Theoretical Investigation of the Gas-Phase Reaction of CrO+ with

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Theoretical Investigation of the Gas-Phase Reaction of CrO with Propane Jennifer E. Beck, and Timothy J. Dudley J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10909 • Publication Date (Web): 15 Feb 2017 Downloaded from http://pubs.acs.org on February 16, 2017

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The Journal of Physical Chemistry

Theoretical Investigation of the Gas-Phase Reaction of CrO+ with Propane Jennifer E. Beck1† and Timothy J. Dudley1,2* 1.

Department of Chemistry, Villanova University, 800 Lancaster Ave., Villanova, PA 19085

2. Math, Science and Technology Department, University of Minnesota Crookston, 2900 University Ave., Crookston, MN 56716 Corresponding Author Phone: 218-281-8261, Fax: 218-281-8080, Email: [email protected] †Current address: Eurofins Lancaster Laboratories, Inc., 2425 New Holland Pike, Lancaster, PA 17601

1

ACS Paragon Plus Environment


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Abstract Transition metal oxide cations (e.g., MO+) have been shown to oxidize small alkanes in the gasphase. The chromium oxide cation is of particular interest because it is more reactive than oxides of earlier transition metals but is more selective than oxides of later transition metals. The reaction of CrO+ with propane has been shown to produce a number of products: propanol, propene, ethene, and hydrogen. Few theoretical studies exist for reactions of simple transition metal oxide cations with larger alkanes. We have analyzed the potential energy surfaces associated with the reaction of CrO+ with propane using two DFT methods, B3LYP and M06-L. Energetically viable reaction paths leading to each experimentally observed product have been characterized. Each reaction path begins with formation of a reactive intermediate in which either an α- or β-hydrogen from propane is extracted by the oxygen atom of CrO+. While pathways leading to formation of hydrogen and ethene were found to occur on a single spin surface, energetically viable pathways to forming propanol and propene require a transition from the quartet spin surface to the sextet surface. The minimum energy crossing points between the quartet and sextet surfaces were found to be well below the energy level of the reactants and structurally resemble the initial reactive intermediates.

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Introduction Gas-phase reactions of simple transition metal oxide cations (i.e., MO+) with alkanes have been thoroughly studied using numerous mass spectrometry techniques.1-11 The interest in this field can be largely attributed to the insights these reactions can provide to important biological and industrial catalytic processes involving transition metal oxides (e.g., Phillips catalyst).12-14 Besides their usefulness in understanding heterogeneous processes, gas-phase reactions of transition metal oxide cations with organic substrates are in and of themselves worthy of attention due to their complexity. The later transition metal oxide cations (e.g., FeO+) are quite powerful oxidizers2-9 while the earlier transition metal analogs (e.g., CrO+) tend to be less reactive.10-11 The nature of the products formed in these reactions depends heavily on the transition metal found in the oxide. For example, the reaction of CrO+ with ethane leads only to ethanol formation,11 while the corresponding reaction involving MnO+ produces ethanol, ethane, and the ethyl radical.9 Many of the reactions between transition metal oxide cations and organic substrates are only thermodynamically feasible if the reaction proceeds through a spin-inversion process (i.e., change in spin state). This concept of two-state reactivity (TSR)15-18 can be important in understanding the rate of product formation and distribution of products for a given reaction.

TSR is not only pervasive in reactions of transition metal oxide cations with

hydrocarbons, but in many other areas of organometallic chemistry. The reactions described above are well suited for analysis by computational methods and indeed a number of theoretical studies have been reported on such reactions.19-29 Standard computational models (e.g., Density Functional Theory) have been used to provide understanding of the mechanisms associated with both simple and complex reactions of transition metal oxide cations. Many of the reported studies have focused on activation of 3



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methane by cations of late transition metal oxides. While these reactions may seem simple based on the number of experimentally observed products that have been reported (i.e., methanol and methyl radical), the calculations have shown these transformations are anything but simple. Formation of a single product often involves multiple intermediates and transition states regardless of the transition metal oxide considered. In many cases, multiple spin surfaces need to be considered and their crossing(s) localized in order to understand if and why a product was or was not observed.

Recently, theoretical studies involving larger alkanes30-32 have been

reported and two items should be emphasized regarding these studies. First, the increased size of the hydrocarbon requires analyzing larger regions of the necessary potential energy surface(s) to understand the multiple product channels each reaction exhibits. Second, the complexity of the potential energy surfaces increases due to the potential for new chemical processes occurring (e.g., C-C bond cleavage). Reactions involving CrO+ are of special interest for two reasons. First, chromium is the earliest transition metal whose oxide cation shows significant reactivity towards small hydrocarbons. CrO+ does not react with methane, but converts ethane to ethanol and produces a number of products when reacting with propane (see Scheme 1).11 Second, the low-spin form of CrO+ (quartet) is lower in energy than its high-spin counterpart (sextet), which is not true of the bare transition metal cation Cr+. Thus, the formation of products through TSR is likely for many of the products one would expect to observe from the reaction of CrO+ with alkanes (e.g., alcohols). This work focuses on the reaction of CrO+ with propane, for which four products have been reported: propanol, propene, ethane, and hydrogen. Few theoretical studies of reactions of transition metal oxide cations with propane have been reported,33 despite the complexity of the

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reactions based on experimentally observed products. The goal of this work is to characterize the potential energy surfaces associated with the formation of each observed product.

