicates that
metallacyclopropane.13,18 Although several stationary points
the C-H insertion barrier must be lower than the association
along the Zr + C2H4 reaction pathway have been calcu-
barrier. This modeling of the competition between ZrC2H4 decay
lated,13,18,19 the barrier height for formation of ground-state
back to Zr + C2H4 reactants and insertion into the C-H bond
ZrC2H4 from separated Zr + C2H4 has not been calculated
has utilized tight transition states for each process. Since the
explicitly to date. The observation that Zr is removed by C2H4
transition state for dissociation back to Zr + C2H4 is expected
in one out of five gas kinetic collisions at room temperature
to be considerably “looser” than that for C-H insertion, it is
has been taken as supporting evidence for a barrier to reaction
likely that our model overestimates the fraction of complexes
no larger than 2 kcal/mol,11,13,14 but the location of the barrier undergoing C-H insertion. Thus, the energetic difference
along the reaction coordinate has not been determined experi- between the ZrC2H4 association barrier and the C-H insertion
mentally. barrier is likely to be even greater than the 7 kcal/mole difference
We have performed additional RRKM calculations that required to simulate our experimental data using this model.
assumed a barrier of 2 kcal/mol for Zr + C2H4 f ZrC2H4. In Given that the C-H insertion barrier clearly lies below that
this case, the transition state for association was modeled as for association, we expect that certain Zr + C2H4 collision
tight. Since no transition state vibrational frequencies were geometries may lead to direct C-H bond insertion without first
available, they were estimated to be the same as those of the accessing the ZrC2H4 well. It is important to note that our
complex, with the lowest frequency vibration removed. There- RRKM modeling of the Zr + C2H4 system has assumed that
fore, these calculations address only the effects of relative barrier all reactivity occurs through initial formation of ZrC2H4
heights and moments of inertia on kdiss/kinsert. In the absence of complexes prior to C-H insertion. In carrying out the tight
transition state vibrational frequencies, we cannot quantitatively association transition state calculations, we have assumed a
assess the effects of the different vibrational frequencies at the barrier height of 2 kcal/mol, the largest barrier to H2 elimination
respective transition states. In order to reproduce our finding determined in experiments carried out at room temperature by
that there is no decay of ZrC2H4 back to Zr + C2H4 at low Weisshaar and co-workers.11,13,14 The additional possibility exists
collision energies, it is again necessary for the insertion barrier that the barrier to ZrC2H4 complex formation lies even higher
to be lower than the barrier for decay back to reactants. Using than 2 kcal/mol, and most, if not all formation of H2 elimination
a C-H insertion barrier of -5 kcal/mol and a barrier of 2 kcal/ products at low collision energies, including the room temper-
mol for decay back to reactants, kdiss/kinsert ≈ 0.05 at Ecoll ) 6 ature studies, results from direct C-H insertion without initial
kcal/mol. Figure 27 displays the effective centrifugal barriers formation of ZrC2H4 complexes. Unlike in the Nb + ethylene
for various J values, assuming an insertion barrier of -5 kcal/ system, this process is not inhibited by the need for a spin flip,
mol. Note that higher collision energies open up reaction to as both the reaction coordinate and ground state Zr reactant are
larger J values capable of surmounting the centrifugal barrier of triplet spin multiplicity. Indeed, Siegbahn and co-workers
for association. The larger moments of inertia of the association have pointed out that the calculated geometry of the metalla-
transition state (calculated in Figure 27 assuming Zr is located cyclopropane complex differs considerably from the transition
4 Å from C2H4) relative to those of the insertion transition state state geometry for C-H insertion.19 In particular, the metalla-
give rise to smaller centrigual barriers for decay back to cyclopropane complex (of C2ν symmetry) corresponds to a metal
reactants. Thus at low collision energies, provided that the atom lying above the plane of a C2H4 molecule with a
barrier for C-H insertion is below that for dissociation back to considerably lengthened C-C bond and hydrogen atoms
Zr + C2H4, insertion is the dominant channel, in agreement with distorted away from the metal atom (Figure 27).18 The transition
our experimental observations. At the larger values of J state for C-H insertion, on the other hand, has a relatively short
accessible at higher collision energies, dissociation back to Zr CdC bond distance similar to that in free C2H4, with the metal
