Theoretical Study of the Direct Conversion of Methane …
39
a substantial decrease in the barrier heights of the transition states. An intersystem
crossing is expected to occur in the transition state for the C–H bond breaking by the
iron–oxo species.
Figure 8 shows computed potential-energy surfaces in the quartet state at the
CASSCF level and SOC values between the quartet and sextet states as a function
of reaction coordinate s. The reaction coordinate s locates the reactant complex at
s = 0, TS1 at s = 4.0, and the hydroxo intermediate at s = 10.0. According to the
B3LYP results, the energy gap between the low-lying quartet and ground sextet states
decreases to zero in the first crossing seam located near s = 1.3. The four quartet
states (
4
Δ 1 ,
4
Δ 2 ,
4
1 , and
4
2 ) exhibit a gradual and smooth change in potential
energies, as indicated in Fig. 8a. The relative energies are measured from the total
energy of the
4
Δ 1 state in the reactant complex as a standard. In the low-lying
4
Δ 1
state, the activation energy is 22.6 kcal/mol and this reaction step is 17.3 kcal/mol
exothermic. The potential energies of the
4
Δ 1 and
4
Δ 2 states are close-lying prior to
TS1. After the reaction passes through TS1, degenerate energies of the
4
Δ 1 and
4
Δ 2
states are separated. The
4
1 and
4
2 states in the reactant complex lie approximately
30 kcal/mol above the
4
Δ 1 state. After all, the
4
Δ 2 ,
4
1 , and
4
2 states lie much
higher than the
4
Δ 1 state in the hydroxo intermediate. Thus, the
4
Δ 2 ,
4
1 , and
4
2
states can be reasonably neglected in the spin inversion after TS1.
The SOC values between the four quartet states and the sextet state are indicated
in Fig. 8b. The
6
+
−
4
Δ SOC is a key to understanding the spin-forbidden transition
that occurs in the vicinity of the first crossing seam in which the spin multiplicity of
the ground state is changed from the sextet state to the quartet state. Starting from
133 cm
−1 at s = 0, the
6
+
−
4
Δ SOC values increase to 169.2 cm
−1 at s = 4.0.
The strength of the
6
+
−
4
Δ 1 SOC increases and the energy gap between the
6
+
and
4
Δ 1 states decreases as the reaction coordinate progresses. Thus, the
6
+
−
4
Δ 1 SOC is particularly effective in the spin transition. The
6
+
−
4
Δ 1 SOC values
start from 133 cm
−1 at s = 0, resulting in 128.4 cm
−1 at s = 4.0. This value is also
sufficiently large to contribute to the spin transition. Therefore, we expect that the
6
+
−
4
Δ 1 SOC and
6
+
−
4
Δ 2 SOC transitions should occur near the first crossing
seam. The
6
+
−
4
1 SOC and
6
+
−
4
2 SOC values of the reactant complex
are 500 and 430 cm
−1 , respectively. However, the
6
+
−
4
transition is unlikely
to contribute to the low-lying reaction pathway through the spin inversion because
the crossing seam between the
6
+ and
4
states lies above TS1 of the
4
Δ 1 state.
After C–H bond dissociation occurs in TS1, the
4
Δ 2 state lies 80 kcal/mol above
the
4
Δ 1 state. Therefore, only the
6
+
−
4
Δ 1 SOC substantially contributes to the
spin transition once the reacting system passes through TS1. The
6
+
−
4
Δ 1 SOC
value starts with 40.3 cm
−1 at s = 5.0 and continues to decrease to 4.5 cm
−1 at s =
7.0. After this minimum point, the
6
+
−
4
Δ 1 SOC value increases to 21.4 cm
−1 in
the hydroxo intermediate. The
6
+
−
4
Δ 1 SOC is relatively small after TS1. Our
analysis predicts that the spin inversion between the
6
+ and
4
Δ states should occur
in the vicinity of the first crossing seam (s = 1.3), whereas the spin inversion hardly
occurs after TS1 (s = 4.0).
The potential energy of the
4
Δ 1 state decreases after the system passes through
TS1, and the second crossing seam occurs in the vicinity of the hydroxo intermediate.