Scheme 1. Reaction of gas-phase CrO+ with propane.11

Methods All calculations reported in this work were performed using GAMESS.34 Density functional methods (DFT) were used to locate and characterize all stationary points. The stationary points were first located and characterized at the B3LYP/6-31G** level of theory utilizing the default grid size for numerical integration of the DFT energy.

The energy gradient convergence

tolerance (OPTTOL) was set to 0.001 Hartree/Bohr. Vibrational frequencies were calculated using numerical derivatives of analytical energy gradients, utilizing a central difference formula for increased accuracy. The energies for stationary points reported in this work are zero-point energy (ZPE) corrected. Transition states were connected to their respective minima by intrinsic reaction coordinate (IRC) calculations using the second order Gonzalez-Schlegel algorithm35 and the default step size. Further refinement of the geometries and energies was achieved by running M06 calculations with no HF exchange (M06-L)36-37 utilizing a larger basis set. For the main group elements the 6-311+G(2df,2p) basis set was used. For chromium, the Wachters-Hay basis

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set was used along with diffuse and polarization functions.38-40 The number of DFT grid points was increased for the M06-L calculations to improve accuracy (NRAD=144, NLEB=590). The minimum energy crossing points (MECPs) at the B3LYP and M06-L levels were located using the RUNTYP=MEX directive. Default step size and convergence parameters were used in all MECP calculations. One-electron spin-orbit coupling (SOC) matrix elements were calculated at the M06-L MECP geometries using multiconfigurational quasi-degenerate perturbation theory (MCQDPT) from a CASSCF reference wavefunction.41 The active space for the CASSCF calculations consisted of 7 electrons in the highest-lying orbitals involving the chromium atom (7 orbitals total). The orbitals used in the MCQDPT calculations were the converged orbitals from the sextet CASSCF calculation. The only orbitals that were not correlated in the MCQDPT calculations were the 13 chemical core orbitals. The effective nuclear charges used in the SOC calculations were suggested values based on previous studies (3.6 for C, 6.0 for O, and 11.6 for Cr).42,43

Results Determination of Reactant and Product Species. Five product channels have been proposed for the reaction of CrO+ with propane, assuming the alcohol formed can be 1-propanol and/or 2propanol. Table 1 lists the relative energies of the reactants and products determined at the M06L and B3LYP levels of theory. The information in Table 1 indicates that formation of hydrogen and ethene can occur readily on the same spin surface (quartet) as the reactants. The other products require a spin crossing between the quartet and sextet surfaces in order to achieve a thermodynamically stable product, though the quartet dissociation limit leading to propene is only slightly higher in energy than the initial reactants. 6


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Table 1. Relative energies at the M06-L level for the reactants and products associated with the reaction of CrO+ with propane. Values in parentheses are energies determined at the B3LYP level of theory. relative energy (kcal/mol) reaction channel

quartet

sextet

CrO+ + propane

0.0 (0.0)

36.0 (34.3)

CrC3H6O+ + H2a

-45.8 (-51.8)

-25.4 (-31.7)

Cr+ + 1-propanol

34.7 (34.5)

-9.1 (5.6)

Cr+ + 2-propanol

33.4 (30.9)

-10.4 (1.9)

CrOH2+ + propene

0.8 (4.7)

-33.2 (-31.2)

CrCH4O+ + ethene

-16.0 (-22.7)

3.8 (-0.7)

a.) Three dissociation limits were found for the product channel leading to hydrogen. The reported energy is for the lowest energy pathway.

Many of the processes required to form the products in Table 1 have been observed for other reactions of metal oxide cations with chromium11 and other transition metals2-10. The formation of alcohol by addition of the oxygen from the metal oxide cation has been observed in previous studies, with spin inversion being a common theme for early transition metals like chromium.1934

Recent theoretical calculations have also provided insight into how alkenes can form from

similar reactions with higher-order alkanes.31-34 Figure 1 shows the structures of the various chromium-containing products associated with the reaction presented in Scheme 1. One can see that the structures of these small chromium-containing fragments are very similar between the B3LYP and M06-L calculations, despite the differences in the methods and basis sets. Many of the bond lengths between chromium and the other heavy atoms differ by less than 0.02 Å between methods, with 6CrOH2+ having the only large bond length variation between methods (Cr-O bond varies by 0.048 Å). One can also note from Table 1 that while there are some 7



