Methane activation by vanadium(1+): electronic and translational

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J . Phys. Chem. 1987, 91, 6178-6188

6178

Methane Activation by V':

Electronlc and Translational Energy Dependence

N. Aristovt and P. B. Armentrout*t Department of Chemistry, University of California, Berkeley, California 94720 (Received: April 24, 1987)

The reaction of Vf with methane is studied as a function of translational energy in a guided ion beam tandem mass spectrometer. The effect of electronic energy is also probed by varying the conditions for forming V+. All observed processes are endothermic for the quintet ground state of V+. Excited triplet states of V+ are found to substantially enhance the reactivity. The results are interpreted to indicate that reaction occurs via a H-V+-CH3 intermediate which has a triplet ground state. The reactivities of the different electronic states of V+ can be explained by using simple molecular orbital concepts and spin conservation. Bond dissociation energies in VH', VCH', VCH2+,and VCH,' are reexamined and are found to be consistent with previous measurements.

Introduction Recent experiments done in our laboratory by Elkind and Armentrout (EA)'., have been successful in elucidating the effect of electron configuration on reactions of first-row transition-metal ions. These experiments focus on the electronic and translational energy dependences of the reactions of M+ and H2, HD, and D,. In this paper, similar methods are applied to understanding the reaction of M+ with methane where M = V. One question of particular interest is whether the ideas that have been developed by EA to understand the activation of dihydrogen by atomic metal ions will also be useful in describing C-H activation in methane. Studies of the reactions of atomic metal ions with CHI are V+$ Cr+,5 abundant. Recent results include ICR studies of Fe+,6 Nb+,7 Rh+,* and Ta+,9 ion beam studies of Sc+,lo Ti+,Io Cr+,11*12 Fe+,l39I4Co+,15 Ni+,13 Zn+,16 and U+,17and flowing afterglow studies of all first-row transition-metal ions.'* With two exceptions, no exothermic, bimolecular reactions are observed in any of these systems. One exception is that electronically excited states of Cr+ dehydrogenate methane.5*'1,'2A second exception is the observation of a similar reaction by Ta+, although it is unknown whether this result is due to an electronically excited specie^.^ This general lack of reactivity for atomic metal ions toward CH4 at thermal energies is not surprising. With the current pool of thermodynamic data, it can be predicted that all reactions of ground-state M + with CH, are endothermic. This is demonstrated unequivocally by the observation of such processes at elevated kinetic energies in beam studies. In the present study, we make a detailed examination of the reaction of V+ with methane. As with other atomic metal ions, ground-state vanadium ions do not react with methane at thermal energies. Translational energy does promote C-H bond cleavage to produce VH' and VCH3+ and elimination of H2 to form VCH2+. At higher energies, the latter two products lose hydrogen to make VCH'. Electronic energy is found to substantially enhance all reaction efficiencies and to lower the endothermicities of all reaction channels. For each of these products, reaction enthalpies are measured by monitoring the translational energy dependences. From this, the bond strengths in VH+, VCH', VCH2+, and VCH,' are derived and compared with values measured previously in studies of the reactions of Vf with H2,1 C2H2,C2H4, and C2H6.I9 Finally, this information is used to postulate a reaction mechanism for this simple metal ionhydrocarbon system which is compared with the reaction of Vf with dihydrogen. Experimental Section A complete description of the apparatus and its capabilities is given elsewhere.,O Briefly, the instrument used here is a guided ion beam tandem mass spectrometer which lends itself to facile t Present address: MPI fur Stromungsforschung, Bunsenstrasse 10, 3400 Gottingen, Federal Republic of Germany. NSF Presidential Young Investigator 1984-1989; Alfred P. Sloan Fellow. Present address: Department of Chemistry, University of Utah, Salt Lake City, UT 841 12.

0022-3654/87/209 1-6178$0 1.50/0

variation of both translational and electronic energy in the ion beam. The latter is achieved by changing the conditions in which the ions are formed. In this study four sets of ionization conditions are used: a surface ionization source (SI) at two temperatures, and an electron impact (EI) source at two electron energies. In the SI source, VOC13 vapor is allowed to flow over a resistively heated rhenium filament. Decomposition ensues and species with low ionization potentials desorb as ions from the filament surface. The temperature of the filament, 1850 f 100 or 2200 f 100 K, has been calibrated by using optical pyrometry. Assuming a Maxwell-Boltzmann distribution, the populations of the electronic states of Vf produced at these conditions are given in Table I. The average electronic excitation for the ion beam is -0.07 eV at 1850 K and -0.09 eV at 2200 K, with uncertainties of f0.005 eV . The assumption that the ion populations in the S I source are given by a thermal distribution has been tested by determining the dependence of certain reactions on the filament t e m p e r a t ~ r e ' ~ and by comparing experimental cross section magnitudes for specific metal ion states to those calculated by phase space theory,* or to those measured by using an E1 source,1'2or to those measured by using a drift cell source which produces ground-state ions exclusively.2 A more direct test is provided by recent measure(1) Elkind, J. L.;Armentrout, P. B. J . Phys. Chem. 1985,89, 5626-5636. (2) Elkind, J. L.; Armentrout, P. B. J. Chem. Phys. 1986,84,4862-4871; 1987,86, 1868-1877; Inorg. Chem. 1986,25,1078-1080; J. Am. Chem. SOC. 1986, 108, 2765-2767; J . Phys. Chem. 1986, 90, 5736-5745, 6576-6586; 1987, 91, 2037. (3) Byrd, G. D.; Burnier, R. C.; Freiser, B. S. J . Am. Chem. SOC.1982, 104, 3565-3569. (4) Jackson, T. C.; Carlin, T. J.; Freiser, B. S. J . Am. Chem. SOC.1986, 108, 1120-1126. ( 5 ) Reents Jr., W. D.; Strobel, F.; Freas 111, R. B.; Wronka, J.; Ridge, D. P. J . Phys. Chem. 1985, 89, 5666-5670. (6) Jackson, T. C.; Jacobson, D. B.; Freiser, B. S. J . Am. Chem. SOC.1984, 106, 1252-1257. (7) Buckner, S. W.; MacMahon, T.; Freiser, B. S. Organometallics, submitted for publication. (8) Byrd, G. D.; Freiser, B. S. J . Am. Chem. SOC.1982,104, 5944-5950. (9) Wise, M. B.; Jacobson, D. B.; Freiser, B. S. J . Am. Chem. SOC.1985, 107, 1590-1595, 6744. (10) Sunderlin, L.; Armentrout, P. B. J . Phys. Chem., submitted for publica tion. (1 1) Halle, L. F.; Armentrout, P. B.; Beauchamp, J. L. J . Am. Chem. SOC. 1981, 103, 962-963. (12) Georgiadis, R.; Armentrout, P. B., work in progress. (13) Halle, L. F.; Armentrout, P. B.; Beauchamp, J. L. Organomerallics 1982, 1, 963-968. (14) . . Schultz. R. S.: Elkind, J. L.; Armentrout. P. B. J . Am. Chem. Sot., in press. (15) Armentrout, P. B.; Beauchamp, J. L. J . Am. Chem. Sot. 1981, 103, 784-791. (16) Georgiadis, R.; Armentrout, P. B. J . Am. Chem. SOC.1986, 108, 2119-2126. (17) Armentrout, P. B.; Hodges, R. V.; Beauchamp, J. L. J. Chem. Phys. 1977, 66, 4683-4688. (18) Tonkyn, R.; Ronan, M.; Weisshaar, J. C.J . Phys. Chem., submitted for publication. (19) Aristov, N.; Armentrout, P. B. J . Am. Chem. SOC.1986, 108, 1806-1819. (20) Ervin, K. M.; Armentrout, P. B. J . Chem. Phys. 1985,83, 166-189.

