Result and Discussion

3-1. Introduction

As mentioned previously, quinone is a NIL; reduction by one electron yields semiquinone (SQ), and a further reduction by one electron gives catecholato (Cat).

NILs can help disperse the electron density at the metal center and promote electron transfer between the metal center and the ligand. Then, keep the metal center in low oxidation states (Scheme 2).

Scheme 4. Characteristic of quinone ligand.

We used the DFT method to calculate pKa and the standard reduction potential

E

⁰ of Ru(OH₂)(tpy)(tBu₂Qn), Ru(OH₂)(tpy)(Bpm), Ru(OH₂)(tpy)(Bpy) and various intermediate complexes, then used Nernst equation (Eqn. (3)) to construct the Pourbaix diagram and compare with experimental values. In Pourbaix diagram, all lines present the number of protons and electrons are involved in reaction, so we have varies slopes. This process is PCET. First, if the reaction involves one electron transfer, the slope is 0. Second, if the reaction involves one proton transfer and one electron transfer, the slope is -0.05916 units. Third, if the reaction involves the transfer of two protons and one electron, the slope is -0.11832 units. Fourth, if the reaction involves the transfer of one proton and two electrons, the slope is -0.02958

11

units. Finally, if the reaction involves one proton transfer, the slope is a straight line, and these values also represent the pKa values. For example, in Figure 1a, for [Ru^III(OH₂)(tpy)(Bpy)]³⁺_(aq) → [Ru^III(OH)(tpy)(Bpy)]²⁺_(aq) + H⁺_(aq), because one proton transfer is involved, the slope is 1. For [Ru^V(=O)(tpy)(Bpy)]³⁺(aq) + e

-→[Ru^IV(=O)(tpy)(Bpy)]²⁺_(aq), because one electron transfer is involved, the slope is a straight line. For [Ru^III(OH)(tpy)(Bpy)]²⁺(aq) + H⁺(aq) + e^- → [Ru^IV(=O)(tpy)(Bpy)]²⁺_(aq), because one proton transfer and one electron transfer are involved, the slope is -0.05916 units. For [Ru^III(OH2)(tpy)(Bpy)]³⁺(aq) + 2H⁺(aq) + e

-→ [Ru^IV(=O)(tpy)(Bpy)]²⁺_(aq), because the transfer of two protons and one electron is involved, the slope is -0.11832 units. For [Ru^II(OH)(tpy)(Bpy)]⁺(aq) + H⁺(aq) + 2e

-→ [Ru^IV(=O)(tpy)(Bpy)]²⁺_(aq), because one proton and two electrons are transferred, the slope is -0.02958 units.

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3-2. Comparison of Pourbaix diagrams, pKa, and Reduction Potential

For Ru(OH₂)(tpy)(tBu₂Qn), Ru(OH₂)(tpy)(Bpm), and Ru(OH₂)(tpy)(Bpy) complexes and various intermediate complexes, we used an optimized structure in the gas phase to do PCM and SMD; we considered two cases: the addition of water to the structures of the complexes and the absence of any such addition. First, for Ru(OH₂)(tpy)(Bpy), the Bpy ligand is an innocent ligand. For [Ru^III(OH2)(tpy)(Bpy)]³⁺(aq) → [Ru^III(OH)(tpy)(Bpy)]²⁺(aq) + H⁺(aq), the pKa values were 4.3, 0.8, 4.1, 1.6, 3.7, and 8.9 (Table 1). In Figures 1–3, a comparison between the Pourbaix diagrams shows that the pKa values of Ru(OH2)(tpy)(Bpy) were irregular in acidic pH conditions, whereas the pKa values were not influenced in basic pH conditions. The pKa values approached experimental values for acidic pH conditions, but the Ru(OH₂)(tpy)(Bpy) performance was poor in the SMD system when water was added to the system. When SMD was used, the calculated reduction potentials decreased for these complexes. In particular, the pH-dependent [Ru^IV=O]/[Ru^V=O] couples potential decreased considerably. The [Ru^IV=O]/[Ru^V=O]

couples potential values were 2.49, 2.35, 2.52, 2.32, 1.90, and 1.88 V (Table 1).

13

(a)

(b)

Figure 1. Pourbaix diagram for the Ru(OH

2)(tpy)(Bpy) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.

14

(a)

(b)

Figure 2. Pourbaix diagram for the Ru(OH

2)(tpy)(Bpy) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by PCM solvation model. (b) Single-point solvation calculation with extra water by PCM solvation model.

