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

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(1)國立臺灣師範大學化學系 Department of Chemistry, National Taiwan Normal University. 碩士論文. 指導教授：蔡明剛博士. 利用理論計算比較釕金屬錯合物中的 Innocent Ligand 和 Non-Innocent Ligand 之 Pourbaix Diagrams 在水氧化反應差異. Theoretical Pourbaix Diagrams of Ru-Polypyridyl Complexes: A Innocent and Non-Innocent Ligand Comparison for Water Oxidation Catalysis. 研究生：朱書儀撰. 中華民國一○三年七月.

(2) 謝誌在我的學生生涯裡面，我很幸運地遇到了許多好老師，當然研究所也不例外，我遇到了一個慈祥和藹又可愛的老師，這是我第一眼對蔡明剛老師的印象，之所以會進入蔡明剛老師實驗室，要從大學說起，原本預計用考試的方式進入研究所的我，在陳輝龍老師的鼓勵之下，進入到陳老師的實驗室做專題，因此我接觸到了理論計算，那時我對理論計算的印象大概只有實驗課裡的畫結構，但事實上並不是只有畫結構這麼簡單，所以在專題生涯我對理論計算有進一步的了解。之後我順利的推甄到了國立臺灣師範大學然後進入蔡明剛老師實驗室。. 這一本論文能夠順利完成，首先最要感謝的就是蔡明剛老師了，從一開始進入到實驗室到現在，老師永遠不辭辛勞地教我們，鼓勵我們，還有訓練我們，這也讓我們訓練了獨立思考以及解決的能力。其次要謝謝口試委員江志強、李祐慈老師，感謝你們抽空來口試，並且提供非常寶貴的意見，使這一篇論文不論架構的嚴謹性或文字的流暢性，都更加完美。接著要感謝幫助我的學長們：謝謝當初一步一步教的我實驗上的東西，讓我對實驗更快的上手的傅弼豊學長；實驗室開心果之 magic 蔡長誌學長，只要有他在，實驗室永遠都充滿著歡笑聲；教我學習處理報帳的張正明學長；幫忙借教室處理雜事的張均普學長，我永遠記得第一次參與學長姊 meeting 時，張均普學長在 ppt 裡面把「±」打成「士」，然後被大家笑到不行；切蛋糕高手的張財興學長，而且需要拍照時總是少不了他。感謝有他們的幫忙，讓我在碩士班充滿歡笑以及學習到不少東西。. 接著感謝我的同學以及學弟妹們：個性大辣辣又少根筋的超級資優生林亮君學妹；有著健康膚色愛運動的鄒語騏；實驗室大家的救星梁哲銘；有著成大木村之稱的詹堯舜；報告時總會有特別腔調的黎學謙；有著娃娃音的大學同學鄧文霜；擁有無數個口袋名單的美食部落客的廖家惠；個性和諧又好相處的徐郁潔；養著 1.

(3) 可愛 Luffy 以及號稱半專業攝影師的詹侑得。感謝碩班有你們陪伴，讓實驗室充滿歡樂。. 最後感謝我的朋友們，請自行填空. ，在此就不一一點名了，謝謝你. 們陪我度過了許多時光，還有父母一路的支持與鼓勵，也謝謝林則言一路的陪伴我度過艱難的時刻，並給我鼓勵，謝謝你們讓我的生活更加精彩。最後最後，我想跟我的奶奶說：「奶奶，我畢業了!」。. 朱書儀謹誌中華民國 103 年 7 月 2.

(4) 總目錄總目錄............................................................................................................................ I 圖目錄........................................................................................................................... II 表目錄......................................................................................................................... IV 中文摘要....................................................................................................................... V Abstract ...................................................................................................................... VI Chapter 1. Introduction ...............................................................................................1 1-1. Characteristics of Noninnocent Ligands......................................................... 3 1-2. Research Objective ......................................................................................... 3 Chapter 2. Computational Details ..............................................................................5 2-1. Computational Method ................................................................................... 5 2-2. Computational Method of Truhlar .................................................................. 5 2-3. Calculation of Free Energy, pKa, and Potential in Aqueous Solution ............ 5 2-4. Various Computational Methods for Constructing Pourbaix Diagrams ......... 9 Chapter 3. Result and Discussion .............................................................................10 3-1. Introduction .................................................................................................. 10 3-2. Comparison of Pourbaix diagrams, pKa, and Reduction Potential .............. 12 3-3. Comparison of Computational Methods....................................................... 27 Chapter 4. Conclusion ...............................................................................................31 Reference ....................................................................................................................32. I.

