9110
J. Phys. Chem. 1995,99, 9110-9117
The Potential Energy Surface for Activation of Methane by Cos: An Experimental Study Chris L. Haynes, Yu-Min Chen? and P. B. Armentrout" Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 Received: January 13, 1995; In Final Form: March 24, 1995"
+
+
A guided-ion-beam mass spectrometer is used to study the reactions of Co' CD4 and CoCH2+ D2 and thereby experimentally probe the potential energy surface for activation of methane by Co'. The results obtained are compared to recent theoretical results and agree with the conclusion that dehydrogenation of methane by Co+ is hindered by a tight four-center transition state complex. The major discrepancy observed between experiment and theory is in the height of this barrier, which theory predicts is 96- 109 kJ/mol versus our experimental result of 34 f 8 kJ/mol. The endothermicities of all reactions are measured and allow the determination of Do(Co+-CD) = 422 f 37 kJ/mol and Do(Co+-C) = 347 f 29 kJ/mol. We also find extensive hydrogen scrambling in the CoCH2+ DZreaction, a result that is interpreted by using phase space theory to help understand how various features on the potential energy surface control branching ratios among the various channels observed.
+
Introduction
Experimental Section
Over the past two decades, considerable research has focused on understanding the ability of atomic transition metal ions to activate C-H and C-C bonds in saturated hydrocarbons.',2 A particularly interesting aspect of this gas-phase research is the periodic trends in this chemistry. For instance, Armentrout and Beauchamp3 note that in the interactions of methane with early first row transition metal ions, reactions 1-3 are all observed with reaction 1 dominating at low energies and reaction 2 at high energies. In contrast, reaction 1 is a minor process
The experiments are performed on a guided-ion-beam tandem mass s p e c t r ~ m e t e requipped ~~'~ with a dc discharge/flow tube ion source, as described below. The ions generated are extracted from the source, accelerated, and passed through a magnetic sector for mass analysis. The mass-selected ions are decelerated to the desired kinetic energy where they are focused into an octopole ion trap. This device uses radiofrequency electric fields to trap the ions in the radial direction and ensure complete collection of reactant and product ions." The octopole passes through a gas cell of effective length 8.26 cm that contains the neutral collision partner at a pressure sufficiently low that multiple ion-molecule collisions are improbable. It was verified that the results presented here exhibit no dependence on pressure and thus correspond to single ion-molecule collisions. The unreacted parent and product ions drift to the end of the octopole where they are extracted, passed through a quadrupole mass filter for mass analysis, and detected with a secondary electron scintillation ion detector using standard pulse counting techniques. The raw ion intensities are converted to cross sections, as described previo~sly.~ We estimate absolute cross sections to be accurate to f 2 0 % . In some of the systems studied here, series of product ions separated by only 1 mass unit are found, requiring high mass resolution to separate them. However, for some products, such conditions do not permit efficient collection of the ions at higher kinetic energies, as can be verified by lower resolution studies. In such cases, the data shown corresponds to high-resolution conditions over the energy range where product collection is still efficient and low-resolution conditions where it is not. Such low-resolution data needs to be corrected for overlap of adjacent masses and is therefore somewhat less reliable. In the present study, this is the case for the Co+, CoH', and COD' product cross sections at energies greater than about 3 eV in the CoCH2' D2 system. Laboratory (lab) energies are converted to energies in the center-of-mass (CM) frame by using the conversion ECM= Elab MI(M m), where m and M are the ion and neutral masses, respectively. The absolute energy scale and corresponding full width at half-maximum (fwhm) of the ion-beam kinetic energy distribution are determined by using the octopole as a retarding
compared to reaction 2 for late first row transition metal ions, even though it is considerably less endothermic than reaction 2. Some insight into this difference between early and late metals has come recently from a theoretical study of the [CoC&]+ ~ y s t e m .Musaev ~ et al. calculated that the dehydrogenation reaction 1 proceeds via a four-center transition state, in agreement with previous hypotheses (detailed discussions of the possible mechanisms for this dehydrogenation reaction can be found e l ~ e w h e r e ) . ~They ~ ~ ~calculated ~-~ that this transition state occurs at an energy of 96-109 kJ/mol in excess of the reaction endothermicity. This is consistent with the observation of Freiser and Jacobson5 that CoCH2+ does not react with H2 at thermal energies. Because of this large barrier, Musaev et al. "predict" that reactions 2 and 3 will occur while reaction 1 is unlikely at elevated temperatures. In contrast, previous ionbeam experiments of Armentrout and Beauchamp8 found that while reaction 2 dominates the products, both reactions 1 and 3 are also observed at elevated energies. In the present work, we reinvestigate both the reactions of Co' with methane and of CoCH2' with dihydrogen in order to experimentally characterize the [COCH~]'surface in a quantitative fashion.
' Present address: Room 54-1312, Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139. Abstract published in Advance ACS Absrructs, May 1, 1995. @
0022-3654/95/2099-9 110$09.00/0
+
+
0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 22, 1995 9111
Activation of Methane by Cos energy analyzer as described previously? The absolute uncertainty in the energy scale is f0.05 eV (lab). The energy distributions are nearly Gaussian and have a typical fwhm of 0.2-0.5 eV (lab). Ion Sources. Co+ and CoCH2+ ions are made in our flowtube ion source, described in detail previously.12 Co+ is made by using a direct current discharge source13consisting of a cobalt cathode held at high negative voltage (1.5-3 kV) over which a flow of approximately 90% He and 10% Ar passes. Ar+ ions created in the discharge are accelerated toward the cobalt cathode, sputtering off ionic and neutral metal atoms. To quench any excited states of Co+, we add a small amount (-3 mTorr) of methane to the flow tube, a method that we have previously demonstrated is effective.I4 CoCH2+ ions are formed by allowing Co' to react with ~ycloheptatriene,'~ which provides the most intense beams, or ethylene oxide.I6 These reagents are added to the flow gases about 60 cm downstream of the source at small pressures (about 1-3 mTorr), otherwise ions of unknown identity are formed with masses 1-3 mass units above and below the desired CoCH2+ mass. At typical flowtube pressures of 0.5-0.6 Torr, the ions undergo > l o 4 thermalizing collisions as they traverse the flow tube and therefore are expected to be at room temperature. Reactant ions are extracted from the flow tube and gently focused through a 9.5 cm long differentially pumped region before entering the rest of the instrument described above. Before any reaction was run, a high-energy collision-induced dissociation (CID) spectrum was taken of the CoCH2+ beam to ensure that Co+ was the only product observed and that it had a threshold consistent with the previously determined thermochemistry of CoCH2+." This provides evidence that the beams have no appreciable impurities or internal excitation. Thermochemical Analysis. Cross sections for the reaction systems are modeled by using eq 4,l33l8
ENERGY (eV. Lob)
0.0
10.0
20.0
30.0
A
A A
I
A
o.'o
coco;
5:o ENERGY (eV.
