J. Phys. Chem. 1994,98, 11637-11647
11637
Flow Tube Kinetic Study of Mo and Mo2 Reactivity? L. Lian, S. A. Mitchell,* and D. M. Rayner Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Dr., Ottawa, Ontario K I A OR6, Canada Received: January 3, 1994; In Final Form: July 20, 1994@
The reactivity of molybdenum atoms and dimers with respect to H2, Nz, CH4,02, N20, COZ,CO, C2H4, C3H6 (propene), and NH3 in He buffer gas in the pressure range 0.44-8 Torr at room temperature has been investigated by using a flow tube reactor equipped with a laser vaporization source for production of Mo and MOZ. Detection and monitoring of Mo and M02 is by resonance fluorescence excitation. The performance of the flow tube is investigated over a range of operating conditions by studies of several test reactions of Ti and Cr atoms, for which rate constants have been measured in previous work. Factors that contribute to the uncertainty of rate constants measured by using the laser vaporization flow tube reactor are discussed. Molybdenum atoms and dimers show significant differences in reactivity, in particular with respect to adduct formation reactions with rc-acceptor and Lewis base ligands. The possible origins of these differences in features of the valence electronic structures of Mo and M02 are discussed, and the role of repulsive interactions in controlling reactivity is emphasized. In view of parallels with coinage metal atoms and dimers, generalizations of reactivity differences between transition metal atoms and dimers are suggested. Analysis of kinetic data for Mo C2H4 and Moz NH3 association reactions leads to the following estimates for binding energies of the 1:l association complexes: AEa&cal mol-' = 17:: for Mo[C2&] and 14 f 2 for ModNH31.
+
+
Introduction Currently there is widespread interest in studies of the variation of chemical properties of metal clusters with cluster size, including the convergence to bulk metal surface reactivity in the limit of very large clusters.'f2 Such studies have the potential for providing new insights into the factors that govem chemical reactivity at complex metal centers of the type involved in many important catalytic processes. There is in addition a strong scientific motivation to improve our understanding of chemical behavior, on a molecular level, for an as yet poorly understood class of materials. In recent years, the field of metal cluster chemistry has been sparked by technical advances in both experimental and theoretical areas, including the development of laser vaporization techniques for production of clusters of virtually any metal,'S2 and ongoing developments of quantum chemical methods that are making high-level theoretical treatments practical for moderate-sized metal cluster^.^ A significant aspect of the work on neutral transition metal clusters in the moderate size range is that the concept of cluster electronic structure is of limited usefulness for interpreting experimental results on reactivities. This is because very little is known about the details of electronic structure of metal clusters. It is therefore the geometrical structure of the clusters that has been emphasized in discussions of trends in reactivity with cluster size.4 Such interpretations make use of concepts that are well developed in surface science, such as chemically distinct binding sites on the surfaces of clusters. It is of course desirable to find links that exist between electronic structure and reactivity, and it seems clear that this may best be done by focusing on smaller clusters such as dimers, trimers, and tetramers. An attractive approach along these lines is to build up a picture of cluster reactivity by examining the evolution of chemical properties of very small clusters, including the
@
Issued as NRCC No. 37220. Abstract published in Advance ACS Abstracts, October 1, 1994.
0022-365419412098-11637$04.50/0
transition from the isolated atom to the dimer. This first step in particular is attractive because it allows us to build on what has been learned in the areas of (1) chemical studies of transition metal atomic ions and neutral atoms, including many correlations between electronic structure and r e a ~ t i v i t y ; ~and - ~ (2) spectroscopic and theoretical studies of electronic structure of transition metal dimer^.^^,^ It is expected that quite dramatic variations in reactivity with nuclearity occur in the very small cluster size regime. By studying and attempting to understand these variations, we can hope to clarify the link between electronic structure and reactivity. A general approach for kinetic studies of metal cluster reactions is to combine a laser vaporization cluster source with a fast flow reactor and laser-ionization, time-of-flight mass spectrometry (TOFMS) for detection and monitoring of clusters.'.* In recent reports from this laboratory, a fast flow reactor has been described that combines a laser vaporization cluster source with a relatively large-diameter (7.3 cm) flow tube, designed to transport the clusters to the detection region under well-defined temperature and pressure conditions, and with minimal loss of the clusters on the walls of the reactor t ~ b e . ~ - ' ~ The earlier reports described kinetic studies of the coinage metal dimers Cu2, Agz, and AUZ,all of which were monitored by fluorescence excitation spectroscopy using well-characterized electronic transitions. Because of its great specificity, fluorescence excitation is in general preferable to nonresonant ionization and TOFMS as a detection method, but it unfortunately has very limited applicability because very few clusters have known electronic spectra. In this paper we report on further studies of metal dimer reactions, specifically M o ~ ,using fluorescence excitation for monitoring the dimers. Results are also given for reactions of molybdenum atoms, and in the discussion the differences in reactivity between the atom and the dimer are highlighted, and the manner in which these differences may be related to known features of the atom and dimer electronic structure is discussed. Drawing on similar
Published 1994 by the American Chemical Society
Lian et al.
11638 J. Phys. Chem., Vol. 98, No. 45, 1994
P
-R
He Figure 1. Schematic diagram showing flow tube in RT-tube configuration. Vaporization and fluorescence excitation laser beams are illustrated. He and R indicate He carrier gas and reactant gas inlets, P shows position of Baratron pressure gauges, and GV shows position of gate valve. Large arrows indicate direction of gas flow.
comparisons available for copper and silver atoms and dimers, it is suggested that two features of the molybdenum dimer electronic structure are important. The dimer has mechanisms not available to the atom for polarizing valence charge density out of the way of incoming reactant molecules and thereby minimizing repulsive interactions and leading to enhanced reactivity in certain situations. One possible mechanism is mixing of the 5sa bonding and 5sa* antibonding molecular orbitals under the influence of an approaching reactant molecule, leading to polarization of the 5sa charge density away from the reactant. A second important feature of the dimer electronic structure is the presence of strong d-d bonding interactions that stabilize the 4d orbitals. These orbitals therefore become less available for dative bonding with n-acceptor ligands such as carbon monoxide and ethylene, relative to the 4d orbitals of Mo atoms.
