J . Phys. Chem. 1993,97, 1810-1817
1810
Binding Energies of Co+-(H2/CH&Hs)
1,%3 Clusters
Paul R. Kemper,' John Bwhnell, Petra van Koppea, and Michael T. Bowers' Department of Chemistry, University of California, Santa Barbara, California 93106- 9510 Received: October 28, 1992
Using temperature dependent equilibria, binding energies for Co+-CH, and Co+-C2Hawere measured to be 22.9 f 0.7 and 28.0 f 1.6 kcal/mol, respectively. Dissociation energies for loss of Y from Co+*X-Y (X = H2, CH4, C2H6, and H20, and Y = H2, CH4, and C2H6) were also measured. Dissociation energies for loss of CH4 or C2H6 from the three ligand species Co+*(CH& and Co+*(CzH& were estimated. The binding energy of a given ligand is affected by the presence of other ligands through both Co+ 3 d - 4 ~electron hybridization and ligandligand interference. The present results agree well with the recent high level theoretical calculations of Perry, Ohanessian, and Goddard. Finally, entropies for most of the above reactions were also measured.
well depth and barrier height do not solely control the reaction. Orbital occupation (4s vs 3d, 3do vs 3dw vs 3d6, etc.) and spin Recently, we have reported studies of transition metal ion state are known to affect reactions of transition metal ions as binding energiesin complexes with rare gas neutrals' and hydrogen ~e11.3~17.18 molecules.2 In these experiments, clustering equilibria were A second use for the C O + - C H ~ / C Zbinding H~ energies is in measured as a function of temperature and the dissociation obtaining binding energies of more strongly bound Co+-X energies (DE = M)were extracted from a statistical mecomplexes via equilibrium ligand switching. This step ladder chanical fit to the data. In the present study we extend the process may help resolve uncertaintiesnow present in these binding experiments to include Co+ (CH4/C&)l ,2,3. Experimental energies. For example, a number of experimentaland theoretical work on these Co+/alkane systems has shown that, under determinations of Co+-C2H4/C2H2 bond strengths have been multicollision conditions, the only significant reaction products made by Armentrout, Beauchamp, and Bauschlicher (with their are the C O + ( C H ~ / C ~ Hcomplexes.) ~)I.~ In fact, this is true of all numerous co-~orkers).~8J~ The results vary significantly (see the first row transition metal atomic ions except Sc+ and Ti+, Table IV in ref 18). This variation may be due to (M+)' excited which eliminate H2 in reacting with C2H6.3.4Reactions of V+ electronic states, which in many cases are very difficult to with C2Hs under single collision conditions produce V+*C2H4+ deactivate.20 Although the bond energy uncertainty increases H2J,6but form only the adduct under high pressure condition^.^ with the number of ligand switching reactions used to calculate In thermal energy reactions of M+ + C3H8, on the other hand, elimination of neutral H2 and CH4 occurs for M+ = S C + , ~ * ~ .it, ~ we hope to significantlyimprove the accuracy of these binding energies. This will also allow absolutebond energiesto be assigned Ti+,3,6.8V+,3.5,6Fe+,33-l1 Co+,M-I2 and Ni+ 3-8-10 under both single to the numerous, strongly bound M+.X2 complexes in the ligand collision and multicollision conditions. While the Co+/alkane switching equilibrium experiments of Kappes et a1.2' which are reaction kinetics have been investigated,no direct measurements referenced to the Ni+-(C2H2)2 dissociation energy. of the relevant bond energies are available. Estimates of the Finally, accurate knowledge of M+-alkane binding energies Co+-C2H6bond strength have been made on the basis of kinetic promotes theoretical investigation into these association comenergy release measurements done on the unimolecular de"plexes. The experiments both point out possible problems in position of Co+-(acetone) Co+.CzH6 + CO and by phase calculations and serve as a calibration of their accuracy. Several space modeling of temperature dependent Co+ + C2H6 groups are active in this theoretical work. Bauschlicher and coCo+.C2Hs high pressure kinetic data.I4 The Co+-CH4 bond workers have investigated bonding in transition metal ion strength was also estimated in a similar fashi0n.1~Unfortunately, in each of these studies analysis of the experimental data was complexes such as M+-(H& ( n 3 1-3),22 M+-(C2H2),19 M + - C Z H ~CU+.CH4/C2Ha/CaHs/CjH6123 ,~~ and M + - ( C H ~ ) Z . ~ ~ complex and the resulting uncertainties in bond energy were high. Their calculations showed that in complexes involving tbe late Accurate bond strengths for these systems are