10.0 CM)
+
Figure 1. Cross sections for the bimolecular reaction of Co' CD4 as a function of relative energy (lower x-axis) and laboratory energy (upper x-axis). The arrow indicates Do(D-CD3) = 4.58 eV.
0.3% are in their SF first excited state, corresponding to a temperature of 800 K, as determined in previous experiment^.'^ Results and Discussion
+
Co+ CDd. Figure 1 shows our results for the bimolecular reaction of Co+ CD4 which yields five product ions shown in reactions 5-9. The thermochemistry listed with each reaction Co'
+
+ CD, - CoCD3+ + D
-
CoCD,+
A$, = 2.43 f 0.04 eV (5)
+ D2 A,.& = 1.51 f 0.06 eV ( 6 )
where E is the relative translational energy, EO is the reaction threshold at 0 K, Erotis the average rotational energy of the reactant ions (0.039 eV = 3k~T/2for Co+ CD4 and 0.065 eV = 5k~T/2for CoCH*+ D2, T = 300 K), a0 is an energyindependent scaling parameter, and the exponent n is treated as a variable parameter. The internal energy of the CoCH2+ reactant ion is included explicitly as a summation over vibrational energy levels, i, with energies Ei and relative populations gi (Egi = 1). We use the Beyer-Swinehart algorithmI9to calculate a Maxwell-Boltzmann distribution of vibrational energies at 300 K which is used for the factors gi in eq 4. We have described this modeling procedure in detail elsewhere.', The vibrational frequencies for CoCH2+ used in our analysis are those determined in a matrix-isolation study of FeCH2+.20 The vibrational energy contribution from D2 is negligible, and that for CD4 is accounted for by adding its average vibrational energy to our measured thresholds. The average vibrational energy at 300 K for CoCH2+ is 0.015 eV and for CD4 is 0.0012 eV. In the CoCH*+ DZreaction, we assume that the population of any electronic states of the ions have equilibrated to the temperature of the flow gas, 300 K, such that the average electronic energy is negligible. Even if the distribution is somewhat hotter, it seems unlikely that the contributions of electronic excitation will influence the threshold determined here outside of the error limits provided. Thresholds for the reaction of Co+ CD4 are modeled with the assumption that 99.7% of the Co+ ions are in their ground state and
+
+
+
+
-
-
+ D2 + D
CoCD'
CoC+
A,H0 = 4.9 f 0.3 eV
(7)
A$o = 4.3 f 0.3 eV
(8)
+ 2D,
COD+
+ CD, A$, = 2.57 f0.06 eV (9)
is calculated using information in Table 1. Studies of the reaction of Co+ with CHq were also performed and yielded consistent results for all chemically analogous species. Only results from the perdeuterated neutral are presented here because its use enhances mass resolution, thereby allowing intensities of the various products to be measured more accurately. In agreement with the less detailed results of Armentrout and Beauchamp,8 reaction 2 dominates the product spectrum, and reactions 1 and 3 are observed. The improved sensitivity of the present experimental apparatus also allows us to observe the minor products, CoCD+ and CoC+, at higher energies. Each of these cross sections is analyzed with eq 4, and the optimized parameters are listed in Table 2. For the COD+ CD3 product channel, we measure a threshold that is consistent with the threshold calculated from literature bond energies, Table 2. (The apparent threshold for this channel in Figure 1 is much lower
+
Haynes et al.
9112 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 1: Bond Dissociation Enemies, kJ/mol, at 0 Ka bond Co+-H CO+-H~ CO+-C Co+-CH Co+-CH:! CO+-CH~ CO+-C& H-CH3 H-CH2
Do 191 f 6 ' 76i4d 347 f 29,' 376 i 29' 420 37,g 418 f 29' 317 5,b 351 f 2lf 203 i4b 90 f 6,h 96 i 3' 432.3 f 0.8 454.5 f 2 . 9
H2-CH2
454.8 f 2 . 9
H-CH C-H2 H-H
420.6 3.0, 322.9 2 . 9 432.070 f 0.008'
bond Co+-D
+
Do 194f6'
Co+-CD 422 f 37' CO+-CD~ 320 i 5 8 CO+-CD~ 207 f 49
*
441.6 f 0.6k 463.6 i 2 S k 461.3 f 2 S k 448.3 f 2Sk 465.4 f 2.5k 461.5 i 2.5'; 427.0 k 3.0k 326.2 f 2.5'; 439.615 f 0.005' 435.535 i0.01 1'
D-CD3 D-CD2 D-CH:! H-CD:! D2-CD2 D2-CH2 D-CD C-D2 D-D H-D
**
a BDEs for neutral deuterium-containing species are calculated from BDEs for neutral hydrogen-containing species and vibrational frequencies from the literature, as specified. Reference 17. Reference 38. Reference 42. e This work. f Reference 23. Temperature not specified. 8 Estimated from zero point energy differences from analogous systems in Table 3. Reference 39. Reference 40.' AfHo298(C&) taken from Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. AiH0298(CH3)taken from Berkowitz, J.; Ellison, G. B.; Gutman, D. J. Phys. Chem. 1994, 98, 2744. Af110298(CH?)taken from Leopold, D. G.; Murray, K. K.; Stevens Miller, A. E.; Lineberger, W. C. J. Chem. Phys. 1985, 83, 4849. AfHoo(CH)taken from Ervin, K. M.; Gronert, S . ; Barlow, S. E.; Gilles, M. K.; Harrison, A. G.; Bierbaum, V. M.; D e h y , C. H.; Lineberger, W. C.; Ellison, G. B. J. Am. Chem. SOC. 1990, 112, 5750. AfHoo(C)taken from ref 27. AiHo298 values are converted to AfHOo by using information in ref 27. Vibrational frequencies for CH2 and CH3 are taken from ref 27. Vibrational frequencies for CD3 taken from ref 33. Vibrational frequencies for CH4, CD4, and CH2D2 taken from ref 34. Vibrational frequencies for H2, D2, HD, CH, and CD taken from ref 35. The CD2 bend frequency is taken from Jacox, M. E. J. Phys. Chem. Ret Data. 1984, 13, 9451068. The CD2 stretching frequencies (2120 and 2340 cm-') are estimated from CH2 frequencies and a comparison of H20 and D20 frequencies. Uncertainties are taken from non-deuterated species. I Reference 27.