Experimental Section The flow tube reactor was used in two configurations, one for kinetic measurements at room temperature and the second for measurements at slightly elevated temperatures to 353 K. These two configurations will be referred to as RT-tube (RT for room temperature) and T-tube, respectively. The RT-tube is illustrated in Figure 1. The laser vaporization source is housed in a six-way cross with 3 inch 0.d. arms (IS0 NW80 supplied by MDC). A stepping motor is coupled through a vacuum feedthrough to translate and rotate a metal target rod (0.25 in. diameter) past the focus of a XeCl excimer laser beam. The full flow of He carrier gas for the flow tube is directed over the laser vaporization region and entrains the ablated material in a 0.8 cm long, 0.2 cm diameter channel before expanding into the flow tube. For cluster experiments, an extension tube may be added to the source block to promote clustering of the metal atoms. In the M* studies reported here a 4 cm long, 0.2 cm internal diameter tube was used. The Lumonics XeCl excimer laser used for vaporization is equipped with unstable resonator optics, and the beam is focused onto the target rod using a 30 cm focal length lens. The pulse energy used for vaporization is in the range 20-40 mJ, and repetition rate is 10 Hz. The upstream portion of the flow tube is made from three standard components (IS0 NW80) joined by O-rings: a 45”
elbow, a 6.44 in. nipple, and a four-way cross, all with internal diameters of 7.29 cm. The downstream portion of the tube is a 3 inch o.d., 16 in. long stainless steel pipe with an internal diameter of 7.3 cm. This pipe has a sliding brass collar that extends the flow tube to within 1 cm of the detection laser beam axis. Adjoining vacuum chambers enclose the downstream part of the tube and are evacuated through a gate valve connected to the first chamber (tee section). The second chamber houses the laser-induced fluorescence (LIF) detection region. The manually operated gate valve is used to control the pumping speed. The total length of the flow tube between the laser vaporization source and the LIF detection axis is 116 cm. The He flow rate is held constant at 15 OOO (f150) sccm (standard cubic centimeters per minute), using a mass flow controller (MKS Model 1159B). A second mass flow controller is used for the reactant gas, which is mixed into the main flow through a downstream inlet ring. The inlet has a design similar to that of the “ring inlet” described by Upschulte et al.,I3 with the reactant flow directed against the bulk flow. The reactant flow can be adjusted in the range 0-200 ( f 2 ) sccm of N2,the range for a specific reactant depending on the relevant calibration factor for the flow meter. The position of the inlet is adjustable in the range 50-70 cm upstream of the LIF detection axis to vary the length of the reaction zone. The pressure in the flow tube is measured using 0- 1 and 0- 100 Torr Baratron capacitance monomers (MKS Models 310CHS-1 and -100), positioned approximately midway between the vaporization source and the LIF detection axis. The accuracy of the pressure measurement is approximately f 5 % . The flow tube is evacuated by a mechanical booster pump (Edwards Model EH2600 with Model ElM275 backing pump) with an effective pumping speed of 634 Us for air at 0.3 Torr. With the gate valve fully open and with a He flow rate of 15000 sccm, the pump maintains a pressure of 0.44 Torr in the flow tube. By partially closing the gate valve, the pressure is adjustable to approximately 10 Torr. Metal atoms and dimers are detected by resonance fluorescence excitation at the exit of the flow tube. The excitation laser beam from an excimer laser pumped dye laser (Lumonics HD-300) enters and exits the detection chamber through side arms equipped with light baffles. The delay between the
Flow Tube Kinetic Study of Mo and M02 Reactivity
J. Phys. Chem., Vol. 98, No. 45, 1994 11639
TABLE 1: Comparison of Rate Constants Measured by Using RT-Tube and T-Tube with Previous Work reaction measurement techniaue and conditions /d2)/cm3s-l (1.62 f 0.13) x A1 0 2 time-resolved measurement by laser photolysis laser fluorescence in flow cell. T = 298 K, 10- 100 Torr of Ar buffer gas (1.79 f 0.20) x RT-tube. T = 295 K, 0.34-0.70 Torr of He buffer gas (2.3 f 0.3) x Ti + 0 2 time-resolved measurement by laser photolysis laser fluorescence in static pressure cell. T = 296 K, 20- 100 Torr of Ar buffer gas flow tube with laser vaporization source. T = 300 K, 0.75 Torr of He buffer gas (1.5 f 0.4) x 10-l2 flow tube with hollow cathode sputtering source. T = 300 K, 0.4 Torr of He buffer gas (1.9 f 0.2) x (1.60 f 0.25) x time-resolved measurement by laser photolysis laser fluorescence in flow cell. T = 298 K, 20 Torr of Ar buffer gas RT-tube and T-tube, T = 296 K, 0.44-8 Torr of He buffer gas (2.8 f 0.5) x lo-'* (4.0 f 1.4) x Ti N20 flow tube with laser vaporization source. T = 300 K, 0.75 Torr of He buffer gas (4.4 f 0.4) 10-13 flow tube with hollow cathode sputtering source. T = 300 K, 0.4 Torr of He buffer gas (5.9 i 1.1) x 10-13 time-resolved measurement by laser photolysis laser fluorescence in flow cell. T = 298 K, 20 Torr of Ar buffer gas RT-tube, T = 296 K, 0.44-4 Torr of He buffer gas (8.9 f 2) x 10-13 (1.0 f 0.1) x 10-14 Cr + N2O time-resolved measurement by laser photolysis laser fluorescence in static pressure cell. T = 298 K, 50-500 Torr of Ar buffer gas (9.25 f 1.43) x time-resolved measurement by laser photolysis laser fluorescence in flow cell. T = 303 K, 82 Torr of Ar buffer gas RT-tube, T = 296 K, 3-8 Torr of He buffer gas (1.03 f 0.3) x
ref
+
23 9 16 17 18 19 present study 17 18 19
+
vaporization and detection laser pulses, equal to the transit time T L of the detected atoms or dimers in the flow tube, is adjusted to optimize the fluorescence signal. Laser-induced fluorescence is collected with afll two-element condenser (focal length 7.5 cm) and imaged with magnification 0.65 onto a 0.16 x 2.4 cm rectangular slit before impinging on a photomuliplier tube (PMT). The slit has its long axis parallel to the excitation laser beam, so the effective detection zone at the center of the flow tube has dimensions of approximately 0.25 x 3.7 cm. The signal pulse from the PMT is amplified and passed through a sample-and-hold circuit to a data acquisition computer. In the T-tube configuration the four-way cross and nipple sections of the upstream portion of the tube are replaced by a copper pipe with an internal diameter of 7.50 cm. The pipe extends through the flange of the tee section vacuum chamber and ends approximately 1 cm away from the LIF detection axis. The pipe is wound with heating tape on the upstream part and with electrically insulated resistance wire on the downstream part inside the tee section vacuum chamber. A series of five thermocouple junctions are soldered onto the interior surface of the tube at regular intervals along its length and are used to monitor the temperature of the tube during heating. By testing with a thermocouple probe at various positions in the gas flow inside the tube, it was seen that the gas temperature was maintained within f 2 K of the tube wall temperature, which varied by at most f 5 K along the length of the tube, over the temperature range 300-353 K. The total length of the T-tube between the vaporization source and the detection axis is 133 cm, and the length of the reaction zone can be varied in the range 67-87 cm. The Baratron pressure gauges are positioned approximately midway between the vaporization source and detection axis. Molybdenum (99.95%) and titanium (99.99%) metal rods were obtained from Aesar/Johnson Matthey. Chromium(99.95%) rod was from Goodfellow. The helium carrier gas was high purity or ultrahigh purity from Linde or Matheson. Nitrogen, methane, carbon monoxide, carbon dioxide, and nitrous oxide reactant gases were ultrahigh purity or research grade from Matheson. Propene was chemical purity from Linde, ethene was polymer grade from Matheson, ammonia was anhydrous grade, and oxygen was chemical punty from Matheson. All gases were used directly from the gas bottles.