(5) 圖目錄. Scheme. 1.. Structure. of. Ru(OH2)(tpy)(tBu2Qn),. Ru(OH2)(tpy)(Bpm). and. Ru(OH2)(tpy)(Bpy)investigated in this work……………………………………….....3 Scheme 2. Thermodynamic cycle for the acid dissociation reaction in the gas phase and in aqueous solution. .................................................................................................6 Scheme 3. Thermodynamic cycle for the standard free energy of reaction for the proton-coupled reduction of species O to species R in the gas phase and in aqueous solution...........................................................................................................................7 Scheme 4. Characteristic of quinone ligand. ...............................................................10 Figure 1. Pourbaix diagram for the Ru(OH2)(tpy)(Bpy) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model. .................................................................13 Figure 2. Pourbaix diagram for the Ru(OH2)(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............................................................................................................................14 Figure 3. Pourbaix diagram for the Ru(OH2)(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............................................................................................................................15 Figure 4. Pourbaix diagram for the Ru(OH2)(tpy)(Bpm) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model. .................................................................18 Figure 5. Pourbaix diagram for the Ru(OH2)(tpy)(Bpm) complexes in aqueous II.

(6) 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............................................................................................................................19 Figure 6. Pourbaix diagram for the Ru(OH2)(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............................................................................................................................20 Figure 7. Pourbaix diagram for the Ru(OH2)(tpy)(tBu2Qn) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model. .................................................................23 Figure 8. Pourbaix diagram for the Ru(OH2)(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............................................................................................................................24 Figure 9. Pourbaix diagram for the Ru(OH2)(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............................................................................................................................25 Figure 10. Pourbaix diagram for the Ru(OH2)(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. .......................................................30. III.

(7) 表目錄 Table 1. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(Bpy) at the density Functional Theory Level. ................................................................................16 Table 2. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(Bpm) at the density Functional Theory Level. ................................................................................21 Table 3. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(tBuQn) at the density Functional Theory Level. ................................................................................26 Table 4. The pKa error analysis of Ru(OH2)(tpy)(tBu2Qn) without extra water. .......28 Table 5. The Eo error analysis of Ru(OH2)(tpy)(tBu2Qn) without extra water. ..........29. IV.

(8) 中文摘要. 將太陽能做能量轉換是水氧化的一個關鍵的半反應，主要以 PCET 為主，需要牽涉多個質子以及多個電子的轉移(2H2O → O2 + 4H+ + 4e−)，水氧化的 mechanism 和催化劑已經有許多人發表，而 Ru 單核催化劑對於水氧化催化劑是重要的一個類別，NIL 有三種氧化狀態，NILOx 、NIL• 、NILRed ，我們得知 non-innocent ligand (NIL)能夠分散金屬中心的電荷密度使分子的能量降低，而 Tanaka 的雙核催化劑對於 Ru-NIL 是一個有趣的例子,我們利用密度泛涵理論 (DFT)來計算 Ru(OH2)(tpy)(tBu2Qn), Ru(OH2)(tpy)(Bpm) and Ru(OH2)(tpy)(Bpy) (tBu2Q = 3,5-di-tert-butyl-2,2-benzoquinone, tpy = 2,2':6',2″-terpyridine, Bpm = 2,2'-bipy-rimidine, Bpy = 2,2'-Bipyridine) complexes 的 pKa 和還原電位，然後繪製 pourbaix diagram，為了比較 innocent 和 non-innocent ligand 之不同，本篇論文我們主要著重在研究 PCET 的過程和尋找低能量的路徑形成 O-O bond，並且利用計算出的 pKa 以及還原電位( Eo )所繪製出的 pourbaix diagram 來進行比較，然後我們發現在 SMD 系統中[RuIV=O] / [RuV=O] couples 有較低的電位，並且在 quinone 系統中發現了新的中間物[RuIII(3αO·-)(tpy)(βSQ)]+，而這個中間物可以進行 radical-radical coupling 形成 O-O bond ，另外，我們也利用不同的計算方法比較其中的差異，發現在 SMD 系統中確實有較好的表現。. 關鍵字 : 水氧化、 Non-Innocent Ligand 、釕金屬、密度泛函理論、 Pourbaix Diagram。 V.

(9) Abstract Water oxidation is a key half-reaction (2H2O → O2 + 4H+ + 4e−) employed in solar-fuel-based energy conversion, and it is dominated by proton-coupled electron transfer (PCET), given its multi-electron, multi-proton character. Mononuclear Ru-based water oxidation catalysts (WOCs) are a valuable class of WOCs used for water splitting. Noninnocent ligands (NILs) have three oxidation states, NILOx, NIL•, and NILRed, that have an electron redox transformation in common. NILs can help disperse the electron density at the metal center and keep the metal center in low oxidation states. The Tanaka catalyst, an anthracene-bridged dinuclear Ru complex, is an interesting example of a Ru–NIL framework in catalysis. We used density functional theory to calculate pKa and the standard reduction potential of Ru(OH2)(tpy)(tBu2Qn), Ru(OH2)(tpy)(Bpm), and Ru(OH2)(tpy)(Bpy) (tBu2Q = 3,5-di-tert-butyl-2,2-benzoquinone,. tpy. =. 2,2':6',2″-terpyridine,. Bpm. =. 2,2'-bipyrimidine, and Bpy = 2,2'-bipyridine) complexes, and we then constructed the Pourbaix diagram to compare innocent ligands and NILs. We focused on pH-dependent onset catalytic potentials indicative of a PCET-driven low-energy pathway for the formation of products with an O−O bond and investigated the differences between these complexes by using the Pourbaix diagram. We found a lower [RuIV=O]/[RuV=O] couples potential in the solvation model density (SMD) system and a new intermediate complex [RuIII(3αO•-)(tpy)(βSQ)]+ that can promote radical-radical coupling to form an O−O bond. In addition, we used different computational methods to compare the differences and to achieve better performance in the SMD system. Key words: Water Oxidation, Non-Innocent Ligand, Ruthenium, Density Functional Theory, Pourbaix Diagram VI.

