Comparison of structures and energies of CH₅^2+• with CH₄^+• and their possible role in superacidic methane activation

Abstract

Contrary to previous theoretical studies at the UHF/6-31G* level, the methonium radical dication CH₅²⁺ is not a C_s symmetrical structure with a 2e—3c bond but a C_2v symmetrical structure 1 with two 2e—3c bonds (at the UHF/6-31G**, UMP2/6-31G**, and UQCISD(T)/6-311G** levels). The C_s symmetrical structure is not even a minimum at the higher level of calculations. The four hydrogen atoms in 1 are bonded to the carbon atom by two 2e—3c bonds and the fifth hydrogen atom by a 2e—2c bond. The unpaired electron of 1 is located in a formal p-orbital (of the sp²-hybridized carbon atom) perpendicular to the plane of the molecule. Hydrogen scrambling in 1 is however extremely facile, as is in other C₁ cations. It is found that the protonation of methane to CH₅⁺ decreases the energy for subsequent homolytic cleavage resulting in the exothermic (24.1 kcal/mol) formation of CH₄^+•. Subsequent reaction with neutral methane while reforming CH₅⁺ gives the methyl radical enabling reaction with excess methane to ethane and H₂. The overall reaction is endothermic by 11.4 kcal/mol, but offers under conditions of oxidative removal of H₂ an alternative to the more energetic carbocationic conversion of methane.

Activation of alkanes, main components of petroleum and natural gas, is an important area of chemistry. Consequently, knowledge of the parent methane cations and dications are of great significance. There have been many experimental and theoretical studies of methane cations and dications (1–3). The methane radical cation, CH₄^+• is the parent ion in mass spectrometry. In an early PNDO study by Olah and Klopman (4) the structure of CH₄^+• was found to have C_2v symmetry and can be considered as CH₂^+• radical cation complexed with a hydrogen molecule involving a three-center two-electron (2e—3c) bond. The 2e—3c unit is perpendicular to the plane of the molecule. High level ab initio calculations are in agreement with this conclusion (ref. 5 and references therein). Isoelectronic boron analog of CH₄^+• is neutral BH₄^•, also has similar C_2v symmetrical structure (6). Methane dication CH₄²⁺ have also been observed in the gas phase (7–11). Planar C_2v symmetrical structure is preferred for the CH₄²⁺ as shown by Wong and Radom (12). Earlier calculations predicted (13, 14) a square planar D_4h symmetrical structure for the CH₄²⁺ dication. The sp²-hybridized carbon atom of CH₄²⁺ contains a 2e—3c bond and an empty p-orbital perpendicular to the plane of the molecule.

CH₅⁺ is considered the parent of nonclassical carbocations containing a five coordinate carbon atom. Recent extensive ab initio calculations by Marx and Parrinello (15) as well as by Müller and Kützelnigg (16) reconfirmed the preferred C_s symmetrical structure (17, 18) for the CH₅⁺ cation with a 2e—3c bond as originally suggested by Olah and coworkers (19, 20). The structure can be viewed as a proton inserted into one of the C—H σ bonds of methane to form a 2e—3c bond between carbon and two hydrogen atoms. At the same time ready bond-to-bond (polytopal) proton migration makes it a rather fluxional molecule (19, 20), the process involving extremely low barriers (17, 18).

The five-coordinate methonium radical dication, CH₅^2+•, was first observed in the gas phase by charge-stripping mass spectrometry by Proctor et al. (9). Later the dication was also observed in the gas phase by Stahl et al. (10) and by Holmes and coworkers (11). Stahl et al. (10) calculated the structure of CH₅^2+• at the ab initio UHF/6-31G* level. They concluded (10) that the C_s symmetrical structure is the global minimum for the dication with a 2e—3c bonding interactions. We recently reported (21) that the planar D_5h symmetric structure 5 is an energy minimum for the CH₅³⁺ trication. On the other hand, our calculations showed that the energy-minimum structure of isoelectronic boron analog, the BH₅²⁺ dication has the planar C_2v symmetric structure 6, with two 2e—3c bonds (21).