Results and Discussion A. Characterization of Flow Tube. The flow tube used
present study 20 21,22 present study
in the present study employs pulsed methods for production and detection of reactive species and therefore differs from flow tubes conventionally used for chemical kinetics studies. In the conventional approach, continuous production and detection methods are used, and the kinetic analysis is in terms of a steadystate spatial distribution of reactive species along the direction of flow.I4 In an earlier report9from this laboratory it was shown that a straightforward analysis of data obtained by using the RT-tube led to good agreement between measured and literature values of the rate constant for the reaction A1 0 2 A10 0 at room temperature. However, due to the large value of the rate constant for this reaction, it is not a convenient one for testing the flow tube over its full pressure range (0.44-10 Torr). Therefore, as part of the present study, several oxidation reactions of Ti and Cr atoms were investigated. The reactions and their rate constants from previous work and from this study are shown in Table 1. The straightforward analysis of kinetic data for a flow tube of the type used here is made by using eq 1, which is assumed
+
-
+
[M]/[M], = e~p(-k'~'[R]l/(v)>
+
-
to apply for a reaction M R products with second-order rate coefficient k@), where M is a reactive atom or dimer and R is a stable reactant present in great excess in the reaction zone. [M]/[M]o is the ratio of the number of reactive species present in the detection volume of the probe laser beam in the presence and absence of a reactant concentration [R], and (v) is the average flow velocity of the detected atoms in the reaction zone of length 1. (v) is taken to be equal to the average flow velocity of the detected atoms in the tube, given by WTL,where L is the length of the flow tube and TL is the transit time of the detected atoms. The transit time is given unambiguously by the delay time between the vaporization and detection laser pulses. (Due to the high velocity of M in the small diameter channel of the laser vaporization source, the residence time in the channel is a negligible fraction of the total transit time TL.) The concentration of reactant is known from the total pressure and the ratio of the reactant flow rate to the total (reactant plus He) flow rate. Thus the rate constant can be found from the slope of a plot of ln([M]/[M]o) vs the flow rate of reactant. The main assumptions underlying this simple analysis are as follows: (1) the average velocity of the detected atoms in the reaction zone is equal to their average velocity (v) in the flow tube; (2) the reactant concentration [R] is constant over the
11640 J. Phys. Chem., Vol. 98, No. 45, 1994
Lian et al. I
l 0
I
0.44 1.0 2.0
6.0Torr
4.0
-1 -2
-3 -4
I 0
1
2
4
3
P(02) tzI 10-5 torr s
0
+
Figure 2. Kinetic data for Ti 02 reaction obtained by using RTtube at total pressures of 2, 4, 6 , and 8 Torr at 296 K. The abscissa is the product of the partial pressure of 02 and the residence time of Ti
atoms in the reaction zone. The ordinate is the logarithm of the ratio of LIF signal due to Ti in the presence and absence of 02. length I of the reaction zone; and (3) effects due to coupling of chemical reaction and radial diffusion may be neglected. Coupling of this type arises in the case of fully developed viscous flow due to the presence of a parabolic velocity distribution in the flow tube.14 Reaction depletes the concentration of reactive species in the more slowly moving regions of the gas near the tube wall, and the resultant radial concentration gradient sets up a flux of reactive species toward the wall. Diffusion and reaction are coupled because the diffusion flux depends on the extent of reaction. In order to investigate the validity of these assumptions, a series of measurements was made on the test reaction Ti -I- 0 2 Ti0 0. These measurements are described in the following paragraphs. It was seen that plots of the type suggested by eq 1 were in general linear, and furthermore, when data from several runs at different pressures were combined, the composite plots were also linear. This is illustrated in Figure 2 , which shows data obtained at 2 , 4 , 6 ,and 8 Torr total pressure, using the RT-tube with a reaction zone length 1 = 60 cm. Actually, there is a perceptible curvature in this plot, and this will be discussed below, but the curvature is small. The transit time of Ti atoms in the flow tube is strongly dependent on the total pressure, so measurements at different pressures span a range of average velocities (v). The abscissa of Figure 2 is the factor multiplying in the argument of the exponential of eq 1, expressed as the product of the pressure of 0 2 and the residence time in the reaction zone tl, where tl = N(v) = I(tL/L) according to assumption (1) above. Since the transit time t~of the detected atoms in the flow tube is a central parameter in the kinetic analysis, plots were made of the distribution of transit times of Ti atoms at various pressures. Such arrival time distributions for the RT-tube are shown in Figure 3. Note that the peak arrival times vary between 5 ms at 0.44 Torr and 64 ms for 6 Torr total pressure. The broken lines in Figure 3 show simulated arrival time distributions calculated from a simple model described below. An important feature of the distributions in Figure 3 is their widths. It was found that the dependence of the width on the pressure in the flow tube could be approximately reproduced by using the following model. It is assumed that Ti atoms instantaneously adopt the (radial) velocity distribution for fully developed viscous flow of He carrier gas in the flow tube and maintain this velocity distribution over the full distance L
-
u2)
+
20
40
60
80
100
lnterpulse delay / ms Figure 3. Normalized arrival time distributions of Ti atoms in RTtube at various total pressures, showing observed distributions of LIF signal due to Ti as function of delay time ZL between vaporization and detection laser pulses (points connected by solid lines). The transit length was L = 116 cm in all cases. Broken lines are calculated arrival time distributions for the model described in the text. between the laser vaporization point and the detection axis. The initial spatial distribution of Ti atoms is assumed: (1) to be uniform over the cross section of the flow tube; and (2) to have a spread along the flow tube axis described by a Gaussian distribution with a full width at half-maximum (fwhm) length of 25 cm. This particular length was found to optimize the agreement between model and observed distributions; its possible origins are considered below. Axial diffusion of Ti is included in an approximate way by allowing the width of the spatial distribution to increase by an amount equal to the root mean square diffusion distance appropriate for the transit time, assuming a diffusion coefficient of 200 cm2 s-l Radial diffusion is neglected. With these assumptions, it is straightforward to calculate the arrival time distribution of Ti from the velocity distribution for viscous flow, taking into account the total mass flow rate, the pressure, and the dimensions of the flow tube and of the detection volume. Thus, the radial velocity distribution is given by V ( I ) = 2vo[l where a is the radius of the tube and vo is the average ve10city.l~ vo is defined in terms of the mass flow rate Q, the pressure P, and the tube radius a, as follows: vo = Q/(nazP). The model arrival time distributions are shown as broken lines in Figure 3. The most important effect contributing to the width of the distribution was seen from these model studies to be the apparent initial spatial width of the pulse of atoms along the flow direction. This width was fixed at 25 cm for the model distributions shown in Figure 3. Two other effects that contribute to the width of the arrival time distribution were found to be less important: (1) diffusion in the axial direction; and ( 2 ) the spread in the velocities of the detected atoms due to the convolution of the detection geometry with the parabolic radial velocity distribution. In the model distributions, axial diffusion accounted for less than 15% of the total width. The detection geometry contributed approximately 25% to the width and produced a slightly asymmetric broadening. Similar results were obtained for all pressures. The origin of the initial spatial width of the atom pulse is not known, but it could arise from a combination of two effects: thermal expansion of the initially very hot plasma produced by the vaporization laser pulse; and turbulence in the flow of He carrier gas as it expands from the narrow channel of the vaporization region into the flow tube. It
