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Theoretical Investigation of the Gas-Phase Reactions of CrO+ with Ethylene Thomas M. Scupp and Timothy J. Dudley* Department of Chemistry, VillanoVa UniVersity, VillanoVa, PennsylVania 19085 ReceiVed: October 1, 2009; ReVised Manuscript ReceiVed: December 3, 2009
The potential energy surfaces associated with the reactions of chromium oxide cation (CrO+) with ethylene have been characterized using density functional, coupled-cluster, and multireference methods. Our calculations show that the most probable reaction involves the formation of acetaldehyde and Cr+ via a hydride transfer involving the metal center. Our calculations support previous experimental hypotheses that a four-membered ring intermediate plays an important role in the reactivity of the system. We have also characterized a number of viable reaction pathways that lead to other products, including ethylene oxide. Due to the experimental observation that CrO+ can activate carbon-carbon bonds, a reaction pathway involving C-C bond cleavage has also been characterized. Since many of the reactions involve a change in the spin state in going from reactants to products, locations of these spin surface crossings are presented and discussed. The applicability of methods based on Hartree-Fock orbitals is also discussed. SCHEME 1
Introduction Transition-metal oxides are effective catalysts for the oxidation of organic compounds.1-3 Numerous experimental4-20 and theoretical21-41 gas-phase studies have been designed to understand C-H and C-C bond activation processes that occur in these transformations. These gas-phase studies of the reactivity of metal oxides have lent insight into the mechanistic nature of the activation of C-H and C-C bonds in organic substrates. Early transition-metal oxides (Sc, Ti, V) have been shown to have relatively strong metal-oxygen bonds and are not reactive in terms of oxidizing alkanes and alkenes.5,7,42-45 In fact, the bare metal ions can react with oxygen-containing organic compounds to generate metal oxide ions and hydrocarbons.46,47 Conversely, the late transition-metal oxides (Mn, Fe, Co, Ni) have relatively weak metal-oxygen bonds and are known to be very reactive toward hydrocarbons but less selective.8,9,43 The chromium oxide cation (CrO+) is known to be more selective in its oxidation processes due to its intermediate metal-oxygen bond dissociation energy. Thus, reactions of chromium oxides and hydrocarbons have received considerable attention. The complexity of reactions involving metal oxides and hydrocarbons is compounded by the fact that many of these reactions involve intermediates on more than one spin surface. Previous studies11,48-53 involving the reactivity of transitionmetal oxides have shown atypical kinetic phenomena (e.g., inverse temperature dependence) that can be attributed to crossing of spin surfaces. Such crossings have led to the concept of two-state reactivity (TSR) in organometallic chemistry.54-57 TSR can affect both the observed rate and product distribution for chemical reactions involving transition metals. Because theoretical calculations can be used to elucidate the nature of chemical transformations via reaction intermediates and transition states as well as localizing regions of space where different spin surfaces cross, these calculations lend themselves to studying complex systems involving metal oxides. Chromium oxide cations are reactive toward many small hydrocarbons (e.g., ethane, ethylene) in the gas phase.4,5,10 * To whom correspondence
[email protected].
should
be
addressed.