15

(a)

(b)

Figure 3. Pourbaix diagram for the Ru(OH

2)(tpy)(Bpy) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by SMD solvation model. (b) Single-point solvation calculation with extra water by SMD solvation model.

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Table 1. Calculated Values of pKa, E

^o, and E1/2 with Ru(OH2)(tpy)(Bpy) at the density Functional Theory Level.

reactions predictions^a,b predictions^a,c predictions^a,d predictions^a,e predictions^a,f predictions^a,g

Ru(OH2)(tpy)(Bpy)

[Ru^III(OH2)(tpy)(Bpy)]³⁺(aq) → [Ru^III(OH)(tpy)(Bpy)]²⁺(aq) + H⁺(aq) pKa=4.3 pKa=0.8 pKa=4.1 pKa=1.6 pKa=3.7 pKa=8.9 [Ru^II(OH2)(tpy)(Bpy)]²⁺(aq) → [Ru^II(OH)(tpy)(Bpy)]⁺(aq) + H⁺(aq) pKa=19.0 pKa=16.9 pKa=19.0 pKa=17.7 pKa=19.8 pKa=20.1 [Ru^V(=O)(tpy)(Bpy)]³⁺(aq) + e^- →[Ru^IV(=O)(tpy)(Bpy)]²⁺(aq) E^o =2.49 E^o =2.35 E^o =2.52 E^o =2.32 E^o =1.90 E^o =1.88 [Ru^III(OH2)(tpy)(Bpy)]³⁺(aq) + e^- → [Ru^II(OH2)(tpy)(Bpy)]²⁺(aq) E^o =0.86 E^o =1.99 E^o =0.87 E^o =1.21 E^o =0.76 E^o =0.65 [Ru^III(OH)(tpy)(Bpy)]²⁺(aq) + e^- → [Ru^II(OH)(tpy)(Bpy)]⁺(aq) E^o =0.00 E^o =0.24 E^o =-0.01 E^o =0.26 E^o =-0.19 E^o =-0.01

[Ru^III(OH)(tpy)(Bpy)]²⁺(aq) + H⁺(aq) + e^- → [Ru^IV(=O)(tpy)(Bpy)]²⁺(aq) E1/2 =1.32-0.05916×pH E1/2 =1.24-0.05916×pH E1/2 =1.31-0.05916×pH E1/2 =1.23-0.05916×pH E1/2 =1.19-0.05916×pH E1/2 =1.22-0.05916×pH [Ru^II(OH2)(tpy)(Bpy)]²⁺(aq) + H⁺(aq) + e^- → [Ru^III(OH)(tpy)(Bpy)]²⁺(aq) E1/2 =1.12-0.05916×pH E1/2 =1.24-0.05916×pH E1/2 =1.11-0.05916×pH E1/2 =1.30-0.05916×pH E1/2 =0.98-0.05916×pH E1/2 =1.18-0.05916×pH [Ru^III(OH2)(tpy)(Bpy)]³⁺(aq) + 2H⁺(aq) + e^- → [Ru^IV(=O)(tpy)(Bpy)]²⁺(aq) E1/2 =1.57-0.11832×pH E1/2 =1.28-0.11832×pH E1/2 =1.55-0.11832×pH E1/2 =1.32-0.11832×pH E1/2 =1.41-0.11832×pH E1/2 =1.75-0.11832×pH [Ru^II(OH)(tpy)(Bpy)]⁺(aq) + H⁺(aq) + 2e^- → [Ru^IV(=O)(tpy)(Bpy)]²⁺(aq) E1/2 =0.65-0.02958×pH E1/2 =0.74-0.02958×pH E1/2 =0.64-0.02958×pH E1/2 =0.78-0.02958×pH E1/2 =0.49-0.02958×pH E1/2 =0.61-0.02958×pH

aE^o and E1/2 are in units of V relative to the SCE. ^bCalculation without extra water by PCM solvation model. ^cCalculation with extra water by PCM solvation model. ^dSingle-point solvation calculation without extra water by PCM solvation model. ^eSingle-point solvation calculation with extra water by PCM solvation model. ^fSingle-point solvation calculation without extra water by SMD solvation model. ^gSingle-point solvation calculation with extra water by SMD solvation model.