Flow Tube Kinetic Study of Mo and Mo2 Reactivity was observed that the arrival time distributions were rather insensitive to changes in the vaporization source, including addition of the 4 cm x 0.2 cm i.d. extension tube, and even to a change in the metal target rod from titanium to molybdenum. Regardless of the origin of the initial spatial width, it has the consequence that, for arbitrary time delay t~ between the vaporization and detection laser pulses within the arrival time distribution, the residence time of the detected atoms in the reaction zone is not given by a simple fraction of ZL determined by the length of the reaction zone and of the flow tube. Such a proportionality would imply that the detected atoms have a constant average velocity over the full length of the flow tube, according to assumption (1) described following eq 1. This situation could still pertain in the case of a spatial width if the broadening is symmetric (with and against the flow direction) in an otherwise constant average velocity flow, and if t~is fixed in the middle of the arrival time distribution. This is therefore the form of assumption (1) in the case where spatial broadening is important. Observations were made of the effect on the arrival time distributions of the addition of reactant in the reaction zone, and these observations are consistent with the interpretation of the distributions in terms of an axial spatial width. Addition of sufficient 0 2 to remove ~ 7 5 % of the Ti had almost no effect on the arrival times of the unreacted atoms. This shows that the arrival times are not proportional to the residence times in the reaction zone, because if this was the case then addition of reactant would selectively remove atoms with longer residence times and this would cause a shift of the arrival time distribution of unreacted atoms to shorter times. It is seen in Figure 3 that the model distributions reproduce the observed peak arrival times for the RT-tube quite well at low pressure but predict too long arrival times at higher pressure. Similar results were found for the T-tube, so the model reproduced the shifts in the peak times due to the differences in geometry between the flow tubes. For example, there is a shift from 5.5 to 6.7 ms at 0.44 Torr. It was also found that the model reproduced the effect of raising the temperature of the T-tube from 296 to 356 K, which caused a %20% shift in the peak arrival time at 4 Torr. As noted above, very similar arrival time distributions were found for Ti and Mo atoms, with and without the extension tube on the cluster source, so the model applies equally in all these situations. From these results it appears that the transport of metal atoms in the flow tube is approximately described by the simple model outlined above, although there are significant deviations at higher pressures. Although the origin of these deviations is not known, note that the model is highly simplified, so deviations such as those observed are not surprising. The major simplification is in the assumption that the vaporized material has a uniform initial spatial distribution over the cross section of the flow tube, and is accommodated instantaneously to the radial velocity distribution for fully developed viscous flow of the He carrier gas. One interpretation of these results is that the assumption of constant average velocity of the detected atoms over the length of the flow tube, as discussed above, may be considered to be valid to within the maximum deviation between the observed and model distributions, which amounts to approximately 17% for the peak arrival times. In all cases, kinetic data were analyzed by using the assumption of symmetric spatial broadening described above, using ZL at the peak arrival time as a measure of the average velocity of the detected atoms. The nearly linear form of the kinetic plot shown in Figure 2 for the Ti -t 0 2 reaction indicates that the average flow velocities obtained in this way for pressures in the range 2-8 Torr lead
J. Phys. Chem., Vol. 98, No. 45, 1994 11641
4t
r C
RT-tube T-tube
0
t 0
I 1
0
2
4
6
8
1
0
Total Pressure / Torr Figure 4. Rate constants for Ti 02 reaction at 296 K, measured using RT-tube and T-tube at various total pressures. Error bars give
+
relative uncertainties estimated from the scatter in the data. to a consistent set of residence times in the reaction zone. If there are systematic errors in the residence times, they would have to be such that relative residence times are correctly described. The slight curvature of the plot in Figure 2 may indicate that this is not entirely true. The results in Figures 2 and 3 can thus be interpreted to suggest that assumption (1) above is approximately valid. Comparisons between measured and literature values for several rate constants support this interpretation, as discussed below. The Ti 0 2 reaction was investigated at 296 f 1 K at pressures in the range 0.44-8 Torr. Previous work has indicated that this is a bimolecular reaction with a pressure independent rate constant.16 In all cases, rate constants were measured by varying the flow rate of 0 2 at constant total pressure and with a constant reaction zone length. In Figure 4, rate constants measured by using the RT-tube and the T-tube are shown as a function of pressure. There are significant differences among the results. The origin of these differences is not known, but it seems likely that they arise mainly from uncertainties in the average velocities of the detected atoms in the reaction zone. An additional factor may be important at the lowest pressure considered (0.44 Torr). This is due to an expected ~ 2 5 % viscous pressure drop down the length of the flow tube (116 cm), and a correspondingly smaller drop ( ~ 1 5 %in ) the reaction zone (length 70 cm). At higher pressures the pressure drop is reduced in proportion to the reciprocal of the average pressure and becomes insignificant above 2 Torr. The pressure drop at low pressure should result in an underestimate of the measured rate constant, due to an error in the estimated pressure of reactant. This arises because the total pressure is measured at the beginning rather than in the middle of the reaction zone (Figure 1). However, in view of the presence of several sources of uncertainty that are difficult to assess, it was decided not to apply corrections to the low-pressure data. A further effect of the viscous pressure drop at the lowest pressures is that the average flow velocity increases down the flow tube. This should also result in underestimation of measured rate constants, but in view of the uncertainty in the average velocity due to spatial broadening, as discussed above, and considering the probable magnitude of the underestimate (at most ~15%), this effect has been disregarded. Finally, in connection with the viscous pressure drop, note that the width and the position of the maximum of the arrival time distribution are sensitive only to the average pressure in the flow tube, and this is known by measurement, so the pressure drop should not affect the model predictions of the arrival time distributions shown in Figure 3.
+
11642 J. Phys. Chem., Vol. 98, No. 45, 1994
Lian et al. -I
4 t
J,
0 30
0
0.44 1.0 4.0
0
6.0torr
i
70 80 Reaction Length / cm Figure 5. Rate constants for Ti 0 2 reaction at 296 K, measured using RT-tube with different reaction zone lengths and at various total pressures. Error bars give relative uncertainties estimated from the scatter in the data. 40
50
60
+
In Figure 5, rate constants measured using several reaction zone lengths and at various pressures in the RT-tube are shown. The apparent rate constants decrease at shorter reaction zone lengths. This is probably due to mixing effects at the reactant inlet. If the time required for mixing the reactant with the bulk flow is a significant fraction of the residence time of the atoms in the reaction zone, then the effective length of the reaction zone is less than the assumed length 1. This is the point of assumption (2) described following eq 1 (constant reactant concentration in reaction zone). As shown in Figure 5 , rate constants measured by using the RT-tube at 0.44 and 1.0 Torr appear to reach limiting values at the longest reaction zone lengths. This suggests that assumption ( 2 ) is satisfied under these conditions. Similar results were obtained at 0.44 and 4 Torr using the T-tube, for 1 = 67 and 77 cm. The situation appears to be different at 4 and 6 Torr in the RT-tube, as shown in Figure 5. The apparent increase in the rate constant at 1 = 70 cm is surprising and suggests that unusual mixing effects occur under these conditions. These are thought to arise because of turbulence in the bulk flow caused by the presence of the four-way cross (see Figure 1). Thus the anomalous behavior at 1 = 70 cm may be due to the coincidence of the position of the inlet ring with a turbulent zone near the entrance plane of the four-way cross. Consistent with this interpretation is the observation that no such effects were seen for the T-tube, where the four-way cross is replaced by a circular tube. However, it is not clear why this effect appears only at higher pressure (see Figure 5). If we remove from consideration the anomalous rate constants at 1 = 70 cm, then our results indicate a value of kc2) = (2.8 & 0.5) x cm3 s-l for Ti 0 2 at 296 K. The uncertainty limits are estimated from the spread in the results obtained under different conditions. As shown in Table 1, this rate constant is close to the one reported by Brown et a1.16 but is higher than the values reported by Ritter and Weisshaar (RW)l79l8and by Campbell and McClean (CM).19 It is interesting to note that the flow tube used by RW is very similar to the one used in the present study. The main difference is that our laser vaporization source has been designed to produce metal clusters and therefore constrains the vaporization plume in a narrow channel. It should be noted in this connection that all results for Ti were obtained without using the 4 cm cluster extension channel. Our rate constant for the Ti N20 reaction, (8.9 f 2) x 10-13, is also higher than the values reported by RW17,18and CM.19 For Cr -I- N20, our result is in good agreement with two literature values20-22obtained by using different techniques (Table 1).
+
+
389.0
389.5
390.0
Mo
390.5
i
391.0
Wavelength / nm Figure 6. Fluorescence excitation spectrum showing transitions of Mo and Moz that were used to monitor reaction kinetics in RT-tube. Arrows show the 0-OQ head of the MOZband at 389.72 nm and a line due to Mo at 390.30 nm (see the text). Note that the relative intensities of the Mo and Mop features are misleading because the wavelength increment used to record the spectrum (0.005 nm) was too large to show the full intensity of the Mo atomic line. The weak features near 390.75 nm are due to the 1-1 band of Mo2.