thus lacking, transition metal ions (Cr+-Cu+)the bonding was almost entirely although Shultz and ArmentrouP have recently determined the bond energy of the Fe+-C& complex. electrostatic. TheSc+andTi+ions (and sometime V+), however, could insert into the C-C r systems. In calculationson transition A need exists for such bond strengths for severalreasons. First, metal-dimethyl complexes, Rosi et al?' point out that thestructure accurate modeling of M+ alkane reactions requires knowledge of many of these complexes is unknown. Some are clearly of the M+-alkane electrostatic well depth. This initial complex covalent, dimethyl M+-(CH3)2ions (M+ = Sc+, Y+,Ti+, Zr+, binding energy strongly influences the reaction because any and Nb+), while others are obviously M+*C2H6 electrostatic subsequentbarriers to reaction arise relative to the complex energy complexes (M+ = Cr+, Mo+, Cu+, and Ag+). For the latp minimum, Le. the bottom of the electrostatic well.1z Thus, transition metals (eg. Co+and Ni+) the structure depends on the increasing the M+-alkane binding energy effectively lowers the M++H6 binding energy. Unfortunately, only the Co+-(CHJ)2 C-H or C-C insertion barrier of the metal ion. This effect is structure was considered in their calculations, although it is clear clearly seen in the series Co+ + C2H6/C3H8/C4Hlowhere the reactions for eliminating H2 and CH4 are non-existent, slow, and from the present results that the lowest energy structure is the fast (respectively) even though all are exoergic.3*9 The rate of Co+*C2H6complex. Thisstructure has been investigatedby Perry elimination does increase with increasing complex binding energy, and GoddardZ5who are completing high level calculations on and knowing this binding energy allows us to make accurate (Co+/Rh+/Ir+)*(H2/CH4/C*H&Hs) complexes. Their work estimates of the relevant barrier heights. This, in turn, may help was very useful in interpreting the present results. Berthier et resolve such questions as the relative importance of C-H and al. have also calculated binding energies for CU+*(C&)~Jand C-C bond activation by a particular M+ ion.12J3 Of course, the CU+*C~H~.~'
I. Inboduction
+
-
-
+
0022-3654/93/2097-18 lOS04.00/0
Q 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1811
Co+g(H2/CH4/C2H6)1,2,3Clusters In this paper we will briefly discuss the experimental method and how the data are analyzed. This will be followed by a discussionof the results, system by system. A conclusion section will summarize the important findings. 11. ExperimeotaI Metbad
The instrumentused in this work has b~endescribed.2~ Detailed discussions of the data analysis and Co+-X equilibrium studies have also appeared.2 Only a very brief overview is given here. The Instrument. The Co+ ions are formed by electron impact (40eV) on (cp)Co(CO)2. Theions aremassselectedandinjected into a high pressure reaction cell. The pressure in the cell is -4 Torr, and the injection energy (- 3 eV LAB) is quickly lost via collisions with the bath gas. The ions are drifted through the cell with a small electric field. A small fraction of the Co+ parent and resulting product ions exit the cell and are quadrupole mass analyzed and detected using standard ion counting techniques. The cell temperature is variable from 80 to 580 K using a flow of heated or cooled N2 gas. Temperatures are controlled to h0.5 K. The cell temperature is measured with a thin film platinum resistor suspended in the bath gas. The accuracy is -2 K at 80 and580Kandf0.2Kat 300K. Pressuresinthecellaremeasured either directly, using a capacitance manometer connected to the cell, or indirectly, using the ion gauge outsidethe cell. The indirect method is necessary where low pressures of reactants are used. In this case, the ion gauge is calibrated against the manometer at higher pressures to provide an absolute pressure. Equilibrium Experiments. These experiments require determination of the various equilibrium constants (i.e. the reactant neutral pressure and parent/product ion ratio) as a function of temperature. As discussed above, measuring the bath gas temperature is straightforward and presents no significant problem. Pressure measurements were done in two ways and are discussed next. In the Co+ + CH4 experiments, a mixture of H2 (-4 Torr) andCH4(-0.025Torr) wasused. Thiswasdonefor tworeasons. First, the Co+*H2/Co+CH4ligand exchange equilibrium and the direct Co+/Co+CH4 equilibrium could both be measured. The ligand exchange reaction is easier to equilibrate due to the smaller Lw, also, problems with electronically excited Co+ are avoided (see below). The second reason for using a small CH4/ H2 pressure ratio was to reduce the amount of Co+.