(10) Chapter 1. Introduction. Since the industrial revolution, development of high technology is a favorable way of improving our life. In the pursuit of economic development, a considerable amount of coal, oil, gas, and other fossil fuels are extracted. Fossil energy makes life convenient, but causes excessive energy shortages, global weather changes, and serious damage to the global environment, apart from affecting global ecological balance. The large-scale use and the burning of fossil fuels produce an amount of carbon dioxide that is more than what nature can load. Solar energy is the largest renewable energy resource, and the energy produced in one hour can be provided to people for consumption throughout the year. If solar energy is to be used as a major source, its storage and conversion is necessary. We use oxygen as our primary energy source during respiration. In nature, oxygen is produced from water through solar-energy conversion in photosynthetic membranes. In green plants, light absorption in photosystem II (PSII).1-3 PSII is a large protein complex found in the thylakoid membranes of oxygenic photosynthetic organisms, and it drives electron-transfer activation of an oxygen-evolving complex (OEC). An OEC consisting of an Mn4CaO5 cluster1 can oxidize water to oxygen. Water oxidation catalysts are essential components of light-driven water-splitting systems, which consist of two crucial half-reactions: the oxidation of water to O2 (2H2O → O2 + 4H+ + 4e−) and the reduction of water to H2 (4H+ + 4e− → 2H2). It is believed that hydrogen and oxygen are clean gases. In particular, hydrogen is a potentially clean energy carrier and water is an abundant and environmentally resource. Many studies have dealt with the development of molecular catalysts for O2 evolution because of the requirement of the removal of four protons and four electrons through a process called proton-coupled electron transfer (PCET);1,2–5 O2 evolution is considered a 1.

(11) diﬃcult process to accelerate, and therefore, the development of highly active and rugged water oxidation catalysts (WOCs) is a key step. In 1982, Meyer and co-workers discovered that the dinuclear Ru complex (bpy)2(H2O)RuORu(OH2)(bpy)2 (known as “blue dimer”6,7) produces O2 molecules considerably slowly and is unstable.6–9 In 2001, Tanaka and co-workers reported the water oxidation catalytic activity of a new dinuclear Ru complex in which two Ru(OH)(3,6-Bu2Q)(tpy)+ (3,6-Bu2Q = 6-di-tert-butyl-1,2-benzoquinone) molecules are strategically connected by an anthracene bridge to form an O─O bond; they found that the turnover number of the catalyst could reach 33,500. Interestingly, the catalyst has the non-innocent ligand (NIL) characteristics of quonine.10 In 2005, Zong and Thummel reported that mononuclear ruthenium complexes were also active as WOCs, and there has been considerable development in the field following the discovery of these types of complexes.11 This discovery spurred interest in the development of mononuclear ruthenium WOCs.12–22 Moreover, in 2012, Sun and Llobet reported a number of mononuclear ruthenium complexes without water molecules and having an unprecedented high reaction rate with a turnover frequency (TOF) above 300 s-1. This high TOF is comparable with the reaction rate of the OEC of PSII. 23 Numerous water oxidation mechanisms have been proposed.14,16,17,24,25 A Ru complex oxide in a high oxidation state (Ru=O) reacts with water to form oxygen; without oxide to high oxidation state can react with water to produce oxygen. Use two mononuclear to promote radical-radical coupling for producing oxygen. In water oxidation, the O–O bond formation is a key step for producing oxygen. In transition metal complexes, the O-O bond formation has two pathways at high oxidation states. One is water nucleophilic attack,25 and the other is interaction of two mononuclear M=O units.26,27. 2.

(12) 1-1. Characteristics of Noninnocent Ligands. A. NIL consists of 1,2-disubstituted phenylene redox-active subunits, and it can. accept two electrons. These bidentate ligands have three oxidation states, NILOx, NIL•, and NILRed, that have an electron redox transformation in common. NILs can be combined with a transition metal. NILs are capable of redistributing the charge density to stabilize the metal complex. Electron transfer between the ligand and the metal center can lead to the metal center being in a low oxidation state. This characteristic plays an important role in the catalyst.. 1-2. Research Objective We used density functional theory (DFT) to calculate Ru(OH2)(tpy)(tBu2Qn), Ru(OH2)(tpy)(Bpm),. and. Ru(OH2)(tpy)(Bpy). 3,5-di-tert-butyl-2,2-benzoquinone,. tpy. =. (Scheme. 1,. 2,2′:6′,2″-terpyridine,. tBu2Q. =. Bpm. =. 2,2′-bipyrimidine, Bpy = 2,2'-bipyridine) complexes to compare innocent ligands and NILs.28 The reaction mechanism reported by Meyer was used. We focused on pH-dependent onset catalytic potentials indicative of a PCET-driven low-energy pathway for the formation of products with an O−O bond and investigated the differences between these complexes by using the Pourbaix diagram.. 3.