Good agreement between measured and literature rate constants has also been found for the reaction A1 02.9,23 From these comparisons, and considering the results in Figures 3-5, it appears that rate constants measured by using either the RTtube or the T-tube have inherent uncertainties near 20%. This is because the assumptions described following eq 1 may not be strictly valid. It should also be noted that laser vaporization has inherent limitations due to fluctuations in the production efficiencies of vapor species, and this can make a major contribution to measurement uncertainty. For refractory species, there are inevitably possibilities for systematic errors that arise due to the energetic conditions needed for their production, so absolute rate measurements are in any case subject to relatively large uncertainties. B. Reactions of Mo and Moz. Kinetic Results. With the 4 cm extension channel on the laser vaporization source, Mo and M02 could both be detected with good signal to noise ratio by using laser-induced fluorescence (LIF). In Figure 6 a fluorescence excitation spectrum of the B ll-I-XIZ(O-O) transition of Mo224and the z7P20-a7S3 transition of Mo25is shown. These transitions specifically involve Mo and Mol in their ground electronic states. Reactions of ground-state Mo and M02 were investigated by monitoring the decrease in the LIF signal caused by addition of reactant in the reaction zone. In principle, the reactant could quench the fluorescence and thereby cause a decrease in the LIF signal without reacting with Mo or M02. However, since the pressure of the reactant never exceeded 0.08 Torr, and the electronic transitions are fully allowed dipole transitions, fluorescence quenching is expected to be negligible. This was confirmed by the absence of apparent reactivity for gases such as propene in the case of M02 and NH3 in the case of Mo, even at 0.08 Torr partial pressure (see below). No effects due to collisional cascade of metastable excited states were seen in the kinetics. Thus, it was always the case that simple firstorder removal of Mo or M02 occurred over the ranges of total pressure and reactant pressure investigated, according to eq 1, and no significant increase in the LIF signal was seen in the case of unreactive gases. These observations indicate that Mo and M02 were thermalized by collisions with He carrier gas before entering the reaction zone. This is reasonable because
+
J. Phys. Chem., Vol. 98, No. 45, 1994 11643
Flow Tube Kinetic Study of Mo and M02 Reactivity
TABLE 2: Second-Order Rate Coefficients for Reactions of Mo and M02 at 296 Ka !dz)(Mo)/cm3s-l !dz)(Mo2)/cm3 SKI reactant (press.Rorr)b (press./Torr)b NR (8) NR (8) NR (8) NR (8) 1.2 x lO-'O (0.45-0.8) (2.3-8.8) 5.3 x NR (8) NR (8) 2.3 x (7.8) 1.3 x 10-l2(7.8)
N R (8) NR (8) NR (8) NR (8)
1.0 x lo-" (0.45-2.3) 1.6 x lO-I4 (4.8-8.8) 4.4 x lO-Iz (0.45-3.8) 2.5 x lO-I3 (7.8) NR (8) N R (8) NR stands for no reaction (!d2) < 5 x cm3 s-l). Relative and absolute uncertainties are estimated as f 2 0 and &30%, respectively. bTotal pressure or range of total pressure investigated shown in parentheses for each rate coefficient. Rate coefficient for Mo2 reaction estimated from analysis assuming approach to equilibrium conditions in association - dissociation reaction (see the text). Rate coefficient pressure dependent (see Table 3). Values given are for indicated total pressures.
TABLE 3: Pressure Dependence of Second-Order Rate Coefficients for Association Reactions of Mo Atoms with Ethene and Propene in He Buffer gas at 296 K" PZ)(czH4)/10-13 !d2)(c3&)/10-" press.Rorr cm3s-l cm3s-l 0.78 0.8 1.8 0.73 0.86 2.3 1.13 2.8 1.48 1.03 3.8 1.82 (1.04)b 1.05 4.8 1.36 1.05 5.8 1.72 0.99 6.8 2.24 1.14 7.8 2.32 1.35 8.8 3.1 Relative and absolute uncertainties are estimated as f 2 0 and f30%, respectively. * Rate coefficient measured at 353 K. even at the lowest pressure investigated (0.44 Torr) the number of collisions with He upstream of the reaction zone is of the order 104. The reactivities of Mo and M02 with respect to H2, N2, C&, 0 2 , N20, c02, C o , c2&, C3H6 (propene), and NH3 were surveyed by using the RT-tube at 296 f 1 K, and with a reaction zone length 1 = 70 cm. Among these various reactants, Hz, N2, C b , and CO showed no reactivity with either Mo or M02, while C2H4 and C3H6 reacted only with Mo, and N20 and NH3 reacted only with M o ~ . Only 0 2 and C02 reacted with both Mo and M o ~ . Our measurements place upper limits of approximately 5 x cm3 s-l on second-order rate constants for the reactions for which no decrease in the Mo or M02 L F signal was observed. Additional measurements were made using the T-tube at 353 K for the Mo C 2 b reaction, and at 308 and 3 16 K for the M02 NH3 reaction. The kinetic results are summarized in Tables 2 and 3, and data for the reactions of Mo and M02 with 0 2 and COz are shown in Figures 7 and 8. Two categories of reaction could be distinguished on the basis of the dependence of the second-order rate coefficient k(2) on total pressure. The reactions involving 0 2 , C02 and N20 showed no pressure dependence and are therefore interpreted as bimolecular, 0-atom transfer reactions. In these cases, composite plots of the type shown in Figure 2 were such that data obtained at different total pressures fell approximately on the same line. Examples are shown in Figures 7 and 8. In contrast, k(2) for the reactions of Mo with C2& and C3H6, and of Mo2 with NH3, were found to be pressure dependent. This
+
+
I
0.0
0.2
0.4
I
I
0.6
0.8
1.0
~ ( 0 tl/ ~ 10-5 ) torr s Figure 7. Kinetic data for reactions of Mo and Moz with 0 2 at 296 K, plotted as in Figure 2. The data for Mo were obtained using total pressures of 0.45 and 0.80 Torr and those for Moz using total pressures in the range 0.45-2.3 Torr.
0
A
8 & K
-1 -2
-3 -4
I
I
0
50
I
I
1
I
I
100 150 200 250 300
P ( C O ~z) j / 10-5torr s Figure 8. Kinetic data for reactions of Mo and Moz with COz at 296 K, plotted as in Figure 2. The data for Mo were obtained using total pressures in the range 2.3-8.8 Torr and those for Moz in the range 4.8-8.8 Torr.
7v) 3 m
E
0
2 2
-9
1
CI
Yl
0 0
2
4
6
8
1
0
Total pressure / Torr Figure 9. Pressure dependence of second-order rate coefficient for association reaction of Mo atom with ethene in He buffer gas at 296 K. Error bars give relative uncertainties estimated from the scatter in the data. is illustrated for the Mo C2H4 reaction in Figure 9, where it is seen that G2) showed an approximately linear dependence on total pressure. This is consistent with a simple adduct formation
+
11644 J. Phys. Chem., Vol. 98,No. 45, 1994
Lian et al.
51-- - 1
+
4t
M02 t NH3
0 0
and implies an equilibrium constant of 1.5 x cm3 for the Mo;? NH3 association reaction at 296 K. Under lower pressure conditions with shorter residence times, there were apparent departures from equilibrium. An analysis of this data was undertaken using a simple kinetic scheme that incorporated the forward and reverse reactions and used the equilibrium constant from Figure 10. This analysis showed that the kinetic results were consistent with an approximately linearly increasing pressure dependence of the second-order association rate coefficient k(2), with the corresponding limiting low-pressure rate constant given by Id3)KY 1 x cm6 s-l. Thus the anomalous pressure dependence seen when the dissociation reaction was not considered was removed. The origin of this anomaly is in the increasing importance of the dissociation reaction and closer approach to equilibrium conditions at longer residence times, which leads to an apparent decrease in the rate of the association reaction at higher pressure. As discussed in the following section, measurements of the temperature dependence of the estimated equilibrium constant are consistent with this interpretation, and there is consistency between the kinetic and thermochemical parameters derived for the association reaction. Binding Energies of Association Complexes. A third-law analysis26 of the equilibrium constant for the M02 NH3 association reaction at 296 K led to the estimate AE"0 = 14 f 2 kcal mol-' for the binding energy of the complex. The uncertainty limits were obtained by varying the assumed vibrational frequencies and moments of inertia of the complex within ranges that were considered to represent reasonable possibilities. The vibrational frequencies were taken to be those of the separated Mo2 NH3 fragment^^.^' plus a single, 5-fold degenerate frequency (denoted m) to represent the relative motions of the fragments in the complex. m was varied in the range 150-400 cm-'. Moments of inertia were calculated assuming end-on (C3,) and side-on (C,) coordination geometries, and with the Mo-N bond distance in the range 1.9-2.3 A. A series of measurements was made at slightly elevated temperatures to observe the temperature dependence of the equilibrium constant. These measurements were subject to large uncertainties because at elevated temperatures the decrease in the M02 signal due to the reaction at equilibrium was rather low (%25% decrease at 316 K). Better results could possibly be obtained by working at lower temperatures (below room temperature) or by using higher flow rates of NH3, but this was not attempted in the present study. Our results indicate that the equilibrium constant decreased by a factor of KY0.37 between 298 and 316 K. This translates to an enthalpy of dissociation at 309 K, AH0309 = 11 kcal mol-', which is in reasonable agreement with the binding energy estimated from the thirdlaw analysis. The measurements of the temperature dependence of the equilibrium constant, although crude, provide support for the interpretation of the M02 NH3 data in terms of an equilibrium association reaction. In particular, they support the interpretation that the monoligand complex does not undergo subsequent ligand addition reactions, since this is a basic assumption of the analysis underlying eq 2. Because of the uncertainties involved in the temperature-dependent measurements, we consider the estimate of the binding energy from the third-law analysis to be our best estimate. A rough estimate of the binding energy of the M o [ C ~ H ~ ] complex may be made from the kinetic data in Figure 9. From the observation of well-defined first-order kinetics for Mo removal at 296 and 353 K, it can be concluded that the reverse dissociation reaction occurred to a negligible extent. This places a lower limit on the association equilibrium constant, K > 7 x cm3 at 353 K. By using a third-law analysis similar to
1
2
3
4
5
6
P(NH3) / l o 2 torr Figure 10. Kinetic data for reaction of Moz with ammonia in the range of total pressure 2.8-8.8 Torr at 296 K, plotted in the fonn of eq 2. The ordinate is the ratio of LIF signal due to Moz in the absence and presence of ammonia. The slope of the plot is equal to the equilibrium constant for the association reaction.