0 1987 American Chemical Society

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6179

Methane Activation by V+ TABLE I: Electronic States of Vt and Their Populations

% population

electron confign

energy," eV

aSD aSF

3d4 4s3d3

0.02 0.36

a3F

4s3d3

1.10

a3P a3H b3F asp a3G b3G a'G

3d4

1.45 1.57 1.68 1.69 1.81 2.04 2.22

0.004 (2) 0.007 (4) 0.002 (2) 0.001 (1) 0.001 (1) 1.0 eV

1.20

0.99 (38)

0.304 (84)

> 1.4 eV

1.59

0.016 (9)

0.074 (28)

state

1850 Kb

2200 Kb

85.4 (1.4) 14.5 (1.4)

80.6 (1.3)1 19.1 (1.2)

30 eV 40c.d 45c

Estates

3d4 3d4 4s3d' 3d4 4s3d3 3d4

0.083 (30)

0.230 (56)

{ 96 3

jiy(7)d

50 eV -0c.d

7 s 3 (2)'

5

Wd

100. 31 (12)d 25c 32 ( l l ) d

"Energies are averaged over J levels taken from: Sugar, J.; Corliss, C. J . Phys. Chem. R e f Data 1978, 7 , 1191-1262. bMaxwell-Boltzmann distribution. Uncertainties due to the flOO K spread in filament temperatures are in parentheses. CEstimatedvalues from ref 1 . These are most accurately viewed as the true population times a relative reaction probability. dEstimates based on the behavior of the VCH,' product in this study (see text). CEstimatesbased on the behavior of the VHt product in this study (see text).

ments of Weisshaar and co-workers who produced vanadium ions with known state distributions via resonant multiphoton ionization.21 They find that V+(3F) reacts to dehydrogenate ethane with an efficiency of 0.43 f 0.17 at 0.2 eV. In our study of the V+ C2H6 reaction,Ig we observed this same reaction and attributed it to efficient reaction of the very small population of triplet states, primarily V+(3F). Assuming a Maxwell-Boltzmann distribution of states, the efficiency of the reaction in our study can be calculated from our published results to be 0.9 f 0.4 at 0.2 eV, in agreement with Weisshaar's result. Since the appearance potential of V+ from VOC13 is 26.8 f 0.4 eV,22 ionization of VOC13 by 30- and 50-eV electrons can produce highly excited vanadium ions. The distribution of states in these beams has been estimated by EA during their study of the V+ Hz reaction system.' Their results are listed in Table I and were obtained under the assumption that all states have equal reactivity. Thus, the figures listed actually represent the true populations multiplied by the relative reactivities of the different states. If unreactive states are present, these cannot be observed and will have no apparent population. As will be seen, the populations obtained by EA differ from those derived below indicating that the relative reactivities in the H2 and CH4 systems differ, not the true populations. After formation, ions are extracted from the source, focused into a magnetic sector for mass selection, and then injected at a well-defined translational energy into an octopole ion trap which passes through the collision cell containing the neutral reactant. The pressure in the collision cell is low enough, 2.3 eV. The energy dependence of the exothermic component is - p 5 for the 30-eV E1 data, -Eo5

Figure 5. Kinetic energy dependence of a(VCH,+) formed by reaction of methane with Vt produced by SI at 1850 K (-), by E1 at 30 eV ( O ) , and by E1 at 50 eV ( 0 ) as a function of translational energy in the

laboratory frame (upper axis) and the center-of-mass frame (lower axis). Arrows show the thermodynamic thresholds for reaction of V+(aJF)and Vt(a5D) at 1.27 eV and 2.37 eV, respectively, and for process 8 at 4.54 eV . for the 50-eV data below 0.2 eV, and --E' for 50-eV E1 between 0.2 and 1.0 eV. The magnitudes of these data at 0.1 eV are 2.3 X 10-4aLGsand 2.9 X 10-3uLGs,respectively. Thus, the fraction of excited states which this exothermic feature represents may still be a very small fraction of the beam, as small as 0.3% if these states react on every collision. Using a similar assumption, EA estimated that 0.2% of the beam was in states above 2.4 eV for 50-eV EI.' If the reactivity of these states is less than unity, these populations could be much higher. Modeling of a(VCH3+, SI) yields a threshold in excellent agreement with the expected value, Table 11, although with a rather large error. This error is attributable to the difficulty that the models have in reproducing the data precisely in the region between 2 and 3 eV, Figure 4. This difficulty is probably the result of small contributions from excited states. This explanation is plausible since the VCH3+ cross section observed when V+ is formed by 30-eV E1 matches the SI data below -2.5 eV when the former is appropriately scaled, Figure 4. The agreement between the threshold measured here for reaction 10 and that derived from previous workT9means that the structure of VCH3+ must be the same in both cases, that is, methylvanadium ion. We have previously argued by using bond additivity arguments [that is, assuming that Do(AV+-B) = Do(V+-B)] that other isomers (e.g., HVCH2+, H2VCH+, or H3VC+) are much higher energy species (by 1.43, 2.04, and 4.68 eV, respectively) than VCH3+.I9 Further confirmation of the structure is given by the fact that a(VCH3+, SI) reaches a maximum between 4 and 5 eV. This corresponds closely to the energy needed for dissociation of VCH3+ to V+ CH3, reaction 8. This observation contrasts with the results for VH+ and shows that the VCH3+formed in reaction 10 retains much more internal energy than the VH+ formed in reaction 7. This seems resonable considering that the neutral product in reaction 10 is a hydrogen atom which has no internal modes and cannot carry off much translational energy since it is a light particle. Finally, it is interesting to compare the absolute cross sections for formation of VCH3+to those for VH+. When these products are formed in an endothermic reaction by V+(5D) and possibly V+(5F), u(VH+) exceeds a(VCH3+) by a factor of about 4. When formed in endothermic reactions by excited states of V+ (mainly 3F), the factor is about 30 in favor of VH+. The first factor is consistent with concluding that V+(5D) reacts via a statistically behaved intermediate (see Appendix). The second factor indicates

+

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6183

Methane Activation by Vt ENERGY (el',

0.