+
competition with reaction 9. The CoCD2+ D2 cross section rises slowly from a threshold that we measure to be 2.23 f 0.24 eV, 0.72 f 0.24 eV higher than the thermodynamic value of 1.51 f 0.06 eV. This elevated threshold is consistent with the presence of a barrier in this exit channel, but the energy is 33 f 25 kJ/mol lower than that calculated by Musaev et aL4 Definitive analyses of the CoCD+ D D2 and CoC+ 2D2 cross sections are difficult because of the small sizes of these cross sections, but we measure 0 K thresholds for these reactions of 4.86 f0.38 and 4.61 f0.30 eV, respectively. These thresholds correspond to Do(Co+-CD) = 422 f 37 kJ/mol and Do(Co+-C) = 347 f 29 kJ/mol. These values are in reasonable agreement, within the combined experimental errors, with those measured by photodissociation of CoCH2+, Do(Co+-CH) = 418 f 29 kJ/mol and Do(Co+-C) = 376 f 29 kJ/m01.~~ The bond energy of CoCH+ is consistent with triple bond format i ~ n , 'and ~ , that ~ ~ for CoC+ is between this value for the triple bond and that for a double bond, Do(Co+-CH2) = 317 f 5 kJ/mol." The observation that the Co+-C bond is stronger than the Cof-CH2 bond is an indication that Cof can backdonate 3dn electrons into an empty 2pn orbital on C.25 Additional information regarding the character of the potential energy surface comes from an analysis of the magnitudes of the cross sections in Figure 1. Even though the COD+ CD3 and CoCD3+ D products have similar thresholds and can be formed from the same D-Co+-CD3 intermediate, the former product channel is favored by a factor of about 25 in the threshold region. As discussed elsewhere in this difference in the cross section magnitudes can be attributed to angular momentum constraints for the CoCD3+ D product channel. The magnitude of the effect suggests that the reaction intermediate is short lived. At higher energies, the CoCD3+ product dissociates to form Co+ CD3, a process that can begin at 4.58 eV = Do(D-CD3), consistent with the energy where the CoCD3+ cross section begins to decline. The COD+product could also begin to dissociate at this energy, but the observation that this does not occur indicates that the CD3 product carries away most of the excess energy. A more interesting observation is the small size of the CoCD2+ D2 cross section because this channel is energetically favored, even when the barrier is considered. This indicates that dehydrogenation is kinetically disfavored, consistent with the proposed tight four-centered transition state. In contrast, COD+ CD3 formation proceeds over a loose transition state involving simple DCo+-CD3 bond cleavage. The CoCD2+ product cross section is observed to reach a maximum near 5 eV, consistent with dissociation to Co+ CD2, which c& begin at 4.82 f 0.03 eV, Table 1. CoCHz+ Dz. The most direct means of measuring the barrier height for dehydrogenation of methane by Co+ is to run reaction 1 in reverse. Figure 2 shows our results for the bimolecular reaction of CoCH2+ with D2. We observe six products formed in reactions 10- 15. Studies of the reaction of CoCH2+ with H2 were also performed and yielded consistent results. Only results for D2 are presented here because they permit hydrogen scrambling reactions to be observed, although there is then an ambiguity between the CoCH2D+ and CoCD2' product ions. The relative contributions of these species can be checked by comparing them to the absolute magnitude of the CoCH3' cross section observed in the CoCH2+ H2 reaction system. We find that the magnitude of the CoCH3+ cross section is same as the sum of the COCH~D'and CoCHD2' cross sections in the CoCH2+ D2 reaction. This suggests that if CoCD2+ is present, it is a minor component of the cross section shown for COCH~D+ in Figure 2. The accuracy of the
+ +
+
+
+
+
+
+
TABLE 2: Parameters Used in Eq 4 for Fitting Reaction Cross Sections product COCD~' COCD~' CoCD+ coc+ COD+
n 2.0 f 0.2 2.4 f 0.6 3.1 f 0.5 1.0 f 0.6 1.2 i 0.2
3.4 i 0.2 COCH~D' 3.7 f 0.4 CoCHD+ 2 . 5 f 0 . 3 COD+ 2.9 f 0.5 CoH+ 2.7 f 0.8 co+ 1.7 f 0.1 CoCHD:!+
a
EO,eV
00
+
CO+ CD4 0.16 i 0.03 2.63 f 0.07 0.08 i 0.05 2.23 f 0.24 0.008 f 0.004 4.86 f 0.38 4.61 f 0.30 0.02 f 0.01 5.34 f 0.81 2.64 f 0.06
+ D:!