(13) Scheme. 1.. Structure. of. Ru(OH2)(tpy)(tBu2Qn),. Ru(OH2)(tpy)(Bpy) investigated in this work.. 4. Ru(OH2)(tpy)(Bpm). and.

(14) Chapter 2. Computational Details. 2-1. Computational Method The initial structures of all complexes were built with Gauss View 5.0. All calculations were carried out with the Gaussian 09 program package29 at the DFT level of theory with the B3LYP functional.30 LANL0831,32 was used for the central Ru metal, and 6-31G(d,p)33,34 was used for other nonmetal atoms. Furthermore, for all complexes, considering the solvent effect, we used the polarizable continuum model (PCM)35,36 as the solvent model, along with the solvation model density (SMD)37 and the dielectric constant of water.. 2-2. Computational Method of Truhlar38 We used the Gaussian 09 program package and the M11-L39 functional for calculations. The MG3S basis set40 was used for the central Ru metal and the 6-311+G(2df,2p) basis set41 was used for other nonmetal atoms. Furthermore, for all complexes, considering the solvent effect, we used a solvent model and the solvation model density (SMD) along with the dielectric constant of water.. 2-3. Calculation of Free Energy, pKa, and Potential in Aqueous Solution ∗ The free energy ∆𝐺𝑎𝑞 (the superscript * indicates the standard state of 1 M in. both the gas phase and in solution) for an acid dissociation reaction in the 1 M standard state can be calculated using the thermodynamic cycle shown in Scheme 2.. 5.

(15) ∆𝑮∗𝒂𝒒 = ∆𝑮°𝒈 + ∆∆𝑮∗𝑺 + ∆𝑮°→∗ ∆𝑮°𝒈 = 𝑮°𝒈 (𝑨− ) + 𝑮°𝒈 (𝑯+ ) − 𝑮°𝒈 (𝑯𝑨) ∆∆𝑮∗𝑺 = ∆𝑮∗𝑺 (𝑨− ) + ∆𝑮∗𝑺 (𝑯+ ) − 𝑮°𝑺 (𝑯𝑨). Scheme 2. Thermodynamic cycle for the acid dissociation reaction in the gas phase and in aqueous solution.. The ΔGgo value was calculated using DFT at 1 atm standard state; ΔGs* is the solvation free energy. The free energy of the gas-phase proton, Ggo(H+), at 298.15 K (-6.28 kcal/mol) was derived from the Sackur–Tetrode equation.42 The free energy of solvation of the proton, ΔGs*(H+), at 298 K (-265.87 kcal/mol) has been reported by Tissandier et al.43 Here ΔGo→* is the free energy associated with the difference in the standard state between the gas phase and the liquid phase (1.89 kcal/mol). Because of differences in the thermal correction between the gas phase and the liquid phase, it is difficult to make the geometry optimizations in the liquid phase converge and obtain ΔGs*. Thus, no vibrational frequency analysis was carried out with the continuum solvation model. The difference in the thermal correction between the gas phase and liquid phase for each intermediate complex is expected to be quite small because no significant geometric change was observed during the geometry optimization iterations in solution. Consequently, changes in thermal corrections associated with solvation are assumed to cancel in the ΔΔGs* term.. 6.

(16) ∗ After obtaining the free energy (∆𝐺𝑎𝑞 ) of the proton dissociation reaction in. solution from the above calculation, we can use the following formula to calculate pKa. The pKa values of various intermediate complexes were calculated for comparison with the experimental values; pKa is defined as pKa =. ∗ ∆𝐺𝑎𝑞 2.303𝑅𝑇. where R is the universal gas constant and T is the absolute temperature. In the ∗ standard state, ∆𝐺𝑎𝑞 of a proton dissociation reaction changes in 1 M solution. We ∗ can calculate ∆𝐺𝑎𝑞 by using a thermodynamic cycle.. ∆𝑮∗𝑶∣𝑹 = ∆𝑮°𝒈 + ∆∆𝑮∗𝑺 − 𝒎 ∙ ∆𝑮°→∗ ∆𝑮°𝒈 = 𝑮°𝒈 (𝑹) − 𝒎 ∙ 𝑮°𝒈 (𝑯+ ) − 𝑮°𝒈 (𝑶) ∆∆𝑮∗𝑺 = 𝑮°𝑺 (𝑹) − 𝒎 ∙ 𝑮°𝑺 (𝑯+ ) − 𝑮°𝑺 (𝑶). Scheme 3. Thermodynamic cycle for the standard free energy of reaction for the proton-coupled reduction of species O to species R in the gas phase and in aqueous solution... The standard reduction potential in a liquid solution was calculated using an approach similar to that described above. The reduction reaction can be expressed by a thermodynamic cycle in which R is the reduced acidic species and O is the oxidized 7.

