Gas Phase Reactions of Second-Row Transition Metal Atoms with

J. Phys. Chem. 1995,99, 13955--13969

13955

Gas Phase Reactions of Second-Row Transition Metal Atoms with Small Hydrocarbons: Experiment and Theory John J. Carroll, Kerstin L. Haug, and James C. Weisshaar" Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706

Margareta R. A. Blomberg,* Per E. M. Siegbahn, and Mats Svensson Department of Physics, University of Stockholm, Box 6730, S-113 85, Stockholm, Sweden Received: March 23, 1995; In Final Form: July 14, 1995@

For reactions of gas phase, ground state, neutral transition metal atoms from the 4d series with alkanes and alkenes, we combine 300 K kinetics measurements with ab initio electronic structure calculations to infer mechanisms in some detail. The theoretical method PCI-80 with zero-point energy corrections to the bare potential surface apparently produces bond energies, reaction exothermicities, and even saddle point energies accurate to within 2-3 kcal/mol, provided that the correct ground state has been located, which is sometimes difficult. The reactions fall into two general categories: termolecular stabilization of long-lived M(hydrocarbon) complexes and bimolecular elimination of Hz. By using the ab initio energies and vibrational frequencies in a statistical unimolecular rate theory (RRKM theory), we can model the lifetimes of M(hydrocarbon) complexes to assess the plausibility of a saturated termolecular mechanism at 1 Torr He. Termolecular examples include the reactions of Pd with alkanes to form long-range v2 complexes; the reactions of Rh and Pd with alkenes to form n complexes; and probably the reactions of Y, Zr, Nb, Rh, and Pd with cyclopropane to form CH or CC insertion complexes. In other reactions, all of the evidence indicates a bimolecular H2 elimination mechanism. Rhodium is unique among the 4d metal atoms in effecting HZ elimination from ethane and larger alkanes. Yttrium, zirconium, and niobium almost surely insert in CH bonds of ethylene and larger alkenes, ultimately eliminating H2. We discuss the general requirements on the pattern of atomic electronic states that pennit efficient CH bond activation and H2 elimination. The good agreement between the observed reaction rates and the PCI-80 calculations lends confidence to future efforts to apply ab initio techniques to more complicated catalytic systems, including condensed phase reactions involving ligated metal centers.

I. Introduction An important long-term goal is to understand homogeneous catalysis by transition metal complexes at the fundamental level of modem electronic structure theory. As ab initio quantum mechanics becomes increasingly able to treat electronically complicated organometallic systems at useful levels of accuracy, we need experimental data on well-defined systems against which to calibrate quantum chemical techniques. Bimolecular gas phase collisions between bare transition metal atoms and hydrocarbons provide a relatively simple arena for the detailed study of metal-hydrocarbon interactions. Reactions of the transition metal cations (M+) have been studied in great detail using the arsenal of sophisticated mass spectrometric techniques.' As a result, there has emerged a detailed picture of how the pattem of low-lying M+ electronic states of different configurations and spin multiplicities determines chemical reacti~ity.~~~ Much less is known about the gas phase reactivity of neutral transition metal atoms (M) with although they arguably provide more realistic models of condensed phase systems. The long-range M+-hydrocarbon potential is typically attractive due to ion-induced dipole forces, so long-range complexes are often bound and most transition metal cations are highly reactive. Early work found the neutral metal atoms from the 3d series to be completely unreactive with alkanes at 300 K; only Sc, Ti, V, and Ni reacted with alkenes.6 Apparently, neutral metal atoms often encounter potential energy @

Abstract published in Advance ACS Abstracts, September 1, 1995.

0022-365419512099-13955$09.00/0

barriers on approach to hydrocarbons, so their behavior is more analogous to solution phase processes. In this work, we present a comprehensive experimental and theoretical study of the reactivity of neutral transition metal atoms from the 4d series with linear alkanes, cyclopropane, and linear alkenes. The experimental work uses laser-induced fluorescence detection to measure the effective bimolecular reaction rate of ground state metal atoms with hydrocarbons at 300 K in 0.5-1.1 Torr of He buffer gas. We present new kinetics data for Rh, Pd, and Ag and summarize earlier data for Y, Zr, Nb, and M O . ~Unlike the mass spectrometric work on M+, the neutral M kinetics experiments determine only the rate of removal of metal atoms, not the chemical identity of the products. Each measured rate constant could include contributions from either bimolecular elimination reactions or termolecular M hydrocarbon association reactions or both. Consequently, our interpretation of the kinetics data has been quite tentative in the past. In parallel to the experimental work, we have been developing new methods for estimating correlation errors in ab initio treatments of the same systems? The errors at a given level of theory are highly systematic. This leads to the simple procedure we call parametrized configuration interaction.'O The PCI-80 version described below allows rapid exploration of potential energy surfaces leading from M hydrocarbon reactants all the way to elimination products at an accuracy of about 2-3 kcallmol, comparable to the accuracy of experimental bond energies themselves. We present PCI-80 results for the first time for selected points along the reaction path for the reactions

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0 1995 American Chemical Society

Carroll et al.

13956 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 1: Laser-Induced Fluorescence Transitio& atom transition energy (cm-I) Rh d8p,4Gi112 d8s,4F9/2 28 543 Rh dsp,4G9/2 d8s,4F9/2 29 105 Pd

Pd Ag Ag

-'PI 2Pin-

d9p, 3DI dl', 'So d9p, d", 'So d"p, d'%, 2Sl/2 dIop, 'P3/2- d'Os, 2S1/2

40 369 40 839 29 552 30 473

Assignments from ref 30.

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M Cb, M C2H6, M C Z ~and , M cyclopropane, where M is a neutral transition metal atom from the 4d series. The result is a large set of calculations corrected in a consistent manner for correlation error and differential effects of zeropoint energy. The calculations and kinetics data together provide the opportunity to compare theory and experiment for the same simple transition metal reactions at a unique level of detail. When we observe no reaction, the calculations can identify the impediment, typically a potential energy barrier arising from the electron confguration or spin of the ground state metal atom. For systems that do react, the experiments do not identify the products. In these cases we use both experimental data and the calculations to assess the plausibility of different reaction mechanisms. In some M alkane and M alkene reactions, the calculations point to bimolecular H2 elimination and the experiments see no pressure dependence of the rate constant. For example, Rh is unique among the 3d and 4d neutral atoms in its ability to dehydrogenate linear alkanes. The calculations allow us to identify the products and to understand the unique aspects of the electronic structure of Rh that permit efficient reaction. In other cases, the experiments show no pressure dependence of the rate constant, but the calculations indicate a termolecular mechanism. We then use microcanonical RRKM unimolecular rate theory with the ab initio vibrational frequencies and energetics to assess whether or not the termolecular mechanism could be in the saturated regime over the pressure range studied. Overall, we find experiment and theory to be in very good accord. This bodes well for extension of the PCI80 method to more complicated reaction systems, including key intermediates and transition states not easily studied by experiment.

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11. Kinetics Measurements A. Experimental Technique. The kinetics technique uses

a sputtering source to produce gas phase transition metal atoms in a fast flow of He buffer gas at 0.5- 1.1 Torr and 300 f 5 K. The metal atoms are thermalized by about lo5 collisions with He prior to entering the reaction zone, which contains a calibrated number density of the hydrocarbon reactant of interest. At the end of the reaction zone, laser-induced fluorescence (LIF) monitors the decay of the ground state metal atom concentration vs hydrocarbon number density for a fixed reaction time. If significant population survived in excited states which relaxed to the ground state in the reaction zone, we would observe nonexponential decay of the ground state LIF signal vs hydrocarbon number density, which does not occur. Details of the measurements are given The specific spinorbit levels probed and the LIF transitions employed for Rh, Pd, and Ag are given in Table 1. By measuring the logarithmic attenuation of metal atom number density (M) vs hydrocarbon number density (hc) at fixed mean reaction time trxn,we obtain the efective bimolecular rate constant kl from the pseudo-first-order expression ln[(M)/(M)o] = -kl(hc)t,,. The range of observable rate constants in our apparatus is typically 5 x 1 0 - l ~to 2 x cm3 s-I. The rate

TABLE 2: Effective Bimolecular Rate Constants kl (lo-'* cm3 s-l) for Reactions of Transition Metal Atoms with Hydrocarbons at 0.50 f 0.05, 0.80 f 0.05, and 1.10 f 0.05 Torr of He and 300 f 5 Ka Pd(lSo)

m(4D9/2)

reactant

ethylene

0.5 Torr

0.8 Torr

8.6 11.3 f2.6b f l . 1 propylene 115 f12 1-butene 175 180 f52b f 1 8 isobutene 218 *22 cyclo14.2 f1.4 propane methane NR ethane 3.50 3.54 f0.70 f0.35 9.38 propane f0.94 19.9 n-butane 18 k5b f2.0

1.1 Torr

0.5 Torr

12.8 f2.6

11.2 f2.2 -

0.8 Torr

15.0 f1.5 189 f19 351 367 176 f37 f53b f 7 0 301 f30 58.9 f7.7 NR 3.43 0.16 f0.02 f0.69 0.68 1.22 f0.14 f 0 . 1 2 19 3.50 4.63 2 ~ 6 ~f0.70 f0.46

1.1 Torr

Ag('S112) 0.8Torr

15.7 f3.1 -

NR

322 f64

NR

-

NR

-

NR

-

-

1.3 f0.3 5.2 1k1.6~

NR

NR

NR

cm3 SKI; dash "NR means no reaction observed, kl < 3 x means not studied. Error limits refer to the precision of the rates. Absolute accuracies estimated as f 3 0 % . In those cases we have only one measurement. Stated uncertainty is f 3 0 % . of neutral metal atom reactions should not greatly exceed the estimated hard-spheres collision rate khs, which is about 3 x cm3 s-l at 300 K for all reactions studied. We define the reaction efSiciency as kl/khs. The experimental rate constant kl is an average over a 300 K Boltzmann distribution of relative translational energy and hydrocarbon vibrational and rotational energy. Disappearance of M could involve bimolecular elimination reactions, termolecular stabilization of long-lived M(hydrocarbon) complexes, or some combination of both. To check for termolecular components of the rate constant, we can vary the He pressure over the limited range 0.5-1.1 Torr. As discussed in detail previously,6J pressure dependence of kl indicates a termolecular component, but the absence of pressure dependence does not rule out the possibility of a saturated termolecular component of the overall rate constant. We have not yet devised an experiment that directly determines the chemical identity of the reaction products. Theory will be very helpful in this regard. B. Kinetics Results. In earlier work we reported rate constants for reactions of metal atoms from the left-hand side of the 4d series (Y,Zr, Nb, and Mo) with linear alkanes and alkenes and with cyclopropane.8 Our new measurements for Rh, Pd, and Ag are summarized in Table 2. The results for Pd have been refined slightly since an earlier report.' Each entry at 0.8 Torr represents the mean of at least two and as many as five determinations of the rate constant. The error estimates refer to the precision of the rate constants. They represent the larger of &lo% or f 2 standard deviations of the mean of multiple measurements. The absolute accuracy of the rate constants is estimated as f30%. Rh and Pd are both unusually reactive, whereas Ag is inert to all hydrocarbons tested. None of the metals react with methane, but both Rh and Pd react with ethane and larger linear alkanes as well as with cyclopropane. The reaction efficiency with cyclopropane lies between that of propylene and propane. All of the observed Pd alkane reactions show a definite pressure dependence, whereas the Rh alkane reactions do not. Both Rh and Pd react with ethylene at about 5% efficiency, and both reactions show a definite pressure dependence. The

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J. Phys. Chem., Vol. 99, No. 38, 1995 13957

Gas Phase Reactions of Second-Row Transition Metals TABLE 3: Effective Bimolecular Rate Constants kl (10-l2 cm3 s-l) for Reactions of Transition Metal Atoms with Selected Hydrocarbons at 0.80 f 0.05 Torr of He and 300 f 5 K‘

ethene

59 f6 156 f16 NR

314 f31 390 f39

ethane

8.2 f0.8 143 &14 NR

-

2.08 f0.41 NR

n-butane

NR

NR

NR

NR

cyclopropane

0.70 10.07

0.66 f0.13

3.04 10.30

NR

1-butene

NR

11.3 fl.l 180 *18 3.70 f0.37 19.9 f2.0 14.2 f1.4

15.0 311.5 367 f37 0.16 f0.02 4.63 f0.46 58.9 f7.7

NR means no reaction observed, kl < 3 x cm3 s-I; dash means not studied. Error limits refer to the precision of the rates. Absolute accuracies estimated as f30%.