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differences between the relative energies predicted at the B3LYP compared to the M06-L level, the quartet-sextet energy gaps for nearly all of the product channels are very similar between methods. The exceptions are the dissociation limits involving Cr+, where the quartet-sextet energy gap is predicted to be about 44 kcal/mol at the M06-L level and 29 kcal/mol at the B3LYP level. Experimentally the difference in energy between the sextet and quartet chromium cation is 54-58 kcal/mol. While both methods predict significantly lower quartet-sextet energy gaps, B3LYP is well below the expected value. This preliminary analysis suggests that the while geometries predicted at the B3LYP/6-31G** level are likely to be of sufficient accuracy, the relative energies require a more sophisticated treatment. Thus, the analysis of structures and relative energies in this work are based on the values determined with a more robust functional (M06-L) and atomic basis sets (triple-zeta quality). One mechanism that has not been analyzed previously in theoretical studies is the formation of hydrogen by reacting metal oxide cations with alkanes. Since this process has been proposed in the reaction of CrO+ with propane, a more detailed analysis of the associated product structures is warranted. Formation of H2 from propane requires the successive extraction of three hydrogen atoms from the organic fragment (vide infra), giving rise to the three structures presented at the bottom of Figure 1. The most stable of these structures is the one formed via extraction of hydrogen from each of the three carbon atoms, 4CrOH(CH2CHCH2)+.

The

increased stability of this structure can be understood by observing the structure in Figure 1, which resembles η3-binding of chromium to an allyl ligand. The other two structures comprise much more strained configurations, leading to energies that are roughly 12-15 kcal/mol higher in energy than 4CrOH(CH2CHCH2)+.

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2.066 (2.018)

4CrOH + 2

6CrOH + 2

117.2º (118.5º)

1.719 (1.700)

1.760 (1.744)

1.965 (1.960) 4CrCH (OH)+ 3

1.730 1.730 (1.720) (1.720) 2.120 2.120 (2.114) (2.114)

2.127 2.127 (2.149) (2.149)

126.7º (126.2º)

114.1º (130.5º) 2.362 (2.356)

6CrCH (OH)+ 3

1.724 (1.711)

1.883 (1.884)

2.184 (2.207)

1.727 (1.712)

2.135 (2.155)

1.910 (1.901)

2.176 2.176 (2.209) (2.209) 4CrOH(CH CHCH )+ 2 2

4CrOH(CHCHCH )+ 3

4CrOH(CH CCH )+ 2 3

Figure 1. Geometrical structures determined at the M06-L (B3LYP) levels of theory for Crcontaining products from the reaction of CrO+ with propane. Bond lengths are in Ångstroms.

All of the experimentally observed products are predicted to be more thermodynamically stable than the reactants, though some processes require a transition between spin surfaces. All of the mechanisms associated with the formation of these products can be connected to an initial complex that forms between propane and the quartet CrO cation (1q in Figure 2). This complex forms a symmetric structure through a barrierless process and is considerably more stable than the dissociated reactants (-46 kcal/mol).

The associated complex on the sextet surface is

considerably higher in energy than both the quartet complexes (by about 20 kcal/mol at M06-L level), so it is not expected to play a significant role in the reaction. Structure 1q is the starting point for the C-H bond activation processes that are necessary to form the products of the reaction of CrO+ with propane. 9



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1.658 (1.649)

1.732 (1.723)

2.197 (2.228)

2.169 (2.255) 1.720 (1.735)

2.082 (2.103)

1.580 (1.572) 2.342 (2.336)

2.342 (2.336)

4TS

2q

1-2

Erel = -18.8 (-21.2)

Erel = -58.1 (-58.8)

1.663 (1.647)

1.736 (1.724) 1.703 (1.710)

1q Erel = -45.6 (-45.8)

1.987 (1.967)

2.277 (2.293)

2.079 (2.081)

4TS

1-3

Erel = -13.0 (-16.8)

1.974 (1.962)

3q Erel = -55.5 (-63.2)

Figure 2. Geometrical structures and relative energies (in kcal/mol) at the M06-L (B3LYP) levels of theory associated with the initial C-H activation process.

Bond lengths are in

Ångstroms.

Initial C-H Activation Mechanisms. Figure 2 shows the geometrical structures and relative energies associated with the two initial C-H bond activation processes for the reaction of CrO+ with propane. The two processes differ based on the type of C-H bond being activated: Cα-H or Cβ-H.

The initial reactant complex on the sextet spin surface is higher in energy than the

reactants on the quartet surface, suggesting that the initial C-H activation proceeds exclusively on the quartet surface. As reported in a number of studies of metal oxide cations reacting with 10


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small hydrocarbons,18-29 the most energetically viable path to activating C-H bonds is via the extraction of the hydrogen by oxygen, aided through an agostic interaction. The transition state structure for the extraction of an α-H (4TS1-2 in Figure 2) exhibits coordination of Cr to both the β-C and the α-C from which the hydrogen is being extracted. The resulting intermediate (2q) is of similar structure, with the exception that the hydrogen is now attached completely to the oxygen. From Figure 2 it can be seen that the resulting α-H extraction from 1q to form 2q results in a lengthening of the Cr-O bond and a stronger bonding interaction between Cr and the carbons in the organic fragment. Other than the removal of an α-H, the organic fragment exhibits little change, including the apparent sp3-hybridization of the α-C from which the hydrogen was removed. Extraction of a β-H occurs through a similar process in which the transition state structure (4TS1-3 in Figure 2) involves the removal of the hydrogen by the oxygen. One marked difference in this structure from the previously mentioned transition state species is the coordination of Cr to only the β-C. The associated intermediate formed from complete removal of the hydrogen from the organic fragment (3q) resembles the corresponding transition state. As with the previous mechanism, a lengthening of the Cr-O bond is observed and little change can be seen in the organic framework. The energetics of the two H-extraction processes are also given in Figure 2.