(CH4)2. At high CH4 pressures measuring the amounts of Co+ and Co+*CH, was very difficult, due to the overwhelming fraction of CO+.(CH~)~. In this experiment, the CHI and H2pressures were measured by difference, using the capacitance manometer connected directly to the reaction cell. No correction for thermal transpiration was required since a high gas pressure is present during all pressure measurements. The uncertainty in the pressures is -f0.001 Torr. In the Co+ C2H6 experiments, direct equilibration between Co+and Co+*CzH6could not be measured due to the large binding energy. Instead, the CO+*CH~/CO+.C~H~ ligand exchange equilibrium was observed. Again, small pressures of CH4 and C2H6 were needed to give measurable Co+.X/Co+.(X)2 ratios; however, in these experiments He was used as the bath gas to reduce the number of product peaks. In these experiments, the CHI and CzH6pressures were read without He present, using an ion gauge outside the cell. The gauge was calibrated for each gas against the capacitance manometer connected directly to the cell. Thermal transpiration between the cell and manometer head is present at these low pressures, but since a ratio of pressures is used, the effect cancels. However, sincethe pressure measurement is indirect, it is conceivable that an unknown, mass dependent effect could alter the CH4/C& pressure ratio when the Hebath gas is added and the flow out of the cell changes from molecular to enthalpy limited Such an effect would result in a constant (nontemperature dependent) error in our CH4/CzH6
-
+
280
320
360
400
440
480
520
560
600
Temperature (K) Figure 1. Freeenergy vs temperaturedata plots for equilibrium reactions involving Co+ and Hz/CH4. The reactant and product neutrals arc not values are given in Table I. shown. Intercept (AI$) and slope (&T)
pressure ratio. This, in turn, would produce an error in the measured entropies but would not affect the binding energy determinations. The ion intensity ratios are the final quantity needed to determine the equilibrium constants. These were taken from the integrated peak areas in the quadrupole mass spectra. Peaks were base-line resolved to prevent tailing of large peaks. Some mass dependent transmission in the quadrupole is probably present; however, this again affects only the A S values, not the bond energies. In the actual experiment, the peak ratios were measured as a function of decreasing cell drift field (increasing reaction time) until a constant ratio wasobserved. Thiscondition indicated both that equilibriumwas achievedand that the increase in effective ion temperature (due to the drift field) was negligible with respect to the thermodynamic temperature. The calculated increase in effective t e m p e r a t ~ r ewas ~ ~ less than 2 K. In the ligand switching experiments (Co+.X + Y e Co+*Y + X) equilibrium was easily achieved, even at short reaction times. In the Co+ CH4 Co+*CH4clustering reaction, equilibrium was harder to achieve due to the presence of electronically excited Co+ (aSF and b3F 4s3d7). As discussed in ref 20, these states are difficult to collisonally relax. Further, the excited Co+ ions have very low cluster binding energies (due to the large, repulsive 4s orbital). Thus, the ground-state Co+ (a3F3d8)clusters far more efficiently, leaving the excited (Co')' as unclustered reactant. The end result is a perturbed equilibrium constant for the first clustering reactions if care is not taken to ensure complete deactivation. In the present experiments, (Co+)*causeddramatic nonlinearities in the AGO vs T plots (Figures 1 and 2). The reactions also become very difficult to equilibrate. These effects became larger as the temperature decreased (due to the smaller amount of Co+ reactant). Only data which were clearly equilibrated and in line with higher temperature results were included. In the worst case, highly linear data could be taken over at least a 100K range. The second and subsequent clustering reactions are not affected by the presence of excited Co+ since the first clustering reaction effectively selects out only groundstate Co+. In summary, there are several factors which may affect the present entropy measurements,however none should significantly affect the measured reaction enthalpies. The reproducibility of the individual AGO measurements was better than 10.1 kcal/ mol (reproducibility in Keq better than -10%) for a range of neutral gas pressures.
+
-
Kemper et al.
