Theoretical Study of the Direct Conversion of Methane …
35
been analyzed in terms of the corresponding potential-energy surfaces. In this reaction, the crossing of the quartet and sextet potential-energy surfaces occurs twice:
once in the entrance channel, and once in the exit channel. The extent of spin–orbit
coupling (SOC) is relatively large in the entrance channel, and it decreases along
the oxidation process, approaching zero in the exit channel. The overall reaction is
limited by SOC effects at spin-inversion points. It turns out that, in addition to the
classical factors such as the potential barrier heights, the surface crossing and the
SOC factor play important roles because a crossing between the high-spin and the
low-spin states constitutes a distinct mechanistic step along the reaction coordinate.
This phenomenon, known as “two-state reactivity,” is likely to be a key feature in
organometallic chemistry [65].
4.1 Crossing Seams of Potential-Energy Surfaces
Crossing seams and spin-inversion processes are discussed in this subsection. The
B3LYP functional predicts a lowering of the activation energy to 22.1 kcal/mol
through spin inversion. As previously discussed, the transition is expected to occur
from the ground sextet state to the lowest quartet state in the region prior to TS1. To
obtain more detailed information about the potential-energy surfaces, we performed
single-point computations of the sextet state as a function of the structural change
along the intrinsic reaction coordinate (IRC) of the quartet state and vice versa; such
analyses will indicate the energy-minimum and energy-maximum crossing points
[34]. The crossing seam of high- and low-spin potential-energy surfaces satisfies
the constraint of high-spin energy = low-spin energy. Because the crossing seam
shows the line as a ridge between potential-energy surfaces, a crossing seam plays an
important role in the nonadiabatic transition between the potential-energy surfaces.
The energy profiles for the high- and low-spin states are displayed in Figs. 6 and 7.
One crossing-seam point (SI) is on the quartet IRC path, and three crossing-seam
points (SII, SIII, and SIV) are on the sextet IRC path.
The solid and the dotted lines in Fig. 6 indicate the computed potential-energy
profiles of the quartet and the sextet states, respectively, as a function of the structural change along the quartet IRC. The relative energies are measured from the
total energy of the reactant complex of the sextet state as a standard. The activation energy for TS1 on the sextet surface is 38.5 kcal/mol, and the exothermicity
is ~20.0 kcal/mol. The potential energy for the TS1 on the quartet surface is lower
than the sextet potential energy by 13.9 kcal/mol. As shown in Fig. 6a, the first
crossing-seam point, SI, is observed at s = −2.80 with an energy of 13.9 kcal/mol.
The quartet energy surface begins to cross the sextet surface from SI because the
sextet energy on the sextet IRC is still more stable than the quartet energy on the
quartet IRC. Once SI has been reached, the quartet IRC continues a stable pathway
toward PC and the energy gap is ~15 kcal/mol in the region between TS1 and TS2.
The relative energies for TS2 in the quartet and sextet states are 5.93 kcal/mol and
21.8 kcal/mol, respectively. Because the relative energy for TS2 in the sextet spin
35
been analyzed in terms of the corresponding potential-energy surfaces. In this reaction, the crossing of the quartet and sextet potential-energy surfaces occurs twice:
once in the entrance channel, and once in the exit channel. The extent of spin–orbit
coupling (SOC) is relatively large in the entrance channel, and it decreases along
the oxidation process, approaching zero in the exit channel. The overall reaction is
limited by SOC effects at spin-inversion points. It turns out that, in addition to the
classical factors such as the potential barrier heights, the surface crossing and the
SOC factor play important roles because a crossing between the high-spin and the
low-spin states constitutes a distinct mechanistic step along the reaction coordinate.
This phenomenon, known as “two-state reactivity,” is likely to be a key feature in
organometallic chemistry [65].
4.1 Crossing Seams of Potential-Energy Surfaces
Crossing seams and spin-inversion processes are discussed in this subsection. The
B3LYP functional predicts a lowering of the activation energy to 22.1 kcal/mol
through spin inversion. As previously discussed, the transition is expected to occur
from the ground sextet state to the lowest quartet state in the region prior to TS1. To
obtain more detailed information about the potential-energy surfaces, we performed
single-point computations of the sextet state as a function of the structural change
along the intrinsic reaction coordinate (IRC) of the quartet state and vice versa; such
analyses will indicate the energy-minimum and energy-maximum crossing points
[34]. The crossing seam of high- and low-spin potential-energy surfaces satisfies
the constraint of high-spin energy = low-spin energy. Because the crossing seam
shows the line as a ridge between potential-energy surfaces, a crossing seam plays an
important role in the nonadiabatic transition between the potential-energy surfaces.
The energy profiles for the high- and low-spin states are displayed in Figs. 6 and 7.
One crossing-seam point (SI) is on the quartet IRC path, and three crossing-seam
points (SII, SIII, and SIV) are on the sextet IRC path.
The solid and the dotted lines in Fig. 6 indicate the computed potential-energy
profiles of the quartet and the sextet states, respectively, as a function of the structural change along the quartet IRC. The relative energies are measured from the
total energy of the reactant complex of the sextet state as a standard. The activation energy for TS1 on the sextet surface is 38.5 kcal/mol, and the exothermicity
is ~20.0 kcal/mol. The potential energy for the TS1 on the quartet surface is lower
than the sextet potential energy by 13.9 kcal/mol. As shown in Fig. 6a, the first
crossing-seam point, SI, is observed at s = −2.80 with an energy of 13.9 kcal/mol.
The quartet energy surface begins to cross the sextet surface from SI because the
sextet energy on the sextet IRC is still more stable than the quartet energy on the
quartet IRC. Once SI has been reached, the quartet IRC continues a stable pathway
toward PC and the energy gap is ~15 kcal/mol in the region between TS1 and TS2.
The relative energies for TS2 in the quartet and sextet states are 5.93 kcal/mol and
21.8 kcal/mol, respectively. Because the relative energy for TS2 in the sextet spin