E-mail:
Previous experiments, however, were not able to identify with certainty the products formed in such reactions because the products were analyzed using mass spectrometry. Recently, theoretical studies of the reactions of chromium oxide cations with small hydrocarbons have been reported.25,27,30,32,37 Most of these have focused on reactions in which methane is converted to methanol. Surprisingly few theoretical studies have focused on reactions involving other simple hydrocarbons,32,37 considering that CrO+ is reactive toward larger hydrocarbons but does not readily react with methane.5 Since reactions of CrO+ with larger hydrocarbons are known to generate multiple products, theoretical studies of such reactions are certainly warranted. The limited number of calculations involving hydrocarbons other than methane have shown that each reaction mechanism associated with a given product can involve numerous intermediates and transition states, some of which have different spin than the initial reactants. This work focuses on the reactions of CrO+ with ethylene. Previous mass spectrometry experiments have shown that interaction of CrO+ with ethylene can lead to one of two products, with one reaction being exothermic and the other endothermic.4 The exothermic reaction involves a simple reductive elimination process to form C2H4O (Scheme 1a). The product was determined to be acetaldehyde rather than ethylene oxide based on the reactivity of the bare metal ion (Cr+) toward each isomer of C2H4O. It is also known that the spin state of the product (sextet) is different than that of the reactants (quartet). The product for the endothermic process was shown to be CH2O, presumably formaldehyde (Scheme 1b). The goal of this work is to characterize the potential energy surfaces associated with the two reactions depicted in Scheme 1, as well as other energetically favorable reaction pathways. Since ethylene is the simplest alkene, understanding the mechanisms associated with oxidation by CrO+ will be helpful in studying
10.1021/jp909455a 2010 American Chemical Society Published on Web 12/18/2009
Theoretical Investigation of CrO+ with Ethylene reactions with larger alkenes, which have been shown to possess numerous exothermic reaction pathways.4
J. Phys. Chem. A, Vol. 114, No. 2, 2010 1135 TABLE 1: Relative Energies (kcal/mol) of Products Associated with the Reaction of CrO+ with Ethylenea BLYP M06-L UCCSD(T)b MRPTc
Methods Density functional theory (DFT) was used to locate all stationary points presented in this work. Initially, these stationary points were localized using the unrestricted B3LYP/6-31G* level of theory as implemented in Spartan06.58 The structures were then reoptimized using the nonhybrid BLYP functional and the 6-311+G(2df,2p) basis set for the nonmetal atoms. The Wachters-Hay triple-ζ quality basis set was used for chromium, with diffuse and polarization functions added.59-61 Only the spherical components of the d and f orbitals were used in the calculations. Vibrational frequencies were obtained at the BLYP level for all stationary points via a central difference formula using numerical derivatives of analytic gradients. Transition states were connected to their respective minima by intrinsic reaction coordinate (IRC) calculations using the second-order Gonzalez-Schlegel algorithm (step size ) 0.25 (amu)1/2bohr).62 Using the BLYP geometries, the structures were then optimized using the M06 functional with no Hartree-Fock exchange included, referred to as M06-L.63 Recent work by Truhlar and Zhao64 suggests that exclusion of Hartree-Fock exchange leads to more accurate results for transition-metal complexes of this nature. The Supporting Information section includes further data supporting the use of BLYP and M06-L. UCCSD(T) and multireference perturbation theory65,66 (MRPT) energies were calculated at the M06-L-optimized geometries, unless otherwise noted, using the same basis set utilized in the geometry optimizations. The energies reported in this work were not zero-point energy (ZPE)-corrected. The UCCSD(T) energies were evaluated using Gaussian03,67 and the Stable)Opt command was used to ensure that the underlying Hartree-Fock orbitals were the ground-state orbitals. The BLYP, M06-L, and MRPT calculations were performed using GAMESS.68 The underlying CASSCF in the MRPT calculations consisted of 11 electrons in 11 orbitals. The orbital set included all orbitals containing unpaired electrons and all bonding and correlating antibonding orbitals between heavy atoms. For both the MRPT and UCCSD(T) calculations, only valence electrons were correlated. Minimum-energy crossing points (MECP) between spin surfaces were localized using analytic energy gradients in GAMESS. MECPs were evaluated at the BLYP and CASSCF levels using default convergence parameters. The active space in the CASSCF calculations was the same one as that used in the previously mentioned MRPT calculations. Results This section outlines the structural and energetic data, determined at various levels of theory, for mechanisms associated with the reaction of CrO+ with ethylene. First, the results of calculations on the possible products of this reaction are reported. Next, the mechanisms on the quartet and sextet surfaces for the various oxygen addition processes (i.e., formation of C2H4O) are discussed. Finally, the mechanism associated with formation of formaldehyde is presented. The addition of oxygen to ethylene via CrO+ has been observed in mass spectrometry experiments, though the nature of the product was deduced through further experiments. These experiments studied the reverse reactions involving a chromium cation and one of two possible products, acetaldehyde and ethylene oxide. Table 1 lists the relative energies of the various products studied in this work with respect to the reactants on the quartet surface. All of the products involving addition of
CrO+ (4Σ) + C2H4 0.0 Cr+ (6S) + acetaldehyde -40.2 Cr+ (6S) + ethenol -30.0 Cr+ (6S) + ethylene oxide -15.2 CrCH2+ (4B1) + H2CO 14.3
0.0 -38.3 -24.4 -13.6 9.0
0.0 -48.5 -37.3 -21.6 14.3
0.0 -40.8 -32.7 -16.2 16.9
a
All structures were optimized at the corresponding level of theory. b Geometries were optimized using numerical gradients and default parameters in Gaussian03. c Geometires were optimized using numerical gradients and a central difference formula in GAMESS.