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Second, for Ru(OH2)(tpy)(Bpm), the Bpm ligand is an innocent ligand. For [Ru^III(OH₂)(tpy)(Bpm)]³⁺_(aq) → [Ru^III(OH)(tpy)(Bpm)]²⁺_(aq) + H⁺_(aq), the pKa values are -7.5, -0.9, -7.9, -0.6, 2.4, and 6.3 (Table 2). In Figures 4–6, a comparison between the Pourbaix diagrams indicates that after the addition of water to u(OH2)(tpy)(Bpm), the pKa values moved to the right in acidic pH conditions; however, the pKa values were not influenced in basic pH conditions. These results are similar to those for Ru(OH₂)(tpy)(tBuQn). When SMD was used for calculating the reduction potentials of these complexes, the reduction potentials were observed to decrease. In particular, the pH-dependent [Ru^IV=O]/[Ru^V=O] couples potential decreased considerably. The [Ru^IV=O]/[Ru^V=O] couples potential values were 2.50, 2.46, 2.66, 2.44, 1.96, and 2.06 V (Table 2). In Figures 5b and 6b, the reduction potentials between [Ru^II(OH₂)(tpy)(Bpm)]²⁺ and [Ru^III(OH)(tpy)(Bpm)]²⁺ and between [Ru^III(OH)(tpy)(Bpm)]²⁺ and [Ru^IV(=O)(tpy)(Bpy)]²⁺ are identical, implying that the reduction potential between [Ru^II(OH2)(tpy)(Bpm)]²⁺ and [Ru^IV(=O)(tpy)(Bpy)]²⁺

should be double of the identical values. This result is similar to that obtained from an experimental diagram.¹⁴

18

(a)

(b)

Figure 4. Pourbaix diagram for the Ru(OH

₂)(tpy)(Bpm) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.

19

(a)

(b)

Figure 5. Pourbaix diagram for the Ru(OH

₂)(tpy)(Bpm) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by PCM solvation model. (b) Single-point solvation calculation with extra water by PCM solvation model.

20

(a)

(b)

Figure 6. Pourbaix diagram for the Ru(OH

2)(tpy)(Bpm) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by SMD solvation model. (b) Single-point solvation calculation with extra water by SMD solvation model.

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Table 2. Calculated Values of pKa, E

^o, and E1/2 with Ru(OH2)(tpy)(Bpm) at the density Functional Theory Level.

reactions predictions^a,b predictions^a,c predictions^a,d predictions^a,e predictions^a,f predictions^a,g

Ru(OH2)(tpy)(Bpm)

[Ru^III(OH2)(tpy)(Bpm)]³⁺(aq) → [Ru^III(OH)(tpy)(Bpm)]²⁺(aq) + H⁺(aq) pKa=-7.5 pKa=-0.9 pKa=-7.9 pKa=-0.6 pKa=2.4 pKa=6.3 [Ru^II(OH2)(tpy)(Bpm)]²⁺(aq) → [Ru^II(OH)(tpy)(Bpm)]⁺(aq) + H⁺(aq) pKa=15.3 pKa=15.7 pKa=16.9 pKa=16.7 pKa=18.6 pKa=18.1 [Ru^V(=O)(tpy)(Bpm)]³⁺(aq) + e^- →[Ru^IV(=O)(tpy)(Bpm)]²⁺(aq) E^o =2.50 E^o =2.46 E^o =2.66 E^o =2.44 E^o =1.96 E^o =2.06 [Ru^III(OH2)(tpy)(Bpm)]³⁺(aq) + e^- → [Ru^II(OH2)(tpy)(Bpm)]²⁺(aq) E^o =1.48 E^o =1.36 E^o =1.60 E^o =1.41 E^o =0.88 E^o =0.78 [Ru^III(OH)(tpy)(Bpm)]²⁺(aq) + e^- → [Ru^II(OH)(tpy)(Bpm)]⁺(aq) E^o =0.13 E^o =0.37 E^o =0.13 E^o =0.39 E^o =-0.08 E^o =0.08