or association reaction mechanism. The slope of the line drawn through the data points in Figure 9, constrained to pass through the origin, gives the limiting low-pressure, third-order rate constant for the association reaction at 296 K, p3)= 1 x cm6 s-l. It was found that the second-order rate coefficient kc2) decreased when the temperature of the reaction zone was increased to 353 K (see Table 3). This is consistent with the occurrence of an association reaction, as is further discussed in the following section. The dependence of p2)on total pressure for the M02 NH3 reaction was different from that shown in Figure 9 for Mo C2&, in that p2)apparently decreased with increasing total pressure. Such a pressure dependence is anomalous and inconsistent with a simple association reaction mechanism. In a previous study of the Ag2 NH3 association reaction using the RT-tube,12 it was found that the reverse (dissociation) reaction occurred to a significant extent in the flow tube, and the data could be understood in terms of an approach to equilibrium. Under higher pressure conditions, with relatively long residence times in the reaction zone, the data were consistent with the attainment of equilibrium in the association reaction forming the 1:l Ag2[NH3] complex. The present results for M02 NH3 can be understood in the same way. However, due to the smaller apparent magnitude of the association equilibrium constant in this case, the decrease in the Mo2 concentration due to complex formation was relatively small, amounting to at most a 70% decrease. This made it difficult to distinguish, on the basis of measurements at constant total pressure, a mechanism involving only an association reaction from one involving coupled association and dissociation reactions. As discussed in ref 12, in the case of fully established equilibrium conditions for formation of a 1:1 complex, and if the complex does not undergo further ligand addition reactions, then a simple analysis may be carried out that allows the equilibrium constant K for the association reaction to be evaluated. The concentration ratio of M02 in the detection zone in the absence and presence of ligand concentration [NH3] is given in terms of the equilibrium constant K as follows.
+
+
+
+
Thus a plot of the M02 concentration ratio against ligand concentration should be linear with slope equal to K. Such a plot is shown in Figure 10. The plot is approximately linear
+
+
+
Flow Tube Kinetic Study of Mo and M02 Reactivity that described above, this implies a lower limit for the binding energy of the Mo[C2H4] complex, B o o > 14 kcal mol-'. A further estimate can be made by modeling the low-pressure association rate constant, kc3) PZ 1 x cm6 s-' at 296 K, using unimolecular reaction theory. In previous work it has been shown that reliable estimates of binding energies of atomligand complexes can be obtained in this way.7,28 In the present study the simplified unimolecular rate theory calculations described by T r ~ were e ~ used. ~ As described the calculations are used to determine a range for the assumed binding energy that approximately reproduces the observed lowpressure rate constant for a range of guessed but "reasonable" molecular parameters, including particularly vibrational frequencies of the association complex. In this approach, it is necessary to assume that there is no activation barrier for formation of the complex. This assumption is justified in the present case by the observation that the second-order rate coefficient for the association reaction has a negative temperature dependence (see Table 3). As in the case of the third-law calculations, the vibrational frequencies were taken to be those of the fragments plus one degenerate frequency (w) to represent the interfragment modes in the complex. w was varied in the range 200-400 cm-', and structural parameters for the Mo[C2H4] complex in the 5B2 ground state were taken from results of electronic structure calculations reported of Blomberg et aL30 Collision parameters for the He-complex interaction (a = 3.9 8, and E = 48 K) were estimated using standard method^,^' and the collision efficiency factor was varied in the range ,& = 0.050.2. These calculations led to M o o = 17 f 4 kcal mol-' for the binding energy of the complex. Combining this with the limiting value from the third-law calculations, our best estimate for the binding energy of Mo[C2&] is 17: kcal mol-'. The unimolecular rate calculations qualitatively reproduced the negative temperature dependence of the rate coefficient, as expected for an association reaction with no activation barrier. A similar analysis was made for the low-pressure association rate constant estimated for the M02 NH3 reaction at 296 K, kc3) x 1 x cm6 s-', and it was seen that this rate constant is consistent with the binding energy of the Mo2[NH3] complex estimated from the third-law analysis of the equilibrium constant. C. Electronic Structure and Reactivity of Mo and Moz. Experimental and theoretical studies of the reactivity of neutral 3d transition metal atoms with respect to adduct formation reactions with simple molecules have shown that repulsive interactions are of dominant importance and lead in many cases to very low r e a ~ t i v i t y . ~This , ~ is in contrast to the situation for singly charged transition metal atomic cations, which are generally very r e a ~ t i v e . ~This , ~ difference in reactivity can be understood in general terms by simple considerations of the nature of the ground-state and low-lying excited-state electronic configurations. Thus, the ground-state neutrals often have the configuration 3dnw24s2,in which the relatively diffuse, closed 4s shell effectively shields the chemically active but compact ion core from interaction with ligand molecules. In the groundstate cations, the 4s shell is either vacant or singly occupied, and in addition, attractive electrostatic interactions with ligand molecules counteract to some extent electronic repulsion effects. For the neutrals, it is expected that reactivity is governed in large part by the availability of a low-lying state with configuration 3dn-'4s1 and by the extent to which electronic repulsion with ligand molecules may be minimized in this configuration by orbital hybridization effects. The latter depends on the occupancy and coupling of electron spins in the 4s and 3d shells. If the 4s electron is low-spin coupled with a singly occupied 3d orbital, then sd hybridization may occur.32 This provides a
+
J. Phys. Chem., Vol. 98, No. 45, 1994 11645 very effective mechanism for reducing electron repulsion and helps to explain, for example, many of the chemical properties of nickel atoms (with a low-lying 3d94s1 'D state), including reactivity with respect to oxidative addition to the 0-H bond of water,33 and formation of strongly bound, singlet spinmultiplicity monoligand complexes with n-acceptor ligands such as carbon monoxide, alkenes and alkynes.34 In the case where singly occupied 4s and 3d orbitals are high-spin coupled, sd hybridization is no longer effective, and instead electronic repulsion is reduced by 4sI4p hybridization, although at a greater energetic cost. These considerations that focus on the role of repulsive interactions in the entrance channel in controlling reactivity with respect to adduct formation apply also for 4d transition metal atoms such as Mo. In the case of the complex Mo[C2&], Blomberg et aL30 have predicted a dissociation energy of approximately 6.5 kcal mol-' for the (5B2)ground state. Our results indicate a significantly higher binding energy of 17: kcal mol-' and show that there is no barrier to complex formation. The absence of a barrier is an indication of a small or negligible net repulsive interaction on the septet potential surface that correlates with ground-state Mo (4d'5~')~S C2H4 reactants, up to the point where this surface is crossed by the quintet surface that correlates with the ground-state complex. This can be understood in terms of 5sf5p hybridization of Mo in the case of the septet surface, which corresponds with the high-spin coupled case described above. The preference for the quintet state as the ground state of the complex is due to the important role of n-back-donation, which is maximized for double occupancy of the dn(b2) orbital.30 It is interesting to note that our results show that binding between Mo and N H 3 is much weaker than that for Mo[CzH4], since no reaction was observed for Mo -t N H 3 . Thus, the reduction of electronic repulsion on the septet surface by 5s15p hybridization is apparently insufficient to allow bond formation in this case, and since NH3 is not a n-acceptor ligand, the quintet state is not sufficiently stabilized to form the ground state of a bound complex. These interpretations are somewhat speculative, but they provide a useful rationalization of the bonding capabilities of Mo atoms with respect to n-acceptor and Lewis base ligands. How are the bonding capabilities of Mo atoms influenced by formation of the metal-metal bond in the dimer M o ~ ?Our results show that the influence is toward greater reactivity in the case of the Lewis base ligand NH3 and less reactivity in the case of the n-acceptor C2H4. Thus, whereas Mo atom forms a bound complex with C2H4 and not with NH3, the reverse is true for MOZdimer (Table 2). The lower reactivity of Mo2 in the case of C2& is undoubtedly due to the presence of strong d-d bonding in the dimer, which stabilizes the d-orbitals and makes them available for backdonation of charge to the n-acceptor. Experimental and theortical studies show that d-d bonding is very important in Mo2; all d-electrons are present in a closed shell of bonding orbitals that makes a major contribution to the large binding energy and short internuclear distance of the dimer (DO= 101 kcal mol-', and re = 1.938 Since n-back-donation is essential to the stability of the Mo[C2&] it is expected that strong stabilization of the d-orbitals on Mo would have an adverse effect on the strength of the MoC2& bond. It could be argued that the ds-orbitals of Mo are not greatly stabilized in the dimer and should be available for n-back-donation. However, this could only occur for a sideon coordination geometry, with the metal-metal bond parallel to and below the plane of C2H4, and perpendicular to the CC axis, as illustrated in Figure 11. It is argued below that electronic repulsion effects cause this geometry to be strongly
