J. Phys. Chem. 1987, 91, 5307-5314 Ru(001) is more active than both the polycrystalline iron and nickel surfaces by a factor of approximately 5-10 at 1250 K, for example. The apparent activation energy of decomposition at high temperature E, - Ed,NH, of 5.0 kcal-mol-' on Ru(001) is similar to those that were determined on polycrystalline iron (10 kcal. m01-I)'~and polycrystalline nickel (6.0 kcal-m~l-').'~ The desorption of N2*with 20 kcal-mol-' of vibrational excitation has been observed in threshold ionization studies of ammonia decomposition on a polycrystalline platinum ribbon at pressures of 0.1-1.4 Torr and temperatures between 773 and 1373 K.sO On this basis, it was suggested that the bimolecular reaction of two adsorbed N H species is the dominant reaction producing molecular nitrogen and limiting the rate of ammonia d e c o m p o ~ i t i o n . ~ ~ However, the thermal desorption experiments conducted during the steady-state decomposition of ammonia at temperatures between 500 and 950 K demonstrate that nitrogen adatoms are the predominant surface species during ammonia decomposition at 2 X 10" Torr on Ru(001) (cf. Figure 3), and the recombinative desorption of nitrogen adatoms is the major reaction producing molecular nitrogen during the steady-state decomposition of amm~nia.~' The fact that the activation energy of desorption of nitrogen is essentially constant for fractional surface coverages of nitrogen greater than approximately 0.1 (cf. Figure 5a) may be interpreted in either of two different ways. First, this could indicate that both the heat of adsorption and the activation energy of adsorption of nitrogen are independent of coverage on Ru(OO1). Alternatively, these data could imply that the activation energy of adsorption increases with surface coverage, whereas the magnitude of the heat of adsorption decreases by the same amount. The second ~
~~
(50) Foner, S . N.; Hudson, R. L. J . Chem. Phys. 1984, 80, 518. (51) The same conclusion was reached for the decomposition of ammonia on the Pt(llO)-(lX2) ~ u r f a c e . ' ~
5307
of these two possibilities is more likely to be the correct explanation. The fact that the activation energy of desorption increases at fractional surface coverages below 0.1 implies that the magnitude of the heat of adsorption increases by more than the decrease in the activation energy of adsorption. Studies currently under way are aimed at disentangling the activation energies of adsorption and desorption of nitrogen on R u ( O O ~ ) . ~ ~ V. Conclusions The steady-state decomposition kinetics of ammonia on Ru(001) are controlled at high temperatures by a competition between the desorption of ammonia and a surface reaction involving the dissociation of a N-H bond in molecularly chemisorbed ammonia. The apparent activation energy in this regime is 5.0 f 0.3 kcal-mol-', and the rate of decomposition, which is first-order in ammonia pressure, exhibits a primary kinetic isotope effect. At low temperatures, the steady-state decomposition kinetics are controlled by the desorption of nitrogen, and the rate is independent of ammonia pressure. The apparent activation energy in this regime is 43 f 3 kcal-mol-I and is equal to the measured activation energy of desorption of nitrogen. The previously proposed reaction mechanism for ammonia decomposition on platinum describes quantitatively the decomposition on ruthenium. Nitrogen adatoms are the dominant surface species during the decomposition of ammonia at 2 X Torr, and the nitrogen overlayer gives rise to a (2x2) LEED pattern that corresponds to an absolute fractional surface coverage of 0.47 at saturation. Acknowledgment. This research was supported by the National Science Foundation under Grant CHE-8617826. Registry No. Ru, 7440-18-8; ammonia, 7664-41-7; nitrogen atom, 17778-88-0;deuterium, 7782-39-0. (52) Tsai, W.; Weinberg, W. H., manuscript in preparation.
Gas-Phase Chemistry of Transition-Metal Ions with Alkanes: Do Initial Electrostatic Interactions Control Final Product Distributions? Deborah J. Hankinson and John Allison* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received: December 22, 1986; In Final Form: April 13, 1987)
There are features of the dynamics of gas-phase ion/molecule reactions that make them unique when compared to neutral/neutral reactions and solution processes. Exceedingly rich and complex chemistry can be observed in gas-phase systems in which a reactant is charged, due, in part, to the relatively long lifetime of the ion/molecule complex that is initially formed. Here possible correlations between final reaction products and geometry-specific complexes that are initially formed are discussed. The chemistry under study is that for univalent first-row transition-metal ions with n-butane, in which cleavage of C-H and C-C bonds is observed for some metals.
Introduction In the past several years, gas-phase studies of the chemistry of transition-metal and metal-containing ions with organic molecules has been an active area of research.' Of the organic molecules studied to date, alkanes2-'* have received considerable (1) Allison, J. Prog. Inorg. Chem. 1986, 34, 627.
(2) Allison, J.; Freas, R. B.; Ridge, D. P. J . Am. Chem. SOC.1979, 101,
,*-a
133L.
(3) Radecki, B. D.; Allison, J. Organometallics 1986, 5 , 411. (4) Freas, R. B.; Ridge, D. P. J . Am. Chem. SOC.1980, 102, 7129. (5) Jackson, T. C.; Carlin, T. J.; Freiser, B. S. J . Am. Chem. SOC.1986, 108, 1120. (6) Mestadagh, H.; Morin, N.; Rolando, C. Terrahedron L e f t . 1986, 27, 33.
