32
Y. Shiota and K. Yoshizawa
3.3 Conversion of Methane to Methanol by FeO + , CoO + ,
and NiO +
Figure 4 shows the potential-energy diagrams for FeO
+ , CoO
+ , and NiO
+ with CH 4
along the entire reaction pathway. FeO
+ exhibits close-lying sextet and quartet spin
state potential energies that differ by 5.8 kcal/mol. A low-lying energy pathway in the
FeO
+ /CH 4 system is opened by a crossing of the sextet and quartet potential-energy
surfaces. Two spin-inversion junctions between the quartet and doublet surfaces are
involved near the RC, OFe
+ (CH 4 ), at the entrance channel and near the product
complex Fe
+ (CH 3 OH) at the exit channel. The energy profiles of the high-spin
and low-spin potential surfaces in the CoO
+ /CH 4 and NiO
+ /CH 4 systems are quite
similar to those of the FeO
+ /CH 4 system. In the sextet ground state, the interaction
between FeO
+ and CH 4 results in the formation of an RC with a binding energy
of 25.4 kcal/mol, as measured from the dissociation limit. The binding energies of
OCo
+ –CH 4 in the quintet ground state and ONi
+ –CH 4 in the quartet ground state
were calculated to be 25.4 kcal/mol and 28.9 kcal/mol, respectively, as measured
from the dissociation limit.
The TS1 of the sextet spin state in the FeO
+ /CH 4 system lies higher in energy than
the dissociation limit of FeO
+
+ CH 4 by 8.3 kcal/mol, whereas the potential energy
of TS1 in the quartet spin state decreases to −0.7 kcal/mol if we consider a quartet–
sextet spin inversion near TS1. The crossing between the sextet and quartet energy
surfaces leads to a substantial lowering of the activation energy. Similar crossing
points have been observed in the CoO
+ /CH 4 and NiO
+ /CH 4 systems. TS1 of the
quartet spin state in the NiO
+ /CH 4 system lies higher in energy than the dissociation
limit of NiO
+
+ CH 4 by 9.0 kcal/mol, whereas the potential energy of TS1 in the
doublet spin state decreases to −3.5 kcal/mol if we consider a quartet–doublet spin
inversion. These computational results readily explain the experimental observation
of high reactivity of FeO
+ and NiO
+ in the low-spin state. The relative energies of
TS1 in CoO
+ were 10.7 kcal/mol in the quintet state and 5.5 kcal/mol in the doublet
state. Despite a quintet–triplet spin inversion leading to a lowering of the activation
energy, the TS1 in the triplet state lies higher in energy than the dissociation limit.
Therefore, the C–H activation via TS1 in the CoO
+ /CH 4 system requires not only the
spin-inversion process but also additional energy. The HIs, HO–Fe
+ –CH 3 , HO–Co
+ –
CH 3 , and HO–Ni
+ –CH 3 are energetically more stable than with the corresponding
RCs by ~20 kcal/mol. The relative energies of TS2 in the FeO
+ /CH 4 system are −
7.7 kcal/mol in the sextet state and −16.4 kcal/mol in the quartet state. The relative
energies of TS2 in the CoO
+ /CH 4 and NiO
+ /CH 4 systems are −20.0 kcal/mol in the
triplet state and −32.9 kcal/mol in the doublet state. Because the potential energies
of TS2 are lower than those of TS1 in the FeO
+ /CH 4 , CoO
+ /CH 4 , and NiO
+ /CH 4
systems, the rate-determining step in the two-step concerted mechanism is not the
second-step reaction with the methyl migration but the first-step reaction that includes
C–H bond cleavage.
For a comparison of the reactions of MnO
+ , FeO
+ , CoO
+ , and NiO
+ with CH 4
on the basis of experimental data [28], the reaction efficiencies φ and the product
Y. Shiota and K. Yoshizawa
3.3 Conversion of Methane to Methanol by FeO + , CoO + ,
and NiO +
Figure 4 shows the potential-energy diagrams for FeO
+ , CoO
+ , and NiO
+ with CH 4
along the entire reaction pathway. FeO
+ exhibits close-lying sextet and quartet spin
state potential energies that differ by 5.8 kcal/mol. A low-lying energy pathway in the
FeO
+ /CH 4 system is opened by a crossing of the sextet and quartet potential-energy
surfaces. Two spin-inversion junctions between the quartet and doublet surfaces are
involved near the RC, OFe
+ (CH 4 ), at the entrance channel and near the product
complex Fe
+ (CH 3 OH) at the exit channel. The energy profiles of the high-spin
and low-spin potential surfaces in the CoO
+ /CH 4 and NiO
+ /CH 4 systems are quite
similar to those of the FeO
+ /CH 4 system. In the sextet ground state, the interaction
between FeO
+ and CH 4 results in the formation of an RC with a binding energy
of 25.4 kcal/mol, as measured from the dissociation limit. The binding energies of
OCo
+ –CH 4 in the quintet ground state and ONi
+ –CH 4 in the quartet ground state
were calculated to be 25.4 kcal/mol and 28.9 kcal/mol, respectively, as measured
from the dissociation limit.
The TS1 of the sextet spin state in the FeO
+ /CH 4 system lies higher in energy than
the dissociation limit of FeO
+
+ CH 4 by 8.3 kcal/mol, whereas the potential energy
of TS1 in the quartet spin state decreases to −0.7 kcal/mol if we consider a quartet–
sextet spin inversion near TS1. The crossing between the sextet and quartet energy
surfaces leads to a substantial lowering of the activation energy. Similar crossing
points have been observed in the CoO
+ /CH 4 and NiO
+ /CH 4 systems. TS1 of the
quartet spin state in the NiO
+ /CH 4 system lies higher in energy than the dissociation
limit of NiO
+
+ CH 4 by 9.0 kcal/mol, whereas the potential energy of TS1 in the
doublet spin state decreases to −3.5 kcal/mol if we consider a quartet–doublet spin
inversion. These computational results readily explain the experimental observation
of high reactivity of FeO
+ and NiO
+ in the low-spin state. The relative energies of
TS1 in CoO
+ were 10.7 kcal/mol in the quintet state and 5.5 kcal/mol in the doublet
state. Despite a quintet–triplet spin inversion leading to a lowering of the activation
energy, the TS1 in the triplet state lies higher in energy than the dissociation limit.
Therefore, the C–H activation via TS1 in the CoO
+ /CH 4 system requires not only the
spin-inversion process but also additional energy. The HIs, HO–Fe
+ –CH 3 , HO–Co
+ –
CH 3 , and HO–Ni
+ –CH 3 are energetically more stable than with the corresponding
RCs by ~20 kcal/mol. The relative energies of TS2 in the FeO
+ /CH 4 system are −
7.7 kcal/mol in the sextet state and −16.4 kcal/mol in the quartet state. The relative
energies of TS2 in the CoO
+ /CH 4 and NiO
+ /CH 4 systems are −20.0 kcal/mol in the
triplet state and −32.9 kcal/mol in the doublet state. Because the potential energies
of TS2 are lower than those of TS1 in the FeO
+ /CH 4 , CoO
+ /CH 4 , and NiO
+ /CH 4
systems, the rate-determining step in the two-step concerted mechanism is not the
second-step reaction with the methyl migration but the first-step reaction that includes
C–H bond cleavage.
For a comparison of the reactions of MnO
+ , FeO
+ , CoO
+ , and NiO
+ with CH 4
on the basis of experimental data [28], the reaction efficiencies φ and the product