We report now that at the higher levels of theory the methonium radical dication CH₅^2+• has not a C_s symmetrical structure with a 2e—3c bond but a C_2v symmetrical structure with two 2e—3c bonds. The C_s symmetrical structure is not even an energy minimum at this higher levels of calculations. We also report the results of our theoretical investigations of the reactions of CH₄^+• 4 with H^• and for comparison the related reaction of protonation of methane.

The geometry optimizations and frequency calculations were performed at the ab initio unrestricted UHF/6-31G**, UMP2/6-31G**, and UQCISD(T)/6-311G** levels (restricted calculations were performed for CH₄, C₂H₆ and CH₅⁺) (22; note that all calculations were performed by using Gaussian 94). From calculated frequencies, the optimized structures were characterized as minima or transition structure. For improved energy, single point energies at UMP4(SDTQ)/6-31G** level on UMP2/6-31G** optimized geometries and at UCCSD(T)/cc-pVTZ (23) level on UQCISD(T)/6-311G** optimized geometries were computed. Calculated energies are given in Table 1. The ab initio calculation using unrestricted (U) approach and frozen-core (fc) approximation were performed throughout. The symbols U and fc have been dropped for simplicity.

The C_2v symmetrical structure 1 and C_s symmetrical structure 2 were found to be minima on the potential energy surface (PES) of CH₅^2+• at the HF/6-31G** level as indicated by their frequency calculations (NIMAG = 0) at the same level.

The structure 2 lies 1.0 kcal/mol higher than 1 at this level of calculations (Table 1). At the higher correlated level of MP2/6-31G** structure 1 was found to be the only minimum on the potential energy surface of CH₅^2+•. At the MP2/6-31G** level 2 is not even a minimum on the PES. The structure 2 turned out to be the transition state of the rotation of one of the 2e—3c unit around its axis as indicated by the frequency calculations (NIMAG = 1) at the same level. The structure 2 lies only 1.3 kcal/mol higher than 1 at the this level of calculations. Rotation of 2e—3c unit of 1 around its axis therefore would be facile. We have located C₂ symmetrical transition structure 3 for intramolecular hydrogen transfer in the cation 1. For comparison we also calculated the structure of CH₄^+• 4. Structure 1 can be viewed as a proton inserted into one of the σ non-2e—3c C—H bonds of CH₄^+• 4 to form an additional 2e—3c bond between carbon and a hydrogen atom. The dissociation of 1 into CH₄^+• 4 and H⁺ was found to be exothermic by 80.1 kcal/mol (Eq. 1). We also calculated the adiabatic ionization energies (IE_a) of CH₄ and CH₅²⁺ (Table 2). Calculated IE_a of CH₄ and CH₅⁺ are 12.6 eV and 21.7 eV, respectively, agree very well with the experimental ionization energies of 12.6 eV (24) and 21.6 eV (10).

Another possible C_s structure 5 of CH₅^2+• was found to be 1.6 kcal/mol less stable than the structure 1 at the MP4(SDTQ)/6-31G**//MP2/6-31G** level. This is also a transition state of the rotation of the 2e—3c unit around its axis as indicated by its frequency calculations (NIMAG = 1) at the MP2/6-31G**//MP2/6-31G** level which again indicates the facile rotation of 2e—3c unit around its axis in 1.

Calculations at even higher level of theory also favor the C_2v structure 1. Optimization at the QCISD(T)/6-311G** level shows that structure 1 is 1.8 kcal/mol more stable than the structure 2. Frequency calculations at the QCISD(T)/6-311G**//QCISD(T)/6-311G** level again show that structure 1 is a minimum and structure 2 is a transition state. Our highest level of calculations [at the CCSD(T)/cc-pVTZ//QCISD(T)/6-311G** level] similarly show that 1 is more stable than 2 by 1.6 kcal/mol.