0022-36541871209 1-5307$0 1.50/0
attention. Detailed studies using labeled alkane^'^*'^ have revealed that the mechanisms through which the observed product ions are formed are varied and complex. B. S. J . Am. Chem. SOC.1983, 105, 5191. (8) Halle, L. F.; Armentrout, P. B.; Beauchamp, J. L. Organometallics 1982, I , 963. (9) Byrd, G . D.; Burnier, R. C.; Freiser, B. S. J . Am. Chem. SOC.1982, 104, 3565. (10) Houriet, R.; Halle, L. F.; Beauchamp, J. L. Organomerallics 1983, 2, 1818. (11) Tolbert, M. A.; Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J . Am. Chem. SOC.1986, 108, 5675. (12) Mandich, M. L.; Steigerwald, M. L.; Reents, W. D. J . Am. Chem. SOC.1986, 108, 6197. (13) Jacobson, D. B.; Freiser, B. S . J . Am. Chem. SOC.1983, 105, 736. (7) Jacobson, D. B.; Freiser,
0 1987 American Chemical Society
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Hankinson and Allison
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Consider the reaction of Co' with butane. Three product ions are observed: CO"
+ n-C4Hlo
-+
+
+
(1)
+ H2
(3)
C O C ~ H ~ ' C2H6
CoC4Hg"
Some transition-metal ions (M') also form MC4H6+ in their chemistry with butane, eliminating two molecules of hydr~gen.~,' Obviously, in reactions such as (1) and (2), C-C bond cleavage occurs. Some transition-metal ions do not appear to cleave C-C bonds but will react by eliminating one or more molecules of hydrogen in reactions with straight-chain alkanes.' A mechanism commonly used in discussing such reactionsk4 involves insertion of the metal ion into a bond (oxidative addition), followed by a /3-H shift (this mechanism may be indistinguishable from one in which insertion into a C-H bond occurs first, followed by the shift of some group that is p to the initial insertion site, although the original mechanism is more consistent with endothermic reaction products that have been observed15and a large body of literature'). In the case of n-butane, transition-metal ions such as Co' appear to insert into C-H and C-C bonds, with products from insertion into the interior C-C bond being favored over those following insertion into the terminal C-C bond. While labeling and collision-induced dissociation s t ~ d i e s ~ , ~have ~'~.'~ provided insights into the mechanisms involved in forming specific products, the factors that control the final product distributions have been elusive. A variety of thermodynamic explanations have been proposed for explaining why the CoC2H,+ product is formed to a greater extent than the CoC3H6' product in the reaction of Co+ with n - b ~ t a n e . ~ .For ' ~ example, the strengths of the bonds being broken and formed have been cited as important factor^,'^^'^ although an explanation that could adequately explain the product distributions for larger alkanes has yet to be concisely defined. Work in characterizing the chain-length effects in reactions of alcohols,lg alkyl halides," nitriles, and alkanes3 has suggested that the chemistry of transition-metal ions with organic molecules should be considered, in most cases, as occurring through a series of four steps: complexation,lg insertion,I4 P-H shift,I4 and competitive ligand loss.19 It has been suggested that the geometry of the initial ion/molecule complex that is formed has a strong influence on where the metal will i n ~ e r t . ~If, ' ~ the distribution of initial insertion intermediates was known, the final products and their distributions would, in many cases, be simple to predict.20 Presented here are the results of simple electrostatic calculations that were designed for investigating the stability of various transition-metal-ion/n-butanecomplexes, in an attempt to probe the relationship between final product distributions and the complexation step-Le., what happens before the "chemistry" (bond cleavage and formation) begins. For example, which of these two electrostatic complexes is more stable:
rl+
I -
II -
In the electrostatic complex I the transition metal is in close proximity to the terminal C-C bond and may thus lead to formation of the CH3-M+-C3H7 insertion intermediate and then to (14) Allison, J.; Ridge, D. P. J. Am. Chem. SOC.1976, 98, 7445. (15) Armentrout, P. B.; Beauchamp, J. L. J . Am. Chem. Soc. 1981, 103, 784. (16) Larsen, B. S.; Ridge, D. P. J . Am. Chem. Soc. 1984, 106, 1912. (17) Armentrout, P. B.; Halle, L. F.; Beauchamp, J. L. J . Am. Chem. SOC. 1981, 103, 6501. (18) Tsarbopoulos, A,; Allison, J. J . Am. Chem. Soc. 1985, 107, 5085. (19) Tsarbopoulos, A,; Allison, J . Organometallics 1984, 3, 86. (20) For example, trends in initial sites of insertion have been used to predict reaction products: Lombarski, M.; Allison, J. Int. J . Muss Spectrom. Ion Processes 1985, 65, 3 1.
the MC,H," product. Thus, the assumption being made here is that the metal ion must be close to a bond for chemistry involving that bond to occur. Our interest in the electrostatic interactions of metal ions and alkanes is also related to the fact that "ligand substitution" reactions are observed in the gas p h a ~ e , ~in. ~which ' alkanes may displace CO, e.g. NiCO'
+ C5H12
-
+
NiCsH12+ CO
(4)
There are a number of possible explanations'6*21 for reactions such as (4). One is that, unlike in solution, pentane is more strongly bound to a transition-metal ion than is CO. Another is that the reaction is more complex and the product exists not as an electrostatically bound ion/alkane complex, but in some other form such as C2H5-Ni+-C,H7. Thus, investigations into the nature of electrostatic ion/molecule interactions may provide insights into such reactions. In this study, a simple model will be used to investigate the electrostatic interactions of Cr' and n-butane. Cr" was chosen because of its spherically symmetric d5 ground state. Thus, the calculations were much simpler than if the ion chosen had a quadrupole moment. Ground-state Cr' is not, itself, reactive with small alkanes, but other first-row transition-metal ions are. The n-butane molecule was chosen because it is the smallest alkane in which two types of C-C bonds are present.