+
Lian et al.
11646 J. Phys. Chem., Vol. 98, No. 45, 1994
side-on end-on Figure 11. Side-on and end-on coordination geometries for complexes of Mo2 with ethene and ammonia. disfavored relative to the end-on geometry, with the metalmetal bond perpendicular to the C& plane. n-back-donation from occupied &bonding orbitals is not feasible in the case of the end-on geometry. The end-on and side-on geometries are illustrated in Figure 11 for C2H4 and NH3 ligands. In an end-on approach of Mo2 to the lone pair of electrons of a ligand such as NH3, repulsion between the electrons of the ligand and those of M02 may be reduced by polarization of charge from the “front” of the dimer to the “rear”. In particular, it is the relatively diffuse, closed-shell 5so electrons on M02 for which polarization away from the ligand is most important. It is significant that such a polarization may be accomplished without admixture of Mo 5p-orbital character in the end-on geometry, but must involve such admixture in the side-on geometry. In the end-on case, a mixing between the filled 5sa bonding and vacant 5so* antibonding orbitals can produce the front to rear polarization. In the side-on case, a polarization directly away from the ligand must involve mixing of 5sa with the vacant 5pn orbital. The population of the energetic Mo 5p-orbitals in M02 is therefore larger in the side-on case, and this favors the end-on geometry. Another way of saying this is that the polarizability of the dimer is greater in the direction parallel to the bond axis than perpendicular to the axis. The importance of charge polarization within the metal fragment has been demonstrated in several theoretical studies35 of the binding of ammonia to metal atoms and clusters. From a series of extended Hiickel calculations for the dimers Cu2, Agz, and M02 interacting with NH3, we have found that simple concepts of orbital interactions are useful for describing the bonding, and provide a viewpoint that is complementary to the picture of electrostatic bonding that has been described for related system^.^^,^^ Thus the calculations indicated a clear preference for the end-on geometry in all cases, due to strong destabilization of the highest occupied molecular orbital when the dimer was rotated toward the side-on configuration. Local spin density calculations on CU~[NHJ] and A ~ z [ N Hhave ~ ] ~also ~ indicated a preference for the end-on geometry. This argument can be generalized and points to a simple but important difference between atoms and small clusters including dimers-electronic repulsion effects that restrict the reactivity of atoms are alleviated in clusters, because clusters have polarization mechanisms that are not available to atoms. An example of this is found in the relative binding energies of complexes of n-acceptor ligands C2& and CO with copper atoms and dimers: AE”0 E 6 kcal mol-’ in the case of Cu3* and ~ 2 kcal 5 mol-’ for Cu2.12 Cu2 forms a similarly strongly bound complex with NH3,12 and in this case also the binding energy of the Cu complex Cu[NH3] is considerably lower.39A
similar trend holds for the comparison between Ag and Ag2 complexes with NH3,12,39and the results of the present study show that this situation pertains also for M o m 3 1 and Mo2W31 complexes. There is strong evidence to indicate that Ag212 and Mo2 bind only one NH3 ligand molecule. This is consistent with the picture of front to rear polarization of charge in the dimer in the end-on bonded configuration, since the metal atom to the rear is thereby made unsuitable as a binding site. These results suggest the following generalizations, which are based on the concept that repulsive interactions associated with occupied valence s-orbitals of the metal atoms exert a dominant influence on their ability to form bonds with simple ligand molecules: complexes with dimers tend to be more strongly bound than those with atoms; and end-on geometries are in general favored over side-on geometries for the dimer complexes. Exceptions to the first generalization may be expected in cases where there are important bonding interactions involving the ion core of the atom, including the d-orbitals. This is the case for the comparison between Mo and M02 complexes with C z b , although this particular case has the unique feature that the d-orbitals form a very stable closed shell in the dimer. The generalization does apply to complexes of Cu and Cu2 with the n-acceptor ligands CO and C2H4. It is interesting to note that theoretical studies@of the bonding of CO on Cu, clusters in the size range n = 3-20 suggest that in all cases CO binds more strongly to the cluster than to a single copper atom. This is consistent with the simple concept of the generalizations above. The large difference in reactivity of Mo and M02 with respect to N20, as shown in Table 2, may have a similar origin in the reduced importance of repulsive interactions in the case of M02. 0-atom transfer reactions involving NzO and metal atoms have been extensively studied, and recently it has been shown41that correlations exist between experimental activation energy barriers for the oxidation reactions and atomic parameters of the metal atoms including ionization potential and certain promotion energies. These correlations point to a dominant role of repulsive interactions in controlling the rate of the reaction. Therefore, the considerations above concerning polarization mechanisms that reduce repulsion are relevant. Reactivity with respect to N20 may be determined by the same factors that govern complex formation with NH3: the inadequacy of 5s15p hybridization of Mo in comparison with 5so/5sa* mixing in Mo2, as a mechanism for reducing repulsion. Note, however, that these considerations do not seem to apply for the oxidation reactions of Mo and M02 with C02 and 0 2 . As Table 2 shows, the reactions with Mo are significantly faster in both cases. In the CO2 case this could arise because of significantly different preexponential factors for the Mo and M02 reactions, due to differing properties of the transition states. This could be further investigated by measurements of the activation energies of the reactions. The higher reactivity of Mo relative to M02 in the reaction with 0 2 is most likely a reflection of the radical-radical nature of the Mo reaction, which should favor high reactivity due to chemical bonding interactions in the intermediate complex.16
Conclusions In the first part of the paper we have described measurements of rate constants for several oxidation reactions of Ti and Cr atoms that were carried out to characterize the flow tube and laser vaporization source for kinetic studies in the range of total pressure 0.44-8 Torr near room temperature. Amval time distributions of Ti atoms were found to be approximately described by a simple model that assumes that the metal atoms
Flow Tube Kinetic Study of Mo and Mo2 Reactivity are instantaneously accommodated in the bulk flow of He carrier gas but have a significant initial spatial distribution along the flow direction. From the results of measurements of rate constants over the accessible range of total pressure, and by comparison with previous kinetic measurements using different experimental methods, it is concluded that the present method is subject to inherent uncertainties of approximately f 2 0 % in measured rate constants. Molybdenum atoms and dimers show interesting differences in reactivity under room temperature conditions. In several cases these differences can be rationalized by considering simple bonding mechanisms and by focusing on the role of repulsive interactions in the entrance channel. Dimers, and clusters in general, have mechanisms for reducing repulsive interactions that are not available to atoms, and this simple effect is expected to lead to enhanced reactivity relative to atoms. This is borne out by several comparisons of the reactivities of atoms and dimers of copper, silver, and molybdenum. Simple considerations of hybridization mechanisms lead to the expectation that in many cases end-on coordination geometries of ligands on dimers with valence sa2configurations are favored over side-on coordination geometries.