COCH~' 0.03 i 0.01 0.09 f 0.03 0.11fO.03 0.06 i 0.03 0.04 f 0.03 0.57 f 0.12
1.00 i 0.13
&(literature), eVa 2.43 f 0.04 1.51 f 0.06 4.9 i 0.3 4.3 i 0.3 2.57 f 0.06 0.94 f 0.08
1.02 f 0.08 0.96 iz 0.07 1.11f0.09 -0.03f0.02 1.15 f 0.16 1.05 f 0.08 1.18 f 0.25 1.10 f 0.09 0.40 i 0.05 -1.50 f 0.06
Calculated using information in Table 1.
because of the energy broadening and the logarithmic scale.) The threshold measured for the CoCD3+ D product channel is slightly higher than the thermodynamic value which is a weighted average" of several previous determinationsfrom our but within the range of the individual measurements of these determinations. It is possible that the slightly higher value may be due to kinetic shifts induced by strong
+
+
+
+
+
+
Activation of Methane by Co+
J. Phys. Chem., Vol. 99, No. 22, 1995 9113
ENERGY (eV.
0.0 CoCH:
0:o
Lob)
50.0
1 :o
+
0,
2:o ENERGY (eV,
+
-+
3.'0
4.'0
5.0
CM)
Figure 2. Cross sections for the bimolecular reaction of CoCH2+
+
DZas a function of relative energy (lower x-axis) and laboratory energy (upper x-axis). The arrow indicates Do(Co+-CHz) = 3.28 eV.
comparison between reaction systems can be verified by also examining the cobalt-hydride ion channels. We find that the cross section magnitudes of the CoH+ in the CoCH2+ H2 reaction system are the same as the sum of the CoH+ and COD+ cross sections in the CoCH2+ D2 reaction system.
+
CoCH,'
+ D2 -COCHD,'
-
-
+ +H
go = 0.94 f 0.08 eV
(1 1a)
+ H2 A,Ho = -0.06 f 0.02 eV (1 lb)
+
COCHD+ HD A,Ho = -0.03 f 0.02 eV (12) COD+
+ CH,D A,Ho = 1.05 f 0.08 eV
-
(10)
+
COCH,D+ D A,Ho = 0.96 f 0.07 eV
CoCD,'
CoH'
(13)
+ CHD, A,H0 = 1.10 f 0.09 eV
Co'
(14)
+ CH2D, A,Ho = -1.50 f 0.06 eV (15)
At low energies, the neutral product accompanying Co+ must be CH2D2, but at higher energies, additional neutral products are possible. Experimentally, these channels correspond to the increase in the Co+ cross section observed above -3 eV. This feature can be attributed to the CID reaction to form Co+ f CH2 f D2, with a threshold equal to Do(Co+-CHz) = 3.28 f 0.05 eV.I7 In agreement with the results of Jacobson and Freiser, we observe no reaction at thermal energies even though formation of Co+ CHzD2 is exothermic by 1.50 f 0.06 eV. Instead, this process exhibits a reaction threshold. Analysis of this cross section yields a threshold for this reaction of 0.40 f 0.05 eV (38 f 5 kJ/mol) at 0 K. This value indicates that the barrier for dehydrogenation in the Co+ CD4 reaction should be 1.91 f 0.08 eV, lower than that measured above, 2.23 f
+
+
0.24 eV, but within combined experimental errors. The lower value measured here is expected to be more accurate because there are fewer problems associated with kinetic shifts and strong competition that could plague the Co+ CD4 system. This barrier height of 38 kJ/mol is much different than the height calculated by Musaev et u L , ~96-109 kJ/mol. We. note, however, that the higher theoretical barrier height lies above the thresholds for all other product channels as well, which would predict that all products should exhibit a common threshold. Instead, we find that the COD+,CoH+, CoCHD2+, and CoCHzD+ product cross sections rise from thresholds consistent with the calculated thermochemistry, Table 2, about 1 eV in all cases. This agreement demonstrates that the CoCH2+ reactant does not have appreciable internal excitation and that the barrier cannot lie above 1 eV. A result that appears to be in conflict with this conclusion is our analysis of the thermoneutral exchange reaction to form CoCHD+ HD. This product channel has an apparent and measured threshold that is about 1 eV above its thermodynamic limit. This reaction almost certainly requires that one passes over the four-centered tight transition state to form a D-CofCH2D intermediate, but the apparent threshold is still 0.7 eV above this barrier height. The reaction must correspond to neutral products of HD, because formation of CoCHD+ H 4-D cannot occur until 4.514 eV.27 We believe that the elevated threshold is a result of competition with the thermodynamically favored formation of Co+ CH2D2. After formation of the D-Co+-CH2D intermediate, elimination of CH2D2 is thermodynamically and kinetically favored compared with retuming over the tight transition state in the entrance channel. Thus, the intensity of the CoCHD+ f HD product is too small to observe at energies below 1 eV. This conclusion can be tested further by using phase space theory to model this competition, as discussed below. Formation of Cof CH2D2 is thermodynamically preferred by over 200 kJ/mol compared with formation of the cobalthydride and cobalt-methyl ions in reactions 10, 11, 13, and 14. Thus, the reverse of reaction 1 dominates at low energies, but the other reaction channels reach comparable magnitudes at higher energies. It is hard to reconcile this observation unless there is some restriction to reaction 15, such as a tight transition state in the exit channel for methane elimination. Such a restriction would mean that the simple bond cleavage reactions leading to cobalt-hydride and cobalt-methyl ions would be kinetically favored at higher energy, consistent with observation. This conclusion appears to be at odds with the results of Musaev et aL4 and Peny2*who find that the H-Co+-CH3 intermediate is not a minimum on the potential energy surface at the highest levels of theory and that there is no barrier to methane elimination along the reaction coordinate. We believe, however, that this restriction can be in the degrees of freedom other than the reaction coordinate, an idea that is explored more thoroughly by using phase space theory to model these results, as described below. Additional support for such a restriction comes from the observation of extensive isotope scrambling in this reaction, Figure 2. Without such a restriction, methane elimination from the D-Co+-CH2D intermediate should be facile and it is hard to imagine why isotope scrambling would occur. With such a restriction, the lifetime of the intermediate can be longer, thereby permitting rearrangement to compete with the thermodynamically preferred methane elimination channel. The energy dependencies of the CoH+ and COD+ cross sections are comparable, with COD+comprising 64% of both products. This preference is consistent with initial formation of a D-Co+-
+
+
+
+
Haynes et al.