1812 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
A rough idea of the accuracy of this method can be obtained by comparison with the stretch frequencies calculated by Perry et al.25for Co+.CH4 and Co+*C2Hs. The frequencies we estimate are higher by 1&30%. Considering the first order nature of the estimation, this is encouraging. We have generally set uncertainties of 20% in the estimated frequencies, although some are much higher. This range of frequencies contributes 0.2 1.0 kcal/mol to the uncertainty in AH(vib) and hence to that in W OThis . is the largest source of error in the dissociation energies.
-
IV. R e s u l Q m d M S C d o ~ A list of the experimental MTvalues is given in Table I along with the corresponding derived values. The various ligand dissociationenergiesderived from these reaction enthalpies are listed in Tables I1 and 111. The results are discussed below for each cluster. Co+*W.The Co+-CHd binding energy was determined both by direct equilibration of Co+ and Co+*CH4,and by Co+*H2/ Co+CH4ligand switching. The results were 22.4 f 0.5 and 23.5 f 0.8 kcal/mol, respectively. The average value is 22.9 f 0.7 kcal/mol. The experimental clustering entropy ( e 3 0 ) was -19.8 f 1.5 cal/(K mol). Calculations by Perry et al.25 indicate Co+-CH4 has C, symmetry with the Co+coordinated to two hydrogens. The Co+-C bond distance was calculated to be 2.24 A. This structure is entirely analogousto theCo+-H2structure.2v22Using this structure and the vibrational frequencies from Table IV, a statistical mechanical entropy of - 20.1:; cal/(K mol) can be calculated.28 The close agreement between the calculated and experimental values indicates that fixed errors in the molecular parameters used in the calculation or in our measured equilibrium constants (e.g. mass discrimination) are small. Our average binding energy (22.9 f 0.7 kcal/mol) can be compared with the value calculated by Perry et al. (De = 21.4 kcal/mol).25 Subtracting the cluster mode zero-point energies gives D: = 20.1 kcal/mol or about 88% of the experimental value. This underestimation is expected and is due to basis set incompleteness, limitations in correlation, and underestimation of the ligand geometry changes.25 This binding energy was also estimated from phase space fitting of Co+ + CH4 kinetic data to be 20.5 f 2 k~al/mol.’~ This result is in reasonable agreement with the present results. The importance of the partial covalent interaction in Co+*CH4 is clear when the differencein binding energiesbetween Cu+.C& (- 14.8 kcal/m01~~ or 18.1kcal/mo126)and Co+-CH4(22.9 f 0.7 kcal/mol) is noted. In Cu+-CH4,the Cu+ coordinates with three hydrogens and the interaction is almost entirely electrostatic due to the closed shell Cu+ d10 ion (a small amount of Cu+ d r CH4 T * donation does occur).23 In Co+-CH4a half-filled du orbital is available, as well as a filled d r for back-donation. The result is a much stronger covalent interaction. On the other hand, a fully covalent bond (e.g. Co+-CH3) has a bond strength of -48 f 4 kcal/mol.lOJ6 The increase in binding energy for Co+CH4relative to Co+.H2 (BE = 18.2 f 1 kcal/mol)2 may be due to several factors. The CHI neutral has a far greater polarizability (2.58 A3 vs 0.79 A3 for H2) leading to increased charge-induced dipole attraction. Perry and Goddard argue that there must also be much greater charge transfer from CHI to the C0+.25 In contrast to these electrostatic complexes, the covalent interaction dominates the M+*Hand M+.CHp interactions, and the resulting bond strengths are quite similar.’OJ6 Co+.(CH& Again, the cluster binding energy was measured both by direct equilibrium (Co+ + 2CH4 Co+*(CH&) and by H2/CH4 ligand exchange (C0+9(H2)2+ 2CH4 i=t Co+-(C&)2 + 2H2). The two experiments measured the total cluster binding energy to be 46.1 f 1.0 and 48.3 & 2.1 kcal/mol, respectively
A@
280
320
360
400
440
480
520
560
600
Temperature (K) Figure 2. Free energyvs temperature data plots for equilibrium reactions involving Co+ and CH4/C2H6. The reactant and product neutrals are not shown. Intercept (At@ and slope (A$) values are given in Table I.