39
a substantial decrease in the barrier heights of the transition states. An intersystem
crossing is expected to occur in the transition state for the C–H bond breaking by the
iron–oxo species.
Figure 8 shows computed potential-energy surfaces in the quartet state at the
CASSCF level and SOC values between the quartet and sextet states as a function
of reaction coordinate s. The reaction coordinate s locates the reactant complex at
s = 0, TS1 at s = 4.0, and the hydroxo intermediate at s = 10.0. According to the
B3LYP results, the energy gap between the low-lying quartet and ground sextet states
decreases to zero in the first crossing seam located near s = 1.3. The four quartet
states (
4
Δ 1 ,
4
Δ 2 ,
4
1 , and
4
2 ) exhibit a gradual and smooth change in potential
energies, as indicated in Fig. 8a. The relative energies are measured from the total
energy of the
4
Δ 1 state in the reactant complex as a standard. In the low-lying
4
Δ 1
state, the activation energy is 22.6 kcal/mol and this reaction step is 17.3 kcal/mol
exothermic. The potential energies of the
4
Δ 1 and
4
Δ 2 states are close-lying prior to
TS1. After the reaction passes through TS1, degenerate energies of the
4
Δ 1 and
4
Δ 2
states are separated. The
4
1 and
4
2 states in the reactant complex lie approximately
30 kcal/mol above the
4
Δ 1 state. After all, the
4
Δ 2 ,
4
1 , and
4
2 states lie much
higher than the
4
Δ 1 state in the hydroxo intermediate. Thus, the
4
Δ 2 ,
4
1 , and
4
2
states can be reasonably neglected in the spin inversion after TS1.
The SOC values between the four quartet states and the sextet state are indicated
in Fig. 8b. The
6
+
−
4
Δ SOC is a key to understanding the spin-forbidden transition
that occurs in the vicinity of the first crossing seam in which the spin multiplicity of
the ground state is changed from the sextet state to the quartet state. Starting from
133 cm
−1 at s = 0, the
6
+
−
4
Δ SOC values increase to 169.2 cm
−1 at s = 4.0.
The strength of the
6
+
−
4
Δ 1 SOC increases and the energy gap between the
6
+
and
4
Δ 1 states decreases as the reaction coordinate progresses. Thus, the
6
+
−
4
Δ 1 SOC is particularly effective in the spin transition. The
6
+
−
4
Δ 1 SOC values
start from 133 cm
−1 at s = 0, resulting in 128.4 cm
−1 at s = 4.0. This value is also
sufficiently large to contribute to the spin transition. Therefore, we expect that the
6
+
−
4
Δ 1 SOC and
6
+
−
4
Δ 2 SOC transitions should occur near the first crossing
seam. The
6
+
−
4
1 SOC and
6
+
−
4
2 SOC values of the reactant complex
are 500 and 430 cm
−1 , respectively. However, the
6
+
−
4
transition is unlikely
to contribute to the low-lying reaction pathway through the spin inversion because
the crossing seam between the
6
+ and
4
states lies above TS1 of the
4
Δ 1 state.
After C–H bond dissociation occurs in TS1, the
4
Δ 2 state lies 80 kcal/mol above
the
4
Δ 1 state. Therefore, only the
6
+
−
4
Δ 1 SOC substantially contributes to the
spin transition once the reacting system passes through TS1. The
6
+
−
4
Δ 1 SOC
value starts with 40.3 cm
−1 at s = 5.0 and continues to decrease to 4.5 cm
−1 at s =
7.0. After this minimum point, the
6
+
−
4
Δ 1 SOC value increases to 21.4 cm
−1 in
the hydroxo intermediate. The
6
+
−
4
Δ 1 SOC is relatively small after TS1. Our
analysis predicts that the spin inversion between the
6
+ and
4
Δ states should occur
in the vicinity of the first crossing seam (s = 1.3), whereas the spin inversion hardly
occurs after TS1 (s = 4.0).
The potential energy of the
4
Δ 1 state decreases after the system passes through
TS1, and the second crossing seam occurs in the vicinity of the hydroxo intermediate.