Computational Details A simple model was constructed that would allow the study of electrostatic interactions between Cr+ and n-butane, with the molecule fixed in specific configurations. For a selected configuration of butane, with an ion at some specific position relative to the molecule, the ion/molecule interaction energy calculated is of the form
Three sets of terms are calculated. The first are ion/induced dipole attractive terms. In this model, these terms are approximated by using individual bond polarizabilities. The ion interacts with each of the 13 bonds in the molecule, leading to 13 terms having the form22
E l l d ( r )= -az2e2/8stor4 Here, an ion with a charge ze at a distance r from a bond center induces a dipole in the polarizable bond. The bond polarizability a has the form23 a = a cos2 O
+ a,
sin2 O
where 8 is the angle formed between the ion-to-bond-center and bond vectors. Each bond is characterized by a parallel and perpendicular p ~ l a r i z a b i l i t ya,, ~ ~and a,. In units of cubic cenfor timeters per molecule, a,, = 18.8 X low2',a , = 0.2 X al = 5.8 X for C-H bonds. C-C bonds and a,,= 7.9 X The second set of terms recognizes the fact that C and H atoms do not have the same electronegativity; thus each C-H bond represents a (small) local dipole. That is, each atom in butane carries either a small positive or negative charge. The ion interacts with each of these small permanent charges to yield repulsive or attractive interactions having the form2, Ei,(r) = z,z2e2/4ator
for an ion of charge zle interacting with a charge z2e (localized on an atom), separated by a distance r. The charges on the atoms in butane that were used are25methyl C (89.2 me), methylene (21) Radecki, B. Ph.D. Thesis, Michigan State University, 1985. (22) Benson, S. W.The Foundations of Chemical Kinetics; McGraw-Hill: New York, 1960. (23) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Mo[ecu[arTheory of Gases and Liquids; Wiley: New York, 1954. (24) Halliday, D.; Resnick, R. Physics, Parrs I and 11; Wiley: New York, 1966.
Chemistry of Transition-Metal Ions with Alkanes
Figure 1. Configuration 1 of butane. Atomic numbering scheme and relationship to axes shown.
C (84.8 me), methyl H (-32.4 me), methylene H (-38.4 me). Thus, we have chosen the local dipoles to be of the form C6+H”. To represent the repulsive interactions between the ion and the atoms in the molecule, an &dependent term was chosen, similar to that used in the Lennard-Jones 6-12 potential.26 The repulsive interaction takes the form
E,(r) = 4d(a/r)I2 where the ion and atom are separated by a distance r. By use of the potential curves for Cr+-H and Cr+-C that have been generated from a b initio calculation^,^^^^^ values were extracted for d and a, where d is the depth of the well and a is one value of r for which the potential has a value of zero (a # m). On the basis of these potential curves, we have chosen for Cr+-C interJ molec~le-~, a = 1.41 A; and for Cr+-H actions d = 22.78 X interactions d = 17.44 J molecule-’, a = 1.18 A. Figure 1 shows the system that will be used for labeling the atoms in butane. Bond lengths of 1.54 8, (C-C) and 1.10 A (C-H) and tetrahedral angles were used to construct the molecule. All calculations were performed on a DEC VAX 11/750, at a double-precision level. Programs were written in VAX-77 Fortran. Two types of calculations were performed that will be referred to as “Cartesian” and “radial”. Consider butane in the configuration shown in Figure 1 , with the center of mass at the origin of the coordinate system as shown. In a Cartesian calculation, we choose a plane such as the XY plane, place the ion at some initial point such as (-5,-5,0) (distances are in angstroms), and calculate the potential. Then the ion is moved about a designated region of the plane in 0.01-A steps, to yield an array of position/energy data pairs. This data can then be read to locate all of the points that correspond to, for example, an energy of -10 kcal/mol. In this way families of potential curves about the molecule can be generated. Note that, as the ion approaches the molecule along a vector, two points corresponding to -10 kcal/mol may be found-on the falling and rising portions of the potential well. For fixed step size, the points on the rapidly rising repulsive portion of the potential may not always be found, within the limits defined (within 1.5% of the value chosen). These calculations, in various planes about the molecule, show where potential gradients are steepest and where high attractive potential regions exist about the molecule. In radial calculations, the ion is brought toward the molecule along some ray that extends from the center of mass, again confined to some defined plane. In this calculation, the bottom of the potential well for this approach is found and its position noted. The ray is then moved in two degree steps and the calculation repeated. In this way, the bottom of the well about the molecule in a particular plane can be visualized and the energies corresponding to these points identified. The results of these radial calculations graphically suggest which ion/molecule complex geometries would be most strongly bound. These two types of calculations have been performed in a variety of planes for a variety of configurations of n-butane, chosen to sample the various chemical environments that a metal ion may sample. Of course, in addition to determining total potentials for various ion/molecule configurations, the variations of individual (25) Fliszar, S. Charge Distributions and Chemical Effects; SpringerVerlag: New York, 1983. (26) Daniels, F.; Alberty, R. A. Physical Chemistry, 3rd ed.; Wiley: New York, 1966. (27) Alvarado-Swaisgood, A. E.; Allison, J.; Harrison, J. F. J. Phys. Chem. 1985, 89, 2517. (28) Harrison, J . F. J. Phys. Chem. 1986, 90, 3313.