III. Data Analysis The equilibrium constantswere converted to free energiesusing eq 1. The resulting AGO values were plotted against temperature (Figures 1 and 2). The intercept of the plot gives AH!T where AGO = -RT In Kq
(1)
Tis the “average” experimental temperature. The slope equals the reaction entropy. The reaction enthalpy does, of course, change with experimentaltemperature. The change is small over our experimental range, however, and the results plots are very nearly linear. The corresponding value is derived using
A@
MT=@+CACpdT
(24
= @+ Mdtrans) + Mdrot.)
+Mdvib)
(2b)
The translational and rotational modes are fully active in all clusters, and the corresponding enthalpy corrections are trivial to calculate. The derivation of the vibrational enthalpies is described below (details of the frequencydeterminationsare given in the Appendix). In order to calculate the necessary AH(vib) values, the vibrational frequencies of the reactants and products are needed. Our method of determining these involved four steps. First, the cluster structures were determined (these were largely based on theoretical calculations and are detailed in the next section). Second, the vibrational modes present in the clusters were determined from a normal mode analysis together with the geometry. Third, we assumed that no change in the ligand “internal”modes occurred between thecluster and the free ligand. These modes could then be subtracted leaving only the “cluster” modes. This assumption introduces error. However, these internal modes generally have very high frequencies (>1300cm-1 except for one ethane mode) and are not active at our experimental temperatures. Thus, any changes in the frequenciesof these modes are not expected to affect the calculated M(vib), and the associated error should be small. Fourth, once it is known which cluster modes are present, estimates of their frequencies can be made on the basis of the fairly well-known Co+~(H2)~,2 frequenThe estimationtakes into account changes in reduced mass, geometry, and bond strength. Details are given in the Appendix.
-
*
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1813
C O + * ( H ~ / C H ~ / C1.2.3 ~ HClusters ~)
TABLE I: Experimental Enthalpies and Entropies from Equilibria reaction no.
reaction obsd
P
-M,
1 2 3 4 5 6 7 8 9 10 11 12
CO++ CH4 --L Co+*CH4 CO+*CH~ + CH4 --L Co+.(CH4)2 CO+.H~ CH4 Co+*CH4 + H2 Co+*(H2)2 + CH4 CO+.H~*CH~ + H2 Co+-(H2)2 2CH4 Co+*(CH4)2 + 2H2 Co+*CH4 C2H6 COt'C2H6 + CHI Co+.(CH4)2 C2H6 CO+*CH4*C2&, CH4 Co+*(CH& + 2C2H.5 COt*(C2H6)2 i-2CH4 CO+*C2H6 C2H6 CO+*(C~H& COt*C2H6 CH4 COt*C2H6*CH4 Co+*H20 H2 Cot*H20*H2 Co+*H20 + CH4 Co+.H20*CH4
530 f SO 500 f 80 500 f 80 440 f 140 460 f 120 500 f 80 480 f 100 480 f 100 490 f 90 490 f 90 530 f 50 525 f 55
23.0 f 0.3 24.2 f 0.3 4.1 f 0.2 4.6 f 0.3 10.4 f 0.4 5.4 f 0.3 3.8 f 0.3 7.1 f 0.3 26.5 f 0.3 23.7 f 0.3 20.9 f 0.3 25.3 f 0.2
+
+ + + + +
--
+
-
+
+
-
+
+
-&T
19.8 f 1.0 26.1 f 0.8 -1.1 f 0.4 -2.7 f 0.3 0.6 f 0.5 2.5 f 0.7 -0.2 f 0.7 2.4 f 0.8 27.8 f 1.2 26.4 f 0.8 24.7 f 0.9 27.0 f 0.6
-Mo d 22.5 f 0.5 24.8 f 1.0 5.2 f 0.4 5.6 f 0.8 1 3 . 0 f 1.2 5.1 f 0.9 3.6 f 1.3 6.7 f 1.3 27.0 f 1.0 2 4 . 4 f 1.1 19.8 f 0.6 25.9 t 0.7
a In kelvin. The f value indicates the experimental temperature range, not an uncertainty. In kcal/mol. The uncertainties are two standard deviations in the linear least squares fit. In cal/(K mol. The uncertainties are three standard deviation in the linear least squares fit. d In kcal/mol. The error limits reflect both the experimental uncertainties and possible errors in M ( v i b ) (due to uncertainties in vibrational frequencies).