9114 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 3: Molecular Constants (in em-') Used in Phase Space Calculation@ species
B
@e
CD4' CoCHD+ HDf COCH~'9 DZf COCH~D'* COD+) CH2Dk COCHD~'* CoH+ CHD2 CH2D2 TSl" TS2"
'
996(3), 1092(2), 2109,2259(3) 400,600,650, 1000,2300,3000 3813 452,624,700, 1319,2942,3012 3116 300(2), 400(2), 1200(2), 2800(2), 3002 1350 580, 1200(2), 2800(2), 3002 400(2), 500(2), 1383(2), 3002, 3184(2) 1888 480, 1300(2), 2900(2), 3050 1033, 1090, 1234, 1333, 1436,2202,2234,2974,3013,2974,3013 400,588,608,617,837, 1010, 1135, 1242, 1271,3012,3087 75,300,700,800, 1239, 1409, 1464, 1607,2935,3049,3111
2.62' 0.91' 45.66 1.07' 30.44 0.90' 3.61 7.59' 0.75' 7.10 7.10k 4.00" 0.50," 0.40 0.75"
Degeneracies in parentheses. Reference 34. Reference 33. Estimated from vibrational frequencies given in ref 20. e Calculated using the geometry of CoCH2+ calculated in ref 4. f Reference 35. 9 Taken from FeCH2' vibrational frequencies given in ref 20. * Estimated from the Co+CH3 stretching frequency in ref 36 and from CH3 vibrational frequencies taken from ref 27. ' Estimated using information from refs 27 and 36. Vibrational constant is estimated by using a Morse potential to scale the frequency of CoH+ from ref 37. The rotational constant is calculated from the bond length given there. Estimated from information for CH3 taken from ref 27. CoH+ vibrational frequency from ref 37. The rotational constant is calculated from the bond length given there. Estimated from information given for C& in ref 27. Frequencies obtained from D. G . Musaev and K. Morokuma, personal communication. Frequencies are scaled down by 9% to account for differences in experimental and theoretical frequencies and for deuterium substitution in TS1 and TS2. Calculated using information from ref 4.
'
TABLE 4: Parameters Used in Phase Space Calculations reaction channel
reduced mass (amu)
polarizability of neutral (A3)
symmetry n 0 . O
no. of surfacesb
C O C H ~ + ( ~+ A D2('Xg) ) CO'(~F) CHZD~('AI) COCH~D+(~E)D(2SJ COCHD~+(~E)H(*S,) COD+(^@) CHzD('A1) COH+(~@) CHD2(2AI)
3.82 13.82 1.96 0.99 12.70 13.27
0.775' 2.56d 0.67' 0.6671 2.229 2.229
4 2 1 1 2 2
3 (3) 21 (3) 16 (3) 16 (3) 16 (1,3)* 16 (1,3)*
+
+ +
+ +
a Product of the symmetry numbers for the ionic and neutral species. Electronic degeneracy (assumed number of reactive surfaces). Hirschfelder, J. 0.;Curtiss, C. R.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1954; p 947. a(CH2D2) assumed to equal a(CH4) given in Rothe, R. W.; Bernstein, R. B. J. Chem. Phys. 1959, 31, 1619. e a(D) assumed to equal a(H). /Miller, M. T.; Bederson, B. Adv. Atom. Mol. Phys. 1977, 13, 1. 9 a(CH2D) and a(CHD2) are assumed to equal a(CH3) which is estimated by using the empirical method given in Miller, K. J.; Savchik, J. A. J. Am. Chem. SOC. 1979, 101,7206. * Three accessible electronic states are used if no TS2 is included in the TD-PST calculation and one is used if TS2 is included. See text.
CH2D intermediate formed by addition of D2 across the Cof=CH2 n bond. The branching ratio for the methyl channels cannot be elucidated unambiguously because CoCH*D+ and CoCD2+ have the same nominal mass. If we presume that there is no CoCD2+ product present, as indicated by the CoCH2+ H2 results, then the CoCHzD+ product comprises 82% of the CoCH2D+ and CoCHD2+ products. If we presume that the CoCD2+ product cross section has a comparable magnitude to that for the CoCHD+ product (this must be an upper limit to the contribution because the CoCH2D' cross section is smaller than the CoCHD+ cross section at the highest energies), then CoCH*D+ comprises about 64% of the CoCH*D+ and CoCHD2+ products. In either case, the preferred product is again consistent with initial formation of a D-Co+-CHzD intermediate. Both the CoCHzD+ and CoCHD2+ cross sections reach maxima near 3 eV, consistent with dissociation to Co+ CH2D (CHD2) which can begin at 3.0 eV. The CoCHD2+ product cross section is observed to decline more rapidly than the CoCH2D+ product cross section. We can think of three possible explanations for this observation. (1) There could be contributions of CoCD2+ in the CoCH2D+ cross section shown, giving it a larger cross section magnitude at higher energies similar to the CoCHD+ cross section. (2) It could be because the heavier neutral product D is able to remove more energy from the CoCH2D+ than the neutral product H removes from CoCHDz', which has a higher internal state density than CoCH2D+, thus stabilizing the former product. (3) It could be because the CoCH2D+ product can also be formed by more direct pathways
+
+
at higher energies, while formation of CoCHD2+ requires a longer-lived intermediate to facilitate more extensive exchange. Phase Space Theory Calculations. The CoCH2+ DZ reaction system can be elucidated further by using phase space theory (PST) to model the results, although additional assumptions are required because of the tight transition state in the entrance channel. As we have discussed elsewhere,29 the modification to PST is a theory for translationally driven (TD) reactions as outlined by Chesnavich and Bowers,30who adapted a treatment of M a r ~ u s . ~Codes ' for PST are adapted from those of Bowers, Chesnavich, and others32 and modified to include the translationally driven assumptions. Table 3 lists the molecular constants for reactants and products, and Table 4 gives other parameters needed for the calculation^.^^-^^ We have successfully used TD-PST to describe reactions of 0 2 + with HZ29 and recently applied it to the COO+ D2 reaction,22 directly analogous to the present system. At low energies (below -1 eV), formation of Co+ CH2D2 and the return to reactants (including the hydrogen scrambling channels, CoCHD' HD and CoCD2+ H2) are the only channels accessible. Using TD-PST, we can reproduce the energy dependence of the Co+ product cross section in this threshold region with a barrier height of 0.3 f 0.1 eV for the four-centered transition state (TS1) where D2 adds across the Co+=CH2 n bond, a value that agrees with our empirically determined threshold for reaction 15 within the experimental errors. Lower and higher barrier heights were explicitly tested and could not reproduce the Co+ cross section. In order to reproduce the absolute magnitude of the Co+ cross section in
+
+
+
+
+
Activation of Methane by Co+
J. Phys. Chem., Vol. 99, No. 22, 1995 9115
ENERGY (eV,
10.0
0.0
Lob)
30.0
20.0
ZO-/
50.0
40.0
I
CCoCH41+ P o t e n t i a l Energy S u r f a c e
! 3,O
2.0
"
CoCH2++ H2
x
m
w
1.0
-1.0
H-c~+-cH~
CO+
Co+-CH+
"1
Reaction Coordinate
Figure 4. [CoCH.#
potential energy surface derived from experimental
results.