As

mentioned earlier, the only energetically feasible reaction path for both processes is on the quartet surface. The reaction barriers to forming the Cr-hydroxide complexes 2q and 3q are relatively large (27 and 33 kcal/mol respectively), but the considerable stability of the initial complex 1q (-46 kcal/mol) means these barriers are still lower in energy than the initial reactants on the quartet surface. Though the initial structures on the sextet surface are considerably higher in energy than their quartet counterparts, the associated Cr-hydroxide complexes 2s and 3s (see 11



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Figure 3) are quite low in energy with respect to both the sextet and quartet reactants. These structures, despite their inaccessibility via typical reaction processes, are important in understanding the product distribution observed in the reaction of CrO+ with propane (vide infra). Thus, it is useful to relate these structures to their quartet counterparts. The α-H extraction product 2s has a significantly different structure than 2q for two reasons. The first is that the Cr-hydroxide moiety is coordinated only to the α-C from which the hydrogen was removed.

The second difference is that the corresponding α-C exhibits sp2-hybridzation,

suggesting that this carbon has radical or cationic character.

The Cr-C bonding orbital

determined from a CASSCF calculation indicated that this bond involves only one electron since the natural orbital occupation number (NOON) is 1.0. Thus, the sp2-hybridization observed for this carbon is likely due to it having radical character.

The structural differences between 3q

and 3s are less drastic, the only significant one being the Cr-C distance for the sextet structure being much greater (1.97 Å for 3q, 2.26 Å for 3s). The energy difference between 2q and 2s is nearly twice as large as that observed between 3q and 3s, likely due to the significant structural differences between 2q and 2s as well as the difference in the electronic structure associated with the α-C in the two structures. All of the final intermediates in the C-H activation mechanisms (2q, 2s, 3q, 3s) are important because each mechanism associated with an observed product from the reaction of CrO+ with propane can be traced back to one or more of these species.

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1.769 (1.759)

1.767 (1.755)

2.327 (2.312)

2.364 (2.369)

2s

MECP1

Erel = -39.3 (-40.0)

Erel = -37.3 (-37.7)

1.766 (1.755)

1.765 (1.752)

2.387 (2.397)

2.262 (2.258)

2.390 (2.426)

2.289 (2.298)

3s

MECP2

Erel = -44.7 (-45.5)

Erel = -43.4 (-44.0)

Figure 3. Geometrical structures and relative energies (in kcal/mol) at the M06-L (B3LYP) levels of theory of the two intermediates associated with C-H activation on the sextet surface (2s and 3s) and the associated minimum energy crossing points (MECPs) between the sextet and quartet surfaces. Bond lengths are in Ångstroms.

For the mechanisms associated with propanol and propene formation, a crossing between the initial reactant surface (quartet) and the higher lying sextet surface is necessary.

The

previously mentioned sextet minima 2s and 3s are very close in energy and structure to two minimum energy crossing points (MECPs), shown in Figure 3. In both cases, the MECP is 13



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nearly identical in energy to the associated sextet minimum (within 2 kcal/mol) and the bond lengths associated with the chromium atom are very similar as well.

These energies are

significantly higher than the associated quartet minima, but are quite thermodynamically stable with respect to the reactants. Thus, the possibility of a transition between spin states is not restricted by accessibility of the spin crossing in terms of energy or structure. Propanol Formation Mechanisms. Formation of both isomers of propyl alcohol requires a transition from the quartet spin surface to the sextet one. Figure 4 shows the two potential energy diagrams associated with the formation of 1-propanol and 2-propanol from CrO+ and propane. The formation of 1-propanol essentially begins with the formation of 2q and the corresponding transition through MECP1 to the sextet spin surface. The geometry and energy of the crossing point is very close to the sextet chromium hydroxide intermediate (2s), so the process resembles a single surface reaction once the spin transition occurs. Thus, the formation of the very stable chromium-propanol complex 4s is achieved by passage through the transition state (6TS2-4) in which the hydroxyl group in 2s is added to the unsaturated terminal carbon atom. The transition state leading to 4s is significantly higher in energy than intermediates 2q and 2s but is well below the initial reactant energy (-20 kcal/mol). The transition state on the quartet surface (4TS2-4) is around 24 kcal/mol higher in energy than its sextet counterpart. This is likely due to the difference in the coordination of the chromium atom in the two structures, with the CrC bond length in the sextet transition state being 2.33 Å while the corresponding bond length in the quartet structure is 2.84 Å. This weak interaction between chromium and carbon in the quartet transition state is a drastic change from intermediate 2q, where chromium forms two relatively strong bonds with carbon (2.17 and 1.99 Å from Figure 2). This leads to a very large energy barrier on the quartet surface of over 60 kcal/mol. The barrier on the sextet surface is 14