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
5309
contributing terms can also be studied. Obviously, such a model is limited. Other approaches to modeling ion/atom and ion/molecule electrostatic potentials should be n ~ t e d . ~ ’The ~ ~ bond polarizability description is a crude approximation; however, it allows for a simple calculation that utilizes the fact that the ion will be closer to some parts of the molecule than others. The point multipole model is again an approximation. Other models could predict a distribution of charges about the butane molecule that would more closely mimic its response to an electric field; however, again, it provides a simple picture for such interactions. Our experience with the atomic charge distribution utilized is that these terms do not dramatically affect the results, at least in calculations at this level for alkanes, since the ion-partial charge terms are the most long range. Thus, if the ion is interacting with a number of H atoms, on which are localized small negative charges, the ion is also near a C atom that carries a small positive charge. Thus, the contribution due to the sum of the Eipterms is always small. We have varied the magnitude and signs of these terms, with only minor effects on the results and no effects on the observed trends. It should be noted that the direction of the dipole for C-H bonds is not well understood, with literature supporting both the C6+-H6-3640and C6--H6+ m ~ d e l s ~available. l-~~ It has been suggested that the C6+-H& polarity of the C-H bond is consistent with the inductive effect concept that -CH3 is a better electron donor than -H.37s38 The uncertainty concerning the relative sign of the C-H dipole arises because the charge distribution for a molecule cannot be uniquely resolved into a collection of localized component^.^^ The same can, of course, be said for the bond-localized polarizability description. New approaches continue to be pursued for calculating charge distributions in molecules.44 Finally, the model is most sensitive to the repulsive terms. We have chosen a simple form for these terms, derived from potential curves. Such terms should have a strong dependence on r; however, it may not actually be an rI2 dependence. This model was developed for studying the interactions of metal ions with organic molecules such as alkanes of varying size and also with polar compounds such as alcohols and alkyl halides. Like all simple models, their utility is not in producing absolute results, but in suggesting possibilities. Ion/molecule interaction energies presented here should not be taken literally; however, it is useful to compare relative values. We are investigating here that “fuzzy region” between long-range interactions (that are predominantly ion/induced dipole interactions for ion/alkane systems at large separations) and that region where electron exchange can occur, and ab initio electronic structure calculations must be utilized. That is, we are interested in what happens as the molecule and ion approach and form an electrostatic complex before the chemistry starts. We fully realize the limitations of these calculations but nonetheless find them exceedingly useful in investigating possible ion/molecule complex configurations and interactions.
Results and Discussion To demonstrate the types of results that can be generated and the relative contributions of the various terms that are calculated (29) Spears, K. G.J. Chem. Phys. 1972, 57, 1842. (30) Spears, K. G. J. Chem. Phys. 1972, 57, 1850. (31) Gowda, B. T.;Renson, S. W . J . Chem. Phys. 1983, 79, 1235. (32) Gowda, B. T.; Benson, S. W. J . Comput. Chem. 1983, 4, 283. (33) Hase, W. L.; Feng, D. F. J . Chem. Phys. 1981, 75, 738. (34) Berthod, H.; Pullman, A. Chem. Phys. Lett. 1980, 70, 434. (35) Gowda, B. T.; Benson, S. W. J . Phys. Chem. 1982.86, 1544. (36) Gordon, M. S.; England, W. J . Am. Chem. SOC.1972, 94, 5168. (37) Fliszar, S. Can. J. Chem. 1976, 54, 2839. (38) Fliszar, S.; Goursot, A.; Dugas, H. J . Am. Chem. Soc. 1974,96,4358. (39) Bader, R. F.; Preston, H. J . T. Theor. Chim. Acta 1970, 17, 384. (40) Pritchard, R. H.; Kern, C. W. J. Am. Chem. SOC.1969, 91, 1613. (41) Mullay, J. J. Am. Chem. SOC.1986, 108, 1770. (42) Fliszar, S.; Kean, G.; Macaulay, R. J . Am. Chem. SOC.1974, 96, 4353. (43) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657. (44) Mortimer, W. J.; Ghosh, S. K.; Shankar, S.J . Am. Chem. SOC.1986, 108, 4315.