(17) basic species, as shown in Scheme 3. The free energy of the electron in the gas phase is -0.006 kcal/mol.44 If m > 0, the reduction reaction is coupled with proton transfer and represented as a PCET process. The total free energy change in the aqueous phase is obtained from the thermodynamic cycle shown in Scheme 3.. The standard reduction potential can also be obtained using a thermodynamic cycle. The standard reduction potential is defined as: ∗ 𝐸𝑂/𝑅. ∗ ∗ (∆𝐺𝑂/𝑅 − 𝑛∆𝐺𝑁𝐻𝐸 ) ∆𝐺0∗ ∗ ∗ =− − 𝐸𝑆𝐶𝐸 = − − 𝐸𝑆𝐶𝐸 𝑛𝐹 𝑛𝐹. ∆𝐺0∗ is the standard free energy change relative to the normal hydrogen electrode (NHE) and ΔGNHE* has previously been reported as 4.28 eV. The standard reduction potential reported in the current study was shifted by -0.24 V with respect to the NHE because of the standard reference electrode (ESCE* = +0.24 V vs NHE) used in the experiments. The pH-dependent reduction potential was determined using the Nernst equation: ∗ 𝐸 = 𝐸𝑂/𝑅 +. 𝑅𝑇 𝑎𝑂 𝑚 ln ( ) − ∙ 0.0591 ∙ 𝑝𝐻 𝑛𝐹 𝑎𝑅 𝑛. If m > 0, the reduction reaction is coupled with proton transfer and represented as a PCET process. where, m is the number of protons, n is the number of electrons, R is the universal gas constant, T is the absolute temperature, F is the Faraday constant, and ai is the chemically active species ( i = R or O, where R is the reduced acidic species and O is the oxidized basic species ). At the half-potential for the reduction reaction, the second term is equal to zero. From the values of pKa and E obtained, we can draw the Pourbaix diagram.. 8.

(18) 2-4. Various Computational Methods for Constructing Pourbaix Diagrams 1. B3LYP/LANL08_PCM: Optimized in the gas phase. The PCM solvation model with B3LYP/LANL08 is used. 2. B3LYP/LANL08_PCM_SP: Optimized in the gas phase. Single-point solvation calculation is performed using the PCM solvation model with B3LYP/LANL08. 3. B3LYP/LANL08_SMD_SP: Optimized in the gas phase. Single-point solvation calculation is performed using the SMD solvation model with B3LYP/LANL08. 4. M11-L/MG3S_SMD_SP: Optimized in the gas phase. Single-point solvation calculation is performed using the SMD solvation model with M11-L/MG3S.. 9.

(19) Chapter 3. 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 E0 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 10.

(20) 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 [RuIII(OH2)(tpy)(Bpy)]3+(aq) → [RuIII(OH)(tpy)(Bpy)]2+(aq) + H+(aq), because one proton transfer is involved, the slope is 1. For [RuV(=O)(tpy)(Bpy)]3+(aq) + e→[RuIV(=O)(tpy)(Bpy)]2+(aq), because one electron transfer is involved, the slope is a. straight. line.. For. [RuIII(OH)(tpy)(Bpy)]2+(aq). +. H+(aq). +. e-. →. [RuIV(=O)(tpy)(Bpy)]2+(aq), because one proton transfer and one electron transfer are involved, the slope is -0.05916 units. For [RuIII(OH2)(tpy)(Bpy)]3+(aq) + 2H+(aq) + e→ [RuIV(=O)(tpy)(Bpy)]2+(aq), because the transfer of two protons and one electron is involved, the slope is -0.11832 units. For [RuII(OH)(tpy)(Bpy)]+(aq) + H+(aq) + 2e→ [RuIV(=O)(tpy)(Bpy)]2+(aq), because one proton and two electrons are transferred, the slope is -0.02958 units.. 11.

(21) 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. [RuIII(OH2)(tpy)(Bpy)]3+(aq) → [RuIII(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 [RuIV=O]/[RuV=O] couples potential decreased considerably. The [RuIV=O]/[RuV=O] couples potential values were 2.49, 2.35, 2.52, 2.32, 1.90, and 1.88 V (Table 1).. 12.

(22) (a). (b). Figure 1. Pourbaix diagram for the Ru(OH2)(tpy)(Bpy) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.. 13.

(23) (a). (b). Figure 2. Pourbaix diagram for the Ru(OH2)(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. 14.

(24) (a). (b). Figure 3. Pourbaix diagram for the Ru(OH2)(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. 15.