TABLE 4: Comparison of Reactivity of 3d- and 4d-Series Congeners with Propane, Propene, and Cyclopropane in 0.80 Torr of He at 300 f 5 K‘ (Effective Bimolecular Rate Constants in cm3 s-l) atom propane propene cyclopropane NR 9.5 f 1.0 0.01 f 0.02 Sc (ds2,2D) NR 141 f 14 0.70 f 0.07 Y (ds2,2D) NR NR Ti (d2s2,3F) 6.2 f 0.6 0.66 f 0.13 153 f 15 NR Zr (d2s2,SF) 0.02 f 0.02 NR 9.6 f 1.0 V (d3s2,4F) 360 f 36 3.04 f 0.30 NR Nb (d4s,6D) NR NR NR Cr (d5s,7S) NR NR Mo (d5s,7S) 0.38 f 0.19 NR NR NR Co (d7s2,4F) 115 f 12 14.2 f 1.4 Rh (d%, 4D) 9.38 f 0.94 NR 11 f 4 10f 1 Ni (d8s2,3F) 58.9 f 7.7 1.22 f 0.12 189 f 19 Pd (d’O, IS) NR NR NR Cu (dIos,2S) NR NR NR Ag (d’Os,2S) cm3 s-I. Error NR means no reaction observed, kl < 3 x limits refer to the precision of the rates. Absolute accuracies estimated as &30%. 3d-series data from ref 6. Early 4d-series data from ref 8. (I

Rh and Pd reactions with larger alkenes are quite efficient and show no pressure dependence. The reaction rates for Rh and Pd increase as the number of carbon atoms in the alkane or alkene increases. For a given carbon chain length, the alkene reaction rates are substantially larger than those for the corresponding alkane. One of the primary goals of this paper is to explain trends in reactivity across the 4d series. In Table 3, we compare rate constants at 0.8 Torr for Y, Zr, Nb, Mo, Rh, and Pd with the representative hydrocarbons ethylene, 1-butene, ethane, nbutane, and cyclopropane. Nb, Rh, and Pd are unusually reactive with alkenes and with cyclopropane. Rh and Pd stand but as the only 4d-series atoms that react with alkanes. In Table 4, we compare reaction rates for both 3d-series and 4d-series atoms with propane, propylene, and cyclopropane. In general, the 4d atoms are substantially more reactive than their 3d congeners.

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HI. Ab Initio Energetics

We have carried out extensive calculations of both potential minima and saddle points along possible reaction paths for the systems M Cfi, M C2H6, M C Z ~and , M cyclopropane, where M is one of the second-row transition metal atoms Y, Zr,Nb, Mo, Tc, Ru, Rh, and Pd. Before presentation

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of the results we describe some general features of the calculated energies. Appendix A gives further details of the basis sets and levels of theory employed. First, the geometry of stationary points is typically optimized at the Hartree-Fock level. This has been shown previously to give reliable results; the errors introduced in the relative energies due to the exclusion of correlation effects in the geometry optimizations are estimated to be less than 2 kcdmol in wellbehaved cases, like most of the present systems.lZ For comparison with experiment it is important to add zero-point vibrational energy to all stationary points, since differential zeropoint effects can be as large as 10 kcaymol. Vibrational frequencies and zero-point corrections are computed for the optimized Hartree-Fock geometries. Second, the relative energies of the stationary points are calculated using the modified coupled pair functional (MCPF) method with a larger basis set than was used for the geometry optimization. The final energies reported here were obtained by applying the parametrized configuration interaction scheme called PCI-8010to the computed MCPF energy. PCI-80 corrects the energy by assuming that the MCPF technique obtains a uniform 80% of the correlation energy at all stationary points. From detailed calibration studies, we expect this method to give relative energies of potential minima on the ground state surface that are typically reliable within 3 kcaymol on average. For bond energies of stable ligated transition metal species, this is comparable to the accuracy of experimental bond energies. All energies in this study are given relative to ground state M hydrocarbon reactants and corrected for zero-point effects and correlation effects as described. One important goal of the present study is to assess the reliability of our procedure in computing barrier heights as well. In some cases a transition state obtained at the Hartree-Fock level disappears at the correlated level. Nevertheless, for completeness we include the energies of such points in the table of transition state energies below. The energy of such a structure may lie below the reactant atomic ground state asymptote, resulting in reported “barrier heights” below 0. For a particular reaction this normally happens only for one or two of the metals. Even if these energies do not correspond to a saddle point on the potential surface, they are characteristic of the bond-breaking process since the structure is similar to the saddle point structures for the other metals in the series. Third, for each type of stationary point the energy of the lowest electronic state is given, regardless of its electron spin multiplicity. This means that in many cases the spin multiplicity changes along the lowest energy reaction path. When ground state asymptotes have higher spin than key intermediates and elimination products, the energy of the crossing point of two spin-conserving surfaces and the probability of a spin change during the collision may determine the reaction rate. Inclusion of spin-orbit coupling, which is beyond the scope of this work, might lower the barrier on the lowest energy surface compared with the curve-crossing point computed without spin-orbit coupling. A. Reactions with Linear Alkanes. Only Rh and Pd react with linear alkanes at 300 K, and these two metals react only with C2H6 and larger alkanes. For the reactions M Cfi, we have investigated CH activation paths leading from ground state reactants to the intermediate H-M-CH3 and on to MCHz HZelimination products. For the M CzH6 reactions, we have investigated CC insertion to CH3-M-CH3, which is always accessible only by passage over a highly energetic transition state. The calculated barriers to CH and CC insertion are given in Table 5 , while the calculated potential minima are given in Table 6. The H-M-CzHs insertion product energies are taken

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Carroll et al.

13958 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 5: Calculated Barriers (kcavmol) for Alkane Activation by Second-Row Transition Metal Atoms, Corrected for Zero-Point Energy Difference# C'Hq CH activation atom

state

barrier

Y

*D

Zr Nb

3F

Mo

'S

Tc Ru Rh Pd

6S 5F 4D

20.7 16.9 15.6 37.8 23.8 10.9 -1.4 3.6

6D

'S

spin mult

c2H6 CC activation barrier

spin mult

28.5 35.8 24.6 41.2 42.0 38.4 21.8 19.5

6

Figure 1. Transition state geometry for CH insertion of Rh

Energies calculated relative to the ground state reactant asymptote using the PCI-80 scheme with corrections for differential zero-point energy effects. Geometries of the transition state structures optimized at the Hartree-Fock level. See text and Appendix A.

+ C'Hq.

M + CH4 Energetics 50

TABLE 6: Calculated Reaction Energies (kcavmol) for Alkane Activation by Second-Row Transition Metal Atom#

40 30

z

3 20

Y Zr Nb

Mo Tc

Ru Rh Pd

-20.9 -20.5 - 17.3 3.2 -1.8 -9.7 -18.8 -2.3

21.3 5.7

10.3 22.9 28.2 17.8 19.5 48.1

-30.8 -3 1.4 -27.7 -4.9 -7.6 -13.6 -20.9 -5.5

-20.2

5.O

-49.8 -36.2 0.4 -4.4 - 14.6 -21.6 - 15.6

-5.3 -3.3 15.4 12.8 -1.3

\

73 10

-5.2

-10

-1.9

Energies calculated relative to the ground state reactant asymptote using the PCI-80 scheme with corrections for differential zero-point energy effects. In each case, the energy reported is for the lowest electronic state, regardless of its spin multiplicity. See text.

to be the same as for H-M-CH3. It could be argued that the presence of /3-agostic bonding could make the H-M-C2H5 systems more stable than the H-M-CH3 systems, but this was checked for in Pd and Rh, and no /3-agostic bonding effect was found. For all eight metal atoms, the energy of the M(H)2C2& dihydrido intermediate is also given in Table 6. As described below, for Rh and Pd only we further investigated the barrier to /3-H transfer from H-M-C~HS to the dihydrido intermediate M(H)2C2& and on to the H2 elimination products MC2& H2, since this is a likely important rearrangement step. In general we expect that neutral bare metal atoms will not form stable molecular complexes M(alkane), although Pd (4d10) is an exception. Thus, the first important stationary point along the reaction path is a transition state to CH or CC insertion. The most likely elimination reactions involve H2 elimination, which must go through a CH insertion intermediate and which yields a metal-carbene in the methane case and a metalethylene n complex in the ethane case. For the methane reaction to be exothermic the metal carbene binding energy must be at least 106 kcal/mol (calculated value; the experimental value is 110 kcal/m01'~),which does not occur. For the ethane reaction to be exothermic, the metal-ethylene binding energy must be at least 33 kcal/mol (calculated; experimental = 31 kcal/m01'~), which occurs for several systems. 1. CH and CC Insertion Steps. Structures of the transition state and insertion product for CH activation of methane and CC activation of ethane were determined. The transition state geometry of the typical example H- - -M- - -CH3 is shown in Figure 1. All bond-insertion transition states occur at small M-hydrocarbon distance, which guides our use of a tight

-20

-30

1

1

1

1

1

I

I

I

Y Zr N b M o Tc Ru Rh Pd Figure 2. PCI-80 energetics for M + C h , including transition state for CH insertion and potential minima as labeled. All energies are measured relative to ground state reactants and corrected for zero-point energy.

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transition state when modeling lifetimes of such complexes in section IV below. The calculated energies of these structures relative to the ground state atomic metal asymptote are given in Table 5 (transition states) and Table 6 (insertion and elimination products) and plotted in Figures 2 and 3. The main features of these results have been discussed in previous publications.15J6 It should be noted that for some of the metals (yttrium, zirconium, niobium, and technetium) new and lower CC activation barriers have been found compared with earlier results.I6 Both CH and CC insertion steps are exothermic reactions for most metals. The exothermicity is largest to the left in the periodic table and smallest for molybdenum, technetium, and palladium. However, with the exception of Rh and Pd insertion into the CH bond of methane, we calculated barriers in excess of 10 kcdmol for all CH and CC insertion steps. The maximum of the barrier heights in the middle of the periodic table (molybdenum) is primarily due to loss of exchange energy on bond insertion. This effect diminishes away from Mo in either direction. The barriers to the left of the series are higher than the barriers to the right, with a minimum for rhodium for the case of CH activation. The insertion barriers are invariably much larger for CC insertion than for CH insertion due to the directionality of both active orbitals in the CC case, as discussed earlier.