5310
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Hankinson and Allison 5007
- 4 6 -35-30 - 2 0
I l l
4’0°1 00
I
400-
300-
a
300-
-35
200-
200-
I00-
100-
Y
Y 000000-I 00-
- I 00-
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-200-
- 30 -300-
-300-
0
-400-
-400-
-5OOJ
-35 -30 -20 -10
- 5 0 0 - 4 0 0 - 3 0 0 - 2 0 0 -100 0 0
100 2 0 0 3m 4 0 0 100
X
-500 - 5 0 0 - 4 0 0 -300 -200 -100 00
100 200 300 4 0 0
500
X
Figure 2. Constant-potential curves in the X Y plane for configuration 1.
for each point, the interaction of Cr+ with one configuration of butane will be discussed and highlights of the calculations for other configurations presented. Figure 1 shows the first configuration of butane that was considered, the numbering system used for the atoms, and the relationship to the Cartesian axes. All four C atoms and two methyl H atoms are in the XYplane. The origin is at the center of mass of the molecule. If calculations are performed in the XY plane and points corresponding to selected energies plotted, the resulting contours are shown in Figure 2. This figure shows that there is a potential region encircling the molecule in this plane, where the ion/molecule attraction is 10 kcal/mol. There are only selected locations where larger binding energies are realized. The largest negative energy found in this plane is -47 kcal/mol, at a position on top of the molecule. At this point, the ion is nested between four methyl C-H bonds. There are some other interesting “hot spots”, where the metal ion is in close proximity to the various C-C bonds. Figure 3 shows the results of radial calculations in the XYplane for configuration 1 of butane. Figure 3a shows the points corresponding to the minima, Le., the bottom of the potential well about the molecule in this plane. Figure 3b shows the energies that correspond to these points (solid line). In Figure 3b, an angle of 90° corresponds to that shown by the arrow in Figure 3a. Angles greater than 90° correspond to points found by moving along the curve shown in Figure 3a counterclockwise, starting froim point A. This shows a number of interesting points at which the Cr+ may be situated. Point A corresponds to the most attractive interaction, -47 kcal/mol. Moving to the left along the curve in Figure 3b, the energy goes up, and a local minimum is found at point D, where the metal ion is situated atop the methyl group, interacting with the three C-H bonds, the three methyl hydrogens, and the parallel polarizability of the C,-C2 bond. The energy goes up as the metal ion passes around the methyl H that is in the XY plane and goes through two more local minima-point C (in close proximity to the terminal C-C bond) and point B (in close proximity to the interior C-C bond). Point B corresponds to a more attractive interaction than does point C. The hot spots found for configuration 1 in the X Y plane correspond to the metal ion in close proximity to either three C-H bonds (points D and C) or four C-H bonds (points A and B) with the latter yielding the more attractive interactions. Table I shows the individual terms that yield the overall energy calculated for point A. The charge/induced dipole contributions are greatest for the C-H bonds that are closest to the ion. The parallel and perpendicular polarizabilities for C-H and C-C bonds suggest that, while orientation is important with respect to C-C bonds, it is not the case for C-H bonds. When the charge is close to a C-H bond, a large ion/induced dipole term is realized, regardless of orientation relative to that bond. A summary of the terms contributing to the energies realized at points B, C, and D, and other points that will be discussed
b
90
126 162 198 234 270 306 342 378 414 450
8 Figure 3. Results of radial calculations in the X Y plane for configuration 1. Panel a shows the minima about the molecule, and panel b shows the
corresponding energies (solid line based on C6+-H6-model, dashed line based on Cb-H6+description). In (a), and all similar figures that follow, 8 = 90’ corresponds to the point lying on the positive side of they axis (here A), with larger angles corresponding to counterclockwise motion about the curve in (a). TABLE I: Values of Individual Terms for Point A
E::ATerms
bond
energy. kcal/mol
HrC1 H2-Cl H944 C1-C,
-3.9
H4-C2
H6-C3
H,-C4
-12.6 -12.6 -4.7
-0.9 -0.9 -3.9
atom HI, H8 H?, H3, H,, HI, CI, c4 H4, H5, H,, H7
c2, c3 totals
bond
energy, kcal/mol
H3-C,
-12.6 -1 2.6 -4.7
H10-C4
c3-c4 H5-C2
-0.9
H,-C3
-0.9
c2-c3
-0.05
total E,,, kcal/mol -3.7 ea. r 6 . 6 ea 14.8 ea.
-3.3 ea.
9.1 ea. 0.8
-71.3
E,, kcal/mol 0.0045 ea 4 25 ea. 3.24 ea. 0.0002 ea
0.016 ea. 23.5
shortly, is given in Table 11. It is interesting to note how the energy arises at points B and C, where the ion is close to the two types of C-C bonds. At point B, the ion is interacting with the parallel polarizability of the two terminal C-C bonds. Thus, while the ion is closest to the interior bond, it is not interacting with it as much as the other C-C bonds. Also, the metal interacts with four C-H bonds at point B. In contrast, point C corresponds to a less attractive interaction than does B. At C, the metal ion interacts with three C-H bonds, with one C-C parallel polarizability, and, again, not to a significant degree with the C-C bond to which it is closest. Figure 4 shows how selected components of the calculated total energy vary for the points plotted in Figure 3a. Figure 4
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Chemistry of Transition-Metal Ions with Alkanes
5001
TABLE 11: Data" on Points A-J -71.3 -59.3 -54.3 -52.5 (0.0,-0.05,l.l5) -57.8 (-1.79,3.10,0.0) -51.4 -54.5 (-2.5 ,-0.26,0 .O) -70.2 (0.51,1.78,0.0) -47.1 (0.72,2.52,0.0) (0.0,-2.38,0.0) -59.3
A
(0.0,2.12,0.0) (0.0,-2.38,0.0) (-2.5,-1.01 ,O.O) (-1.72,2.37,0.0)
B C D E F G H I
J
0.8 4.1 2.6 0.8 7.2 0.7 2.7 4.8 -0.7 4.1
23.5 16.1 16.6 16.2 15.4 16.0 16.5 20.5 13.7 16.1
-47.0 -39.1 -35.1 -35.5 -35.2 -34.7 -35.3 -44.9 -34.1 -39.1
300200-
loo-
z
ow-I00.