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much smaller (about 18 kcal/mol) and is likely due to the less drastic change in the Cr-C bond between 2s (2.31 Å) and the associated transition state (2.33 Å). The sextet intermediate 4s is considerably lower in energy than its quartet counterpart 4q (about 35 kcal/mol). This is not surprising since the structures are very similar in that they look like 1-propanol coordinated to the chromium cation, but the cation in the sextet state is known to be over 40 kcal/mol more stable than the quartet cation. While formation of both chromium-propanol intermediates 4q and 4s are feasible energetically, the final dissociation of the chromium ion is only thermodynamically favorable on the sextet surface.

1.831 (1.813) 1.831 1.831 (1.813) (1.813 (1.813) 2.116 ) (2.087)

1.981 (1.959)

1.833 (1.815)

2.116 (2.087) 1.480 (1.496)

1.983 (1.967)

2.300 (2.184)

1.500 (1.515)

1.881 (1.844)

2.332 (2.352)

2.097 (2.098)

1.876 (1.839)

2.050 (1.996) 1.458 (1.483)

2.494 (2.430)

2.208 (2.156)

2.049 (2.000)

1.495 (1.483)

Figure 4. Potential energy diagrams for the formation of 1-propanol (left) and 2-propanol (right) from CrO+ and propane. The relative energies (in kcal/mol) and geometrical structures (bond lengths in Ångstroms) are based on M06-L (B3LYP) calculations.

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The mechanism associated with the formation of 2-propanol resembles that of 1-propanol in many aspects. The process proceeds almost immediately through MECP2 which is close both structurally and energetically to the chromium hydroxide intermediate on the sextet surface (3s). A relatively small barrier (about 18 kcal/mol) on the sextet surface exists in which the hydroxyl group is added to the unsaturated interior carbon to form another very stable (-58 kcal/mol) chromium-propanol intermediate (5s). Formation of the associated quartet intermediate (5q) does occur through an overall energetically favorable process, but the barrier to this process is quite large (about 50 kcal/mol) and the resulting intermediate is about 33 kcal/mol higher in energy than the corresponding sextet intermediate (5s). As was the case for 1-propanol, the formation of 2-propanol is only energetically favorable on the sextet surface. Propene Formation Mechanisms. The formation of propene begins as all other mechanisms do, through the formation of either intermediate 2q or 3q. Since the second hydrogen required to be removed from the organic fragment must come from the carbon adjacent to the unsaturated carbon created in making either 2q or 3q, both structures lead to the same intermediate structure 6q (see Figure 5). A similar mechanism can be found on the sextet surface, leading from structures 2s and 3s to the CrOH2+-propene intermediate 6s. Extraction of the second hydrogen from the organic fragment is achieved in a manner similar to the first extraction, through the coordination of the hydrogen to the oxygen atom. While the energies of many of the quartet structures in Figure 5 are lower in energy than their sextet counterparts, the final intermediates (6q and 6s) show a different order, as do the dissociated products (see Table 1). The formation of propene from CrO+ and propane is likely due to a spin inversion based on thermodynamic arguments, though the quartet products are not much higher in energy than the initial reactants. It should also be noted that a number of factors have not been included in the reported energies (e.g., entropy), thus a determination of the thermodynamic stability cannot be absolutely made. The potential energy diagram in Figure 5 indicates 16


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that the surface crossings needed to form propene occurs after passing through the barriers associated with the second hydrogen extraction (4TS2-6 and 4TS3-6). Another crossing point between the quartet and sextet surfaces was located (MECP3 in Figure 5) and it resembles the quartet intermediate 6q both structurally and energetically. This MECP is considerably lower in energy than the previous two found in the propanol mechanisms (-55 kcal/mol).

1.904 (1.888) 1.771 (1.785) 2.068 (2.048) 2.116 (2.123)

1.889 (1.881)

1.987 (1.993)

2.090 (2.108)

1.965 (1.972)

2.057 (2.059)

MECP3

1.737 (1.756)

Erel = -54.1 (-54.6)

2.118 (2.157)

2.055 (2.038) 2.037 (2.074)

1.991 (2.020)

2.076 (2.068) 2.254 (2.261)

2.314 (2.308)

Figure 5. Geometrical structures and relative energies (in kcal/mol) determined at the M06-L (B3LYP) levels of theory for the intermediates and transition states associated with the formation of propene. Bond lengths are in Ångstroms.

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Ethene Formation Mechanism. The only thermodynamically favorable dissociation limit corresponding to ethene formation is of the same spin as the reactants. Thus, only quartet structures will be considered in the proposed mechanism. The formation of ethene from propane requires activation of both a C-H and a C-C bond. Thus, two possible mechanisms can be imagined for such a process: C-H activation followed by C-C activation or vice versa. For the reaction of FeO+ with propane, both mechanisms were characterized theoretically33 with the C-H activation followed by C-C activation being much more viable. Figure 6 shows the structures and energetics of the mechanism found for ethene formation from propane using CrO+.