TABLE II: Summary of Bond Strengths reaction no.
bond(s)
dissociation energya
13 14 15 16 17 18 19 20 21 22 23 24 2s 26 27 28 29
Co+-H2 CO+*H~-H~ Co+-(H2)2 CO+-& CO+.CH~-CH~ Co+-(CH4)2 CO+*H 2-C Hq Co+*CHd-H2 Cot-C2H6
18.2 f l.Ob 17.0 f 0.4b 35.2 f l.Ob 22.9 f 0.7c 24.8 f O A d 47.7 f 1.w 22.6 f 1.Y 17.4 f 0.88 28.0 f 1.6* 26.8 f 1.0' 54.6 f 2.W 28.4 f 1.3k 24.0 f 1.2' 19.8 f 0.6 25.9 f 0.8 -11m C12"
COt'C2H6-C2H6
Co+-(C2H6)z COt*CH4-C2H6 COt*C2H6-CH4
Cot-H20-H2 Cot.H20-CH4 CO+.(CH~)~-CH~ Cot'(C2H6)2-C2H6
a In kcal/mol. From ref 2. Average of reaction 1 (22.5 f 0.5 kcal/ mol) and reactions 3 13 (23.4 f 1.4 kcal/mol). Average of reaction 2 (24.8 f 1.0 kcal/mol) and reactions 5 + 14- 3 (24.8 f 2.0 kcal/mol). e Average of reactions 1 + 2 (47.3 f 1.O kcal/mol) and reactions 5 15 (48.2 f 2.2 kcal/mol). f From reactions 4 + 14. 8 Average of reactions 4 + 14 - 3 (17.4 f 0.8 kcal/mol) and reactions 4 17 - 5 (17.4 f 1.2 kcal/mol). From reactions 16 6. Average of reaction 9 (27.0 f 1.0 kcal/mol) and reactions 8 + 2 - 6 (26.4 f 2.2 kcal/mol). J Average of reactions 21 22 (54.8 f 2.6 kcal/mol) and reactions 8 + 18 (54.4 f 2.3 kcal/mol). From reactions 7 + 17. Average of reaction 10 (24.4 f 1.1 kcal/mol) and reactions 22 + 7 - 8 (23.7 f 1.3 kcal/mol). m Estimated; see text. Upper limit only; see text.
+
+
+
*
+
+
TABLE IIk Second Ligand Bond Strengths (Co+-X-Hz/ CHJCz&) for Various First Ligands (Co+.X) bond strengths (kcal/mol) Co+*H20 Co+*CzHs CO+.CH~ Co+*H2 a
40.1," 37.1b 28.0 f 1.6 22.9 f 0.7 18.2 f 1.0
19.8 f 0.6 17.4 f 0.8 17.0 f 0.4
25.9 f 0.8 24.0 f 1.2 24.7 f 0.9 22.6 f 1.2
26.8 f 1.0 28.4 1.3
Reference 3 1. Reference 32b.
(47.2 f 1.5 kcal/mol, average). The experimental values for the bond dissociation energy of the second methane are then 23.7 f 1.0 (direct equilibrium) and 24.8 f 2.1 kcal/mol (ligand exchange). In both the direct equilibrium and ligand exchange experiments, the second CH4 is bound 1.3 f 0.6 kcal/mol more strongly than the first. Perry and Goddard25 have very recently investigated the structure and bonding in this cluster. They find the lowest energy structure has a linear C-Co+-C axis with the methane hydrogens eclipsed ( D z symmetry). ~ The eclipsed form was 6.6 kcal/mol more stable than the staggered. This is surprising considering the analogous Co+.(H2)2 cluster where the staggered form is definitely the morestable becauseit allowsdr-. u* back-donation
from two separate filled d a orbitals on CO+to the hydrogens.22 A detailed explanation of the Co+-(CH4)2calculationand structure is in preparation.25 The calculated bond energy for the second methaneis De = 23.1 kcal/mol. Correcting for zero-point energies gives a D: = 21.4 kcal/mol, an increase of 1.3 kcal/mol relative to the first methane binding energy. This theoretical D: is 88% of our experimental determination. The same limits on the accuracy of the calculation are present as in the Co+.CH4 calculation, and this level agreement is quite good. The exact agreement between experimental and theoretical values for the increase in bond strength between the first and second methanes is probably fortuitous. It does, however, confirm the presence of the increase and its approximate size. Again, details of the calculation are not yet available, but this effect has been both predicted and observed for several transition metal containing clusters (e.g. Co+*X2where X = He, Ar,1329H2:922.30 H20,3i932 and NH331.33).The effect is due to 3 d - 4 ~hybridization in the first cluster (Co+.X). This increases the Co+-X bond strength by reducing electron density on the bond axis. The effect is symmetric, and when the second ligand approaches, it benefits from the reduced electron-electron repulsion without paying the energy cost