1'.
-''4
o A
'
'
0.0
'
'
I - .
1.0 ENERGY (eV.
ENERGY (eV,
10.0
0.0
20.0
I
'
"
2.0 CM)
'
f
3.0
Lob)
30.0
50.0
40.0
reach a magnitude of A2 until about 1 eV, consistent with experiment, Figure 2. Above about 1 eV, reproduction of the experimental data requires that the exit channel for loss of methane be carefully considered. If the transition state for this channel is treated as loose, Le., parameters associated with Co+ CH2D2 are used, TD-PST predicts a low magnitude for the CoCHD+ cross section (even though the reaction path degeneracy of two from a D-CO+-CH~D intermediate is included) but shows good agreement with the other experimental cross section magnitudes, Figure 3a. We then performed TD-PST calculations that included a transition state (TS2) with a barrier height ranging from 0 to 1.2 eV below the CoCH2+ D2 asymptotic limit. The best results are obtained when the barrier height is about 1.15 eV below the CoCH2+ D2 asymptotic limit, approximately equal in energy to the D-Co+-CHzD intermediate (see below). This is in agreement with the theoretical calculations of Musaev et aL4 who state that no barrier relative to the H-Co+-CH3 intermediate is present for TS2 and those of Perry who calculated only a 4 kJ/mol barrier.28 This calculation now fails to reproduce the data because the cross section calculated for the Co+-hydride channels is about a factor of 3 larger than the experimental results. We adjust for this by decreasing the number of accessible electronic states for the Co+-hydride products from 3 to 1, Table 4. With this change, the addition of TS2 to the calculation now yields cross sections for all channels having similar magnitudes to the experimental data, Figure 3b. Whether TS2 is included in the calculation or not, our TDPST results find that COD+ comprises 67% of the CoH+ and COD+cross sections, in good agreement with the experimental value of 64%. The TD-PST results show that CoCHzD+ comprises 83% of the CoCH2D' and CoCHD2+ cross sections, also consistent with the experimental value of 82% obtained if no CoCD2+ is formed. This good agreement is consistent with little or no contribution of the CoCD2+ product to the CoCH*D+ cross section. It also means that the observed predominance of the COD+ CH2D and CoCH2D+ D channels over CoH+ CHDz and CoCHD2+ H, respectively, is a statistical phenomenon rather than a dynamic one having to do with the initially formed intermediate. [CoCI€# Potential Energy Surface. Overall, the present results combined with previous determinations of the thermochemistry for C O + - H , I ~ ,Co+-CH2,I7 ~~ Co+-CH 3, 17,21,22 and Co+-C& 39-41 allow us to construct a detailed potential energy surface (PES), Figure 4. We take the barrier for TS1 as 34 zk 8 kJ/mol, the average value obtained from our empirical and PST analyses of the data. We presume that Do(HzCCo+-H*) Do(Co+-H2) = 0.79 eV42 and that the H-Co+-CH3
+
N "
0
"
-
10-1:
+
5
t-
u w
+
v)
VI VI
0
s
10-2
: I
0.0
"
0.0
I
-3.0
10-2
2 E!
+ C H ~
"
I
.
"
'
1.0 ENERGY (0'4.
I
"
.
.
l
2.0 CM)
Figure 3. Comparison of experimental results for CoCH2'
3.0
+
DZwith translationally driven phase space theory calculations as a function of kinetic energy in the center-of-mass frame (lower x-axis) and laboratory frame (upper x-axis). Symbols show the experimental results, which are the same as in Figure 2, although only the sums of the cross sections for CoH' and COD' (open circles) and for CoCH2D' and CoCHDz+ (open triangles) are shown for clarity. The TD-PST theoretical calculations detailed in the text (after convolution over the experimental energy distributions) are shown as solid lines for Co', Co+-methyls, and Co+-hydrides and as a dashed line for CoCHD+. Calculations without and with TS2 included are shown by parts a (top) and b (bottom), respectively.
the threshold region, the rotational constant for TS1 is lowered slightly to B = 0.40 cm-', from a value of 0.50 cm-' calculated from the theoretical geometry of Musaev et aL4 (This result suggests a slightly different geometry for TS 1, consistent with our finding that the experimental energy of TS1 also differs from the theoretical value; however, the absolute magnitudes of the TD-PST calculations are not sufficiently reliable that such a conclusion is definitive.) After convoluting over the experimental energy distributions, the TD-PST result is shown along with the experimental data in Figure 3. The TD-PST results also demonstrate that a retum to reactants (including hydrogen scrambling) is very inefficient. Indeed, the calculations show that the thermoneutral ligand exchange reactions to form CoCHD+ HD and CoCD2+ H2 rise slowly from a threshold of 0.3 f. 0.1 eV but do not
+
+
+
+
+
+
9116 J. Phys. Chem., Vol. 99, No. 22, 1995
Haynes et al.