oxygen to ethylene are exothermic at all levels of theory considered. The one endothermic process involves the formation of formaldehyde. The BLYP energies compare quite well to the MRPT energies for all products considered, while the M06-L energies do not agree well with any of the MRPT calculations. Surprisingly, the UCCSD(T) results are also in relatively poor agreement compared to the MRPT calculations. This may be due to the significant multireference character of quartet CrO+, which exhibits a T1 diagnostic of 0.102. The natural orbital occupation numbers (NOONs) from the CASSCF in the MRPT calculations also suggest significant multireference character. Two degenerate π-orbitals have occupation numbers of 1.81, with the corresponding antibonding orbitals having occupation numbers of 0.19. Though formation of ethylene oxide in metal oxide reactions is common,69 it was determined that the product in this case was acetaldehyde due to the lack of a reaction of Cr+ with acetaldehyde to generate ethylene. Due to the simplicity of the mechanism for ethylene epoxidation, it will be considered first. Figure 1 shows the structures associated with the formation of ethylene oxide on both the quartet and sextet surfaces, determined using DFT methods. One can see that the structures associated with epoxide formation are very similar between surfaces. Both mechanisms start with the formation of a metallacycle intermediate (1s and 1q), though the ring in the sextet structure 1s is not as pronounced. This is evidenced by the lack of sp3-hybridization at the carbon closest to the chromium in 1s, especially when compared to the same carbon atom in 1q. A simple transition state corresponding to formation of the second carbon-oxygen bond is observed on both surfaces (2q and 2s), and each leads to the formation of an epoxide-Cr+ complex (3q and 3s), where the chromium is coordinated to the oxygen atom. Compared to the M06-L calculations, BLYP consistently underestimates the length of the Cr-O bond in every structure and by as much as 0.08 Å. Considerably better agreement is observed for the other bonds between heavy atoms. Figure 2 is a potential energy diagram of the epoxidation mechanism evaluated at the DFT level of theory. The formation of the metallacycle is very favorable on both the quartet and sextet surfaces. The process of forming the epoxide-Cr+ complex (3q) on the quartet surface proceeds through a significant barrier and is predicted to be overall exothermic, though 3q is significantly higher in energy than the metallacyle intermediate 1q. The overall endothermicity of the ethylene oxide formation process on the quartet surface supports the experimental determination that this reaction was not observed in previous experiments. Table 2 lists the energies of the intermediates and transition states associated with the epoxidation mechanisms at the DFT, UCCSD(T), and MRPT levels. A few discrepancies are observed between the various methods.
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Figure 1. Quartet (top) and sextet (bottom) structures associated with epoxide formation from CrO+ and ethylene. Bond distances (in Å) are reported at the M06-L and BLYP (in parentheses) levels. Imaginary modes are displayed for transition-state structures.
Figure 2. Potential energy diagram (kcal/mol) of epoxidation mechanisms on the quartet and sextet surfaces, determined at the M06-L and BLYP (in parentheses) levels of theory. The structure of the ion at the spin inversion point, determined at the CASSCF level, is also included.