Gas Phase Reactions of Second-Row Transition Metals

50

r

M + C2H6Energetics E, cc ins. /

1

J. Phys. Chem., Vol. 99, No. 38, 1995 13959 TABLE 7: Calculated Barriers ( k d m o l ) for Cyclopropane Activation by Second-Row Transition Metal Atom@ CH activation CC activation metal (M) state barrier spin mult barrier spin mult Y Zr Nb Mo

7S

Tc

6S

Ru

Rh

ZD

3F 6D

5F 4D

11.3 7.2 4.3 28.0 17.8 4.5 -5.6 0.5

'S See footnote to Tabie 5 and text. Pd

Y Zr Nb Mo Tc Ru Rh Pd Figure 3. PCI-80 energetics for M -t C&, including transition state for CC insertion and potential minima as labeled. All energies are measured relative to ground state reactants and corrected for zero-point

energy.

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2. Elimination of Molecular Hydrogen. In M C&, the only potentially feasible bimolecular reaction is a-hydrogen elimination. However, as shown in Table 6 and Figure 2, none of the metal-methylene complexes have a binding energy larger than 106 kcdmol. This means that H2 elimination from methane is endothermic for all metals. The metal-methylene binding energy is largest on the left of the series, where electron-electron repulsion is smaller, as discussed earlier. The lowest calculated endothermicities are 5.7 kcallmol for Zr and 9.7 kcaUmol for Nb, but both of these atoms have calculated barriers to CH insertion in excess of 15 kcdmol. Thus, the ab initio calculations immediately explain why no second-row metal atom has been observed to react with C&. For all metals, H2 elimination from ethane is energetically more favorable than H2 elimination from methane. The difference is particularly large to the right of the series. For all metals except Mo, the dihydrido intermediate M(H)2C2& lies below reactants (Table 6). For Y, Zr, and Nb,the calculations find H2 elimination only mildly endothermic or slightly exothermic. However, we expect that the substantial barrier to CH insertion for these metals precludes elimination chemistry at 300 K, in accord with experiment. For Rh and Pd, the same two metals that had small barriers to CH insertion, H2 elimination from ethane is calculated to be exothemic by 5.2 and 1.9 kcdmol, respectively. Consequently, for these two atoms we pursued the reaction path further. The next plausible step following CH insertion is a /3-hydrogen shift to the metal, yielding the dihydrido complex M(H)2C2& (Table 6). For Rh, the calculated barrier to the dihydrido intermediate lies 0.6 kcaVmol below the reactants, which is consistent with a bimolecular elimination mechanism. For Pd the barrier lies 15.4 kcal/mol above reactants. This indicates that the observed Pd reactions with alkanes larger than C& must be termolecular, and indeed those reactions show a pressure-dependent rate constant. The ab initio calculations thus indicate that Rh is unique in having no barrier to CH insertion on the ground state adiabatic surface, no barrier to a subsequent exothermic @-hydrogenshift, and exothermic RhC2H4 H2 elimination products. This occurs in spite of the need for quartet ground state Rh to change spin

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9.6 14.4 8.1 9.3 26.4 5.5 -16.6 -13.6

prior to bond insertion. Rh is special in having a low excitation energy to the doublet 4d9 configuration, which minimizes electron-electron repulsion as the metal approaches a CH bond, and also a low excitation energy to the doublet 4d85s configuration, which is essential for hybridization and formation of two covalent bonds on insertion. Accordingly, Rh reacts with ethane and larger linear alkanes at 300 K, and no pressure dependence of the rate is observed. In contrast, Pd has a 4d'O ground state but a substantially larger promotion energy to the low-spin 4d95s configuration, which raises the barriers to CH insertion and /3-H migration. B. Reactions with Cyclopropane. Experimentally cyclopropane is found to react with all metals investigated except molybdenum (Table 3). However, the reaction efficiencies are only 2 x for yttrium and zirconium and 0.01 for niobium. Reaction with cyclopropane is moderately rapid for Rh and quite rapid for Pd. In the 3d series, only Ni reacts modestly rapidly with cyclopropane; very slow reaction rates near the detection limit were also observed for Sc and V. Thus, cyclopropane is much more reactive with neutral metal atoms than ethane or propane. In addition, cyclopropane is one of the few molecules for which intermolecular CC bond activation by transition metal complexes is observed experimentally in solution. Cyclopropane has substantially weaker CC bonds than the linear alkanes, which makes bond-breaking reactions energetically more favorable. This is due to the ring strain making the CC bond in cyclopropane unusually weak. In contrast to the linear alkanes, the activation energies needed for breaking the CC and the CH bonds are of similar size. Therefore, reactions involving breaking of a CC bond are much more probable for cyclopropane than for the linear alkanes. 1. Initial CH and CC Activation. The calculated barriers for CH and CC activation of cyclopropane are given in Table 7 and shown in Figure 4. The CH activation energy curve for cyclopropane is almost parallel to the corresponding curve for methane but lower by 3- 11 kcdmol. Thus, rhodium has the lowest CH activation barrier, and molybdenum has the highest one for cyclopropane as well as for CH4. The CH bond in cyclopropane is stronger than in methane (calculated 108 vs 103 kcaymol). Nevertheless, the barriers to CH insertion are lower in cyclopropane than in methane. The same factors that give rise to a stronger CH bond in cyclopropane also make a stronger M-C bond in the insertion product and a lower activation barrier in the cyclopropane case. The key effect is the larger ionicity of the CH bond in cyclopropane compared to the CH bond in methane. Experimentally, the amount of ionicity of a CH bond can be seen from the acidity of the system, since ionicity and acidity are clearly related. It is found that there is a clear correlation between acidity and the strength of a CH bond,17bwhich thus demonstrates the importance of the ionic contribution for the strength of these bonds. When the ionic contribution is important, the effect is

Carroll et al.

13960 J. Phys. Chem., Vol. 99, No. 38, 1995

M + c-C3H6Energetics

=:

z

3

0-

4 -20 -30 -40 -10

Y

-

-%I-I

1

1

I

I

I

I

14

Y Zr Nb Mo Tc Ru Rh Pd

Figure 4. PCI-80 energetics for M + cyclopropane, including transition states for CH and CC insertion and the potential minima for H-Mcyclopropyl and the metallacyclobutane (labeled MC3H6). All energies are measured relative to ground state reactants and corrected for zeropoint energy. TABLE 8: Calculated Reaction Energies (kcaVmol) for Cyclopropane Activation by Second-Row Transition Metal Atoms' MC3H6

HMC3H5

(CC insert)

(CH insert)

allene

propyneb

Pd

-28.2

-26.9 -27.4 -24.8 -2.6 -6.8 -15.4 -24.4 -5.5

-3.6 -5.6 -9.3 9.8 6.9 -4.8 -9.8 -3.7

-22.7 -29.6 -25.5 -0.9 -1.0

Rh

-40.0 -47.0 -36.8 -21.0 -8.7 -32.8 -42.6

metal (M) Y

Zr Nb MO

Tc Ru

MC3H4+Hz

-11.8 -12.5 -2.2

MCHz+ CZ&

4.1

-11.5 -6.9 5.7

11.0 0.6 2.3 30.9

See footnote to Table 6 and text. For H2 elimination, only the M-allene energies are explicitly calculated. M-propyne energies are estimated from previous calculations on metal-acetylene bonding. a

larger for the MC bond than for the CH bond since the metal has a lower ionization potential than hydrogen. As a result, the insertion product is much more exothermic in cyclopropane than in methane (Table 8) and the CH insertion barriers are lower. The effect is larger in the transition state region than in the insertion products themselves. For the insertion products, cyclopropane binds 3 -7 kcal/mol stronger than methane, compared with differences in barrier heights of 3 - 11 kcal/mol. Yttrium and zirconium, which react very slowly with cyclopropane, have substantial calculated barriers to CH insertion, 11.3 and 7.2 kcaymol, respectively. For these metals there is no change of spin multiplicity involved in the ground state reaction. For niobium, which shows significantly greater reactivity with cyclopropane, the PCI-80 energy on the quartet surface at the SCF transition state to CH activation lies only 4.3 kcal/mol above ground state (sextet) reactants. The spin must change from the 6D atomic ground state to the quartet CH insertion intermediate, and it is possible that the two spinconserving curves cross at higher energy than 4.3 kcaumol and thus determine the reaction rate. For molybdenum the very high CH activation barrier of 28.0 kcal/mol agrees with the fact that no reaction is observed with cyclopropane. For rhodium a negative energy (-5.6 kcal/mol) is obtained in the transition

state region, and for palladium the value is close to 0 (0.5 k c d mol). Rhodium requires a change in spin from quartet reactants to doublet insertion intermediate, as discussed above for the linear alkanes. Once again, we do not expect the spin-crossing to result in a significant barrier, since the doublet energy in the transition state region (-5.6 kcal/mol) is even lower than in the methane case (- 1.4 kcdmol). These results indicate little or no barrier to CH activation of cyclopropane by Rh and Pd, and these two atoms are indeed the most reactive. For cyclopropane the CC activation barriers are similar to the CH activation barriers (Table 7, Figure 4). This is in contrast to the linear alkanes, for which the CC activation barriers are on the order of 10-30 kcdmol higher than the CH activation barriers (Table 5, Figures 2, 3). In fact, for the three metals molybdenum, rhodium, and palladium, cyclopropane CC activation has a considerably lower barrier than CH activation. Comparing the CC activation of cyclopropane with ethane, we see that for all metal atoms the activation energies are lower for cyclopropane. This is due to the weakened CC bond in cyclopropane. The difference in CC insertion barriers lies in the range 15-40 kcal/mol, with the largest values to the right of the 4d series. Comparing Figures 3 and 4, we find a striking difference in behavior between Mo and Tc. For ethane, Mo and Tc have quite similar barriers to CC insertion, while for cyclopropane Tc has a much higher barrier than Mo and all other metals as well. The same effect is observed in the CC insertion product; that is, Tc binds to cyclopropane much more weakly than the rest of the metals. The reason for this behavior is simple to understand from the atomic structure. The Tc atom has a 6S,4d55s2 ground state. For ethane, the bond-breaking occurs through an sp hybridization mechanism, and both the transition state and CC insertion products are sextets. For cyclopropane, however, the ring structure requires smaller C-M-C bond angles so the bond-breaking must occur through an sd hybridization. As a result, both the transition state and CC insertion products are now quartets. The higher barrier and insertion product energies in cyclopropane are thus due to the loss of exchange stabilization in passing from sextet reactants to quartets. In ethane, the exchange stabilization is quite similar in reactants, transition state, and CC insertion products. The low CC activation barriers for Y, Zr, Nb, Rh, and Pd reactions with cyclopropane may open up this pathway, as discussed further below. For niobium, the CC activation barrier is higher than the CH activation barrier, 8.1 and 4.3 kcal/mol, respectively. For both rhodium and palladium negative energies are obtained in the transition state region (-16.6 and -13.6 kcal/mol, respectively), indicating that for these metals there are no barriers to CC activation. For rhodium the spin-crossing is expected to introduce at most a very low barrier. For molybdenum, where the cyclopropane CH activation barrier is prohibitively high (28.0 kcal/mol) the CC activation barrier is considerably smaller, 9.3 kcal/mol on the low-spin surface. However, the reaction between molybdenum and cyclopropane involves a spin-crossing, which will determine the actual barrier height in excess of the low-spin barrier. This is consistent with the fact that no reaction was observed experimentally between molybdenum and cyclopropane. The metallacyclobutane product of CC insertion in cyclopropane is the lowest of the investigated points on the interaction surface for all metals (Table 8, Figure 4). For all metals except technetium the binding energy is very large, in the range 2147 kcdmol. The RRKM modeling will show that for a metallacyclobutane well depth as large as 40 kcal/mol, any M cyclopropane reactants that reach the well will never return to reactants on the 100 ns time scale of termolecular collisions