1.750 (1.738) 2.009 (2.017)

2.096 (2.099)

2.300 (2.295)

1.732 (1.721)

1.732 (1.723) 2.169 (2.255)

2.267 (2.325) 1.987 (1.967)

1.973 (1.974) 2.312 (2.366)

Figure 6. Potential energy diagram and structures associated with the formation of ethene from CrO+ and propane via intermediate 2q. Relative energies (in kcal/mol) and bond lengths (in Ångstroms) were determined at the M06-L (B3LYP) level of theory.

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As was the case for FeO+, the most viable mechanism first involves C-H activation followed by C-C activation. Thus, the mechanism in Figure 6 begins at structure 2q followed by a transition state structure (4TS2-7) associated with the breaking of the bond between the saturated carbons on the organic fragment. As the C-C bond is breaking, the chromium atom forms a strong interaction with all three carbon atoms rather than just two as observed in structure 2q. Once the C-C bond is completely cleaved, the resulting intermediate structure 7q appears as though the chromium atom is binding two organic fragments: an ethene molecule and a methyl fragment. The ethene fragment bound to chromium appears to do so as one would expect for a cationic metal complex, via the π-bond. The methyl fragment appears to be bound through formation of a Cr-C σ-bond based on the bond distance and the sp3-hybridized nature of the carbon atom. All of the structures in Figure 6 are considerably lower in energy than the reactants, suggesting they readily form. However, the removal of the ethene molecule from the final intermediate complex 7q requires a significant amount of energy (36 kcal/mol), leading to a dissociation limit that is only slightly lower in energy than the reactants (-16 kcal/mol). H2 Formation Mechanisms. Based on previous experimental mass spectrometry experiments11, H2 is the most abundant product when CrO+ reacts with propane. While the thermodynamics and the fact that no spin surface crossing is needed to form H2 offer a good explanation as to why this process is the most highly favored, further analyses of possible mechanisms are needed to make a more definitive conclusion. The formation of H2 requires the extraction of two hydrogen atoms from the propane fragment. Both intermediates 2q and 3q are starting points for the mechanisms associated with forming H2, but not for the reasons one may initially consider. While both intermediates were formed via an H-atom extraction from the propane fragment, this H-atom does not appear to be one of the hydrogens found in H2. Thus, two more H-atoms must be extracted from the organic fragment to make H2. The next H-atom removed depends on which initial intermediate is considered, 2q or 3q. In either case, the most stable organic fragment one can imagine forming is propene. For both intermediates 2q and 3q, this is achieved by extraction of the corresponding H-atom (β-H for 2q, α-H for 3q) by the chromium atom (see Figure 7).

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Figure 7 shows the structures and energies associated with the formation of the first intermediates for the H2-formation mechanisms. One can see that the energetics of both processes parallel one another and lead to a single metal-hydride intermediate, 8q.

1.733 (1.720)

1.724 (1.713)

1.612 (1.606)

2.144 (2.139)

2.197 (2.221)

1.730 (1.718)

2.094 (2.097)

1.620 (1.615)

1.601 (1.591)

1.739 (1.728)

2.224 (2.251)

1.684 (1.680) 1.088 (1.041)

1.962 (1.943)

0.776 (0.766) 1.957 (1.938)

1.773 (1.758) 2.231 (2.258)

Figure 7. Potential energy diagram for the formation of H2 from CrO+ and propane. Reported relative energies (in kcal/mol) and bond lengths (in Ångstroms) were determined at the M06-L (B3LYP) levels of theory.

Upon formation of the metal-hydride intermediate 8q, three mechanisms associated with the final H-atom extraction are possible due to there being three distinct types of carbon atoms on the organic

20


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fragment. An interesting feature of each mechanism is that the associated transition state (4TS8-9, 4TS8-10, 4

TS8-11 in Figure 7) corresponds to the extraction of one of the H-atoms on the propene fragment by the

hydrogen atom attached to the chromium (see 4TS8-9 in Figure 7). Extraction of protons from sp2hybridized carbons in the propene fragment leads to quite large reaction barriers (20-25 kcal/mol) compared to the extraction of one of the protons from the sp3-hybridized carbon (about 4 kcal/mol) to form an allyl ligand. The resulting intermediates from the proton extraction (9q, 10q, 11q in Figure 7) show one similarity in that they exhibit an H2 molecule loosely coordinated to the cationic CrOH-organic fragment. The rest of the organometallic framework resembles the products these intermediates are associated with (see Figure 1). The potential energy diagram in Figure 7 shows that all three mechanisms are energetically favorable compared to the initial reactants, but the mechanism that forms the η3-complex with the organic fragment (9q) involves a low-energy barrier and leads to the most thermodynamically stable product. The lower energy barrier to forming 9q compared to those forming 10q and 11q is likely due to the difference between extracting a hydrogen atom from a saturated carbon to form a stable allyl ligand as opposed to an unsaturated carbon to form much more strained organic fragments (see Figure 1).