0.5

ENERGY (eV, Lab)

Lob)

1.0

I. 5

2.0

ENERGY (eV, CU)

€"Y

Figure 6. Variation of the VCH2+cross section for reaction of V+ produced by SI at 1850 K (0)and 2200 K).( with methane as a function of translational energy in the laboratory frame (upper axis) and the

center-of-mass frame (lower axis). The solid lines through the points are the optimum fits to the data, convoluted over the experimental energy broadening. The dashed lines show convoluted fits for the individual components which comprise the optimum fit to the 1850 K data. Curves a, b, anc c represent contributions from Vt(a3P, or higher lying states), V+(a3F),and V+(aSD),respectively. that excited states react via a more direct process (see Appendix). EA drew similar conclusions for the endothermic reactions of these V+ states with dihydrogen based on branching ratios in the reactions of V+ HD.' Interestingly, a(VCH3+) is larger than a(VH+) by about 2.5 for the very small exothermic components. This could be the result of statistical behavior (now influenced by the fact that production of VCH3+is 0.08 eV more exothermic than VH' production), or of formation of a different isomer of VCH3+; however, it is unknown whether the same excited states are responsible for the exothermic formation of VH+ and VCH3+. VCH2+. As can be seen in Figure 1, the onset of the vanadium carbene ion occurs well below the thermodynamic threshold for reaction 11. Figure 6 shows a detailed view of a(VCH2+)in the

+

V+

+ CHI -,VCH2+ + H2- 1.48 f 0.07 eV

(11)

threshold region and compares the cross sections for V+ formed at filament temperatures of 1850 and 2200 K. As with VH+ formation, a large enhancement of the cross section occurs at the higher filament temperature. Clearly. the VCH2+ cross section contains significant contributions from reactions of electronically excited V+ that are proceeding with much greater efficiency than those of the ground state. This behavior is similar to dehydrogenation of ethane by V+.19 There, S I filament temperature dependence studies implicate the triplet states as the major reactant species and suggest that they react at close to the collision rate (=90 f 40% efficiency below 0.2 eV). This conclusion has been confirmed by Weisshaar and co-workers.21 Figure 6 clearly shows that there are exothermic reaction components at both 1850 and 2200 K. Energetically, the states responsible for these components should have electronic energies in excess of 1.48 f 0.07 eV. This identifies the responsible states as the a3P or above, Table I. The magnitudes of the cross sections below 0.15 eV are 0.4 X lo-4qGS (1850 K data) and 1.2 X 1 O 4 q G S (2200 K data). The ratio of these cross sections is about 3, close to the proportions of the states above 1 eV in the V+ beams, Table I. Note that no single state above the b3F has sufficient population to account for the magnitudes of the exothermic cross sections even if it reacted on every collision. This means that the primary reacting state (or states) of V+ responsible for the exothermic component is probably the a3P, a3H, or b3F; however, higher lying states may also contribute.

(eV, CH)

Figure 7. Kinetic energy dependence of a(VCH2+)formed by reaction of methane with V+ produced by SI at 1850 K (-), by E1 at 30 eV (0),

and by E1 at 50 eV ( 0 ) as a function of translational energy in the laboratory frame (upper axis) and the center-of-mass frame (lower axis). The dashed line shows the collision cross section, eq 5 , divided by 20. The fact that excited states are responsible for the low-energy behavior of reaction 11 is also verified by examination of beams produced by EI. Figure 7 shows that under both 30- and 50-eV EI, the cross sections are almost completely dominated by exothermic reactions. The change in slope of the cross section in the 30-eV E1 data near 0.6 eV indicates a contribution from endothermic reactions. The exothermic feature in the 30-eV E1 data below falls off as -E".5 and the 50-eV E1 data decline as 0.2 eV and as -E-'.5 between 0.2 and 0.5 eV. Their magnitudes at low energies are 0.020uLGs and 0.060aLcs,respectively. These values indicate an increase of 500 and 1500, respectively, over the 1850 K data, and 170 and -500, respectively, over the 2200 K data. These ratios lead to the estimated populations for the states above 1.4 eV listed in Table I. These values are in reasonable accord with the estimates of EA.' Three regions of varying energy dependence are evident in the SI data of Figure 6: the exothermic component, an endothermic component beginning about 0.2 eV, and a second endothermic component which starts at about 1 eV. We tentatively assign the reactivities of these regions to a3P or higher lying states: the a3F, and the aSDor aSF,respectively. Note that the separation between the two endothermic components is about 0.8 eV, in reasonable agreement with the aSF-a3Fsplitting of 0.74 eV. To determine VCH2+thermochemistry from the thresholds of the endothermic components in Figures 6 and 7, the three regions must be resolved from one another. We assume that the exothermic cross section behaves like the 50 eV data at low energies, but continues to decline as above 0.5 eV. A cross section with this behavior is shown in Figure 8. When this cross section is scaled by the populations given in Table I for states with Eel above 1.4 eV, the low-energy behavior for all four source conditions is reproduced nicely. This is shown explicitly in Figure 6 for the 1850 and 2200 K data. The curve in Figure 8 therefore represents our best estimate of the true cross section for states with Eel above 1.4 eV, the a3P and above. If these exothermic components of the cross sections are subtracted from the S I and E1 data, the remaining cross sections for all four source conditions can then be modeled with the forms of eq 2 given in Table 11. The average value of A E derived is 0.20 & 0.05 eV and the best value of n is 1 for all source conditions. A cross section with this behavior is shown in Figure 8 and attributed to the V+(3F) state as discussed above. The absolute magnitude of this curve is determined by the 3Fpopulations in the SI beams, Table I. In order to reproduce the E1 data as well, this cross section must be scaled by the populations of the a3F