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J. Phys. Chem., Vol. 99, No. 38, I995 13961

Gas Phase Reactions of Second-Row Transition Metals with He. However, only rhodium and palladium have calculated barriers to the metallacyclobutane structure so low as to ensure that access to the deep well is possible. 2. Possible Elimination Products. H2 elimination from cyclopropane can lead to several different products: allene (H2C=C=CH2), propyne (H3CCWH), or cyclopropene. In the gas phase the allene and propyne products are close in energy, while the cyclopropene product is much less favorable. Only the metal-allene final product is explicitly calculated, and the energies of this reaction are given in Table 8. The metalpropyne final product is estimated from previous calculations on the metal acetylene bonding,'* and"these results are also given. H2 elimination from cyclopropane to yield the metal-allene product is an exothermic reaction for all metals except molybdenum and technetium. The metal-propyne product is estimated to be even more exothermic for all metals except palladium, where the energies are quite close. Thus, for all metals that are experimentally observed to react with cyclopropane the metal-allene and the metal-propyne complexes are energetically possible final products. However, there must be several steps between the initial activation reaction and these final products, and the barriers involved in these steps have not been investigated. It can further be noted that the propyne final product requires more rearrangements within the cyclopropane molecule, including migration of a hydrogen atom from one carbon to another. At least for palladium, which reacts the fastest of all atoms studied, there are probably substantial barriers since palladium can form only two covalent bonds and some of the transition states will involve more than two bonding interactions. Therefore, the rapid reaction observed experimentally for palladium is .probably CC insertion reaction ending with the metallacycle. The metal-allene bonding can be compared to metalethylene bonding described previously.16 For all second-row metals allene binds stronger than ethylene. The difference is larger for the metals to the left in the periodic table, where allene binds about 10 kcdmol stronger than ethylene. To the right in the periodic table the difference is 3-5 kcdmol. The free allene molecule is linear, with the two end CH2 groups twisted; that is, the two n bonds are perpendicular to each other. The stronger metal-allene bonding seems to be, at least in part, explained by an extra bonding interaction between the metal and the allene n system perpendicular to the molecular plane. To the left in the periodic table this extra bonding occurs through donation from the allene n orbital into empty d orbitals on the metal. To the right in the periodic table it occurs through donation from occupied metal d orbitals into the n* orbital on allene. The bonding interaction between the metal atom and the perpendicular allene n system can occur because the allene, which is linear as a free molecule, bends upon coordination, such that two carbons are coordinating symmetrically to the metal and the third carbon is bending away (Figure 5). The bonding interaction in the perpendicular n system is seen from the elongation of this CC distance. In the free allene the calculated CC bond lengths are 1.31 A. In the zirconium complex, for example, the directly coordinating CC bond length increases to 1.50 A, while the other CC bond length is 1.34 A. There is a mild interaction between the metal and the perpendicular n bond. For metals to the right in the periodic table, e.g. ruthenium, the two CC distances are found to be 1.42 and 1.33 A, respectively. The difference in CC distance in the part of the molecule that is not directly coordinating to the metal indicates that the interaction is stronger to the left in the periodic

Figure 5. Geometry of Pd-allene complex. TABLE 9: Calculated Energies (kcavmol) of Minima and CH Insertion Saddle Points on Potential Energy Surfaces for Ethylene Activation by Second-Row Transition Metal Atom# Y Zr

Nb Mo Tc Ru Rh Pd

-27.7 -38.0 -35.9 - 17.3 - 19.8 -34.0 -37.9 -34.6

1.9 1.8

-1.3 18.2 14.5 -1.6 -11.9 -4.4 '

-27.4 -28.7 -24.0 -2.2' -6.9 - 14.8 -25.4 -7.2

-11.5 -18.5 - 14.4 12.1 12.2 -0.7 -1.3

9.0

See footnotes to Tables 5 and 6 and text.

table, in agreement with the energetic results that show a larger difference between ethylene and allene in the left part of the periodic table. The possibility of ethylene elimination was also investigated, yielding a metal-carbene complex. These reaction energies are also given in Table 8. For the metals to the left in the periodic table the metal-carbene bond is fairly strong, so the H2 and ethylene elimination reactions are approximately equally favorable energetically. To the right, the metal-carbene bond is weaker, and therefore the ethylene elimination is less favorable than the H2 elimination. C. Reactions with Alkenes. The alkenes are the most reactive of the hydrocarbons included in the experimental study (Tables 2-4). All alkenes investigated, ethylene, propylene, 1-butene, and isobutylene, react with all second-row metal atoms studied, except that ethylene does not react with molybdenum. Molybdenum is unusually inert to alkenes, and Nb is the most reactive with alkenes. Our calculations focus on M C2H4. The simplest reaction between a metal atom and ethylene is termolecular stabilization of a n coordination complex. The exothermic elimination of H2 from ethylene requires a metalacetylene binding energy of at least 45 kcal/mol (calculated; experimental = 40 kcal/mol19). This elimination process must be initiated by CH activation. For all second-row metal atoms, we have investigated the energetics of n complex formation with ethylene, the transition state between the n complex and the CH insertion intermediate H-M-C2H3, the CH insertion intermediate itself, and the H2 elimination products MC2H2 H2. For two examples, Zr and Nb, we also investigated the barrier to and energetics of the @-hydrogen shift intermediate M(H)2C2H2. I . Formation of M(C2H4) n Complexes. The calculated results for n coordination of ethylene to the low-spin states of second-transition-row metals are given in Table 9 and in Figure 6. These results have been discussed in detail in a previous publication.2o Ethylene binds fairly strongly to all second-

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13962 J. Phys. Chem., Vol. 99, No. 38, 1995

M + C2H4Energetics

0--

-

10

M + CZH4+ M + CzHz

+lo--

-lo--

-

”-

-

-30.-

0-

z8 -: h

3

-10

3. W -20

4--M--

-

60-1-

-

Figure 7. PCI-80 reaction path energetics for Nb, Zr

-30 -

+ C2&.

All

energies are measured relative to ground state reactants and corrected for zero-point energy.

c

-4OCI

AE (kcaVmol)

I

I

I

I

I

I

I4

Y Zr Nb Mo Tc Ru Rh Pd Figure 6. PCI-80 energetics for M iC2&, including transition state for CH insertion and potential minima as labeled. All energies are

measured relative to ground state reactants and corrected for zero-point energy. transition-row metals, by 17-38 kcaYmo1. The largest binding energies are found to the left and right in the periodic table; the binding energy goes through a minimum in the middle of the row. The 3t complexes are formed without breaking any bonds, so we expect no barriers on the diabatic potential surface connecting the metal-ethylene complex with the atomic state having the same spin. However, for Zr, Nb, Mo, Ru, and Rh, the most strongly bound 3t complexes have lower spin multiplicity than the atomic ground states,20and therefore barriers due to spin-crossings of diabatic surfaces could occur. In many of those cases ( Y , Zr, and Nb), the high-spin state of the 3t complex is also bound, typically with smaller binding energy than for the low-spin states.20 The binding involves donation from the doubly occupied ethylene n orbital into an empty dn orbital on the metal. Only Y , Zr, and Nb can have such an empty orbital in the high-spin state. Since the spin-crossings occur in a region where the energy of both high- and low-spin diabatic surfaces is likely to be below ground state reactants, there should be no barriers to ethylene coordination due to the spin-crossings in Y , Zr, and Nb. In Mo, we found only slight binding (1-2 kcaYmo1) between the high-spin 4d55s ground state and ethylene, apparently for lack of an empty dn orbital. Thus we expect a large “spin barrier” to formation of MoC2h from ground state reactants. For the Y , Zr, Nb, Rh, and Pd, all of which react rapidly with alkenes, we find large MC2& complex binding energies of 28-38 kcal/mol (Table 9). Since the experiments do not identify products, this leads naturally to the possibility that some or all of the observed M alkene reactions involve collisional stabilization of long-lived 3t complexes. We use RRKM theory to investigate this possibility further in section IV. 2. CH Insertion and H2 Elimination in Alkenes. The CH activation barriers for ethylene are given in Table 9 and in Figure 6. These results have been described in a previous publication.2’ As can be seen from Figure 2 the CH activation barriers for ethylene parallel those for methane, with the ethylene curve below the methane curve for all metals. This difference in CH activation energy provides part of the explanation for the higher reactivity of the alkenes compared with the linear alkanes. Of the metals studied experimentally, the transition state to

+

CH insertion lies below reactants for Nb, Rh, and Pd. In spite of the negative energies, these are true transition states lying between the 3t complex and the CH insertion intermediate. Furthermore, for niobium and rhodium the spin-crossing is expected to occur earlier in the reaction and should therefore not introduce any additional barriers. Thus, we expect no barriers to CH activation for these three metals. For yttrium and zirconium, which are also found to be reactive with alkenes experimentally, CH activation barriers of 1.9 and 1.8 kcaYmol are obtained in the present study. As compared with previous work, new and lower transitions states have been found for these metals. The reactivity of these two metals is considerably lower than that of niobium. Molybdenum, which is found to be unreactive with ethylene and to have a very low reactivity with the larger alkenes, has a substantial CH activation barrier of 18.2 kcaVmol. Even if this barrier height should decrease somewhat on going to the larger alkenes, it is unlikely that it is low enough to make CH activation possible for any of the alkenes in the reaction with molybdenum. The very low reactivity observed for molybdenum with the larger alkenes probably involves formation of the high-spin 3t complex, which is bound by only 1-2 kcaYmol in the calculations for ethylene. We discuss bimolecular vs termolecular mechanisms further in section V after we have obtained the RRKM modeling results. H2 elimination from an alkene gives a metal-alkyne complex as the product. The product energetics for HZelimination from ethylene are given in Table 9 and in Figure 6. Acetylene binds very strongly to the metal atoms, in particular to the left in the periodic table, as discussed earlier.I8 The reaction is exothermic only if the M-CzH2 binding energy exceeds 45 kcaYmol (calculated; 40 kcal/mol experimental]9), which occurs for Y , Zr, Nb, Ru, and Rh. The calculations thus tend to rule out H2 elimination for reactions of Mo and Pd with ethylene; the H2 elimination reactions with larger alkenes should be slightly less endothermic. 3. Reaction Paths for Zr and Nb. For the metals zirconium and niobium, a more complete reaction path for the H2 elimination from ethylene was investigated, and the results are shown in Figure 7. For both metals the B-hydrogen shift from the CH insertion intermediate lies well below the energy of the reactants. In fact, we expect that there is no barrier whatsoever between CH insertion and the H2 elimination product. The transition state for the final elimination step should lie low in energy since it involves formation and breaking of bonds by the spherical 1s orbitals of H, as discussed in an earlier paper.22 In the case of Nb the alkene reaction can proceed all the way to H2 elimination with no barriers lying above the reactant

Gas Phase Reactions of Second-Row Transition Metals

J. Phys. Chem., Vol. 99, No. 38, 1995 13963

asymptote. In zirconium, we find a small barrier to CH activation, but no subsequent barrier.