Discussion Experimentally, the reaction of CrO+ with propane leads to four distinct product distributions: hydrogen (47%), ethene (20%), propanols (20%), and propene (13%).11 The first two products can form without a crossing between spin surfaces, while the final two products do require a transition from the quartet spin surface to the sextet surface. Thus, it is not surprising that the majority of products formed are those that are found on the same spin surface as the reactants. The minor products propene, 1propanol, and 2-propanol appear to proceed through a crossing of the quartet and sextet potential energy surfaces. A quantitative analysis of product distributions would require dynamics calculations, which is beyond the scope of this work. However, comparison of proposed mechanisms based on gas-phase reactions of deuterated propane11 (propane-2,2-d2) to our computational results can lead to a better 21



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Page 22 of 33

qualitative understanding of the processes involved in the oxidation of propane by CrO+. For example, the reaction of propane-2,2-d2 with CrO+ leads to the formation of two forms of hydrogen in nearly identical amounts, H2 (25% total product) and HD (24% total product). The mechanisms suggested by Kang and Beauchamp11 that account for the formation of H2 and HD are essentially the same ones shown at the bottom of Figure 7. Successive extraction of hydrogen from each carbon atom can start with either extraction of a terminal hydrogen (2q) or an interior hydrogen (3q). The formation of HD would proceed through intermediate 2q while H2 would form through intermediate 3q, both mechanisms passing through intermediates 8q and 9q. Once the activated intermediate(s) are formed (2q, 3q), the reaction essentially proceeds completely downhill and is the most energetically favorable reaction path despite having the most intermediate steps. The formation of ethene leads to the highest energy dissociation limit of any of the products observed experimentally (see Figure 6). While this might not seem surprising, the reason for it being the least energetically favorable might be. The required cleavage of a C-C bond is surprisingly of little consequence energetically, particularly when compared to the initial C-H activation process. The barrier to breaking the C-C bond is about 39 kcal/mol lower in energy than the initial reactants and 20-25 kcal/mol lower in energy than the initial C-H activation barriers. The final dissociation step is the most energetically demanding process in the formation of ethene, with the dissociated products lying about 32 kcal/mol higher in energy than the final reaction intermediate (7q). Deuterated propene has been shown to produce two forms of ethene from the reaction with CrO+, C2H2D2 (13% total product) and C2H3D (10% total product). Based on this result, a mechanism was proposed11 in which CrO+ directly inserted into the C-C bond and various hydride shifts led to the distribution of the two deuterated forms of ethene. Our calculations suggest that direct insertion of CrO+ into the C-C bond is not occurring, but insertion does occur after the initial hydrogen extraction by oxygen (see Figure 6), specifically in structure 2q. However, the mechanism shown in Figure 6 can only account for the formation of C2H2D2. One possible mechanism that accounts for the formation of C2H3D is the insertion of the metal into one of the C-C

22


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bonds in 3q. Figure 8 shows the structures and energetics associated cleaving a C-C bond in 3q to form ethene. The overall process on the quartet surface is completely downhill in energy compared to the initial reactants and all barriers and intermediates are lower in energy than the final products as well. The process differs in two ways from the associated pathway involving intermediate 2q. First, the cleavage of the C-C bond in 3q occurs through what appears to be a barrierless process, as opposed to the activation barrier observed in the similar process involving 2q. The potential energy surface in the region of the resulting intermediate (12q) is relatively flat and attempts to locate a transition state at the B3LYP and M06-L levels were unsuccessful. A set of constrained optimizations in which the C-C bond was fixed at various intermediate lengths to those found in 12q and 3q led to a monotonically decreasing set of relative energies. The second difference in the mechanism is that formation of the product complex 7q requires a hydrogen-shift, the barrier to that shift (4TS12-7 in Figure 8) being relatively small and lower in energy than the reactants and associated products.

1.736 (1.724)

1.732 (1.721) 2.277 (2.293)

1.974 (1.962)

2.267 (2.325) 1.973 (1.974) 2.312 (2.366)

Figure 8.

Potential energy diagram and structures associated with the formation of ethene from

intermediate 3q. Relative energies (in kcal/mol) and bond lengths (in Ångstroms) were determined at the M06-L (B3LYP) levels of theory.