 Reaction Dynamics of Zr and Nb with Ethylene J. Phys. Chem. A, Vol. 103, No. 19, 1999 3719

atom lying near the plane of C2H4, indicating that no strong rotational periods. Wide-angle inelastic scattering of atomic M
chemical interaction exists between Zr and the C-C π-bond at resulting from the decay of long-lived MC2H4 complexes was
the transition state for C-H insertion.19 Consequently, the height also observed for both transition metal reactants. For the Zr
of the barrier for direct C-H insertion, without initial formation system, this was only observed for Ecoll g 9.1 kcal/mol,
of a metallacyclopropane, is also likely to lie below the indicating that an adiabatic barrier exists for formation of ZrC2H4
asymptotic energy of the Zr + C2H4 reactants. In this regard it complexes. RRKM calculations modeling the competition
is interesting to note that Stoutland and Bergman45 have studied between decay back to Zr + C2H4 reactants and C-H bond
the reaction (η5-C5Me5)(PMe3)Ir + C2H4 in solution. Their insertion require that the insertion barrier be lower than the
results indicated the involvement of a direct insertion reaction barrier for association. Reaction of Zr atoms at low collision
without the initial formation of a complex, as well as a separate energies via initial formation of ZrC2H4 is likely to be hindered
channel forming complexes. Subsequent extended Hückel by this barrier to association. The Nb reaction can occur at low
calculations suggest that the most favorable approach of the collision energies by initial NbC2H4 complex formation without
metal center for insertion is along the H-C bond axis in a barrier above reactants, which facilitates the spin flip necessary
ethylene.46 Further calculations on the Zr + C2H4 system for C-H bond insertion. At increasing energies, Zr becomes
focusing on transition states for direct C-H bond insertion and the more reactive atom as the barrier for complex formation is
insertion starting from ZrC2H4 would be interesting. surmounted. Alternatively, direct C-H insertion without met-
In the case of the Nb reaction, at the lowest studied collision allocyclopropane formation is fully spin-allowed in the Zr +
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energy of 4.8 kcal/mol, decay of complexes is clearly observed. C2H4 reaction and may play an important role. Our finding that
In addition to reforming reactants, these complexes can readily the barrier for C-H insertion must be below that for ZrC2H4
undergo intersystem crossing and then C-H insertion. Direct formation suggests that such a direct mechanism is in fact likely.
C-H bond insertion by Nb is likely to be inhibited by spin Future experiments include a more quantitative determination
conservation. The intersystem crossing necessary for C-H bond of the branching ratios between nonreaction and reaction as a
Publication Date (Web): April 24, 1999 | doi: 10.1021/jp9846633

insertion by Nb is enhanced by multiple recrossings in the region function of collision energy. These studies, together with careful
of the surface crossing for long-lived NbC2H4 complexes. Such modeling, should facilitate a precise determination of the
complex-mediated spin-forbidden processes in bimolecular potential energy barrier for ZrC2H4 complex formation and may
reactions are well-known, for example, Ba + SO2.47 better assess the role of direct C-H insertion.
Comparison of Nb and Zr Reactivity. At 6 kcal/mol, the
reactivities of Nb and Zr are comparable (Figure 25). However, Acknowledgment. This work was supported by a National
there is a clear trend toward greater reactivity of Nb with Science Foundation Faculty Early Career Development Award,
decreasing collision energies. This trend is in agreement with and by an NSF Equipment Grant. Some of the equipment used
the room-temperature flow-tube result of Carroll et al.13 Under in this work was funded by an ONR Young Investigator Award.
the conditions of their experiment, corresponding to a mean Support by the Exxon Eduational Foundation is also gratefully
collision energy of approximately 0.9 kcal/mol, ground state acknowledged. H.S. thanks the Link Foundation for a Graduate
Nb was depleted by ethylene approximately five times more Fellowship. R.H. thanks the Department of Education for a
efficiently than ground-state Zr (i.e., kdiss/kinsert ) 0.2). The Graduate Fellowship. The authors thank B. Carpenter, J.
greater reactivity of Nb at low collision energies is attributable Weisshaar, S. Klippenstein, and P. Wolczanski for valuable
to the absence of any significant barrier above the ground-state discussions and suggestions.
reactants for complex formation, leading to a large capture cross-
section. Because the C-H insertion barrier for Nb lies below References and Notes
the reactants, a substantial fraction of these complexes go on
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