- -

-

-

6184

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 ENERGY (eV, Lab) 100

Aristov and Armentrout at 1.16 f 0.05 eV is consistent with these if contributions from V+(aSF),AE = 1.30-0.36 = 0.94 eV, are considered. The best estimate of D0(V+-CH2)from the present experiment comes from the V+(a3F)threshold and is 3.47 f 0.14 eV. The uncertainty has been increased to account for errors introduced by subtraction of the exothermic component. This value is somewhat larger than those derived from previous measurements, 3.28 f 0.06 eV (from V+ C2H6) and 3.32 f 0.1 1 eV (from Vc + C,H,).19 However, the present data cannot be quantitatively interpreted if the bond energy is this low. Therefore, the present value is believed to be the best determination of Do(V'-CH2). This discrepancy is not believed to be due to structural differences in the VCHz' produced in these reaction systems. In all cases, the structure of the VCH2+species is believed to be the vanadium methylidene ion. By use of bond additivity arguments, the estimated enthaplies of formation of alternate isomers, HVCH' and H2VC+,are 0.65 and 3.17 eV more endothermic, respectively. The discrepancy may be due to activation barriers in the previously studied reactions. This possibility is consistent with the observation of an activation barrier of 0 . 6 4 . 9 eV in the reaction of SC' C2H6 to form SCCH,'.*~ Figure 1 shows that u(VCH,+) begins to decay above 2.3 eV. This is much lower than the thermodynamic thresholds of the dissociation reactions of VCH2+,reactions 12-14. This type of

+

ENERGY (eV, CV)

Figure 8. Approximate state-specific cross sections for formation of VCH,+ by reaction of methane with Vt(a5D) (dotted line, multiplied by a factor of IOO), Vt(a3F) (full line), and V+(a3P,or higher lying states) (dash-dot line) as a function of translational energy in the laboratory

frame (upper axis) and the center-of-mass frame (lower axis). The dashed line shows the collision cross section, eq 5 , divided by 4. state given in Table I. Note that the populations for the 3F state derived in this way are in reasonable agreement with those estimated above from a similar analysis of the VH' product channel. The discrepancies illustrate that absolute errors intrinsic in these kinds of population estimates. To extract the threshold for the second endothermic component of the SI data, fits to the low-energy endothermic component are subtracted from each of the curves. Modeling of the second threshold for the SI data by the parameters of Table I1 gives an overall AI? of 1.16 f 0.05 eV. The best value of n again appears to be near 1.0. A cross section with this behavior is shown in Figure 8. To reproduce the 30- and 50-eV E1 data, 40% and 0% contributions of this endothermic curve, respectively, are necessary. This gives populations of the a5D and aSFstates in the E1 beams which are in good agreement with those derived by EA, Table

I.' In this analysis, we have derived models for the three main components which contribute to reaction 11, and approximate populations for the states responsible for each component, Table I. W e therefore have been able to estimate the absolute cross sections for these states, Figure 8. By combination of these cross sections with the state populations listed in Table I, the experimentally observed cross sections for the SI and E1 data can be accurately reproduced. This is shown explicitly for the S I data in Figure 6. Note, however, that the populations for the excited states may be in error by as much as 50%. This means that the absolute cross sections for these states may vary from that shown in Figure 8 by a comparable amount. Even given this rather large uncertainty, it is clear that the excited triplet states are much more reactive than the quintet states. By comparing these cross sections with the collision cross section according to eq 5, we can estimate the reaction efficiencies for the various states. For the states with E,, > 1.4 eV, V+(3P, ...), the reaction efficiency is about 20 f 10% below 0.1 eV. The cross section for V+(3F) reaches a similar efficiency at about 1.5 eV. In contrast, the ground state cross section reaches a maximum efficiency of only 0.08% at about 2 eV. Thus, the triplet states are well over 2 orders of magnitude more reactive than the quintet states. The thermochemical implications of this analysis are as follows. If reaction 11 is exothermic for V+(a3P),E,, = 1.45 eV, then the threshold of reaction of ground state V+ must be 5 1.45 eV. This is consistent with assignment of the 0.20 f 0.05-eV threshold to reaction of V'(a3F), E,, = 1.10 eV, since this means that the ground-state threshold is 1.30 f 0.05 eV. The second threshold

+

V'

-

+ CH4

-

+ H + H2

VCH'

4.25 f 0.09 eV (12)

+ 2H2 - 4.24 f 0.04 eV

VC' V+

-

+ C H 2 + H, - 4.78 f 0.04 eV

(13) (14)

result can occur when the intermediate which is the precursor to VCH2+ is depleted by other processes. Reactions 7 and 10 are likely candidates since both have ground-state thresholds in the vicinity of 2.3 eV. Because the increase of reaction 10 (-0.0015 A* between 2 and 3 eV) is much smaller than the decrease in u(VCH2+) (-0.006 A2 between 2 and 3 eV), reaction 7 (which increases -0.02 A2) is clearly the major competitor. The fact that VH' competes so strongly with VCH,' is evidence that these two products come from the same reaction intermediate. For the E1 data under both sets of ionization conditions, the VCH2+ cross sections decrease sharply near 1.5 eV. A 2-eV downward shift in the thresholds of processes 12-14 still places them above this energy. Thus, it is most likely that the falloff is again due to competition from VH' production by excited states. A second reaction which produces VCH2+ can be seen by the rise in its cross section near 6 eV, Figure 1. This is due to process 15, corresponding to hydrogen atom loss from VCH3+. A similar reaction was also observed in our study of the reaction of V+ C2H6.'9 This cross section reaches a maximum at about 9 eV corresponding to competition from reactions 16-1 8 at higher energies. Since VC' is not observed and g(VCH') does not

+

V+

+ CH,

-

-

VCH,'

VCH+

+ 2H - 6.0 f 0.1 eV

+ 3H - 8.8 f 0.2 eV

(15) (16)

VC'

+ H, + 2H - 8.76 f 0.04 eV

(17)

V+

+ CH2 + 2H - 9.30 f 0.04 eV

(18)

increase near 9 eV, process 18 is probably the major decomposition channel. Process 15 was not studied under E1 conditions. VCH'. Reaction 12 produces the vanadium methylidyne ion, Figures 1 and 9. This corresponds either to decomposition of VCH3+by loss of H, or to decomposition of VCH2+ by H atom loss. There is no SI filament temperature effect in u(VCH+). This suggests that VCH3+is the major precursor since u(VCH3') has no temperature dependence while a( VCH2+)does. Analysis of the VCHf cross section yields APE = 4.05 f 0.29 eV, Table I1 and Figure 9. This leads to Do(V+-CH) = 5.13 f 0.29 eV which is consistent with our previously reported value of 5.00 f 0.06 eV (from V+ + C,H,) and 4.86 f 0.1 1 eV (from an evaluation CH4 data).I9 The result from this study of preliminary V' replaces the previous CH,-based value, so that the best value of

+

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6185

Methane Activation by V+ ENERGY (eV, Lab) 10.0

0. oo!