-200.
-300.
Coordinates are in angstroms; energies are in kilocalories per mole.
I
-30.20
-500 -500-400 -3m- 2 0 0 -100 00 7
l
O
100 2 0 0 300 4 0 0 Loo
Y
k
I\
/c'
2
4 z
I
.
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5311
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540-
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I-
n
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-1410 -1800 900
\
'
\ L'I
1260
00-
1620
1980
2340
2700 3060
3420
3780
W O
4500
e Figure 4. Dependence of various terms that contribute to the overall energies shown in Figure 3b (solid line). Shown are Elldterms for the C2-C3 and Hl-CI bonds, E,, terms for the atoms H I and CI, and the repulsive E , terms for C, and H9 (labeled with an R).
graphically shows a number of features of the interaction as described in this model. Ion/point multipole interactions are the most long range and thus have nonzero values for all points in Figure 3a. Those shown are for the ion interacting with the small charges that are localized on CI and HI. Also shown are the values for selected repulsive interactions, which obviously only contribute when the ion is close to that particular atom. Finally, two ion/induced dipole terms are plotted. The energy corresponding to the ion/C2-C3 bond interaction shows that, at the location corresponding to point B, where the metal ion is closest to this interior C-C bond, the induced dipole term for this bond is very small due to the orientation and the small perpendicular polarizability for C-C bonds. Similar calculations were performed in the X Z and Y Z planes for configuration 1 of butane. We believe that investigations in these three planes sample the extremes in chemical environments that could be experienced by the ion for this configuration of the molecule. Figure 5 shows the results of studies in the Y Z plane. Figure 5a shows a number of potential curves. Figure 5b shows the minima points found by the radial calculation, with Figure 5c showing the energies corresponding to the points in Figure 5b. As in the previous figures, an angle of 90° corresponds to the ray extending from the center of mass pointing up (here parallel to the Z axis, extending toward positive values of Z ) . Note that points A and B are also present in the YZ plane. An additional point of interest is labeled E. This is another location where the metal ion is surrounded by four C-H bonds, although the attractive energy at point E is smaller than that calculated for points A and B. Figure 6 shows the results of calculations for configuration 1 of butane in the X Z plane. Figure 6a shows selected potential curves; Figure 6b,c show the results for radial calculations in the X Z plane. The one point of interest in this plane that has appeared previously is point E. These results again show how the metal ion can be strongly bound at locations where it is surrounded by three or four C-H bonds. Point E corresponds to an interaction energy of -35 kcal/mol. Thus, for configuration 1 of butane, the
'" 1
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lation for configuration 1 in the YZ plane.
highest interaction energy found was at point A, -47 kcal/mol. Similar calculations were performed for other configurations of butane. The anti configuration (configuration 2), shown in Figure 7 , was also investigated. This is the lowest energy configuration for butane. Rotational energy barriers for butane about the interior C-C bond are in the 4-7 kcal/mol range.45,46 Panels a, b, and c of Figure 7 show potential curves, minima points, and corresponding energies, respectively, in the X Y plane for this configuration. In contrast to configuration 1, in which the two methyl groups were in (relatively) close proximity, the interactions with "isolated" methyl groups can be seen with configuration 2. Three points of interest are labeled F, G, and H (there are, of course, unlabeled symmetric counterparts to these three points). Again, there are two locations where the metal ion is close to three C-H bonds ( F and G), which contrasts to the more attractive point (45) Morrison, R. T.; Boyd, R. N. Organic Chemistry; Allyn and Bacon: Boston, 1973. (46) Streitwieser, A.; Heathcock, C. H. Infroduction to Organic Chemistry, 3rd ed.; Macmillan: New York, 1985.