IV. RRKM Modeling of Complex Lifetimes Statistical modeling of unimolecular decay rates23 complements the analysis of the experimental kinetics data and the ab initio calculations of the potential surfaces. Since our experiments do not identify the reaction products, the measured rate constant could include contributions from bimolecular reactions or from collisional stabilization of long-lived M(hydrocarbon) complexes or from both. Our goal is to infer from the ab initio calculations and statistical modeling under what circumstances we might expect M(hydrocarbon) complexes to be sufficiently long-lived to permit stabilization by collisions with the third body He at 0.5-1.1 Torr to contribute to a measured rate constant. We confine ourselves to a very simple model of the termolecular process:

M

+ hc 2M(hc)* 2 M(hc) kuu

This model includes formation of long-lived complexes (kf), unimolecular decay back to reactants (kuni), and collisional stabilization or quenching (h) by the He buffer gas, whose number density is [He]. Much more elaborate treatments of the collisional activation of the complex are but we seek a simple result here. The steady state approximation on the M(hc)* density yields the effective bimolecular rate constant:

At sufficiently low He pressure, this predicts a linear increase of the observed reaction rate constant with [He]. Eventually, P2)begins to saturate vs [He]; in the high-pressure limit, P2) becomes equal to kf, independent of He pressure. Physically, this means that the complexes are so long-lived that every complex is stabilized by He collisions. A rough estimate of the pressure at which saturation begins can be obtained by equating kq[He] with kuni. As a rough estimate, we assume that only 20% of the He M(hc)* hard-spheres collisions remove sufficient energy from the complex that it never dissociates, since He has no rotational or vibrational degrees of freedom to help absorb energy. This gives the estimate k~ FZ 1 x cm3 s-I. Then at 1 Torr He, we expect that roughly half the complexes will be stabilized if kuni = 3 x lo6 s-’, which corresponds to a complex lifetime of 300 ns. While we do not expect to model specific lifetimes to high accuracy, we do hope to obtain a good quantitative sense of how kui varies with the size of the hydrocarbon and with binding energy DO. In particular, we want to know under what conditions kuni could be so slow compared with the He-complex collision rate that saturated termolecular kinetics would occur over the entire pressure range studied, 0.5-1.1 Torr of He. In that limit, the mechanism would be termolecular, but we would observe no pressure dependence of the measured effective bimolecular rate constant. In RRKM mce-Ramsburger-Kassel-Marcus) the microcanonical unimolecular rate constant is given by

+

kuni(E,J) = Wt(E,J)/WE+DO,J)

(3)

where W’ is the sum of vibration-rotation states at the transition state, is the density of vibration-rotation states for the bound

complex, and h is Planck’s c o n ~ t a n t . ~Here ~ , ~we ~ define E as the total energy relative to ground state M hydrocarbon reactants; the complex then has energy E DOrelative to its ground state, where DOis the dissociation energy. J is the orbital angular momentum of the collision, which is assumed to be conserved throughout the reaction. The two overall rotational modes about axes perpendicular to the line of approach are thus “inactive” and do not exchange energy with the vibrational and active rotational modes and are not included in the state densities. A fraction of the total energy is fixed in these inactive rotational modes. Moreover, the amount of unavailable rotational energy changes during the course of the reaction, since the moments of inertia for these inactive rotations change as the geometry changes. We have calculated microcanonical RRKM unimolecular decay rates for the representative cases of q2 Pd(akane) complexes; of CH insertion complexes of Rh with linear alkanes; of both CH and CC insertion complexes of Y with cyclopropane; and of n complexes of Pd with alkenes. Details of the calculations are given elsewhere.25 The inputs include vibrational frequencies and rotational constants for both the M(hydrocarbon) complex and the transition state. Two different models of the transition state were employed. For formation of q2 Pd(alkane) complexes and of Rh(akene) JC complexes, no covalent bonds are broken and we expect no potential barrier. In these cases, the transition state is modeled as loose. The (3N-6) vibrational modes of the complex become in the transition state (3N-9) vibrational modes, two completely free internal rotations, plus translation along the reaction coordinate. One metal-hydrocarbon stretch and two bends are lost from the complex to the transition state. The bare potential (corresponding to J = 0) at long-range was approximated by the van der Waals interaction -c@. c6 coefficients were calculated from polarizability data using the Slater-Kirkwood formula.26 The effective long-range potential for each value of J was determined by adding the repulsive centrifugal term, h2J(J 1)/8z2pR2, to the attractive c6 term. Here, p is the reduced mass, and R is the distance along the reaction coordinate. For representative calculations with J = 50, the position of the transition state, Rt(J), was determined as the maximum of this effective long-range potential. For CH or CC insertion (Rh -t alkane, Y cyclopropane), the transition state is modeled as tight. The (3N-6) vibrational modes of the complex become (3N-7) vibrational modes of the transition state plus the reaction coordinate. The long-range potential was taken as 0 for J = 0; for J = 50, an appropriate centrifugal potential was added. In these cases, we model bending modes of the complex as bending vibrations in the transition state. In the q2 Pd(C&) and Pd(C2H6) complexes, appropriate frequency sets and geometries were available from the ab initio calculations. To model the Pd(C2H4) JC complex, we substituted the ab initio geometry and vibrational frequencies for the Zr(C2H4) complex. In the loose transition states, we used the frequencies of the bare hydrocarbon. When frequencies of only the complex were available, as in Y(cyclopropane), we kept two soft bending frequencies from the complexes in the transition state and added the bare hydrocarbon frequencies. To model the H-Rh-CH3 complex, we substituted the available frequencies for H-Pd-CH3 for both complex and transition state. For larger hydrocarbons for which no calculations were available, we borrowed two or three soft frequencies from the calculations on smaller cases and augmented the frequency set with bare hydrocarbon frequencies. Vibrational frequencies for the bare hydrocarbons were taken from the l i t e r a t ~ r e . ~ ’ - ~ ~

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Carroll et al.

13964 J. Phys. Chem., Vol. 99, No. 38, 1995 H-Rh-Alkyl Complexes

2

Pd(alkane) q Complexes

1oI2

1

10"

lo9

i . C4HlO

lo8

5

10

15

I

C4HlO

loo 5

10

Geometries for the larger M-hydrocarbon complexes and transition states were taken as composites of ab initio geometries for the smaller species and fragments of the bare hydrocarbon geometry itself. Rotational constants were then calculated using the GEOM portion of the UNIMOL suite of programs.23 Sample calculations indicate that inaccuracies in the frequency sets should affect the model results by less than a factor of 10. For example, the gross change of doubling or halving the three lowest frequencies, which make the largest contributions to the density of states, changes the calculated rate constants only by about 1 order of magnitude. Most importantly for present purposes, the trend in ku,i vs DOor size of hydrocarbon is quite insensitive to the vibrational frequency set. We did not attempt to average the microcanonical kuni(E,J) over a Boltzmann distribution of collision energies and angular momenta, nor were effects of internal energy in the hydrocarbon reactant included. In general, kuni is larger near threshold for the loose transition state than for the tight transition state because free internal rotation contributes to the sum of states at threshold, while bending vibrations tum on more slowly. The loose model probably overestimates kuni since the free rotor states dominate the sum of states in the numerator of eq 3 at the low collision energies of interest in our 300 K measurements, In Figure 8, we show calculated kuni vs DOfor dissociation of long-range q2 complexes of Pd (loose transition state) with different alkanes for E = 200 cm-' and J = 50, typical values in our Boltzmann distribution of collisions at 300 K. The figure shows at a glance how we might expect complex decay rates to vary with binding energy and with the size of alkane. In Figure 9, we show calculated kuni vs DO for CH insertion complexes of Rh with different alkanes with E = 200 cm-' and J = 0, using the tight model of the transition state. We use J = 0 to illustrate this trend, because in the case of CH insertion for the smaller alkanes the centrifugal barrier for J=50 is larger than the energies of most collision complexes. In Figure 10, we compare calculated kuni vs DO for the CH and CC insertion products of Y cyclopropane at E = 200 cm-I and J = 50, using the tight model of the transition state, since these reactions proceed through a chemical barrier. Finally, in Figure 11, we show calculated kuni vs DO for Pd(alkene) n

+

15

20

25

30

35

40

Do (kcal/mol)

Do (kcal/mol) Figure 8. RRKM microcanonical unimolecular decay rates of q2 Pd(alkane) complexes vs dissociation energy DO.Loose transition state, E = 200 cm-I, J = 50. See text for details.

I

Figure 9. RRKM microcanonical unimolecular decay rates of H-Rhalkyl complexes vs dissociation energy DO.Tight transition state, E = 200 cm-I, J = 0. See text for details.

Y(cyc1opropane) Complexes

Do (kcal/mol) Figure 10. RRKM microcanonical unimolecular decay rates of H-Ycyclopropyl and yttrium-metallacyclobutane complexes vs dissociation energy DO.Tight transition state, E = 200 cm-I, J = 50. See text for

details. complexes at E = 200 cm-' and J = 50 using the loose model of the transition state. The trends in Figures 8-1 1 are much more significant than the absolute rates, which could easily be in error by a factor of 10 or more. We use these representative estimates of kuni and how they vary with DOand with size of hydrocarbon to reason about reaction mechanisms in the next section.