30.0

20.0 I

I

L

ENERGY (eV, Lab)

40.0 I

I ' I I

t

t'

1

.

50 eV

*.

0

H

c 0.

8 0

I

0.

4.0

2.0

6.0

8.0

10.0

ENERGY (eV. CM)

D"(V+-CH) is taken as 5.00 f 0.06 eV. At about 6 eV, o(VCH+) begins to decrease. This does not correspond to either of the two possible decomposition pathways, H atom loss in reaction 17 or reaction 19. The only reasonable

+ CH4

-

V+

+ C H + H2 + H - 9.2 eV

e,

100

10'

cn) Figure 10. Kinetic energy dependence of a(VCH+) formed by reaction of methane with V+ produced by SI at 1850 K (-), by E1 at 30 eV ( O ) , and E1 at 50 eV (0) as a function of translational energy in the laboratory frame (upper axis) and the center-of-mass frame (lower axis). ENERGY (ev.

Figure 9. Variation of the cross section for formation of VCH' by reaction of V+ (produced by SI at 1850 K) with methane as a function of translational energy in the laboratory frame (upper axis) and the center-of-massframe (lower axis). The line is an m = 1 fit to the data, using the average AE given in Table 11, convoluted over the experimental energy distribution. The dashed line shows the unconvoluted fit.

V+

10-1

anisms for this dehydrogenation step: via intermediate I1 or via the four-center transition state, 111. We believe that the former H

\+ V,

H *- H

I+

H'

(19)

explanation for this behavior is that the precursor to VCH+ is being depleted. This is further evidence that VCH+ is formed via VCH3+, since u(VCH3+) declines in this energy region due to reaction 8. This indicates that a viable but minor decay route for methylvanadium ion is dehydrogenation. The same conclusion was reached for decomposition of VCH,' produced by reaction of V+ + C2H6.I9 Under 30-eV E1 conditions, (r(VCH+) has only an endothermic component which begins at 2.11 f 0.17 eV and peaks between 4 and 5 eV, Figure 10. This is a -2-eV shift down from the threshold and peak for process 12 observed under SI conditions. In the 50-eV E1 data, an exothermic component is again observed and declines as --E-'. The presence of this component means that excited states with E,, = 4.25 f 0.1 eV or higher are formed. This corresponds to the 25th excited state of V+ or above. The fraction of these states can be calculated as 4.4 X l@ by assuming that the reaction proceeds at the LGS limit. This value is a lower limit to the true fraction since these states may be less reactive than this.

Discussion In this section, the information presented above is used to postulate a mechanism for the reaction of V+ with methane. This mechanism must not only explain the observed products but also the dependence on electronic excitation. The presence of exothermic channels and the 1-2-eV downward shift of endothermic components in all products in the electron impact data indicate that electronic energy is efficiently coupled into the reaction coordinates. However, the data also indicate that the effect of electronic energy differs for different reaction channels. For example, production of VH+ and VCH2+ is strongly enhanced by the triplet excited states while the effect on the VCH3+ product is considerably less dramatic. A simple reaction mechanism for the interaction of V+ with methane involves oxidative addition of the C-H bond at the metal center to form intermediate I, HVCH3+. Indeed, it is difficult to imagine how the production of VCH2+ + H 2 could occur without such an insertion step. We envision two possible mech-

I

V ;;CHZ

=CH2

I11

I1

mechanism is unlikely for several reasons. First, by using bond additivity arguments, we estimate the production of I1 from V+(5D) + CH4 to cost 1.7 eV. This is -0.4 eV higher than the measured threshold for dehydrogenation. Second, we observe that both Sc+ and Ti+ also dehydrogenate CH4 at low kinetic energ i e ~ . " . ~ Intermediates ~ similar to I1 for these metals must be even higher energy species since Sc+ and Ti' do not have enough valence electrons (2 and 3, respectively) to form a covalently bound structure like 11. The second mechanism, four-center elimination via 111, is quite reasonable based on calculations of Steigerwald and G ~ d d a r and d ~ ~R a ~ p e .They ~ ~ find that such eliminations can be facile if the metal-ligand bonds are covalent and have significant d character. Both of these conditions are probably met by intermediate I.40s41 An intermediate such as I also cleanly explains the observed competition between VCH,+ and VH+ products. Clearly, VH+ can be formed by cleavage of the V-C bond in I. Since this process is a simple bond cleavage while dehydrogenation proceeds through a tight transition state, this competition favors VH+. Likewise VCH3+ can be formed by cleavage of the V-H bond in I. The feasibility of intermediate I is further strengthened by the fact that we have observed VCH4+ as a product in the reaction of V+ with 2-methylpropane and 2,2-dimeth~lpropane.~~ From analysis of the observed cross sections, we have measured the sum of the V+-H and V+-CH3 bond energies in this species to be 4.03 f 0.25 eV. Since D"(H-CH,) = 4.54 eV, this thermochemistry indicates that formation of VCH4+ from V+(5D) CH4 is endothermic by 0.51 f 0.25 eV. As a consequence, this value cannot refer to a structure where methane is loosely bound to the vanadium ion, Le., V+-CH4, since this adduct must be lower in energy than separated V+ CH4. However, this value is very

+

+

(32) Armentrout, P. B. "Gas Phase Inorganic Chemistry", in Modern Inorganic Chemistry; Russell, D. H., Ed.; Plenum: New York, in press. (33) Steigerwald, M. L.; Goddard, W. A. J . Am. Chem. SOC.1984, 106, 308-3 1 1 . (34) Rappe, A. K. Organometallics 1987, 6, 354-351. (35) Aristov, N.; Armentrout, P. B., work in progress.