Structure 1 resembles a complex between CH^2+• and two hydrogen molecules resulting in the formation of two 2e-3c bonds. The sp²-hybridized carbon atom of 1 possesses a formal p-orbital (containing a single electron) perpendicular to the plane of the molecule. The plane of each of the 2e—3c units are rotated 90° around its axis from the plane of the molecule. The C—H bond distance in the 2e—3c bonds is 1.238 Å at the MP2/6-31G** level. This is slightly longer than that found in the 2e—3c C—H bonds (1.181 Å) of CH₄^+• 4 at the same theoretical level. The non-2e—3c interacting C—H bond distance of 1.101 Å in 1 is also slightly longer than that of 4. On the other hand, the calculated H—H distance in the 2e—3c interactions of 1.005 Å is only slightly shorter than that of 2e—3c interaction of 4 (1.077 Å).

Optimizations of the structures 1–4 at the QCISD(T)/6-311G** level changed the geometries very little. The C—H and H—H bonds become slightly longer. The transition structure 3 for intramolecular hydrogen transfer in the cation 1 lies only 3.9 kcal/mol higher in energy than structure 1 at the CCSD(T)/cc-pVTZ//QCISD(T)/6-311G** level. However, including zero point vibrational (ZPE) energy this is reduced to 1.0 kcal/mol (Table 1). Hydrogen scrambling in 1 therefore is extremely facile. This type of facile hydrogen scrambling was also found for CH₄²⁺ (12), CH₅⁺ (16–18), CH₆²⁺ (25, 26), and CH₇³⁺ (27). Thus, it is clear that the most of the C₁ carbocations containing one or more 2e—3c bond can undergo very readily low energy bond to bond rearrangements as postulated in case of CH₅⁺ by Olah et al. as early as 1969 (19, 20).

We have also investigated the related reactions of CH₄^+• 4 with H^• and with methane, as well as the protonation of methane. The reaction of H^• with CH₄^+• 4 (Eq. 2; see Table 3) was found to be exothermic by 105.1 kcal/mol. In comparison the reaction of H⁺ with CH₄ is exothermic by 129.2 kcal/mol (Eq. 3). These results suggest that the gas phase dissociation of CH₅⁺ into CH₄^+• 4 and H^• is about 24 kcal/mol more favorable than the gas phase dissociation of CH₅⁺ into CH₄ and H⁺. On the other hand, the reaction of CH₄^+• 4 with methane to form CH₅⁺ and CH_3• is only exothermic by 1.2 kcal/mol (Eq. 4).

In fact, the radiolysis of solid methane in liquid argon at 77 K by γ rays was shown by Libby and coworkers (28–30) to give polycondensates of an average molecular formula C₂₀H₄₀. It was considered that the radiolysis of methane gives CH₄^+•, which in the presence of excess methane reacts according to CH₄^+• + CH₄ = CH₅⁺ + CH_3⋅. Subsequent polymerization would involve ion molecule reactions (CH₄ + C_n⁺H_2n+1 = H₂ + C_n+1⁺H_2n+3) followed by neutralization to form the heavier hydrocarbons (29, 30).

The exothermic protonation of methane offers a possibility for subsequent more facile homolytic cleavage resulting in overall exothermic formation of CH₄^+• by 24.1 kcal/mol.

In contrast, the one electron oxidation of methane requires 289.6 kcal/mol.

Subsequent reaction with neutral methane while reforms CH₅⁺ gives the methyl radical enabling reaction with excess methane to give ethane. The overall reaction is endothermic by 11.4 kcal/mol.

H⋅ can give subsequently H₂ (2 H^• → H₂) or react further with CH₄ (CH₄ + H^• → CH₃^• + H2). The protolytic activation of methane with subsequent homolytic cleavage offers an alternative to the carbocationic higher energy conversion of methane.

Hydrogen must be oxidatively removed as the overall reaction of 2 CH₄ → C₂H₆ + H₂ is endothermic by 15.4 kcal/mol.