[Ru^III(OH)(tpy)(Bpm)]²⁺(aq) + H⁺(aq) + e^- → [Ru^IV(=O)(tpy)(Bpm)]²⁺(aq) E1/2 =1.17-0.05916×pH E1/2 =1.27-0.05916×pH E1/2 =1.34-0.05916×pH E1/2 =1.26-0.05916×pH E1/2 =1.21-0.05916×pH E1/2 =1.26-0.05916×pH [Ru^II(OH2)(tpy)(Bpm)]²⁺(aq) + H⁺(aq) + e^- → [Ru^III(OH)(tpy)(Bpm)]²⁺(aq) E1/2 =1.03-0.05916×pH E1/2 =1.30-0.05916×pH E1/2 =1.13-0.05916×pH E1/2 =1.38-0.05916×pH E1/2 =1.02-0.05916×pH E1/2 =1.15-0.05916×pH [Ru^III(OH2)(tpy)(Bpm)]³⁺(aq) + 2H⁺(aq) + e^- → [Ru^IV(=O)(tpy)(Bpm)]²⁺(aq) E1/2 =0.73-0.11832×pH E1/2 =1.22-0.11832×pH E1/2 =0.87-0.11832×pH E1/2 =1.22-0.11832×pH E1/2 =1.35-0.11832×pH E1/2 =1.63-0.11832×pH [Ru^II(OH)(tpy)(Bpm)]⁺(aq) + H⁺(aq) + 2e^- → [Ru^IV(=O)(tpy)(Bpm)]²⁺(aq) E1/2 =0.66-0.02958×pH E1/2 =0.96-0.02958×pH E1/2 =0.75-0.02958×pH E1/2 =0.88-0.02958×pH E1/2 =0.54-0.02958×pH E1/2 =0.61-0.02958×pH

aE^o and E1/2 are in units of V relative to the SCE. ^bCalculation without extra water by PCM solvation model. ^cCalculation with extra water by PCM solvation model. ^dSingle-point solvation calculation without extra water by PCM solvation model. ^eSingle-point solvation calculation with extra water by PCM solvation model. ^fSingle-point solvation calculation without extra water by SMD solvation model. ^gSingle-point solvation calculation with extra water by SMD solvation model.

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Third, Ru(OH2)(tpy)(tBu2Qn) has a quinone ligand, which is a NIL often seen in chlorophyll and which has high redox activity. For [Ru^II(OH2)(tpy)(Q)]²⁺(aq) →

however, the pKa values were not influenced in basic pH conditions. When SMD was used to calculate the reduction potentials of these complexes, the reduction potentials were observed to decrease. In particular, the pH-dependent [Ru^IV=O]/[Ru^V=O]

couples potential decreased considerably. The [Ru^IV=O]/[Ru^V=O] couples potential values were 2.58, 2.38, 2.43, 2.36, 1.95, and 1.97 V (Table 3).

When compared with Ru(OH2)(tpy)(Bpm), Ru(OH2)(tpy)(Bpy), and Ru(OH2)(tpy)(tBu2Qn) complexes, Ru(OH2)(tpy)(tBu2Qn) showed a new intermediate complex, [Ru^III(^3αO^·-)(tpy)(^βSQ)]⁺, which could undergo radical-radical coupling to form an O−O bond and produce oxygen. The Ru(OH₂)(tpy)(tBu₂Qn), Ru(OH2)(tpy)(Bpm), and Ru(OH2)(tpy)(Bpy) complexes in the SMD system showed the same result: a decrease in the reduction potentials. In high oxidation states, the pH-dependent [Ru^IV=O]/[Ru^V=O] couples potential is not influenced by any ligand because of the reaction acting on the metal center.

23

(a)

(b)

Figure 7. Pourbaix diagram for the Ru(OH

2)(tpy)(tBu2Qn) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.

24

(a)

(b)

Figure 8. Pourbaix diagram for the Ru(OH

₂)(tpy)(tBu₂Qn) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by PCM solvation model. (b) Single-point solvation calculation with extra water by PCM solvation model.

25

(a)

(b)

Figure 9. Pourbaix diagram for the Ru(OH

2)(tpy)(tBu2Qn) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by SMD solvation model. (b) Single-point solvation calculation with extra water by SMD solvation model.

26

Table 3. Calculated Values of pKa, E

^o, and E1/2 with Ru(OH2)(tpy)(tBuQn) at the density Functional Theory Level.

reactions predictions^a,b predictions^a,c predictions^a,d predictions^a,e predictions^a,f predictions^a,g

Ru(OH2)(tpy)(tBuQn)

aE^o and E_1/2 are in units of V relative to the SCE. ^bCalculation without extra water by PCM solvation model. ^cCalculation with extra water by PCM solvation model. ^dSingle-point solvation calculation without extra water by PCM solvation model. ^eSingle-point solvation calculation with extra water by PCM solvation model. ^fSingle-point solvation calculation without extra water by SMD solvation model. ^gSingle-point solvation calculation with extra water by SMD solvation model.