6186

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987

, 2-

/

A

>

Aristov and Armentrout erations indicate that the surface evolving from a3F crosses that evolving from a3P. As shown in Figure 11, this surface crossing may be avoided such that a3F could form I by mixing with the attractive surface of the a3P or higher states. This corresponds to moving the electron originally in the 4s orbital into a 3d orbital to remove the repulsive interactions. Now consider the spin states of the dehydrogenation products, VCHz+ HZ(lZg+).The metal methylidene is presumed to have a triplet ground state since its bond energy indicates a double V-C bond leaving two unpaired electrons on the meta1.38139 The enormous enhancement in the dehydrogenation reaction observed for the triplet states can therefore be explained as a result of favorable energy and spin, Figure 11. (We and Sanders et al. have drawn a similar conclusion for dehydrogenation of ethane by V+.)19*2'Reaction of the quintet states to form VCH,' must occur via a crossing from a quintet surface to a triplet surface. Such a crossing clearly exists, Figure 11, but to occur must involve spin-orbit coupling of these surfaces. The relative inertness of the quintet states therefore suggests that such spin-orbit coupling is rather inefficient in this system. For the high energy endothermic processes, production of VCH3+and VH', the spin states of the products are CH3(zA2/'), ~ ~VH+. , ~ ~ For H(*S), and a quartet state (4A ground ~ t a t e ) ' , for VCH3+,we assume that the V-C bond is a single covalent bond leaving three unpaired electrons on the metal such that this species also has a quartet spin.39,42Thus, formation of VH+ and VCH3+ are spin-allowed from both quintet and triplet V+ states. Because of this, these reactions may not be as sensitive to the reactant state as the dehydrogenation reaction. Indeed, the absence of a temperature effect in a(VCH3f) is consistent with this argument. However, a(VH+) does exhibit an enhancement with increasing triplet state fraction at low energies. One explanation for this recalls that the excited states form VH+ preferentially by a factor of about 30 over VCH3+,as noted in Results. As discussed in the Appendix, this is taken to indicate that these states react to form VH+ via a direct process. If viewed as an abstraction or stripping process, a direct reaction would not be expected to produce much VCH3+ but could yield VH+ with high efficiency. In contrast, the ground state reacts to form only -4 times as much VH+ as VCH3+ in the threshold region. This result is taken to indicate that the quintet states (dominated by the 5D react via a more statistically behaved intermediate. This intermediate could be the ground state of HVCH3+ accessed via spin-orbit coupling, or it could be an excited state of this species having quintet spin. A final point of interest concerns the persistence of the VH+ product to very high energies. As noted in Results, the SI cross sections begin to increase starting -4.5 eV. This reactivity is attributed to the quintet states of V+ and is consistent with an impulsive type of mechanism due to a repulsive reaction surface. The explanation for this first points out that for the V+(aSD,3d4) state, there is a single hole in the five 3d orbitals. For this state, the 3da orbital is empty in only one out of five possible electron configurations. As discussed above, molecular orbital arguments contend that occupation of the 3da is unfavorable to reaction. As V+(aSD) approaches CHI, the surface degeneracy breaks such that five quintet surfaces evolve (some of these may be degenerate depending on the symmetry). One of these surfaces (corresponding to a 3da hole) should be most reactive and is probably responsible for the reactivity of V+(a5D) observed at the thermodynamic threshold. Four of these surfaces have the repulsive character induced by occupation of the 3da orbital which can lead to an

+

Figure 11. Semiquantitative potential energy diagram for the interaction of V+ with methane.

reasonable for structure I since it is close to the value predicted by simple bond additivity, Do(V+-H) Do(V+-CH3) = 4.26 f 0.12 eV, Table 111. Further, it also agrees with a more sophisticated estimate which includes the energy due to electron-exchange interactions, 4.0 f 0.1 eV.36 Note that this thermochemistry suggests that reductive elimination of methane from I to form ground-state species is exothermic. Since VCH4+ is observed, however, I must be at least metastable which indicates the presence of a barrier to this reductive elimination. We propose that the origin of this barrier is due to differences in spin of the various species involved. If I truly contains covalent V-H and V-C bonds, then two of the four valence electrons on V+ are involved in bonding. Therefore, the ground state of I must be a triplet, while the ground-state reactants are a quintet, V+(a5D),and a singlet, CH,('A,). These considerations lead to the conclusions that formation of I is both endothermic and spin-forbidden for reaction of either the V+(SD) or the V+(5F) state. However, the triplet states of V+ can form I in exothermic and spin-allowed processes. A more detailed understanding of how individual states of V+ will interact with methane can be obtained by using simple molecular orbital arguments which have been quite successful in elucidating the reactivities and mechanisms of atomic transition metal ions with dihydrogen.'q2 Oxidative addition of an H-H or C-H bond to a metal center is achieved by donation of the bonding a electrons into empty 4s and 3da orbitals of the metal and back-donation of metal 3d7r electrons into the a* antibonding 0rbita1.'*~*~' This synergistic effect both increases the electron density between the metal and the molecular fragments and lengthens the H-H or C-H bond. This picture further predicts that metals in states having electron configurations with occupied 4s (and to a lesser extent 3da) orbitals will have repulsive interactions with the H-H or C-H bonding a electrons.'Bz Thus, these states are generally much less reactive with H-H or C-H bonds than those with empty 4s and 3da orbital^.^*'^ This implies that of the lower electronic states, the a 5 F and a3F (which have 4s3d3 configurations), will have repulsive surfaces. In contrast, the states having 3d4 configurations, e.g., a5D, a3P,a3H, b3F, avoid these repulsions and have more attractive surfaces. Based on these ideas, the correlations shown in Figure 11 can be drawn. This diagram shows an initial interaction for all states that is attractive due to the ion-induced dipole potential. Both the aSFand the a3F states have repulsive surfaces at closer distances since the 4s orbital is occupied. The a5D surface is presumably less repulsive than these states since it has a 3d4 configuration; but this state has the wrong spin to produce groundstate HVCH3+. Therefore, this surface also must rise at close interaction distances. The a3Pstate (which we let represent other higher lying states as well) has both the correct spin and electron configuration to smoothly generate I. Notice that these consid-

+

~~

~

(36) Tolbert, M A , Beauchamp, J L J Am Chem Soc 1986, 108, 7509-7517 (37) Saillard, J Y , Hoffmann, R J A m Chem Soc 1984, 106, 2006-2026

(38) Simple atomic coupling arguments as outlined in ref 1 can be used to suggest that the ground state should be either 3BI or 'B2 (two nonbonding electrons, one in the remaining P orbital and one in a 6 orbital). (39) Aristov, N.; Armentrout, P. B. J . Am. Chem. Soc. 1984, 106, 4065-4066. (40) Schilling, J. B.; Goddard, W. A,; Beauchamp, J. L. J . Am. Chem. Soc. 1986, 108, 582-594; to be published. (41) Pettersson, L. G. M.; Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. J . Chem. Phys. 1987, 87, 481-492. (42) Simple atomic coupling arguments as outlined in ref 1 can be used to suggest that the ground state of VCH3+should be either 4AIor 4Az(three nonbonding electrons, one in each of the two P orbitals and one in a 6 orbital).