(25) Table 1. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(Bpy) at the density Functional Theory Level. reactions. predictionsa,b. predictionsa,c. predictionsa,d. predictionsa,e. predictionsa,f. predictionsa,g. pKa=4.3. pKa=0.8. pKa=4.1. pKa=1.6. pKa=3.7. pKa=8.9. pKa=19.0. pKa=16.9. pKa=19.0. pKa=17.7. pKa=19.8. pKa=20.1. Ru(OH2)(tpy)(Bpy) [RuIII(OH2)(tpy)(Bpy)]3+(aq) → [RuIII(OH)(tpy)(Bpy)]2+(aq) + H+(aq) II. [Ru (OH2)(tpy)(Bpy)] V. 2+. (aq). → [Ru (OH)(tpy)(Bpy)]. +. (aq). + e →[Ru (=O)(tpy)(Bpy)] IV. +H. 2+. (aq). E =2.35. E =2.52. E =2.32. E =1.90. Eo =1.88. [RuIII(OH2)(tpy)(Bpy)]3+(aq) + e- → [RuII(OH2)(tpy)(Bpy)]2+(aq). Eo =0.86. Eo =1.99. Eo =0.87. Eo =1.21. Eo =0.76. Eo =0.65. [RuIII(OH)(tpy)(Bpy)]2+(aq) + e- → [RuII(OH)(tpy)(Bpy)]+(aq). Eo =0.00. Eo =0.24. Eo =-0.01. Eo =0.26. Eo =-0.19. Eo =-0.01. 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. 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. 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. 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. (aq). -. +. E =2.49. [Ru (=O)(tpy)(Bpy)]. 3+. II. o. (aq). [RuIII(OH)(tpy)(Bpy)]2+(aq) + H+(aq) + e- → [RuIV(=O)(tpy)(Bpy)]2+(aq) II. [Ru (OH2)(tpy)(Bpy)]. 2+. III. [Ru (OH2)(tpy)(Bpy)] II. [Ru (OH)(tpy)(Bpy)] a o. +. (aq). 3+. +. +H. + e → [Ru (OH)(tpy)(Bpy)]. 2H+(aq). (aq) +. (aq) +. (aq). +. H. (aq). -. III. 2+. + e → [Ru (=O)(tpy)(Bpy)] -. IV. + 2e → [Ru (=O)(tpy)(Bpy)] -. IV. 2+. (aq). 2+. (aq). (aq). o. o. b. o. o. c. E and E1/2 are in units of V relative to the SCE. Calculation without extra water by PCM solvation model. Calculation 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.. 16.

(26) Second, for Ru(OH2)(tpy)(Bpm), the Bpm ligand is an innocent ligand. For [RuIII(OH2)(tpy)(Bpm)]3+(aq) → [RuIII(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 [RuIV=O]/[RuV=O] couples potential decreased considerably. The [RuIV=O]/[RuV=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 [RuII(OH2)(tpy)(Bpm)]2+. and. [RuIII(OH)(tpy)(Bpm)]2+. and. between. [RuIII(OH)(tpy)(Bpm)]2+ and [RuIV(=O)(tpy)(Bpy)]2+ are identical, implying that the reduction potential between [RuII(OH2)(tpy)(Bpm)]2+ and [RuIV(=O)(tpy)(Bpy)]2+ should be double of the identical values. This result is similar to that obtained from an experimental diagram.14. 17.

(27) (a). (b). Figure 4. Pourbaix diagram for the Ru(OH2)(tpy)(Bpm) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.. 18.

(28) (a). (b). Figure 5. Pourbaix diagram for the Ru(OH2)(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.. 19.

(29) (a). (b). Figure 6. Pourbaix diagram for the Ru(OH2)(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.. 20.

(30) Table 2. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(Bpm) at the density Functional Theory Level. reactions. predictionsa,b. predictionsa,c. predictionsa,d. predictionsa,e. predictionsa,f. predictionsa,g. pKa=-7.5. pKa=-0.9. pKa=-7.9. pKa=-0.6. pKa=2.4. pKa=6.3. pKa=15.3. pKa=15.7. pKa=16.9. pKa=16.7. pKa=18.6. pKa=18.1. Ru(OH2)(tpy)(Bpm) [RuIII(OH2)(tpy)(Bpm)]3+(aq) → [RuIII(OH)(tpy)(Bpm)]2+(aq) + H+(aq) [Ru. II. (OH2)(tpy)(Bpm)]2+(aq). V. → [Ru (OH)(tpy)(Bpm)]. +. (aq). + e →[Ru (=O)(tpy)(Bpm)] IV. +. E =2.46. E =2.66. E =2.44. E =1.96. Eo =2.06. [RuIII(OH2)(tpy)(Bpm)]3+(aq) + e- → [RuII(OH2)(tpy)(Bpm)]2+(aq). Eo =1.48. Eo =1.36. Eo =1.60. Eo =1.41. Eo =0.88. Eo =0.78. [RuIII(OH)(tpy)(Bpm)]2+(aq) + e- → [RuII(OH)(tpy)(Bpm)]+(aq). Eo =0.13. Eo =0.37. Eo =0.13. Eo =0.39. Eo =-0.08. Eo =0.08. 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. 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. 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. 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. (aq). -. 2+. H+(aq). E =2.50. [Ru (=O)(tpy)(Bpm)]. 3+. II. o. (aq). [RuIII(OH)(tpy)(Bpm)]2+(aq) + H+(aq) + e- → [RuIV(=O)(tpy)(Bpm)]2+(aq) [Ru. II. (OH2)(tpy)(Bpm)]2+(aq). III. [Ru (OH2)(tpy)(Bpm)] II. [Ru (OH)(tpy)(Bpm)] a o. +. 3+. +. +H. +. (aq) +. (aq) +. (aq). + e → [Ru (OH)(tpy)(Bpm)] -. III. + e → [Ru (=O)(tpy)(Bpm)] -. IV. 2H. (aq). +. + 2e → [Ru (=O)(tpy)(Bpm)]. H. (aq). 2+. -. IV. 2+. (aq). 2+. (aq). (aq). o. o. b. o. o. c. E and E1/2 are in units of V relative to the SCE. Calculation without extra water by PCM solvation model. Calculation 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.. 21.