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3-3. Comparison of Computational Methods

Finally, we used Truhlar’s computational method to calculate Ru(OH2)(tpy)(tBuQn) and examine differences between B3LYP/LANL08 and M11-L/MG3S (Tables 4 and 5). For all methods, ∆∆Gsol showed superior contribution to the SMD system, and therefore, pKa and the oxidation potential showed good performance. In addition, M11-L/MG3S was better than B3LYP/LANL08 in alkaline pKa and for low oxidation potential ∆EDFT. It representative M11-L/MG3S has good description of the structure of energy for alkaline pKa and low oxidation potential. A comparison between B3LYP/LANL08, M11-L/MG3S, and experimental values obtained from the Pourbaix diagram (Figure 10), we found M11-L/MG3S to be close to experimental values, once again proving that M11-L/MG3S was better than B3LYP/LANL08. Truhlar’s method is a good way to calculate pKa and oxidation potential. We shall also use Truhlar’s method for calculations in another project.

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Table 4. The pKa error analysis of Ru(OH

2)(tpy)(tBu2Qn) without extra water.

pKa Composition (kcal/mol) ∆EDFT ∆ZPE ∆Gcor ∆∆Gsol

[Ru^III(OH)(tpy)(Q)]²⁺_(aq) → [Ru^III(^3αO^‧-)(tpy)(^ßSQ)]⁺_(aq) + H⁺_(aq)

B3LYP/LANL08/PCM

^a

200.66 -7.34 -7.05 82.22

B3LYP/LANL08/PCM_SP

^b

200.66 -7.34 -7.05 80.96

B3LYP/LANL08/SMD_SP

^c

200.66 -7.34 -7.05 87.27

M11L/MG3S/SMD

^d

199.56 -7.72 -6.94 88.49

[Ru^II(OH2)(tpy)(SQ)]⁺(aq) → [Ru^III(OH)(tpy)(Cat)]⁰(aq) + H⁺(aq)

B3LYP/LANL08/PCM

^a

276.61 -8.61 -8.08 26.80

B3LYP/LANL08/PCM_SP

^b

276.61 -8.61 -8.08 23.11

B3LYP/LANL08/SMD_SP

^c

276.61 -8.61 -8.08 24.54

M11L/MG3S/SMD

^d

264.67 -8.67 -7.98 29.01

aCalculation without extra water by PCM solvation model with B3LYP/LANL08. ^bSingle-point solvation calculation without extra water by PCM solvation model with B3LYP/LANL08. ^cSingle-point solvation calculation without extra water by SMD solvation model with B3LYP/LANL08. ^dSingle-point solvation calculation without extra water by SMD solvation model with M11-L/MG3S.

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Table 5. The E

^o error analysis of Ru(OH2)(tpy)(tBu2Qn) without extra water.

E^o Composition (kcal/mol) ∆EDFT ∆ZPE ∆Gcor ∆∆Gsol

[Ru^III(O^•-)(tpy)(Q)]²⁺_(aq) + e^- →[Ru^IV(O^•-)(tpy)(Q)]³⁺_(aq)

B3LYP/LANL08/PCM

^a

301.22 -0.58 -0.18 -142.94

B3LYP/LANL08/PCM_SP

^b

301.22 -0.58 -0.18 -146.32

B3LYP/LANL08/SMD_SP

^c

301.22 -0.58 -0.18 -157.29

M11L/MG3S/SMD

^d

302.86 -1.07 -1.11 -157.31

[Ru^III(OH)(tpy)(SQ)]⁺(aq) + e^- → [Ru^III(OH)(tpy)(Cat)]⁰(aq)

B3LYP/LANL08/PCM

^a

115.43 1.32 0.99 -24.09

B3LYP/LANL08/PCM_SP

^b

115.43 1.32 0.99 -22.10

B3LYP/LANL08/SMD_SP

^c

115.43 1.32 0.99 -24.22

M11L/MG3S/SMD

^d

126.88 1.90 2.59 -25.30

aCalculation without extra water by PCM solvation model with B3LYP/LANL08. ^bSingle-point solvation calculation without extra water by PCM solvation model with B3LYP/LANL08. ^cSingle-point solvation calculation without extra water by SMD solvation model with B3LYP/LANL08. ^dSingle-point solvation calculation without extra water by SMD solvation model with M11-L/MG3S.

30 (a)

(b)

Figure 10. Pourbaix diagram for the Ru(OH

2)(tpy)(tBu2Qn) complexes in aqueous solution. (a) Single-point solvation calculation without extra water by SMD solvation model with M11-L/MG3S. (b) Single-point solvation calculation without extra water by SMD solvation model with B3LYP/LANL08.

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在文檔中 利用理論計算比較釕金屬撮合霧中的Innocent Ligand 和 Non-innocent Ligand 之 Pourbaix Diagrams 在水氧化反應差異 (頁 19-40)