V. Reaction Mechanisms In this section we combine the experimental results, the ab initio energetics, and trends in kuni as estimated from RRKM model calculations to infer whether the observed reactions involve termolecular association or bimolecular H2 elimination. The ab initio results in conjunction with RRKM rates usually

Gas Phase Reactions of Second-Row Transition Metals Pd(alkene) x-complexes lo9

J. Phys. Chem., Vol. 99, No. 38, 1995 13965 Rhodium reacts successively more rapidly with larger linear alkanes. We measure no reaction with methane, 3.5 x cm3 s-' with ethane, 9.4 x cm3 s-' with propane, and 19.9 x cm3 s-l for n-butane. The pressure dependence was investigated for Rh ethane and n-butane, and no dependence was observed over the range 0.5- 1.1 Torr of He. We believe that the Rh reactions with ethane, propane, and n-butane are bimolecular H2 elimination reactions. Rhodium is the only 4d-series metal atom for which the ab initio calculations are completely consistent with bimolecular H2 elimination chemistry. We find no potential barrier to CH insertion in methane on the low-spin (doublet) surface. The calculated energy at the transition state geometry lies 1.4 kcal/ mol below ground state reactants. The potential well for H-Rh-CH3 is 19 kcal/mol deep relative to reactants. In Rh f C2H6, the barrier between H-Rh-CzH5 and the rearranged Rh(H)2C2H4 intermediate also lies below reactants, and H2 elimination is exothermic by 5.2 kcdmol. The only possible impediment to H2 elimination is the spin change necessary for the quartet Rh ground state to access the attractive doublet surface. As Rh approaches CH4, the quartet and doublet surfaces must cross prior to CH insertion. At the calculated CH transition state, the doublet surface lies 1.4 kcal/ mol below quartet reactants. At longer range (Rh-C distance = 2.7 A), we find a weak doublet molecular complex about 1 kcdmol above reactants; at the same geometry, the quartet surface also lies about 1 kcal/mol above reactants. Thus, the best calculations indicate that a substantial fraction of quartet reactants at 300 K should access geometries for which the doublet surface lies very low in energy. The modest increase in bimolecular rate with alkane size could arise from increasingly attractive doublet surfaces at long range or from greater average internal energy at 300 K for the larger alkanes. Methane does not react because the H-Rh-CH3 intermediate lacks a B-hydrogen, and the barrier to a-hydrogen migration to the metal atom is prohibitively high. The greater than 100-fold increase in observed rate constant between methane and ethane, but only a factor of 2-3 increase for each step from ethane to propane to butane, is easily understood by the bimolecular mechanism. The alternative termolecular mechanism would also require access to the CH insertion well, which is approximately 20 k c d mol deep for H-Rh-CH3. Since the measured rates do not depend on pressure, a temolecular mechanism would have to be in the saturated limit already at 0.5 Torr of He for Rh C2H6 yet show no reaction for Rh -t C h . We can assess this possibility by comparing the RRKM decay rates of Figure 9 with our estimate of the effective quenching rate by He collisions at 0.5 Torr, k~[He] 2 x lo6 s-l. For well depths DOof about 20 kcdmol, the RRKM rates span 4.5 decades for the sequence of alkanes; kuni decreases about a factor of 10 from CHq to C2&, another factor of 100 from C2& to C3H8, and still another factor of 25 from C3Hs to C4Hl0. If the trend in kunl with alkane size is roughly correct, then the termolecular mechanism cannot explain the observed rates for all four alkanes. It is plausible that the C3Hg and C ~ H Ireactions O could be saturated termolecular. However, if the C2H6 reaction were also saturated termolecular, implying kuni less than lo6 s-l, the C b reaction should then be. observable. We conclude that bimolecular H2 elimination occurs for Rh C2H6, C3H8, and C ~ H I OIf. H2 elimination were not so readily feasible, a termolecular reaction would be observed at least for C3H8 and C ~ H I OIt. is likely that a termolecular Rh CHq reaction could be detected at higher He pressure. In contrast, the Pd alkane reactions are clearly termolecular. The experiments found no reaction with C&. The effective

+

10'

r

lo6

r

h I

'5

&

lo5

10'

lo3

25

30

35

40

Do (kcal/mol) Figure 11. RRKM microcanonical unimolecular decay rates of Pdalkene n complexes vs dissociation energy DO.Loose transition state, E = 200 cm-', J = 50. See text for details.

allow some conclusions about the chemical identity of termolecular products as well. The degree of consistency between experiment and theory allows us to assess the quantitative accuracy of the ab initio energetics for both potential minima and transition states. With firm mechanistic inferences in hand, we conclude by describing how the pattem of low-lying electronic states govems the reactivity of neutral 4d-series metal atoms. We can sometimes set an approximate upper bound on the height of certain potential energy barriers from the measured reaction efficiency kl/khs,the ratio of the effective bimolecular rate constant to the hard-spheres collision rate. Since khs s 3 x 1O-Io cm3 s-I, the experimental detection limit of ki 2 5 x cm3 s-' corresponds to a reaction efficiency Wkhs L 2 x Direct comparison of a reaction efficiency with an a b initio barrier corrected for zero-point energy differences is complicated by the Boltzmann distribution of reactant translational, rotational, and vibrational energies. In a Boltzmann distrubution at 300 K, 2 x of the collisions have relative kinetic energy in excess of 5.8 kcal/mol. Considering translational energy only, we can detect reaction when potential barriers are smaller than 6 kcal/mol. In addition, the mean vibrational energy at 300 K is 0.03, 0.5, 0.8, 1.2, and 2.0 kcal/mol for methane, ethane, propylene, propane, and n-butane, respectively. Roughly speaking, observation of a reaction in our experiment implies a barrier not larger than about 8-10 kcal/mol, depending on the size of the hydrocarbon. A. Reactions with Linear Alkanes. None of the neutral atoms Y, Zr, Nb, and Mo from the left-hand side of the 4d series react with linear alkanes under our experimental conditions. The calculated barriers in Figures 2 and 3 explain why. As argued above, a potential barrier to bond insertion in excess of 8-10 kcal/mol will cause the insertion rate constant to fall below our experimental detection limit of 5 x lO-I4 cm3 s-l. Thus, barriers to CC insertion are prohibitively high across the entire series. For Y through Mo, the calculated barriers to CH insertion in methane exceed 15 kcal/mol in all cases. The potential barriers to CH insertion could be several kcaYmo1 lower for larger alkanes such as propane and n-butane, but these barriers are still too large.

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13966 J. Phys. Chem., Vol. 99, No. 38, 1995 bimolecular rate constants at 0.8 Torr are C0.05 x 10-l2 cm3 s-l for methane, 0.16 x cm3 s-I for ethane (at least a 3-fold increase), 1.22 x cm3 s-' for propane (&fold increase), and 4.63 x 10-l2 cm3 s-I for n-butane (4-fold increase). In the two cases studied vs He pressure, both the propane and n-butane rates increased with pressure from 0.5 to 1.1 Torr, clearly indicating a termolecular component of the mechanism. If the propane and n-butane reactions are termolecular, the ethane reaction should be also, since we expect larger barriers and a smaller exothermicity for ethane. The ab initio calculations find that Pd is unique in that its ground state forms a long-range q2 complex that is bound relative to ground state reactants, as described earlier.I5 For Pd with its 4di0 (IS)ground state, the entire reaction occurs on the singlet surface. The question for theory is the nature of the long-lived Pd(alkane) complexes and whether or not some fraction of reactants might be able to proceed to H2 elimination products. Our best estimates of the binding energy are 5.1 k c d mol for CH4,6.6 kcdmol for C2H6, and r 6 . 6 kcdmol for C,Hg and C ~ H I OAssuming . 7.5 kcaYmo1 for C3Hg and C4H10, the RRKM estimates of kuniin Figure 8 decrease a factor of 4 from methane to ethane, another factor of 5 from ethane to propane, and another factor of 3 from propane to butane. This is qualitatively consistent with the trend of observed rate constants. However, the absolute magnitudes of the RRKM rates in Figure 8 are too large to explain the data by as much as a factor of 30. The proper average over E and J would probably decrease kun,, especially since the rates are quite sensitive to E near threshold. In addition, the loose transition state assumption also overestimates kun,. The ab initio calculations may underestimate the binding energies as well. Finally, the large calculated barrier to P-hydrogen migration in the H-Pd-alkyl intermediates should preclude any H2 elimination reactions at 300 K, consistent with the observed termolecular mechanism. In H-Pd-C2H5, this barrier lies 15 kcaYmol above reactants. The reason is that Pd(4dio)must use high-energy 5p orbitals to form the rearrangement intermediate Pd(W2C2H4. B. Reactions with Cyclopropane. Under our experimental conditions, the effective bimolecular rate constants for reaction with cyclopropane are 0.7 x cm3 s-l for Y and Zr; 3 x cm3 s-l for Nb; < 3 x cm3 s-I for Mo; 14.2 x lo-'* cm3 s-l for Rh; and 59 x cm3 s-l for Pd (Table 3). Our only investigation of the pressure dependence found similar rates at 0.5 and 0.8 Torr for the reactions of Y and Zr. Among the atoms studied experimentally, the ab initio barrier to CH insertion is prohibitively high only for Mo. From Y to Nb the calculated barrier decreases from 11.3 to 4.3 kcdmol. There is no barrier for Rh and a small 0.5 kcdmol barrier for Pd. The CC activation barriers are 9.6 kcaYmo1 for Y, 14.4 kcaY mol for Zr, 8.1 kcdmol for Nb, and only 9.3 kcaYmo1 for Mo; there is no barrier to CC insertion for Rh and Pd. For those atoms observed to react, the calculations permit either CC or CH insertion. For the most reactive atoms, Rh and Pd, both CC and CH insertion are surely energetically feasible. For Mo, all low-spin states lie at least 30 kcaYmo1 above the 7S ground state. The CH insertion barrier is very high. The stated 9.3 kcaYmo1 barrier to CC insertion is the PCI-80 energy at the geometry of the saddle point on the lowspin surface obtained from the SCF wave function. In fact, there is no barrier to CC insertion on the low-spin PCI-80 surface, which decreases smoothly from low-spin reactants to the CC intermediate. However, the septet surface is purely repulsive, so the highest point on the adiabatic surface leading from ground state Mo cyclopropane to CC insertion will lie

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Carroll et al. substantially higher than 9.3 kcdmol. Accordingly, no reaction with Mo is observed. Termolecular stabilization into the deep metallacyclobutane well (CC insertion) can sensibly explain the observed reactions of Y, Zr, Nb, Rh, and Pd with cyclopropane. For Y, Zr,Nb, and Rh, the ab initio calculations find extremely deep metallacyclobutane well depths of 40,47,37, and 43 kcdmol relative to ground state reactants. The RRKM modeling (Figure 10) shows unequivocally that if M cyclopropane reactants ever access such a deep well with so many vibrational degrees of freedom, they will never return to reactants on the time scale of the termolecular collisions with He. For the representative case of E = 200 cm-' and J = 50, the modeling using a tight transition state finds lifetimes ranging from 1 ms for NbC3H6 to 5 ms for Zc3H6. Even for the more weakly bound case of PdC3H6 (calculated DOof 28 kcaYmol), the RRKM lifetime is 50 ,us, easily long enough for saturated termolecular kinetics. For Y, Zr, Nb, and Rh, we cannot rule out collisional stabilization of CH insertion complexes as well. These are also strongly bound by about 25 kcaYmol. RRKh4 calculations of the CH insertion complex lifetimes (Figure 10) using a tight transition state find a lifetime of about 50 ,us for these complexes for E = 200 cm-' and J = 50. The CH insertion complex for Pd is bound by only 6 kcaYmo1, so the well is too shallow to contribute substantially to a termolecular rate. If the M cyclopropane reactions are indeed dominated by termolecular processes and the RRKM lifetimes are reasonably accurate, then the observed rate constants are governed primarily by the probability that a collision gains access to the deep well(s). For Y and Zr,no spin change is necessary from ground state reactants to insertion intermediates. The efficiency of formation of long-lived complexes is then determined by the substantial potential energy barrier to CC insertion by the 5s2 ground state atoms. The calculated barriers to insertion using the PCI-80 method are 9.6 kcaumol for Y inserting in the CC bond and 7.2 kcaYmo1 for Zr inserting into the CH bond. The calculated barriers are probably 2-3 kcdmol too large to be consistent with the observed reaction efficiencies of about 2 x even taking account of the internal energy in cyclopropane at 300 K. For Nb, as for Mo, the spin must change in order for reactants to access the CC insertion well. The stated CH and CC activation barriers are PCI-80 results at the saddle points located by the SCF technique. There are no barriers on the quartet Nb -tcyclopropane surfaces, but again the crossing point between the repulsive sextet and attractive quartet surfaces must occur at somewhat higher energy than the stated barrier of 8.1 kcaY mol (CC insertion). The atoms on the right-hand side (Rh and Pd) react much more efficiently with cyclopropane, apparently because the barriers to CC or CH insertion are small or nonexistent. For both Rh and Pd, the calculated energy in the transition region for CC activation is negative. Pd should have no difficulty accessing the deep CC insertion well, since the ground state has the appropriate spin for bond insertion. Ground state Rh must change spin to insert, but the low-spin surface is so attractive that we expect only a small barrier to CC insertion. Similar statements hold for CH insertion. The necessary spin change for Rh may partially explain why it is less reactive than Pd in spite of more favorable subsequent energetics. In summary, all of the observed chemistry with cyclopropane could well be due to CC or CH insertion and subsequent collisional stabilization of the metallacycle or CH bond insertion intermediate. Neither the calculations nor the data rule out bimolecular H2 elimination reactions, since we have not