(31) Third, Ru(OH2)(tpy)(tBu2Qn) has a quinone ligand, which is a NIL often seen in chlorophyll and which has high redox activity. For [RuII(OH2)(tpy)(Q)]2+(aq) → [RuIII(OH)(tpy)(SQ)]+(aq) + H+(aq), the pKa values were 7.4, 9.0, 5.9, 9.3, 9.8, and 12.2 (Table 3). For [RuIII(OH)(tpy)(Q)]2+(aq) → [RuIII(3αO‧-)(tpy)(ßSQ)]+ (aq) + H+(aq), the pKa values were 5.5, 7.0, 4.5, 7.4, 9.2, and 10.6 (Table 3). In Figures 7–9, a comparison of the Pourbaix diagrams shows that when water was added to Ru(OH2)(tpy)(tBuQn), the pKa values moved to the right in acidic pH conditions; 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 [RuIV=O]/[RuV=O] couples potential decreased considerably. The [RuIV=O]/[RuV=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, [RuIII(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 [RuIV=O]/[RuV=O] couples potential is not influenced by any ligand because of the reaction acting on the metal center. 22.

(32) (a). (b). Figure 7. Pourbaix diagram for the Ru(OH2)(tpy)(tBu2Qn) complexes in aqueous solution. (a) Calculation without extra water by PCM solvation model. (b) Calculation with extra water by PCM solvation model.. 23.

(33) (a). (b). Figure 8. Pourbaix diagram for the Ru(OH2)(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.. 24.

(34) (a). (b). Figure 9. Pourbaix diagram for the Ru(OH2)(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.. 25.