23



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The other minor products, propene and both propanols, likely form from spin-inversions based on the energies of the dissociation limits when spin is conserved (see Table 1) and these transitions presumably account for the observed lower yields. The crossings between spin surfaces for the propanol formation mechanisms occur very early in the reaction, during the C-H activation step. Whether forming 1-propanol or 2-propanol, the MECPs occur well below the reactant energies and at geometries that are similar to reactive intermediates (2s and 3s, respectively). Thus, the potential for surface hopping is likely not restricted based on energetic and structural factors, but on the coupling between the surfaces. The probability of transitioning between different spin states at an MECP is related to a number of factors, one of which is the size of the spin-orbit coupling (SOC) matrix element between the different spin states. Using a simple one-electron model, SOC matrix elements were determined at the MECP geometries located at the M06-L level. The MECPs located near the entrance channel of the reaction, MECP1 and MECP2, were found to have relatively small couplings, 5 cm-1 and 11 cm-1, respectively. Propene has the lowest yield of all products formed, despite the fact it has a number of viable pathways to formation. It is possible that the process occurs on a single spin surface since the products determined at both the M06-L and B3LYP levels of theory are only slightly higher in energy than the reactants (< 5 kcal/mol). A more likely scenario for the formation of propene involves a spin-inversion process, of which two energetically viable mechanisms have been presented (see Figure 5). One is where the spin transition occurs at the beginning of the mechanism (i.e., MECP1 or MECP2) and the other involves the transition occurring at the end of the reactive process (MECP3). The SOC matrix element determined at the MECP near the exit channel for the reaction forming propene (MECP3) is considerably larger (241 cm-1) than those for MECP1 and MECP2. However, the mechanisms presented in Figure 5 are not able to account for the observed reaction involving propane-2,2-d2. From Figure 5, the product one would obtain would be exclusively C3H5D since both processes involve the extraction of a terminal and interior hydrogen, only the order changes. However, the observed reaction11 indicates that the propene product is C3H4D2, suggesting a 1,3-dehydrogenation from propane. Figure 9 shows a viable

24


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reaction mechanism involving sextet intermediates and transitions states.

Assuming that the spin

transition between structures 2q and 2s is viable (which it would be if 1-propanol forms), the extraction of a hydrogen from the other end of the propane fragment occurs through an energetically favorable pathway and leads to a relatively stable intermediate (13s). The formation of the same cationic CrOH2-propene complex (6s) presented in the earlier mechanisms (see Figure 5) then proceeds through a hydrogen transfer from the interior carbon to a terminal carbon. The associated transition state (6TS13-6) is lower in energy than the reactants, though only slightly lower (7.3 kcal lower). Since no interior hydrogen atoms were abstracted by oxygen in these steps, the use of propane-2,2-d2 would lead to both deuterons remaining on the propene fragment.

2s

6s

Erel = -39.3 (-40.0)

Erel = -73.1 (-73.8)

66TS TS2-13 2-13

13s 13s

-8.0 EErelrel== -12.5 (-11.9) (-16.4)

-18.8 EErelrel == -20.7 (-23.0) (-24.9)

6TS

TS13-6 13-6

= -3.8 Erel rel = -7.3 (-2.1) (-5.6)

Figure 9. Formation of propene from 1,3-dehydrogenation of propane on the sextet surface. Relative energies (in kcal/mol) and bond lengths (in Ångstroms) were determined at the M06-L (B3LYP) levels of theory.

Conclusions Reaction mechanisms for each product formed from the gas-phase reaction of CrO+ with propane have been characterized at the B3LYP and M06-L levels of theory. All reaction paths leading to products begin with a C-H bond activation process initiated by the oxygen atom in CrO+. All intermediates and transition states on the reaction path leading to the most abundant product, H2, are lower in energy than

25



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the reactants and are of the same spin as the reactants (quartet). Similar H2-formation mechanisms have not been previously characterized in reactions of metal oxide cations (MO+) with small hydrocarbons. The dissociation limit associated with formation of H2 is also lower in energy than all other dissociation limits associated with the title reaction. The reaction paths leading to the formation of ethene also involve intermediates and transition states that are lower in energy than the reactants and have the same spin as the reactants. The C-C bond activation steps occur after the initial C-H bond activation and have relatively low activation barriers. Viable reaction paths leading to the least abundant products, 1-propanol, 2-propanol, and propene, likely require a transition between the reactant spin surface (quartet) and a sextet spin surface. Assuming a spin-inversion process occurs, reaction paths for each of these products involve intermediates and transition states lower in energy than the reactants. Minimum energy crossing points (MECPs) for each reaction path have been localized at the DFT level and spin-orbit coupling (SOC) matrix elements have been calculated using a one-electron model. The spin transitions for 1-propanol, 2-propanol, and propene appear to occur during the initial C-H activation process, though simple spin-orbit coupling calculations suggest the surfaces are not strongly coupled. While the likely reason for the lower yields for both isomers of propanol and propene are due to the required spin-inversion to form thermodynamically stable products, dynamics calculations are needed to fully understand the quantitative distribution of products. However, viable mechanisms have been provided to explain the products observed when a deuterated forms of propane is used (propane-2,2-d2).

Supporting Information. Energies and Cartesian coordinates for intermediates, transition states, and minimum energy crossing points. Acknowledgements. This work was supported by Research Corporation (#CC6834/6814). The authors thank the College of Liberal Arts and Sciences at Villanova University for partial financial support.

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References

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TOC Graphic

Reactants

Products C-C bond activation

CrO+ (quartet) + propane

C-H bond activation

Metal-mediated H-transfer

Two-state reactivity or spin-inversion (sextet)

33


ethene

H2

1-,2-propanol propene

Theoretical Investigation of the Gas-Phase Reaction of CrO+ with

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