First, the UCCSD(T) and MRPT calculations predict 1q to be considerably less stable than the DFT calculations. Both the UCCSD(T) and MPRT calculations show that there is significant multireference character, with the UCCSD(T) calculation having a T1 diagnostic of 0.058. The NOONs in the MRPT calculation indicate multireference character as well. The sigma-bonding orbital between the oxygen and chromium atoms has a NOON of 1.82, and the corresponding antibonding orbital has a NOON of 0.20. Thus, the differences between the DFT calculations and the higher-level calculations are not surprising. The barrier to formation of 3q is predicted to be relatively small at the
UCCSD(T) level (about 6 kcal/mol) as opposed to both the MRPT and DFT levels (37-43 kcal/mol). The T1 diagnostic for 2q was determined to be 0.060, again suggesting multireference character. The NOONs from the MRPT calculation suggest that the structure is a low-spin quartet (1.12, 1.00, 1.00, 1.00, 0.88), with the corresponding orbitals residing primarily on the chromium atom. The change in electronic structure in going from a high-spin quartet in 1q to a low-spin quartet in 2q is not surprising since the quartet and sextet surfaces appear to cross in this region (see Figure 2). While both the UCCSD(T) and MRPT calculations indicate that a single determinant wave
Theoretical Investigation of CrO+ with Ethylene
J. Phys. Chem. A, Vol. 114, No. 2, 2010 1137
TABLE 2: Relative Energies (in kcal/mol) of Structures Related to Epoxidation on the Quartet and Sextet Surfaces, Determined at Various Levels of Theorya 1q BLYP M06-L UCCSD(T)//M06-L MRPT//M06-L a
2q
3q
1s
2s
-50.6 -13.6 -29.9 -36.0 -34.9 -50.3 -7.3 -18.3 -34.4 -32.6 -21.4 -15.7 -41.7 -25.7 -23.1 -27.5 12.6 -2.3 -19.5 -30.8
3s -60.6 -50.7 -52.4 -56.9
The energies are relative to the reactants on the quartet surface.
TABLE 3: Geometrical Parameters of the MECP Associated with the Epoxidation Mechanisms on the Quartet and Sextet Surfacesa Cr-O Cr-C O-C C-C a
BLYP
CASSCF
1.775 2.367 1.434 1.485
1.806 2.204 1.472 1.546
Bond lengths are in Å.
function is not an appropriate zero-order approximation for 2q, they predict very different energy barriers. Another discrepancy is that the UCCSD(T) calculation predicts 3q to be significantly lower in energy than the metallacycle intermediate 1q, as opposed to 3q being higher in energy at the DFT and MRPT levels. Again, the T1 diagnostic (0.070) indicates multireference character, and the NOONs from the MRPT calculation (1.02, 1.00, 1.00, 1.00, 0.98) suggest the same. As was the case in 2q, UCCSD(T) appears to overestimate the correlation energy in 3q, thus predicting 3q to be more stable than 1q. More discrepancies are observed on the sextet surface. All of the calculations predict 1s to be stable with respect to the initial reactants, but the UCCSD(T) calculation predicts the sextet structure to be more stable than its quartet counterpart 1q. The T1 diagnostic for 1s (0.034) is considerably smaller than that for 1q but is still relatively high. The process of forming the epoxide-Cr+ complex on the sextet surface (3s) proceeds through a significantly smaller barrier (2s) at the DFT and UCCSD(T) levels (30 kcal/mol) than the initial reactants. The chromium hydride intermediate 5q was calculated to be slightly higher in energy (∼4 kcal/mol) at the DFT levels than the initial reactant complex 1q but still considerably lower in energy than the reactants (>44 kcal/mol). Table 4 lists the energies of structures 1q, 4q, and 5q at various levels of theory. The barrier to chromium hydride formation at the MRPT level is similar to that calculated by the DFT methods (21 kcal/mol), while the barrier at the UCCSD(T) level is considerably lower (9 kcal/mol). The MRPT calculations predict the chromium hydride intermediate 5q to be higher in energy than 1q but by a significantly larger amount than the DFT calculations. The UCCSD(T) calculations predict 5q to be slightly lower in energy than 1q. As was the case for previous structures, the UCCSD(T) calculations have large T1 diagnostic values for 4q (0.057) and 5q (0.051). The NOONs for the bonding and antibonding orbitals between the chromium and the terminal carbon in both
4q (1.76 and 0.25) and 5q (1.80 and 0.20) from the MRPT calculations also suggests significant multireference character. In Figure 5, one can see that both quartet and sextet structures are involved in the process of transferring the hydride from the chromium atom to the terminal carbon. The barrier to the hydride transfer on the quartet surface is relatively small at the DFT levels (