The Journal of Physical Chemistry, Vol. 91, No. 24, 1987 6187

Methane Activation by Vs impulsive reaction mechanism. The observed results at high energies may then be due to reactions on these four surfaces. Similarly, surfaces evolving from V+(a5F) CH4 should also be repulsive due to occupation of the 4s orbital. An argument similar to this was used by EA to explain the absolute magnitude of the cross section for the V+(a5D) + H2 reaction.’

M+

+

Summary The results of this study indicate that the most likely reaction mechanism for the V+ CH4 system proceeds via oxidative addition of a C-H bond to yield I, HVCH3+. Four-center molecular elimination of H2leads to VCH2+ and at higher energies, simple bond cleavages produce VH+ and VCH3+. It would also appear that VH+ can be produced by a direct abstraction mechanism and by impulsive reactions at very high collision energies. VCH+ is formed by decomposition of these products, primarily VCH3+. The triplet states of V+ are found to be much more reactive than the quintet states. This is shown by the approximate state-specific cross sections such as those shown in Figure 8. While there are sizable errors in the determination of the absolute excited-state cross sections, the different reactivities are clear and unambiguous. The rationale for this behavior is that the triplet states can more easily form the triplet ground state of the insertion intermediate I because of spin conservation and thermochemistry, Figure 11. Some reactions of the quintet states of V+, specifically dehydrogenation, must involve spin-forbidden processes which require spin-orbit mixing. This mixing is apparently inefficient in this system. Simple molecular orbital arguments which have been tremendously useful in understanding the reactions of atomic transition metals with H2Iv2appear to remain valid for reactions with CHI. These considerations lead to reasonably detailed potential energy surfaces, some of which are shown in Figure 11. Thermochemistry for VH+, VCH3+, VCH2+, and VCH+ is reevaluated and compiled in Table 111. Good agreement with previous results is found for the first, second, and third molecules. The vanadium methylidene ion bond energy is found to be slightly stronger than previously r e p ~ r t e d . ’ ~This . ~ ~implies that the reactions used to derive this value in our earlier work (V+ + C2H6 VCH2+ + CH,, and V+ + C2H4 VCH2+ + CH2) had activation barriers of about 0.2 eV. This conclusion is consistent with a similar observation for the reaction, Sc+ C2H6 ScCH2+ + CH4.25 It will be interesting to see whether the detailed conclusions of this work are verified by similar studies with other metal ions. Studies evaluating the reactions of methane with Sc’, Ti+,’O Cr+,I2 and Fe+ l 4 in different electronic states are forthcoming. Preliminary results indicate that the picture derived in this study is fairly typical.

+

-

-

+

-

Acknowledgment. This work is supported by National Science Foundation Grant No. CHE-8608847. We also thank the Monsanto Co. for their generous contributions and Y. T. Lee, D. Neumark, R. Schultz, and L. Sunderlin for useful discussions regarding the branching ratio arguments.

Appendix: Reaction Branching Ratios There are several influential factors in determining the branching ratio in a bimolecular reaction. These factors depend heavily on the reaction mechanism. While inferring reaction mechanisms from branching ratios cannot be unambiguous, broad classes of behavior can be illustrated. The first step in this process is to identify those factors which must occur in all reactions, regardless of mechanism. Chief among these is the conservation of energy and angular momentum. We have discussed these factors in earlier r e p ~ r t s ’ ~and ~ Jused ~ ~ ~them ~ to successfully explain the branching ratio between MH+ and MD+ in reaction of M+ with H D and other in other reactions. Here we are concerned with the more complex problem of the branching ratio between processes A1 and A2 (reactions 7 and 10, respectively, for M = V).

+ CH4

-

MH+

+ CH,

(AI)

+H

(‘42)

MCH,’

Consider reactants of relative velocity u and reduced mass p evolving to products with similar quantities denoted by primes. Then L = pub = ( 2 ~ E ) ’ / ~and b L’= (2h’E9’I2b’, where E and b are the translational energy and impact parameter, respectively. We note that the rotational angular momentum of the reactants, J , is small compared with L. As a first approximation, we also presume that J’, the products’ rotational angular momentum, is much smaller than L’. Then, L i= L’ such that eq A3 is found after substitution. If the reactions under consideration are enb = b’(p’E’/pE)’/’

(‘43)

dothermic (as in the case for most states of M+), then E’ IE - AE. Also, p’ < /I for both reactions A1 and A2. Therefore, b must be less than b’, i.e., the entrance channel impact parameter which can lead to products is limited by angular momentum conservation in the exit channel. Hence the maximum cross section for product formation is given by u

= ?rbma2= ?rb’,,,,:(p’E’/FE)

(A4)

The exit impact parameter is limited by the LGS cross section, eq 5, such that bkaX2= (2e2cu’/E91/2. Substituting this into eq A4 gives a = ~e$(2a’E9~/~/pE

(‘45)

This equation can also be derived by using microscopic reversibilit~.~~ Now consider the two different product channels A1 and A2, indicated by subscripts 1 and 2. The ratio of cross sections for = 11.65 these products is given by eq A6. When M = V, u1/ u2 = (d1 E ‘I / af2E‘2) II2p‘]