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J. Phys. Chem., Vol. 99, No. 38, 1995 13967

Gas Phase Reactions of Second-Row Transition Metals investigated the energetics along the appropriate reaction paths. If bimolecular elimination cannot occur, then the estimated lifetimes of the strongly bound complexes (DO> 25 kcal/mol) are sufficiently long to make termolecular stabilization highly probable once the well is reached. Since all exothermic channels involve complicated rearrangements, we suspect the observed chemistry is dominated by termolecular processes. C. Reactions with Linear Alkenes. All of the 4d-series neutral metal atoms except Ag react with linear alkenes of sufficient size. For Y, Zr, Nb, Rh, and Pd, the reactions are quite efficient, whereas Mo reacts only with the larger alkenes and even then only very slowly. The ab initio calculations find strongly bound low-spin R complexes that lie well below ground state M alkene reactants for all the atoms Y through Pd. The key question is whether the observed reactions are always termolecular stabilization into these wells or whether bimolecular elimination chemistry plays a role. In addition, we would like to understand the substantial variation across the 4d series in reaction efficiency with the smallest alkene, ethylene. The most reactive atom is Nb. Indeed, the Nb alkene reaction rates approach the hard-spheres estimate for all alkenes, including ethylene, and show no pressure dependence. The detailed ab initio investigation of the quartet Nb C2H4 potential (Figure 7) shows that there is no barrier to exothermic H2 elimination on that low-spin surface. Since the sextet reactants form a bound high-spin complex?0 we expect no potential barrier on approach of ground state Nb to alkene. Apparently the high-spin complex gives the reactants sufficient time to transfer efficiently from the sextet to the quartet surface, even in ethylene. Thus, we infer that efficient H2 elimination dominates the observed Nb alkene reactions in all cases. In corroboration, the RRKM modeling suggests that the Nb-C2& binding energy of 36 kcal/mol is probably too small to cause saturated termolecular chemistry in the pressure range studied, and indeed no pressure dependence is observed. For Y and Zr,the reaction rates with ethylene are substantially slower than Nb, but the rates for larger alkenes are within a factor of 2 of the estimated hard-spheres rates. No pressure dependence was observed over the limited range 0.5-0.8 Torr. If the Y and Zr mechanisms are termolecular, they must be saturated termolecular even for ethylene, the smallest system. The RRKM modeling (Figure 11) then requires R complex well depths of 40 kcaVmol or greater to provide kuni less than about lo7 s-'. The ab initio calculations do find substantial wells of 28 kcal/mol for Y and 38 kcal/mol for Zr. The calculations make it highly unlikely that the Y C2H4 reaction can be in the saturated termolecular limit. In addition, Rh and Pd have calculated R complex well depths of 38 and 35 kcaVmol (similar to Zr) and exhibit clear pressure dependence in their reactions with ethylene. This suggests that termolecular reactions of both Y and Zr with Cz& would show a pressure dependence, but the experiments find none. Thus, we tend to rule out termolecular reactions for Y and Zr with ethylene. We believe both Y and Zr effect bimolecular HZelimination reactions with ethylene, and by inference with all of the linear alkenes. In both Y and Zr,the low-spin, 5s2 ground state encounters a small barrier to n complex formation, at least with ethylene. In Y and Zr ethylene, the calculated barriers to CH insertion are 1.9 and 1.8 kcdmol, respectively. These insertion barriers may limit the ethylene reaction rates. Once CH insertion occurs, the extensive calculations along the entire reaction path for Zr C2H4 find no further impediment to H2 elimination, and we expect the same to hold for Y C2&. For reactions of Y and Zr with the larger alkenes propylene, 1-butene, and isobutene, we again infer H2 elimina-

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tion reactions since we expect barriers to be lower for the larger systems. Molybdenum again suffers from the extreme stability (and thus energetic isolation) of its 4d55s', 7S ground state. The excitation energy to the lowest 5S state is 31 k~al/mol.~OFor Mo, the energy at the transition state to CH insertion on the low-spin (quintet) surface is in and of itself clearly too high (f18.2 kcaymol) to be overcome at 300 K. In addition, the absence of an empty dn acceptor orbital greatly diminishes the binding energy and increases the equilibrium bond length of the high-spin MoC2€& complex compared with its NbC2H4 counterpart. Thus, crossing from the long-range septet complex to the short-range quintet complex will be inefficient in Mo. Apparently, Mo never accesses the moderately bound (- 17.3 kcal/mol) low-spin well. The slight reactivity of Mo with the larger alkenes probably arises from inefficient collisional stabilization of the weakly bound, high-spin complex. The Rh and Pd reaction rates with ethylene are quite similar to each other and to that of Y, on the order of IO-" cm3 s-l. In contrast to Y, both the Rh and Pd reactions show a definite pressure dependence, clearly indicating a termolecular component of the reactions. The RRKM modeling using the ab initio well depths explains the differences between Rh and Pd vs Y. The calculations find substantially deeper wells for Rh and Pd with ethylene (38 and 35 kcdmol, respectively) than for Y (28 kcal/mol). The RRKM models find that kunl increases rapidly from about lo7 s-' for a MC2H4 well depth of 38 kcal/mol to 2 x lo8 S-I for 28 kcal/mol. For Rh and Pd, this magnitude of kun, can explain the observation of pressure-dependent rate constants in the range 0.5-1.1 Torr quite well. The pressure dependence is in fact weaker than linear, as if the rates are alkene, the necessary spin beginning to saturate. In Rh change from reactants to the low-spin R complex is apparently not a serious impediment, as judged by the highly efficient reactions with larger alkenes. The overall consistency of the observed rate constants, the ab initio well depths, and the RRKM modeling for the reactions of Y, Zr, Rh, and Pd with ethylene is quite satisfying. For both Rh and Pd, the ab initio calculations indicate that the low-spin R complex is separated from the CH insertion intermediate H-M-C2H3 by a barrier that lies substantially below ground state reactants. However, the CH insertion intermediate is much more weakly bound than the R complex; the difference in binding energies is 12 kcal/mol for Rh and 27 kcal/mol for Pd. Thus even though the R complex can access the CH insertion well, there is much more phase space above the n complex well, so we believe the collisionally stabilized adducts have the M-ethylene structure. H2 elimination is slightly exothermic for Rh C2H4 and substantially endothermic for Pd C2&. We have not investigated the energetics of /?-hydrogen migration to M(H)zC2H2 for either Rh or Pd. In Pd C2H4, the calculated endothermicity rules out H2 elimination. In Rh C2H4, we cannot rule out a contribution from H2 elimination, but the pressure dependence indicates that it is at least very slow. Both the Rh and Pd reactions with the larger alkenes are highly efficient and exhibit no pressure dependence, much like the Y, Zr, and Nb reactions with larger alkenes. For Rh, it is possible that bimolecular H2 elimination becomes efficient for the larger alkenes. For Pd, the calculated endothermicity seems to rule this out. As a check, we can ask whether or not the absence of pressure dependence in Rh 1-butene and Pd 1-butene is consistent with a saturated termolecular mechanism. The same RRKM model that was so successful in explaining the ethylene reactions indicates that the Pd reactions with larger

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13968 J. Phys. Chem., Vol. 99, No. 38, 1995 alkenes would easily fall in the saturated termolecular limit. For example, assuming a well depth of 36 kcal/mol, we estimate kunias small as 2 x lo5 s-l already for M propylene, which would be sufficiently slow to place the reaction in the saturated termolecular limit at 1 Torr. For the l-butene complexes, kuni is yet another order of magnitude smaller. In summary, the agreement between experiment and the combination of ab initio bound state energies and RRKM modeling of lifetimes is excellent for the M alkene systems. We conclude that Y, Zr, and Nb gain access to the deep M(alkene) well, insert into a CH bond, and ultimately eliminate H2. With ethylene, Rh and Pd form n complexes which are collisionally stabilized. With larger alkenes, Pd forms n complexes that are so long-lived that they are collisionally stabilized with unit efficiency in 1 Torr of He. Rh may well do the same, but we cannot rule out the possibility of bimolecular H2 elimination reactions between Rh and alkenes larger than ethylene. Finally, we comment that the binding energy of the 4dI05s, 2S ground state of Ag with all alkenes is apparently less than 5 kcaymol, since no reaction is observed. The filled d orbitals preclude any n donation from the alkene, and the half-filled 5s orbital is unable to form a sufficiently stable complex by itself. In contrast, the 4d55s, 7S ground state of Mo, which has halfempty d.z orbitals, apparently forms high-spin complexes which are inefficiently stabilized. The slow but irreversible observed reaction suggests that septet Mo(alkene) complexes are bound by roughly 5 kcaumol for propene and larger alkenes, although the ab initio calculations find a binding energy of only 1-2 kcdmol for the septet of the smaller Mo(C2H4) complex.

In comparing the 4d-series transition metal atoms with their 3d-series congeners (Table 4), we find that the 4d metals are always substantially more reactive. None of the 3d-series atoms reacts with alkanes. Ni (3ds4s2, 3F) is quite reactive with alkenes, presumably due to its unusually low-lying 3d94sexcited states. In both series, electron spin conservation and the chemical importance of SI configurations are recurring important themes. In general, the 4d-series neutral atoms have the advantages of lower energy d orbitals, which favors the s1 and so configurations. In addition, the 4d atoms make significantly stronger covalent chemical bonds to hydrogen and carbon for at least two reasons. The larger absolute size of the valence 4d orbitals improves overlap with ligand orbitals. Furthermore, the smaller size disparity between the 4d and 5s orbitals in the 4d series compared with the 3d and 4s orbitals in the 3d series makes sd hybridization a more effective means of relieving electron -electron repulsion, Overall, our detailed comparison of kinetics measurements and ab initio calculations has been highly satisfactory. While spectroscopic data will eventually provide a more stringent test of the quantitative accuracy of the calculations, we can certainly say that there are no glaring inconsistencies between theory and experiment at this point. Our best analysis suggests that the PCI-80 method can indeed calculate both stable minima and saddle points to an accuracy of several kcaymol. In the future, we will extend both the theoretical and experimental work to the neutral 5d-series transition metal atoms, including Ir and Pt,some of the most important metals in homogeneous catalysis.