SCHEME 1
-
,H. ,
D-Co+-CH2D
-
\
D----H
; co+-
\
cpt-
D-CO+-CH~D
CHD I
.D'
' CHD
;
cot-
+
H-CO+-CHD,
H----D 4
CHD
-
H-Co+-CHD2
intermediate is given by bond additivity to lie 0.4 eV above the Co+ CHq a~ymptote.'~ This value also lies between values calculated by Perry,280.52 eV, and Musaev et al.? 0.02-0.3 eV, depending on the level of theory. Although qualitatively similar to the surface calculated by Musaev et al.: this experimental PES is substantially different in several quantitative aspects, including the endothermicities of reactions 1-3 and especially with regard to the activation barrier associated with dehydrogenation of methane, reaction 1. In this regard, we note that Musaev et al.43 also find a barrier for the reaction of RhCH2+ H2 Rh+ CHq, in contrast to the observation by Jacobson and Freiser that this reaction proceeds efficiently at thermal e n e r g i e ~ .The ~ conclusion that the rhodium reaction is barrierless is supported by complementary experiments performed in our laboratory.u Mechanism for Isotope Scrambling. An interesting issue in the CoCH2+ D2 reaction is the mechanism for hydrogen scrambling. The phase space results indicate that the branching ratios are determined primarily by the densities of states of the various product channels, suggesting that the intermediate lives long enough to behave statistically at lower kinetic energies. This is further evidence for TS2, the restriction in phase space associated with methane elimination. Without this transition state, it is hard to imagine that the intermediate could exist for a sufficiently long time to allow efficient scrambling. The initially formed intermediate, D-Co+-CH2D, formed by addition of D2 across the Co+=CH2 n bond, can eliminate HD to yield CoCHD+, eliminate D to form CoCH2D+, or eliminate CH2D to yield COD+. Formation of CoCHD2+ H and CoH+ CHD2 presumably requires rearrangement to a H-Co+-CHD2 intermediate. This rearrangement could occur by rearrangement of D-Co+-CHlD passing over TS1 to form the CoCHD+-HD complex, which then adds back to form H-Co+-CHD*, but the small cross section for CoCHD+ (which also involves passing over TS 1) demonstrates that this process is inefficient. We speculate that the most likely pathway for scrambling is if D-Co+-CH2D rearranges via TS2 to form the Co+-CH2D2 complex, which then adds back to form H-Co+CHD2. However, if the complex Co+-CH2D2 were to form, we would expect that loss of CH2D2 should strongly dominate the reaction as the energy available to the system increases, in contrast to the results of Figure 2. In turn, this should mean that the formation of CoCHDz+ H and CoH+ CHD2 should become inefficient compared with formation of CoCH2D+ D and COD+ CHzD as the energy increases. This is true for the cobalt-methyl channels but not for the cobalt-hydride channels, Figure 2, a result that casts some doubt on this scrambling mechanism. Altemative mechanisms for scrambling are hard to imagine, but it is possible that they involve concerted interchange of H and D from the D-Co+-CH*D intermediate, ie., through mechanisms such as those shown in Scheme 1. Because a transition metal center is involved, such concerted mechanisms could be low-energy processes.
+
-
+
+
+
+
+
+
+
+
guided-ion-beam mass spectrometry. We are able to map the [CoCH# PES in detail by starting at two different locations on the same global PES, namely, Co+ f CHq and CoCH2+ H2. We directly measure the barrier for the tight four-centered transition state associated with dehydrogenation of methane by Co+ as 34 f 8 kJ/mol. This value is substantially lower than that calculated in a previous theoretical study! We use phase space theory (PST) modified to include assumptions appropriate for a tight transition state in the entrance channel (TD-PST) to model our results for the reaction of CoCH2+ D2. This permits a further refinement of the quantitative details of the [CoCH4]+ PES. TD-PST is able to reproduce the cross section for formation of Co' CH2D2, the elevated threshold observed for CoCHD+ HD, and the branching ratios for hydrogen scrambling in the cobalt-hydride and cobalt-methyl ion channels. The possible existence of a tight transition state for elimination of methane from the D-Cof-CH2D intermediate is also tested. The results are not definitive as TD-PST calculations with and without this transition state reproduce different features of the experimental results well, although if this transition state exists, we find that it has an energy close to that of the D-Co+-CH2D intermediate, in agreement with t h e ~ r y . ~Lastly, . ~ ~ we measure 0 K bond dissociation energies for Co+-CD and Co+-C of 422 f 37 and 347 f 29 kJ/mol, respectively.