for hybridization. The net result is an increased attractive well depth for the second ligand. That fact that this increase in bond strength is present in Co+-(CH4)2also argues that steric interference between the methanes is small. This is apparently not the case for C2Hs ligands for example, and interactions between ligands in these clusters is discussed below. The entropy associated with adding a second methane was measured to be -26.1 2 cal/(K mol). The AS is estimated from statistical mechanics to be -23.3:; cal/(K mol). The measured entropy is significantly more negative than the -19.8 f 1.5 cal(K mol) found for the first methane addition. The difference is due to a major change in AS(rot.) (from +8.8 to -1 1.0 cal/(K mol)), due, in turn, to the presence of rotational modes in the ionic reactant. This is partly compensated for by the increased AS(vib) (from about +9.7 to about +23.9 cal/(K mol)) due to the additional vibrational modes in the CO+.(CH,)~ product. Co+-(CH4)~.The binding energy of the third CHI ligand is much smaller than those of the first two. The amount of CO+.(CH~)~ was too small to measure accurately in the present experiments; however, the ratio of CO+-(CH~)~/CO+*(CHI)~ was about 1.4 X 10-4 at T = 477 K. This corresponds to a AGO -0.7 kcal/mol. Wecanestimate theentropy of the thirdclustering reactions to be roughly -20 cal/(K This indicates that the bond energy of the third CH4 ligand is about 11 kcal/mol, or 13 kcal/mol weaker than the second. This decrease is similar to that found in the CO+.(H~)~/CO+*(H~)~ case, where the respective binding energies are 17.1 and 9.6 kcal/mol.2 A similar decrease in binding energy was also found for C O + * ( N H ~ ) ~ . ~ ) Calculations on CO+.(H~)~ predict22this drop in binding energy
*
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1814 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
e ~ EStimted Vibntiod F"eSi TABLE Iv: S y m ~ t d rad
Kemper et al.
for Co+*(HS/CHJC&)~j cluster vibrational modes
symmetry
no.
Co+*H2
ion
C2,
Co+*(H2)2'
Did
1 2 3 1 2 3 4 5 6 7 1 2 3
CO+.CH~
CO+.(CH4)2
c2
c2
C2,
c 2
a
1 2 3 4 5 6 1 2 3 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8
irred. rep. AI AI
BI AI
B2 AI B2
BI E E AI BI B2
AI
B2 A2
E E E
A
B A A A
2B A 2A
2B AI AI
A2 B2
BI B2
BI + B2
A A A
2B B B B A
mode type
Co+-H2 sym str, ~r= 1.934 H-H str c0-H~asym strlrock sym str (HrCo+-H2), fir = 2.0 asym str (HrCo+.H2), fir = 1.94 sym str (H-H) asym str (H-H) internal rotation (hindered) bend (HrCo+-H2) rock (Hz-Co) sym str (CO+-CH4) bend about H-H axis (Co+-H&H2) bend perpendicular to H-H axis (Co+-HAH2, similar to c 0 - H ~rock) sym str (CHd-Co+-CH4),fir = 16.0 asym str (CH&o+-CH4), = 13.2 internal rotation bend (CH&o+-CH4) bend (H~C-H&O+.CHI) rock (bend perpendicular to no. 5 ) sym str (Co+-C2H6) rock (Co+-C2H6) internal rotation (C2H6 rotation about C-C bond) Sym Str (C2H6-CO+-C2H6) aSym Str (C2H6-CO+-C&) bend (C2H6-CO+-C2H6) internal rotation (about C2 axis) internal rotation (C2H6 rotation about C-C bond) rocklasym str (Co+-C2H6) str (H~-CO+.CHI) str (CH~-CO+.H~) internal rotation rock (H~-CO+.CH~) rock (CH4-Co+.H2) bend (CHrH&o+.H2) bend (CH&o+-H2) str (CH4-CO+*C&j) str (C2H6-Cd-CH4) internal rotation (about C2 axis) bend (CH4-CO+-C2H6) rock (CH~-CO+.C~H~)
rock (C2H6-CO+*CH4)
bend (CHrH&o+.C2&) internal rotation (C2H6 rotation about C-C bond)
freq (cm-1) 863a/9096 3754'135806 1288'1822 834 23800 23900 465 170:; 1245 374 3436 40-3, 520 & 80
+c
332 366 159 70 40;: 530 & 70 3291261 450 & 60
free rotor 270 310 66 60
free rotor 41 1 890 375 272 1280 520 & 80
;:04 170 290 311 140 65 & 20 480 80 410 80
*
;::04 free rotor
Reference 37. Reference 25. E See ref 2 for a discussion of the derivation of these frequencies.