In conclusions, the present high level ab initio study at the HF/6-31G**, MP2/6-31G**, and QCISD(T)/6-311G** levels indicates that the C_2v symmetrical structure 1 is the only minimum on the potential energy surfaces of CH₅^2+•. This is in contrast to the previously reported ab initio calculated C_s symmetrical structure of CH₅^2+• at the HF/6-31G* level (with only one 2e—3c bond) (10). The optimized structure shows that the four hydrogen atoms in 1 are bonded to the carbon atom by two 2e—3c bonds and the fifth by a 2e—3c bond. The sp²-hybridized carbon atom of 1 possesses a formal p-orbital (containing an unpaired electron) perpendicular to the plane of the molecule. The plane of each of the 2e—3c units are rotated 90° around its axis from the plane of the molecule. The transition structure, 3, was located for the intramolecular hydrogen transfer in the cation 1, which indicates that the hydrogen scrambling in 1 should be facile. It was also pointed out that the protonation of methane to CH₅⁺ offers a possibility for subsequent faciliated homolytic cleavage resulting in the overall exothermic formation of CH₄^+• by 24.1 kcal/mol. Subsequent reaction with neutral methane gives the methyl radical-enabling reaction with excess methane to give ethane offering an alternative for the carbocationic condensation of methane. Oxidative removal of hydrogen allows the otherwise overall endothermic (by 11.4 kcal/mol) reaction to proceed.

Figure .

Structure 1

Figure .

Structure 2

Table 1.

Total energies (-au) and relative energies (kcal/mol)

	Energies†			Relative energies
	1	2	3	1	2	3
HF/6-31G**//HF/6-31G**	39.63641 (0)	39.63486 (0)	39.62709 (1)	0.0	1.0	5.9
MP2/6-31G**//MP2/6-31G**	39.77365 (0)	39.77153 (1)	39.76819 (1)	0.0	1.3	3.4
ZPE‡	(25.7)	(24.6)	(22.8)
MP4(SDTQ)/6-311G**//MP2/6-31G**	39.81563	39.81296	39.80950	0.0	1.7	3.9
QCISD(T)/6-311G**//QCISD(T)/6-311G**	39.81777 (0)	39.81493 (1)	39.81129 (1)	0.0	1.8	4.1
CCSD(T)/cc-pVTZ//QCISD(T)/6-311G**	39.84519	39.84258	39.83903	0.0	1.6	3.9
Final relative energies§				0.0	0.5	1.0

^†Number of imaginary frequencies in parentheses.

^‡Zero point vibrational energies (ZPE) at MP2/6-31G**//MP2/6-31G** scaled by a factor of 0.93.

^§Final relative energies based on CCSD(T)/cc-pVTZ//QCISD(T)/6-311G**+ZPE.

Figure .

Structure 3

Figure .

Structure 4

Table 2.

Theoretical and experimental ionization energies in eV (kcal/mol) of CH₄ and CH₅⁺

	Theoretical IEa	Experimental
CH4	12.6† (289.6)	12.6‡ (290.6)
CH5+	21.7† (4.97)	21.6§ (496.8)

^†At the CCSD(T)/cc-pVTZ//QCISD(T)/6-311G** + ZPE level.

^‡Taken from ref. 27.

^§Taken from ref. 10.

Figure .

Structure 5

Table 3.

Computed thermodynamic energies for various reactions

No.	Equation	ΔH† (kcal/mol)
1	CH4+•(4) + H+ → CH52+•(1)	+80.9
2	CH4+•(4) + H → CH5+	−105.1
3	CH4 + H+ → CH5+	−129.2
4	CH4+•(4) + CH4 → CH5+ + CH3•	−1.2
5	CH4 + CH3• → C2H6 + H•	+12.6
6	2 CH4 → C2H6 + H2	+15.4

^†At the CCSD(T)/cc-pVTZ//QCISD(T)6-311G** + ZPE level.