(-46)

amu, wr2 = 0.99 amu, af1= a(CH3) = 1.95 A3, and af2= a ( H ) = 0.67 This gives ul /a2 = 20(E’1/E\)1/2. Since the product channels have nearly equal endothermicities (differing by only 0.1 eV), it is likely that E’I i= E’2. Thus, a first-order approximation for the cross section ratio is 20. Now consider what happens for nonzero J’. If L’ and J’ are parallel, then b’ must be smaller and hence, according to eq A4, so is a. If L’ and J’ are antiparallel, the maximum relative translational energy E’must decrease, again limiting u. Another way of looking at the reaction process considers dynamical constraints in the exit channels. In a reaction like M+ + CH4, the translational energy of the reactants must become internal energy of the transient intermediate. Specifically, the total angular momentum of the intermediate, K, must equal L (since J is negligible), and also K = (21E,)1/2 where I is the moment of inertia and E, is the energy in overall rotation of the complex. As the intermediate evolves to products, it can take on the form of “MH+-CH3” or “H-CH3M+”. These species have approximately the same reduced masses as the products of reaction A1 and A2, respectively, such that for a separation r in the exit channel, I = p ’ 9 and E, = €?/2p‘$. Since K’] > F ’ ~ this , equation shows that if an intermediate with a given K evolves along the A1 channel, it has less energy tied up in rotation (and hence, a lower dynamic barrier) than one evolving along the A2 channel. This dynamic rotational barrier cannot exceed the maximum energy available to the products, E, 5 E - AE. This means that the range of entrance channel impact parameters which can lead to MH+ formation is larger than the range leading to MCH3+ , shown explicitly by eq A7. formation (again because 11’’ > F ’ ~ ) as A3.44345

b = L / p u = K / p u = r(p’Er/wE)’/2

(‘47)

(43) Levine, R. D.; Bernstein, R. B. J. Chem. Phys. 1971, 56, 2281. (44) Miller, T. M.; Bederson, B. Adu. Atomic Mol. Phys. 1977, J3, 1-55. (45) a(CH3) calculated using the methods outlined in Miller, K. J.; Savchik, J. A. J. Am. Chem. SOC.1979, 101, 7206-7213.

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The Journal of Physical Chemistry, Vol, 91, No. 24, 19‘87

By using these same arguments in the exit channel, it must be l I ~ L’ = p’v‘b’ = the case that L’ = (21E’r)1/2= r ( 2 ~ ’ E ’ ~ )and b’(2/1’E’)’12such tbat Etr= E‘(b‘/r)2. Substituting this into eq A7 yields eq A8, comparable to eq A3. Using the same arguments applied above, we can show that the ratio of cross sections is given by eq A9, similar to eq A6. If there is not mechanism for

b = b’(~’E’//IE)1/Z(E,/E’,)’~2 (A8)

converting the overall rotational energy of the dissociating complex into internal rotational energy of the fragments, then E, = Ellr = Elzr, reproducing the result above. (This is equivalent to the contention that L = L’.) Even if this is not strictly true, this same result is obtained as long as E ; , = Etzr,a reasonable proposition since both channels have approximately the same total available energy. The assumption that Etl = E’, is the result of statistical behavior. In an impulsive reaction (spectator stripping is an exa m ~ l e ) ,this ~ , ~assumption ~ is inappropriate. In this limit, the reaction depends on the effective energy between the incoming ion and the atom (or group of atoms) with which it first interacts. It is straightforward to show that the translational energy of the products is given by eq A10, where A, B, and C represent the E’ = E A C / ( A + B ) ( B + C) 6410)

+

-

masses of the species in the general reaction, A BC AB + C. For reactions 7 and 10, this equation gives Etl = 0.92E and E‘, = 0.05E, respectively, such that E’l/E’, = 19. Substituting this back into eq A6 gives the branching ratio, u1/u2 = 88. If the reaction is direct but not impulsive, we would still expect that E’, > El2, but by less than a factor of 19. Experimentally, we observe a large branching ratio (u(VH+)/u(VCH3+) = 30) for reaction of methane with the triplet states of V+. Reaction of the quintet states of V+ yields a much smaller ratio, -4. The angular momentum arguments presented above explain most of the former result, and can be quantitative if the reaction is direct (although clearly not in the impulsive limit). However, these arguments clearly cannot account for the latter experimental result. The simplest approach to explaining this notes that in a direct reaction, the vibrational, rotational, and translational degrees of freedom of the transient intermediate do not (46) Henglein, A. In Ion Molecule Reactions in the Gas Phase; Ausloos, P. J., Ed.: American Chemical Society: Washington, DC, 1966. Ding, A,; Lacmann, K.; Henglein, A. Ber. Bunsen-ges. Phys. Chem. 1967, 71, 596.

Aristov and Armentrout completely equilibrate. The product cross sections therefore depend primarily on the angular momentum arguments described above. If the intermediate is statistically behaved, however, the internal degrees of freedom should equilibrate, and this will change the branching ratio. As a zeroth-order approximation to including the internal degrees of freedom, we treat the methyl group as a structureless species, Me. Since Do(Vf-H) = Do(V+-CH3), Table 111, we presume that VH+ and VMe+ have similar force constants and bond distances. Then, VH+ and VMef will differ in their vibrational frequencies and rotational constants primarily due to changes in the reduced mass, m, of the diatom or pseudodiatom since w a m-ll2 and B a m-l. Given that m(VH+) = 1 amu and m(VMe+) = 11.6 amu, the internal density of states for VMef formation is greater than that of VH+ by 11.63/2= 40. If we now consider that the methyl group is not structureless, we find that the M-C-H bending vibrations (doubly degenerate) in MCH3+ become free rotations of the methyl group in the MH+ + C H 3 channel. This increases the density of states for VH+ formation relative to VCH3+ production. Most of the other internal motions of CH3 (CH bends, C H stretches, and rotation about the z axis of CH3) do not change a great deal (although the frequency for the umbrella motion decreases somewhat for free CH3). All of these various considerations can be accounted for by using phase space theory which explicitly includes vibrational and rotational states as well as energy and angular momentum con~ervation.~’ Molecular constants are known (either from experiment or theory) for all species here but VCH3+and these are estimated. Test calculations find that the ratio of u(VH+)/u(VCH3+) varies from about 4 to 20 for reasonable values of the molecular constants of VCH3+. This variation depends most heavily on the choice of the average rotational constant (Bavg= 0.3 to 0.9 cm-I) and the V-C-H bending frequencies (400-800 cm-I). Nevertheless, this calculation demonstrates that a statistically behaved intermediate can produce a branching ratio of about 4. We therefore believe that branching ratios which are less than a factor of 20 in favor of reaction A1 probably indicate a statistically behaved intermediate while ratios which are greater than 20 indicate a direct reaction. Registry No. V+, 14782-33-3; CH,, 74-82-8; VCH2’, 110638-17-0; VCH’, 101653-82-1; VC*, 110638-18-1; VH’, 83018-01-3; HV’CH,, 110638-19-2. (47) Details of the phase space theory programs used here are outlined in Grice, M. E.; Song, K.; Chesnavich, W. J. J . Phys. Chem. 1986, 90, 3503-3509 and references therein.