VI. Conclusions The special reactivity of certain atoms with alkanes or alkenes can be traced directly to the electronic structure of the bare atoms themselves. In terms of bimolecular H2 elimination reactions, Rh (4d85s, 4D)is especially reactive with alkanes and Nb (4d45s, 6D) is especially reactive with alkenes. Both atoms have high-spin, 5s' ground state configurations, which minimizes electron-electron repulsion at long range compared with 5s2 configurations. The only other atom with 5s' configuration studied experimentally is Mo (4d55s, 7S), whose low-spin states lie so high in energy that formation of two covalent bonds is energetically impossible for 300 K collisions. The key to the efficiency of the Nb reaction with ethylene is the barrierless formation of the high-spin (sextet) n complex, which relies on the availability of an unoccupied d.z orbital on the metal atom. The substantial lifetime of this sextet complex apparently gives reactants sufficient time to cross very efficiently onto the quartet surface, on which H2 elimination is facile. The unusual reactivity of Rh with alkanes apparently arises from its uniquely balanced pattem of low-lying atomic states. Both 4d85s and 4d9 configurations lie at low energy, allowing the atom to minimize repulsion at long range yet readily form the sd hybrids necessary to make two CJ bonds. In Pd, the unique 4dI0 ground state is ideal for formation of n complexes with alkenes and the unusual q2complexes with alkanes. In addition, the low-lying 4d95s' excited state makes CH bond insertion relatively facile as well. However, formation of more than two covalent bonds requires involvement of highly excited states. This pushes the key P-hydrogen migration transition state between Pd(H)(C2H5) and Pd(H)zC2& to prohibitively high energy and prevents elimination chemistry at 300 K. Furthermore, the large number of valence electrons in Pd have a repulsive effect, which causes the PdC2H2 binding energy to be too small to make the elimination reaction Pd C2H4 PdC2H2 H2 exothermic.

Reasonably large basis sets were used in a generalized contraction scheme. All valence electrons were correlated using size-consistent methods. The basis sets and underlying methods are identical to those used in the previous studies of the same type.'5,'6,'8,20,2',31In short, the geometry optimizations are performed at the SCF level using the GAMESS set of programs32using double-g quality basis sets. Computed Hessians were always used to locate the transition states. In a few cases, e.g. Pd-alkene complexes, the geometry optimizations were performed at the MP2 level, using the GAUSSIAN-92 The accuracy of the geometry optimization step has recently been systematically tested and found to be adequate for both equilibrium and transition state geometries for cases where no coefficient in the configuration expansion of the subsequent correlation calculation is larger than 0.20.12 To be directly comparable to experiments, the calculated energies have to be corrected for zero-point vibrational effects. These were evaluated using the GRADSCF program.34 The correlated calculations are performed using the modified coupled pair functional (MCPF) method,35 which is a sizeconsistent, single reference state method. The zeroth-order wave function is determined at the SCF level. The basis sets in these calculations are larger than those used in the geometry optimization, with polarization functions on all atoms including an f set on the metal. Because rotation between valence and core orbitals sometimes occurs, the core orbitals are localized using a procedure in which (9) of the core orbitals is minimized. Relativistic effects were accounted for using first-order perturbation theory including the mass-velocity and Darwin terms.36 All the calculations were performed on an FX-80 ALLIANT and on an IBM Risc 6000 computer, and the final energy evaluations were performed using the STOCKHOLM set of programs.37 Even though the absolute accuracy of the MCPF calculations is not very high, the fact that the errors are highly systematic

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Appendix A: Computational Details

Gas Phase Reactions of Second-Row Transition Metals can be used to significantly reduce the errors. The accuracy is mainly limited by the basis set size in the final MCPF calculations. The lack of triple excitations is another important factor. In comparison to these other errors, the error in the geometry optimization step can normally be neglected. On the basis of comparisons to calculations of high accuracy and comparisons to experiments, it has recently been demonstrated that the present type of treatment gives a remarkably stable fraction of the correlation effects. Using the present basis sets and methods, it has been shown that this fraction is close to 80%. A simple estimate of the remaining correlation effects is then obtained by simply adding 20% correlation energy to each system. This is the general idea behind the PCI-80 (parametrized configuration interaction with parameter 80) scheme which has recently been proposed.I0 This parametrization gives a major improvement of the results compared to an unparametrized treatment. For a benchmark test consisting of the atomization energies of 32 neutral first row systems, the PCI80 method gives an average absolute deviation compared to experiments of only 2.4 kcaVm01.~~Pople et ~ 2 1 have . ~ ~ shown that for the same systems the MP2 method using polarized basis sets gives an average absolute deviation of 22 kcal/mol and for the QCISD method the deviation is actually larger, 29 kcaV mol. For transition metal systems the improvement at the PCI80 level compared to an unparametrized treatment is sometimes quite dramatic. Tests against a large number of experimentally studied small second-row transition metal complexes show that the accuracy of the PCI-80 method for bond strengths is probably at least as high as that available from experiments for these systems.'O Finally, all the results reported here are for the ground state of each system. Since in most cases the ground state of the reactants has a different total spin than the ground state of the products, the energies in the tables often correspond to states of different spin in the beginning and at the end of the reaction. It has been shown in detail by Mitchell@that in the case of the association reaction between the nickel atom and carbon monoxide, the crossing probability between different spin surfaces is near unity due to the large spin-orbit coupling. Also, to rationalize the experimental results for the oxidative addition reaction between the nickel atom and water, a high crossing probability has to be as~umed.~' The crossing probability should be even larger for the present second-row transition metal systems. Acknowledgment. J.C.W. thanks the U.S. National Science Foundation (CHE-9303918) and the donors of the Petroleum Research Fund (Type AC) for generous support of this work. References and Notes (1) For a comprehensive review of M+ chemistry, see: Eller, K.; Schwarz, H. Chem. Rev. 1991, 91, 1121. (2) Weisshaar, J. C. Acc. Chem. Res. 1993, 26, 213. (3) Armentrout, P. B. In Gas Phase Inorganic Chemistry; D. H. Russell, Ed.; Plenum: New York, 1989. (4) Mitchell, S. A. Submitted to the Symposium on Gas-Phase Metal Reactions, 4th Chemical Congress of North America, New York, NY. ( 5 ) Lian, L.; Mitchell, S. A,; Rayner, D. M. J. Phys. Chem. 1994, 98, 11637. (6) Ritter, D.; Carroll, J. J.; Weisshaar, J. C. J. Phys. Chem. 1992, 96, 10636. (7) Carroll, J. J.; Weisshaar, J. C. J. Am. Chem. SOC. 1993, 11.5, 800. (8) Carroll, J. J.; Haug, K. L.; Weisshaar, J. C. J. Am. Chem. SOC. 1993, 115, 6962. (9) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J. Phys. Chem. 1994, 98, 2062. (10) Siegbahn, P. E. M.; Blomberg, M. R. A.; Svensson, M. Chem.Phys. Lett. 1994, 223, 35. (1 1) Ritter, D. Ph.D. Thesis, University of Wisconsin-Madison, 1990.

J. Phys. Chem., Vol. 99,No. 38, 1995 13969 (12) Siegbahn, P. E. M.; Svensson, M. Chem. Phys. Lett. 1993, 216, 147. (13) Experimental value (1 10 kcaYmol endothermic) calculated from heats of formation for C h (Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phys. Chem. ReJ Data 1985, 14, Suppl. 11, CH2 (Lengel, R. K.; Zare, R. N. J. Am. Chem. SOC. 1978,100,7495),and Hz (Huber, K.; Herzberg, G. Molecular Spectra and Molecular Structure 4. Constants of Diatomic Molecules; van Nostrand: Princeton, 1979). (14) Experimental value (31 kcdmol endothermic) calculated from heats of formation for C2H6 (Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Chumey, K. L.; Nuttall, R. L. J. Phys. Chem. Re$ Data 1982,11, Suppl. 2), CzH4 (Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; F ~ r i pD. , J.; McDonald, R. A,; Syverud, A. N. J. Phys. Chem. Re$ Data 1985,14, Suppl. l), and H2 (Huber, K.; Herzberg, G. Molecular Spectra and Molecular Structure 4. Constants of Diatomic Molecules; van Nostrand: Princeton, 1979). (15) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J. Am. Chem SOC.1992, 114, 6095. (16) Siegbahn, P. E. M.; Blomberg, M. R. A. J. Am. Chem. SOC. 1992, 114, 10548. (17) (a) Crabtree, R. H. Chem. Rev. 1985, 85, 245. (b) Shilov, A. E. Activation of Saturated Hydrocarbons by Transition Metal Complexes: D. Reidel: Dordrecht, 1984. (18) Siegbahn, P. E. M. Theor. Chim. Acta 1994, 87, 277. (19) Experimental value (40 kcaVmol endothermic) calculated from heats of formation for C2H4 (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. 1). C2H2 (Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Chumey, K. L.; Nuttall, R. L. J. Phys. Chem. Ret Data 1982, 11, Suppl. 2), and H2 (Huber, K.; Herzberg, G. Molecular Spectra and Molecular Structure 4. Constants of Diatomic Molecules; van Nostrand: Princeton, 1979). (20) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J. Phys. Chem. 1992, 96, 9794. (21) Siegbahn, P. E. M.; Blomberg, M. R. A,; Svensson, M. J. Am. Chem. SOC. 1993, 115, 1952. (22) Blomberg, M. R. A.; Siegbahn, P. E. M.; Nagashima, U.; Wennerberg, J. J. Am. Chem. Sac. 1991, 113, 424. (23) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific Publications: Oxford, England, 1990. (24) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; WileyInterscience: New York, 1972. (25) Carroll, J. J. Ph.D. Thesis, University of Wisconsin-Madison, 1995. (26) Cambi, R.; Cappelletti, D.; Liuti, G.; Pirani, F. J. Chem. Phys. 1991, 95, 1852. (27) Shimanouchi, T. Tables of Molecular Vibrational Frequencies; National Bureau of Standards: Washington, DC, 1967; Vols. 1-3. (28) Herzberg, G. Molecular Spectra and Molecular Structure, 11. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold Co.: New York, 1945. (29) Sheppard, N. J. Chem. Phys. 1949, 17, 74. (30) Moore, C. E. NBS Circ. No. 467; U.S. Dept. of Commerce: Washington, DC, 1949; Vols. 1-111. (31) Siegbahn, P. E. M. Chem. Phys. Lett. 1993, 201, 15. (32) GAMESS (General Atomic and Molecular Electronic Structure System): Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S.; Gordon, M. S.; Nguyen, K. A,; Windus, T. L.; Elbert, S. T. QCPE Bull. 1990, 10,52. (33) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Ragavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Revision A; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1992. (34) GRADSCF is a vectorized SCF first- and second-derivative code written by A. Komomicki and H. King. (35) Chong, D. P.; Langhoff, S. R. J. Chem. Phys. 1986, 84, 5606. (36) Martin, R. L. J. Phys. Chem. 1983, 87, 750. See also: Cowan, R. D.; Griffin, D. C. J. Opt. SOC. Am. 1976, 66, 1010. (37) STOCKHOLM is a general purpose quantum chemical set of programs written by P. E. M. Siegbahn, M. R. A. Blomberg, L. G. M. Patterson, B. 0. Roos, and J. Almlof. (38) Siegbahn, P. E. M.; Svensson, M.; Boussard, P. J. E. J. Chem. Phys., submitted. (39) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1992, 97, 7846. (40) Mitchell, S. A. In Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam, 1992. (41) Mitchell, S. A.; Blitz, M. A.; Siegbahn, P. E. M.; Svensson, M. J. Chem. Phys. 1994, 100, 423. Jp9508261