5312 The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Hankinson and Allison
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F 126 162
198 234 270 306 342 378 414 450
8 Figure 7. Results of (a) Cartesian calculation and (b, c) radial calcu-
lation for configuration 2 in the X Y plane. \
H, where the metal ion is situated among four C-H bonds. In contrast to the results for configuration 1, there are not locations that could be easily perceived as having the metal localized about the various C-C bonds. Point G may be associated with the terminal C-C bond; however, point H is equidistant from two C-C bond centers. Calculations in planes other than the XYplane were performed for configuration 2 of butane; however, no point was found to yield a more attractive interaction than point H for this configuration. On evaluation of points A-H, it becomes apparent that environments in which three to four C-H bonds are nearby are most attractive. This led to the decision to evaluate a third configuration, which is shown in Figure 8. Configuration 3 is formed by rotating the left methyl group by 60’. This creates a region above the molecule where three C-H bonds are close-possibly creating a very attractive hot spot. The results of our calculations, in the X Y plane, are shown in Figure 8. The point of interest was point I, which, as the data shows, is less attractive than the point
similar to D, situated on the end of the methyl group. The most attractive interaction was found to be point J for this asymmetric structure, which is essentially equivalent to point B. There are a number of thermodynamic and chemical implications that result from these calculations. First, concerning the Cr+-n-butane electrostatic “bond energy”, the two largest attractive energies found were at points A and H. Point A yielded an energy approximately 3 kcal/mol greater than that for H. However, the potential energy of configuration 1 is higher than that for configuration 2 by at least 3 kcal/mol; thus this level of calculation yields a maximum bond energy of approximately 45 kcal/mol. While we are not suggesting that this is the true value, the calculations have shown that a nonpolar, polarizable molecule can significantly interact with a transition metal ion located nearby. Calculations at this level for systems such as Cr+-CO suggest that butane does interact more strongly than does CO; thus direct ligand substitution by an alkane would be possible in an ionic, gas-phase system.48 Modeling the M+-CO interaction in this way
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Chemistry of Transition-Metal Ions with Alkanes
a variety of ion/molecule complexes are initially formed, with the distribution of these depending on their relative stabilities. How does the structure corresponding to the metal ion a t point A fit into the chemistry? One possibility is that such intermediates lead to C-H insertion, although any of the other complexes discussed could as well. However, at A, the metal ion is only close to C-H bonds. Transition-metal ions do apparently insert into C-H bonds, leading to H2elimination following a P-H shift. Some transition metals that do not appear to insert into C-C bonds do eliminate H2 from a variety of molecules, possibly from initial complexes similar to A. An interesting possibility for the mechanism leading to H, elimination may be related to point A. For some first-row transition metal ions, the reaction
300-
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5313
500200I00-
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M+ + C4H10 ---* MCdHs' + H2 is more complicated than it appears. The ionic product may not be a metal-butene complex but a bis(ethy1ene) complex, M+(C2H4)2.This structure suggests that a C-C bond and two C-H bonds have been cleaved. It has been proposed that the transition-metal ion inserts into the interior C-C bond to form the insertion intermediate C2H5-M+-C2H5, which undergoes a double P-H shift to yield the bis(o1efin) metal complex and dihydrogen (1,4-elimination of H2). In light of the importance of point A, an alternate mechanism may be envisaged in which the transition-metal ion, starting from point A, inserts into two terminal C-H bonds to form a metallacyclic dihydride intermediate, 111, in which a C-C bond cleaves to yield the same products. A
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is not unreasonable in light of the result of high-level electronic structure descriptions of transition-metal-ion/CO interactions; the bonding appears to be predominantly electrostatic in nature.47 Also, at this level of calculation, Cr+/alkane interaction energies increase as the size of the alkane in~reases~~-consistent with experimental observations.2' These calculations suggest interesting possibilities relating the stability of various transition-metal-ion/ butane complex geometries and the final distribution of products observed from the chemistry that follows complexation. In the Introduction, it was pointed out that metal ions appear to attack the interior C-C bond to a greater extent than the terminal C-C bonds in n-butane. In this regard it is interesting to note that the potential well about point B is deeper than that for C. This suggests that complexation may dictate which bonds will be attacked to a greater extent, Le., that ~~~~~
~~
very similar metallocyclopentane intermediate has been suggested as an intermediate in the reaction of Co+ with 2,2,3,3-tetramethylbutane leading to dihydrogen elimination;l5 however, there is strong evidence, at least in the chemistry of Ni', that dihydrogen elimination from n-butane should not proceed through such a metallacyclic intermediate.49 However, metallacycles such as the vanadacyclopentane ion do appear to convert to a bis(ethy1ene) s t r u c t ~ r e .Through ~ an intermediate such as a metallocyclopentane dihydride generated through complex A, a metal-butadiene product could also be formed (resulting in the elimination of 2 H2), without cleavage of C-C bonds but only of C-H bonds. It was pointed out earlier that the direction of the local C-H dipole is not obvious. On the basis of a body of literature, we chose the C6+-H6- description. We suggest that the interaction of the ion with these small charges on the atoms is negligible in this case, due to the long-range nature of the interaction (see Tables I and 11). To probe this, the magnitude of the partial charges on the atoms of butane were maintained, and the signs were changed. The results are shown as the dotted line in Figure 3a for C6--H6+, in contrast to the solid line that was generated by using the C6+-H" description. The curves are similar, and the conclusions based on the work would not change. This alternate description of the atomic charge distribution makes the difference in energies between points B and C larger, also supporting the proposed link between initial complex formation and sites of subsequent bond insertion. A comment should be made concerning the resultant geometries in which the ion is closer to some atoms in the molecule than would be expected or may seem reasonable. This is, in part, due to the level at which these calculations are performed; the results are obviously sensitive to the repulsive terms used. There is growing
~~
(47) Harrison, J. F.,unpublished results. (48) Hankinson, D. J.; Allison, J , unpublished results.
(49) Halle, L. F.; Houriet, R.; Kappes, M. M.; Staley, R. H.; Beauchamp, J. L. J . Am. Chem. SOC.1982, 104, 6293.
5314
J . Phys. Chem. 1987, 91, 5314-5324
evidence that, in transition-metal-ion/moleculereactions, an electrostatically bound complex exists for some time before bond cleavages occur.Is One possible scenario is that the ion "parks" at some relatively large distance from the molecule to form the complex and the chemistry that follows draws the ion closer to atoms in the molecule. Another possibility is that the ion and molecule are in close proximity in the complex and motion of groups of atoms within the molecule must occur for the chemistry to begin; that is, the events are sequential in time but not necessarily corresponding to radically different separations. While it may be that the repulsive terms are too small in these calculations, it appears that there is little to stop the ion from getting close to the molecule, forming the initial complex, suggesting the latter scenario. This may not be the case for polar and/or unsaturated molecules in which a substantial charge distribution may exist throughout the structure.
first-row transition-metal ions, these calculations suggest that a complex in which an ion is in close proximity to the interior C-C bond is more strongly bound than that for a terminal C-C bond. This is easily visualized in the context of the bond polarizability description utilized here, which suggests that ion/induced dipole interactions involving C-C bonds are more extensive when the metal ion lies along a C-C bond axis than when positioned atop such a bond. Only when the metal ion is close to the interior C-C bond can it interact with two C-C bonds, as opposed to interaction with only one C-C bond when it is close to a terminal C-C bond. This simple approach to the modeling of ion/molecule complexes suggests that the first step in these reactionscomplexation-may be a key factor in determining which bonds are preferentially attacked and, hence, the final product distributions. Work is under way to refine the model and extend this work to larger alkanes, polar compounds, and metal ions with asymmetric charge distributions.