+
Conclusions In these experiments, we probe the potential energy surface (PES) for activation of methane by atomic Co+ ions using
+
+
+
Acknowledgment. This work is supported by the National Science Foundation, Grant No. CHE-9221241. We thank Dr. D. G. Musaev and. Professor K. Morokuma for providing us with calculated frequencies for the TS1 and TS2 complexes. References and Notes (1) Allison, J. Prog. Inorg. Chem. 1986,34,627.Squires, R. R. Chem. Rev. 1987, 87, 623. Gas Phase Inorganic Chemistry, Russell, D. H., Ed.; Plenum: New York, 1989. Eller, K.; Schwarz, H. Chem. Rev. 1991, 91, 1121. (2) Armentrout, P. B. In Selective Hydrocarbon Activation: Principles and Progress; Davies, J. A., Watson, P. L., Liebman, J. F., Greenberg, A,, Eds.; VCH: New York, 1990; pp 467-533. (3) Armentrout, P. B.; Beauchamp, J. L. Acc. Chem. Res. 1989, 22, 315. (4) Musaev, D. G.; Morokuma, K.; Koga, N.; Nguyen, K. A,; Gordon, M. S.; Cundari, T. R. J. Phys. Chem. 1993, 97, 11435. (5) Jacobson, D. B.; Freiser, B. S. J. Am. Chem. SOC.1985, 107, 5870. (6) Aristov, N.; Armentrout, P. B. J. Phys. Chem. 1987, 91, 6178. (7) Sunderlin, L. S.; Armentrout, P. B. J. Phys. Chem. 1988,92, 1209. (8) Armentrout, P. B.; Beauchamp, J. L. J. Am. Chem. SOC.1981, 103, 784. (9) Ervin, K. M.; Armentrout, P. B. J. Chem. Phys. 1985, 83, 166. (10) Sunderlin, L. S.; Armentrout, P. B. Chem. Phys. Lett. 1990, 167, 188. (11) Teloy, E.; Gerlich, D. Chem. Phys. 1974, 4, 417. Gerlich, D. Diplomarbeit, University of Freiburg, Federal Republic of Germany, 1971. (12) Schultz, R. H.; Armentrout, P. B. Int. J. Mass Spectrom. Zon Processes 1991, 107, 29. (13) Schultz, R. H.; Crellin, K. C.; Armentrout, P. B. J. Am. Chem. SOC. 1991, l I 3 , 8590. (14) Haynes, C. L.; Armentrout, P. B. Organometallics 1994, 13,3480. (15) Jacobson, D. B.; Byrd, G. D.; Freiser, B. S. Inorg. Chem. 1984, 23, 553. (16) Armentrout, P. B.; Beauchamp, J. L. J. Chem. Phys. 1981, 74,2819. (17) Our previously published transition metal thermochemistry has been reevaluated in Armentrout, P. B.; Kickel, B. L. Organometallic Ion Chemistry; Freiser, B. S., Ed.; in press. (18) Armentrout, P. B. In Advances in Gas Phase Ion Chemistry; Adams, N. G., Babcock, L. M., Eds.; JAI: Greenwich, 1992; Vol. 1, pp 83-119. (19) Beyer, T.; Swinehart, D. F. Commun. ACM 1973, 16, 379. Stein, S. E.; Rabinovitch, B. S. J . Chem. Phys. 1973,58, 2438; Chem. Phys. Lett. 1977, 49, 183. Gilbert, R. G.; Smith, S . C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, UK, 1990. (20) Hague, R. H.; Margrave, J. L.; Kafafi, 2. H. In Chemistiy ofMatrixIsolated Species; Andrew, L.. Moskovits, M.,Eds.; North-Holland: Amsterdam, 1989; Chapter IO.
Activation of Methane by Co+ (21) Georgiadis, R.; Fisher, E. R.; Armentrout, P. B. J. Am. Chem. Soc. 1989, 111,4251. Fisher, E. R.; Sunderlin, L. S.; Armentrout, P. B. J. Phys. Chem. 1989, 93, 7375. (22) Chen, Y. M.; Clemmer, D. E.; Armentrout, P. B. J. Am. Chem. Soc. 1994, 116, 7815. (23) Hettich, R. L.; Freiser, B. S. J. Am. Chem. SOC.1986, 108, 2537. (24) Armentrout, P. B.; Clemmer, D. E. In Energetics of Organometallic Species; Simoes, J. A. M., Ed.; Kluwer: Dordrecht, the Netherlands, 1992; pp 321-356. (25) Aristov, N.; Armentrout, P. B. J. Am. Chem. SOC.1984, 106,4065. (26) Aristov, N.; Armentrout, P. B. J. Phys. Chem. 1987, 91, 6178. (27) Chase, M. W., Jr.; Davies, C. A,; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Re$ Data 1985.14, Suppl. No. 1 (JANAF Tables). (28) Perry, J. K. Ph.D. Thesis, Caltech, 1994. (29) Weber, M. E.; Dalleska, N. F.; Tjelta, B. L.; Fisher, E. R.; Armentrout, P. B. J. Chem. Phys. 1993, 98, 7855. (30) Chesnavich, W. J.; Bowers, M. T. J. Phys. Chem. 1979, 83, 900. (31) Marcus, R. A. J. Chem. Phys. 1975, 62, 1372. (32) Programs are now available from the Quantum Chemistry Program Exchange, Indiana University, Program No. 557. Contributors to the original and revised programs include Bowers, M. T.; Chesnavich, W. J.; Jarrold, M. F.; Bass, L.; Grice, M. E.; Song, K.; Webb, D. A. (33) Pamidimukkala, K. M.; Rogers, D.; Skinner, G. B. J. Phys. Chem. Ret Data, 1982, 11, 85.
J. Phys. Chem., Vol. 99, No. 22, 1995 9117 (34) Shimanouchi, T. Tables of Molecular Vibrational Frequencies, Consolidated, Vol. I; National Bureau of Standards: Washington, DC, 1972. (35) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure Constants of Diatomic Molecules; Van Nostrand Reinhold Company: New York, 1979. (36) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H.; Barnes, L. A. J. Chem. Phys. 1989, 91, 2399. (37) Pettersson, L. G. M.; Bauschlicher, C. W., Jr.; Langhoff, S. R. J. Chem. Phys. 1987, 87, 481. (38) Elkind, J. L.; Armentrout, P. B. J. Phys. Chem. 1986, 90, 6576. (39) Haynes, C. L.; Armentrout, P. B.; Perry, J. K.; Goddard, W. A., 111. J. Phys. Chem. 1995, 99, 6340. (40) Kemper, P. R.; Bushnell, J.; van Koppen, P.; Bowers, M. T. J. Phys. Chem. 1993, 97, 1810. (41) Perry, J. K.; Ohanessian, G.; Goddard, W. A,, 111. J. Phys. Chem. 1993, 97, 5238. (42) Kemper, P. R.; Bushnell, J.; von Helden, G.; Bowers, M. T. J. Phys. Chem. 1993, 97, 52. (43) Musaev, D. G.; Koga, N.; Morokuma, K. J. Phys. Chem. 1993, 97, 4064. (44) Chen, Y.-M.; Armentrout, P. B. J. Phys. Chem., submitted JP950157R