Acknowledgment. The authors thank Sophie Brunet and Sam Butler for their help as summer student assistants, and Peter Hackett for helpful discussions. References and Notes (1) Jarrold, M. F. In Advances in Gas-Phase Photochemistry and Kinetics. Bimolecular Collisions;Ashfold, M. N. R., Baggott, J. E., Eds.; Royal Society of Chemistry: London, 1989; pp 337-376. (2) Kaldor, A.; Cox, D. M.; Zakin, M. R. Adv. Chem. Phys. 1988, 70, 21 1-261. (3) (a) Salahub, D. R. Adv. Chem. Phys. 1987, 69, 447-520.
(b) Wahlgren, U.; Siegbahn, P. In Metal-Ligand Interactions: From Atoms, to Clusters, to Surfaces; Salahub, D. R., Russo, N., Eds.; Kluwer Academic Publishers: New York, 1992; pp 199-249. (4) Parks, E. K.; Winter, B. J.; Klots, T. D.; Riley, S. J. J . Chem. Phys. 1991, 94, 1882-1902, and references cited therein. (5) Weisshaar, J. C. Ace. Chem. Res. 1993, 26, 213-219. (6) Armentrout, P. B.; Beauchamp, J. L. Arc. Chem. Res. 1989, 22, 315-321. (7) Mitchell, S. A. In Gas-Phase Metal Reactions; Fontijn, A,, Ed.; Elsevier: Amsterdam, 1992; pp 227-252. (8) Morse, M. D. Chem. Rev. 1986, 86, 1049-1109. (9) Lian, L.; Akhtar, F.; Parsons, J. M.; Hackett, P. A.; Rayner, D. M. Z. Phys. D-Atoms Mol. Clusters 1993, 26 (Suppl), S168-170. (10) Lian, L.; Akhtar, F.; Hackett, P. A,; Rayner, D. M. Chem. Phys. Lett. 1993, 205, 487-492. (11) Lian, L.; Akhtar, F.; Hackett, P. A,; Rayner, D. M. Int. J. Chem. Kinet. 1994, 26, 85-96. (12) Lian, L.; Hackett, P. A,; Rayner, D. M. J. Chem. Phys. 1993, 99, 2583-2590.
J. Phys. Chem., Vol. 98, No. 45, 1994 11647 (13) Upschulte, B. L.; Shul, R. J.; Passarella, R.; Keesee, R. G.; Castleman, A. W. Jr. Int. J . Mass Spectrom. Ion Processes 1987, 75, 2745. (14) Ferguson, E. E.; Fehsenfield, F. C.; Schmeltekopf, A. L. Adv. At. Mol. Phys. 1969, 5, 1-56. (15) (a) Diffusion coefficient estimated by using simple hard-sphere model (Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954; p 14). (b) For Q = 15 000 sccm He at 296 K, and a = 3.65 cm (for RT-tube), the average bulk flow velocity [ v d m s-'] is related to the flow tube pressure [PITorr]as follows: vo = 49.2P. The observed peak arrival times of Ti atoms shown in Figure 3 imply velocities approximately two times larger than VO. The reason for this is that only atoms near the centerline are detected, and these atoms travel at twice the bulk velocity. (16) Brown, C. E.; Mitchell, S. A,; Hackett, P. A. J. Phys. Chem. 1991, 95, 1062-1066. (17) Ritter, D.; Weisshaar, J. C . J . Phys. Chem. 1989, 93, 1576-1581. (18) Ritter, D.; Weisshaar, J. C. J . Phys. Chem. 1990, 94, 4907-4913. (19) Campbell, M. L.; McClean, R. E. J. Phys. Chem. 1993,97,79427946. (20) Pamis, J. M.; Mitchell, S. A,; Hackett, P. A. J . Phys. Chem. 1990, 94, 8152-8160. (21) Futerko, P. M.; Fontijn, A. J . Chem. Phys. 1992, 97, 3861-3862. (22) Fontijn, A.; Blue, A. S.; Narayan, A. S.; Bajaj, P. N. Combust. Sci. Technol., in press. (23) Garland, N. L.; Nelson, H. H. Chem. Phys. Lett. 1992,191,269272. (24) Efremov, Yu. M.; Samoilova, A. K.; Kozhukhovsky, V. B.; Gurvich, L. V. J. Mol. Spectrosc. 1978, 73, 430-440. (25) Moore, C. E. Atomic Energy Levels; Natl. Bur. Stand. U.S. Circ. 1952, No. 467, Vol. III. (26) Benson, S. W. Thermochemical Kinetics; 2nd ed.; Wiley: New York, 1976; p 8. (27) Herzberg, G. Molecular Spectra and Molecular Structure I I Infrared and Raman Spectra of Polyatomic Molecules; Krieger: New York, 1991. (28) Mitchell, S. A. Int. J . Chem. Kinet. 1994, 26, 97-111. (29) Troe, J. J . Phys. Chem. 1979, 83, 114-126. (30) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J . Phys. Chem. 1992, 96, 9794-9800. (31) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell: Oxford, U.K., 1990. (32) Blomberg, M. R. A,; Brandemark, U. B.; Siegbahn, P. E. M.; Mathisen, K. B.; Karlstrbm, G. J. Phys. Chem. 1985, 89, 2171. (33) Mitchell, S. A.; Blitz, M. A.; Siegbahn, P. E. M.; Svensson, M. J . Chem. Phys. 1994, 100, 423-433. (34) Mitchell, S. A.; Blitz, M. A,; Foumier, R. Can. J . Chem. 1994, 72, 587-599. (35) Bagus, P. S.; Hermann, K.; Bauschlicher, C. W., Jr. J . Chem. Phys. 1984, 81, 1966-1974. (36) Curtiss, L. A.; Kraka, E.; Gauss, J.; Cremer, D. J . Phys. Chem. 1987, 91, 1080-1084. (37) Private communication of unpublished work by R. Foumier. (38) Blitz, M. A.; Mitchell, S. A.; Hackett, P. A. J . Phys. Chem. 1991, 95, 8719-8726. (39) Unpublished results from this laboratory. (40) Nygren, M. A.; Siegbahn, P. E. M. J. Phys. Chem. 1992,96,75797584. (41) Futerko, P. M.; Fontijn, A. J . Chem. Phys. 1991, 95, 8065-8072.
