Theoretical Study of the Direct Conversion of Methane …
29
The formation of the PC corresponding to M
+ (CH 3 OH) occurs in a concerted
manner via 1,2-methyl migration on HI. The potential-energy surface of the singlet
state in the ScO
+ /CH 4 system lies below that of the triplet state in the ScO
+ /CH 4
system, and their relative order is reversed in TS2, as shown in Fig. 2. Thus, there
should be a crossing of the triplet and singlet potential-energy surfaces that occurs
near the region where TS2 is formed. Similar crossings should also occur in the
TiO
+ /CH 4 and VO
+ /CH 4 systems.
In this section, we consider the reverse reaction: M
+
+ CH 3 OH → MO
+
+ CH 4 .
Irigoras, Fowler, and Ugalde [33] carried out ab initio calculations for the ground
state of the analogous reverse process, MO
+
+ H − H, formed by the reaction of
M
+
+ H 2 O in the gas phase. The potential-energy surfaces indicate that the lowspin first excited state should provide high reactivity because of the low-spin surface
leading to MO
+
+ CH 4 without a spin-forbidden surface crossing. The energetics
of the early transition-metal MO
+ complexes indicate that the reverse reactions are
preferred over the corresponding forward reactions. These calculations explain an
experimental observation that the early transition metals prefer an oxygen acceptor
over an oxygen donor.
3.2 Conversion of Methane to Methanol by CrO + and MnO +
Figure 3 shows computed potential-energy diagrams along the entire reaction
pathway, CrO
+
+ CH 4 → Cr
+
+ CH 3 OH, in the quartet and doublet states. The chemistry of CrO
+ and MnO
+ complexes shows the bridging between the early and the
late transition-metal MO
+ complexes. Kang and Beauchamp [18, 19] carried out the
gas-phase reactions of CrO
+ with alkanes and found that CrO
+ can convert ethane to
ethanol without forming a byproduct. Because the high-spin sextet potential-energy
surface lies above the low-spin quartet potential-energy surface, a crossing between
the sextet and quartet surfaces occurs only once near TS2. In the quartet ground state,
CrO
+ reacts with CH 4 , and the binding energy for the RC, OCr
+ –(CH 4 ), was calculated to be 21.5 kcal/mol. TS1 in the CrO
+ /CH 4 system differs from those in the other
early transition-metal MO
+ /CH 4 systems (e.g., ScO
+ , TiO
+ , and VO
+ /CH 4 ) because
TS1 lies at a lower energy that the dissociation limit CrO
+
+ CH 4 by 0.7 kcal/mol.
Because the initial energy is sufficient for passing over TS1, the reaction efficiency of
CrO
+ for the H-atom abstraction should be substantial compared with those of ScO
+ ,
TiO
+ , and VO
+ . The quartet HI, CH 3 –Cr
+ –OH, was calculated to be −34.2 kcal/mol,
as measured from the dissociation limit.
In TS2, the potential-energy surface of the quartet state lies below that of the sextet
state and their relative positions are reversed. TS2 of the sextet spin state is more
stable than that of the quartet spin state, and the stabilization energy is 16.7 kcal/mol
because of a spin inversion from the quartet state to the sextet state. The spin inversion
contributes to the reaction via TS2. TS2 in the CrO
+ /CH 4 system was calculated to
be −6.3 kcal/mol in the sextet spin sate, whereas the product complex of the sextet
spin state was calculated to be −45.3 kcal/mol. The spin-conserving process in
29
The formation of the PC corresponding to M
+ (CH 3 OH) occurs in a concerted
manner via 1,2-methyl migration on HI. The potential-energy surface of the singlet
state in the ScO
+ /CH 4 system lies below that of the triplet state in the ScO
+ /CH 4
system, and their relative order is reversed in TS2, as shown in Fig. 2. Thus, there
should be a crossing of the triplet and singlet potential-energy surfaces that occurs
near the region where TS2 is formed. Similar crossings should also occur in the
TiO
+ /CH 4 and VO
+ /CH 4 systems.
In this section, we consider the reverse reaction: M
+
+ CH 3 OH → MO
+
+ CH 4 .
Irigoras, Fowler, and Ugalde [33] carried out ab initio calculations for the ground
state of the analogous reverse process, MO
+
+ H − H, formed by the reaction of
M
+
+ H 2 O in the gas phase. The potential-energy surfaces indicate that the lowspin first excited state should provide high reactivity because of the low-spin surface
leading to MO
+
+ CH 4 without a spin-forbidden surface crossing. The energetics
of the early transition-metal MO
+ complexes indicate that the reverse reactions are
preferred over the corresponding forward reactions. These calculations explain an
experimental observation that the early transition metals prefer an oxygen acceptor
over an oxygen donor.
3.2 Conversion of Methane to Methanol by CrO + and MnO +
Figure 3 shows computed potential-energy diagrams along the entire reaction
pathway, CrO
+
+ CH 4 → Cr
+
+ CH 3 OH, in the quartet and doublet states. The chemistry of CrO
+ and MnO
+ complexes shows the bridging between the early and the
late transition-metal MO
+ complexes. Kang and Beauchamp [18, 19] carried out the
gas-phase reactions of CrO
+ with alkanes and found that CrO
+ can convert ethane to
ethanol without forming a byproduct. Because the high-spin sextet potential-energy
surface lies above the low-spin quartet potential-energy surface, a crossing between
the sextet and quartet surfaces occurs only once near TS2. In the quartet ground state,
CrO
+ reacts with CH 4 , and the binding energy for the RC, OCr
+ –(CH 4 ), was calculated to be 21.5 kcal/mol. TS1 in the CrO
+ /CH 4 system differs from those in the other
early transition-metal MO
+ /CH 4 systems (e.g., ScO
+ , TiO
+ , and VO
+ /CH 4 ) because
TS1 lies at a lower energy that the dissociation limit CrO
+
+ CH 4 by 0.7 kcal/mol.
Because the initial energy is sufficient for passing over TS1, the reaction efficiency of
CrO
+ for the H-atom abstraction should be substantial compared with those of ScO
+ ,
TiO
+ , and VO
+ . The quartet HI, CH 3 –Cr
+ –OH, was calculated to be −34.2 kcal/mol,
as measured from the dissociation limit.
In TS2, the potential-energy surface of the quartet state lies below that of the sextet
state and their relative positions are reversed. TS2 of the sextet spin state is more
stable than that of the quartet spin state, and the stabilization energy is 16.7 kcal/mol
because of a spin inversion from the quartet state to the sextet state. The spin inversion
contributes to the reaction via TS2. TS2 in the CrO
+ /CH 4 system was calculated to
be −6.3 kcal/mol in the sextet spin sate, whereas the product complex of the sextet
spin state was calculated to be −45.3 kcal/mol. The spin-conserving process in