Conclusions By use of a simple model, preferred configurations of electrostatically bound metal ion/butane complexes are identified. This work supports the concept that ion/molecule interactions can be substantial, not only for polar molecules but for nonpolar, polarizable species as well. Concerning the chemistry of butane with
The Addition and Dissociation Reaction H
Acknowledgment. Partial support for this project from Professor Paul Hunt, Director of Academic Computing at Michigan State University is acknowledged. Also, we thank J. F. Harrison and K. C. Hunt for helpful discussions. Registry No. CO', 16610-75-6; n-C4H,,,, 106-97-8.
+ CO C HCO. 1. Theoretical RRKM Studies
Albert F. Wagner* and Joel M. Bowman' Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: December 29, 1986)
RRKM calculations of the thermal addition and dissociation rate constants are carried out on the Harding surface for HCO. Structures, frequencies, and energetics at the stationary points on the surface are presented for HCO and DCO. Due to the relatively weak H-CO bond (bond energy of about 16 kcal/mol) and the few degrees of freedom in HCO, the spacing between the vibrational states of the metastable HCO* is quite large. This motivates a form of RRKM theory in which metastable HCO* is explicitly considered to exist only at isolated vibrational resonance energies and all addition and dissociation dynamics is controlled by these isolated resonance states. The rate constant calculations focus on the implications of this isolated resonance model. Several experiments to test the model are indicated. Among the major conclusions of the study are ( 1 ) a standard treatment of tunneling cannot be included in the calculations, (2) explicit summation over total angular momentum must be included in the calculations, (3) interesting isotope effects in addition are predicted in the low-pressure limit of the rate constants, and (4) measurable recrossing effects are predicted in the approach to the high-pressure limit of the rate constants. In the following paper, the isolated resonance RRKM calculations are directly and generally favorably compared to the existing low-pressure measurements for both thermal addition and dissociation.
I. Introduction The collision dynamics of H with CO has been studied over the years in three different energy regimes. In the highest energy regime, hot atom sources for H atoms have been used to probe inelastic dynamics at energies up to several electronvolts. Both e~perimentall-~ and interpretative theoretical studies& have been carried out. In an intermediate energy regime, thermal addition and dissociation of HCO in a buffer gas M
the exception of one model study,I3 there have been no theoretical studies of these rate constants. In the lowest energy regime, there
H + co HCO* 2 HCO (1) have been extensively studied e~perimentally.~-'* The rate constants for these processes are of interest in combustion chemistry. However, essentially all the experimental studies at combustion temperatures (1200-2500 K) are indirect of the dissociation rate constant, and there is no agreement on the rate constant to within at least 1 order of magnitude. There are three experimental studies"'-'2 of the addition process near room temperature, all of which indicate a relatively low rate constant. With
tron-Molecule Scattering, van der Waals Complexes, and Reactiue Chemical Dynamics; Truhlar, D. G:, Ed.; American Chemical Society: Washington, DC, 1984; Chapter 22. (6) Gieger, L. C.; Schatz, G. C.; Harding, L. B. Chem. Phys. Lett. 1985, 114, 520. (7) Baulch, D. L.; Drysdale, D. D.; Duxbury, J.; Grant, S . J. Evaluated Kinetic Data f o r High Temperature Reactions; Butterworths: London, 1976; Vol. 3, p 327 ff. (8) Warnatz, J. In Combustion Chemistry; Gardiner, W. C . , Ed.; Springer-Verlag: New York, 1984; Chapter 5 . (9) Hucknall, D. J. Chemistry of Hydrocarbon Combustion; Chapman and Hall: New York, 1985; p 304 ff. (10) Hikida, T.; Eyre, J. A.; Dorfman, L. M . J . Chem. Phys. 1971, 54, 3422. ( 1 1) Wang, H. Y.; Eyre, J. A.; Dorfman, L. M . J . Chem. Phys. 1973,59, 5199.
'Permanent address: Department of Chemistry, Emory University, Atlanta, GA 30322.
0022-3654/87/2091-5314$01.50/0
(1) Wood, C. F.; Flynn, G . W.; Weston, Jr., R. E. J . Cbem. Phys. 1982, 77, 4776. (2) Wight, C. A.; Leone, S. R. J . Chem. Pbys.'1983, 78, 4875. (3) Wight, C. A,; Leone, S. R. J . Chem. Pbys. 1983, 79, 4823. (4) Gieger, L. C.; Schatz, G. C. J . Phys. Chem. 1984, 88, 214. (5) Gieger, L. C.; Schatz, G. C.; Garrett, B. C. In Resonances in Elec-
0 1987 American Chemical Society