and also indicate that the probable structure is a slightlydistorted T. Several factors are responsible for the reduction in bond energy in Co+*(H2)3:2steric interference, loss of 3 d 4 s hybridization advantage (since the third ligand would be sited at the electron density maximum), and decreased u bonding between Co+ and H2. The greater reduction in the third ligand bond strength observed in the Co+*(CH4),,system may be due to increased steric interference due to the larger CH4 ligands. Co+C& The binding energy for this cluster was too large to measure using a direct equilibrium between Co+and Co+-C2H6. Instead, equilibrium ligand switching between Co+-CH4and Co+C2H6was used to measure the difference in bond energies. The resulting Co+*C& bond strength was 28.0 f 1.1 kcal/mol. The corresponding was -22.3 f 2 cal/(K mol). The increase in binding energy relative to the Co+.CH4 cluster is again due to several factors. First, the polarizability of C2H6 is considerably larger than CH4 (4.44 A3 w 2.58 A3), resulting in a greater chargeinduddipole attraction. Second, a quadrupole moment is present in C2H6, allowing a chargc-quadrupole attraction to occur. The moment is small, however, and its negative value would favor an end-on Co+-C2H6 interaction. A third possible cause of the increased binding is the possible Co+ coordination to the relatively polarizable C-C bond. This might be expected to significantly increase the u bonding between the metal and ligand. Other effects are undoubtedly present as well.
em
For more information as to structure and bonding we turn to theoretical calculations. The experimental results can again be compared with those from the calculations of Perry et al.25 They find three energy structures. In the most stable, the Co+ coordinates to the C-C bond (C2 symmetry, De = 24.9 kcal/mol). Nearly isoenergetic, however, is the structure with the Co+ coordinating to two hydrogens on one carbon (C,symmetry, De = 24.7 kcal/mol). In the third structure, the Co+ coordinates with three hydrogens on the same carbon (C3"symmetry, De = 23.6 kcal/mol). The most stable geometry (C2 symmetry) was used in the derivation of our experimentalbinding energies (see Data Analysisand Appendix); however, little change occurs if the C, symmetry is assumed. Making the usual zero-point energy correctiongives a theoretical, ground-state binding energy of 23.8 kcal/mol. This is 85%of the present experimental value, and the underestimation in BE is about what is expected.25 Because of the possible (unknown) changes in the C2H6 vibrational modes, the zero-point correction is somewhat uncertain. The presence of at least two Co+C2H6structures of similar energy (the C2 and C, structures) issupported by the calculations of Rosi et al.24on Cr+*C2H6.The C,,structure (Cr+coordinated to three hydrogens) was not considered. The calculated binding energy (De)was 10.7 kcal/mol. Only one structure (C2 symmetry) was found for the Cu+.C2H6complex. The binding energy was
CO+.(HZ/CH~/C~H~) I ,2,3 Clusters
The Journal of Physical Chemistry, Vol. 97, NO. 9, 1993 1815
larger (De= 16.2kcal/mol) due to thesmallCu+radius. Extensive C2H6 ligands are much lower than in the H2 ligands, and such effects should be smaller. It appears that calculations on the calculations were not reported for the Co+-C2H6 complex. A cluster ion are needed to understand any changes in bonding re-analysisof the data in ref 13 (assumingthe Co+*CzD6structure) which occur in adding the second C2H6 ligand. gave a cO+-C2D6binding energy of -23 kcal/m~l?~ in agreement with preliminary results of Haynes and Armentrout.15 Some Co+*(C&)p The Co+.(C2&)3 thirdcluster wasnot observable question exists, however, as to the reactant rotational/internal at our experimental temperatures and pressure, with typical energy distribution in the study.35 Phase space fitting of the C O + ( C ~ H ~ ) ~ / C O + (ratios C ~ H
