38
Y. Shiota and K. Yoshizawa
intermediate to another hydroxy intermediate; we can estimate that the activation
energy for this transition state is less than 10 kcal/mol.
We summarize some features of the sextet and the quartet potential-energy
surfaces along the reaction pathway for the CH 4 –to–CH 3 OH conversion. The ground
state of FeO
+ is the sextet state; thus, that of the reactant complex is also the sextet
state because the interaction between CH 4 and FeO
+ is not strong in the reactant
complex. The potential-energy surface of the sextet state begins to increase from the
reactant complex and contacts with the quartet IRC valley at point SI. The sextet
potential-energy surface still continues in increase while maintaining contact with
the quartet potential-energy surface; finally, the sextet IRC valley contacts the quartet
potential-energy surface at point SII. After passing point SII, the sextet potentialenergy surface completely lies above the quartet potential-energy surface. Consequently, there is a crossing seam of the two potential-energy surfaces in the region
between SI and SII, where SI and SII are the energy-minimum and energy-maximum
crossing points, respectively, in the first crossing seam. After the IRCs of the sextet
and the quartet states, the molecular structures become different after passing TS1;
as a result, the second crossing seam appears at point SIII and disappears at point
SIV. The two potential-energy surfaces are separated again after passing point SIV,
with the sextet potential energy lying slightly above the quartet potential energy until
the PC is formed. The third crossing seam exists in the exit channel, and it plays a
dominant role in the elimination of product CH 3 OH.
4.2 Spin–Orbit Coupling of Methane Conversion
The rate-determining step of the CH 4 –to–CH 3 OH conversion was determined by the
activation energies of TS1 and TS2. These results indicate that the first step and the
first crossing seam played a key role in the rate constant of the reaction catalyzed
by FeO
+ because a lower-energy pathway for the CH 4 –to–CH 3 OH conversion by
FeO
+ is opened in the entrance channel by the crossing of the sextet and the quartet
potential-energy surfaces, leading to a substantial decrease in the barrier height of
TS1 from 31.1 to 22.1 kcal/mol at the B3LYP level of DFT. The molecular system
should change its spin multiplicity from the sextet state to the quartet state near this
crossing region.
SOC is important for evaluating the possibility for spin-nonconserving processes
involving high- and low-spin potential-energy surfaces. SOC induces mixing between
the low-lying quartet and sextet states of the bare FeO
+ species. Thus, the strength of
SOC controls the spin-inversion rate in the reaction mediated by FeO
+ . SOC constants
were computed by ab initio complete active space self-consistent field (CASSCF)
theory along the reaction pathway of the oxidation process of CH 4 , CH 4 + FeO
+
→
CH 3 OH + Fe
+ [37]. The process involves three spin crossing seams of the quartet
and sextet potential-energy surfaces. This electronic feature is the most important
aspect in this reaction pathway in that the FeO
+ /CH 4 system should change its spin
multiplicity from the sextet to the quartet state and that this effect should lead to
Y. Shiota and K. Yoshizawa
intermediate to another hydroxy intermediate; we can estimate that the activation
energy for this transition state is less than 10 kcal/mol.
We summarize some features of the sextet and the quartet potential-energy
surfaces along the reaction pathway for the CH 4 –to–CH 3 OH conversion. The ground
state of FeO
+ is the sextet state; thus, that of the reactant complex is also the sextet
state because the interaction between CH 4 and FeO
+ is not strong in the reactant
complex. The potential-energy surface of the sextet state begins to increase from the
reactant complex and contacts with the quartet IRC valley at point SI. The sextet
potential-energy surface still continues in increase while maintaining contact with
the quartet potential-energy surface; finally, the sextet IRC valley contacts the quartet
potential-energy surface at point SII. After passing point SII, the sextet potentialenergy surface completely lies above the quartet potential-energy surface. Consequently, there is a crossing seam of the two potential-energy surfaces in the region
between SI and SII, where SI and SII are the energy-minimum and energy-maximum
crossing points, respectively, in the first crossing seam. After the IRCs of the sextet
and the quartet states, the molecular structures become different after passing TS1;
as a result, the second crossing seam appears at point SIII and disappears at point
SIV. The two potential-energy surfaces are separated again after passing point SIV,
with the sextet potential energy lying slightly above the quartet potential energy until
the PC is formed. The third crossing seam exists in the exit channel, and it plays a
dominant role in the elimination of product CH 3 OH.
4.2 Spin–Orbit Coupling of Methane Conversion
The rate-determining step of the CH 4 –to–CH 3 OH conversion was determined by the
activation energies of TS1 and TS2. These results indicate that the first step and the
first crossing seam played a key role in the rate constant of the reaction catalyzed
by FeO
+ because a lower-energy pathway for the CH 4 –to–CH 3 OH conversion by
FeO
+ is opened in the entrance channel by the crossing of the sextet and the quartet
potential-energy surfaces, leading to a substantial decrease in the barrier height of
TS1 from 31.1 to 22.1 kcal/mol at the B3LYP level of DFT. The molecular system
should change its spin multiplicity from the sextet state to the quartet state near this
crossing region.
SOC is important for evaluating the possibility for spin-nonconserving processes
involving high- and low-spin potential-energy surfaces. SOC induces mixing between
the low-lying quartet and sextet states of the bare FeO
+ species. Thus, the strength of
SOC controls the spin-inversion rate in the reaction mediated by FeO
+ . SOC constants
were computed by ab initio complete active space self-consistent field (CASSCF)
theory along the reaction pathway of the oxidation process of CH 4 , CH 4 + FeO
+
→
CH 3 OH + Fe
+ [37]. The process involves three spin crossing seams of the quartet
and sextet potential-energy surfaces. This electronic feature is the most important
aspect in this reaction pathway in that the FeO
+ /CH 4 system should change its spin
multiplicity from the sextet to the quartet state and that this effect should lead to