(35) Table 3. Calculated Values of pKa, Eo, and E1/2 with Ru(OH2)(tpy)(tBuQn) at the density Functional Theory Level. predictionsa,b. predictionsa,c. predictionsa,d. predictionsa,e. predictionsa,f. predictionsa,g. [RuIII(OH)(tpy)(Q)]2+(aq) → [RuIII(3αO‧-)(tpy)(ßSQ)]+ (aq) + H+(aq). pKa=5.5. pKa=7.0. pKa=4.5. pKa=7.4. pKa=9.2. pKa=10.6. [RuII(OH2)(tpy)(Q)]2+(aq) → [RuIII(OH)(tpy)(SQ)]+(aq) + H+(aq). pKa=7.4. pKa=9.0. pKa=5.9. pKa=9.3. pKa=9.8. pKa=12.2. [RuII(OH2)(tpy)(SQ)]+(aq) → [RuIII(OH)(tpy)(Cat)]0(aq) + H+(aq). pKa=19.8. pKa=18.9. pKa=17.1. pKa=19.1. pKa=18.1. pKa=19.4. [RuII(OH2)(tpy)(Q)]2+(aq) + e- → [RuII(OH2)(tpy)(SQ)]+(aq). Eo =0.46. Eo =0.50. Eo =0.47. Eo =0.49. Eo =0.21. Eo =0.25. reactions Ru(OH2)(tpy)(tBuQn). III. + e → [Ru (OH)(tpy)(Cat)]. E =-0.28. E =-0.08. E =-0.19. E =-0.09. E =-0.28. Eo =-0.18. [RuIV(=O)(tpy)(Q)]2+(aq) + e- → [RuIII(3αO‧-)(tpy)(βSQ)]+(aq). Eo =0.96. Eo =0.93. Eo =0.90. Eo =0.95. Eo =0.56. Eo =0.60. [RuIV(=O)(tpy)(Q)]2+(aq) + e- →[RuV(=O)(tpy)(Q)]3+(aq). Eo =2.58. Eo =2.38. Eo =2.43. Eo =2.36. Eo =1.95. Eo =1.97. E1/2 =1.29-0.05916×pH. E1/2 =1.34-0.05916×pH. E1/2 =1.17-0.05916×pH. E1/2 =1.39-0.05916×pH. E1/2 =1.10-0.05916×pH. E1/2 =1.22-0.05916×pH. E1/2 =1.24-0.05916×pH. E1/2 =1.28-0.05916×pH. E1/2 =1.11-0.05916×pH. E1/2 =1.27-0.05916×pH. E1/2 =1.08-0.05916×pH. E1/2 =1.18-0.05916×pH. E1/2 =1.13-0.05916×pH. E1/2 =1.16-0.05916×pH. E1/2 =1.04-0.05916×pH. E1/2 =1.16-0.05916×pH. E1/2 =1.04-0.05916×pH. E1/2 =1.09-0.05916×pH. E1/2 =0.89-0.05916×pH. E1/2 =1.04-0.05916×pH. E1/2 =0.82-0.05916×pH. E1/2 =1.04-0.05916×pH. E1/2 =0.79-0.05916×pH. E1/2 =0.97-0.05916×pH. E1/2 =1.56-0.11832×pH. E1/2 =1.69-0.11832×pH. E1/2 =1.38-0.11832×pH. E1/2 =1.72-0.11832×pH. E1/2 =1.62-0.11832×pH. E1/2 =1.81-0.11832×pH. E1/2 =0.39-0.02958×pH. E1/2 =0.54-0.02958×pH. E1/2 =0.42-0.02958×pH. E1/2 =0.53-0.02958×pH. E1/2 =0.37-0.02958×pH. E1/2 =0.46-0.02958×pH. [Ru (OH)(tpy)(SQ)]. +. -. (aq). III. 0. o. (aq). [RuIII(OH)(tpy)(Q)]2+(aq) + H+(aq) + e- → [RuIV(=O)(tpy)(Q)]2+(aq) II. [Ru (OH2)(tpy)(Q)]. 2+. (aq). III. +. II. +. [Ru (OH)(tpy)(SQ)]. [Ru (OH2)(tpy)(SQ)] II. [Ru (OH2)(tpy)(Q)] III. 2+. [Ru (OH)(tpy)(Cat)] a o. +. +H. (aq) (aq). +H. (aq) +. +. H. III 3α. 2+. (aq). + e → [Ru ( O )(tpy)( SQ)]. (aq). (aq). III. -. (aq). +. 2H. + e → [Ru (OH)(tpy)(Q)]. (aq). +. +H. (aq) +. 0. (aq). +. -. ‧-. ß. + e → [Ru (OH)(tpy)(SQ)] -. III. III 3α. β. +. +. (aq). + e → [Ru ( O )(tpy)( SQ)] -. III 3α. ‧-. β. +. + 2e → [Ru ( O )(tpy)( SQ)] -. ‧-. (aq). (aq). +. (aq). o. o. b. o. o. c. E and E1/2 are in units of V relative to the SCE. Calculation without extra water by PCM solvation model. Calculation 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.. 26.

(36) 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.. 27.

(37) Table 4. The pKa error analysis of Ru(OH2)(tpy)(tBu2Qn) without extra water. pKa Composition (kcal/mol). ∆EDFT. ∆ZPE. ∆Gcor. ∆∆Gsol. [RuIII(OH)(tpy)(Q)]2+(aq) → [RuIII(3αO -)(tpy)(ß SQ)]+ (aq) + H+(aq) ‧. B3LYP/LANL08/PCMa B3LYP/LANL08/PCM_SP. 200.66. -7.34. -7.05. 82.22. b. 200.66. -7.34. -7.05. 80.96. c. 200.66. -7.34. -7.05. 87.27. 199.56. -7.72. -6.94. 88.49. B3LYP/LANL08/SMD_SP M11L/MG3S/SMD II. [Ru (OH2)(tpy)(SQ)]. +. d. III. (aq). → [Ru (OH)(tpy)(Cat)]. B3LYP/LANL08/PCM. +H. (aq). 276.61. -8.61. -8.08. 26.80. b. 276.61. -8.61. -8.08. 23.11. c. 276.61. -8.61. -8.08. 24.54. 264.67. -8.67. -7.98. 29.01. B3LYP/LANL08/SMD_SP. a. (aq). +. a. B3LYP/LANL08/PCM_SP. M11L/MG3S/SMD. 0. d. Calculation 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.. 28.

(38) Table 5. The Eo error analysis of Ru(OH2)(tpy)(tBu2Qn) without extra water. Eo Composition (kcal/mol) III. •-. [Ru (O )(tpy)(Q)]. 2+. -. (aq). •-. IV. + e →[Ru (O )(tpy)(Q)]. B3LYP/LANL08/PCM. ∆Gcor. ∆∆Gsol. 301.22. -0.58. -0.18. -142.94. b. 301.22. -0.58. -0.18. -146.32. c. 301.22. -0.58. -0.18. -157.29. 302.86. -1.07. -1.11. -157.31. B3LYP/LANL08/SMD_SP M11L/MG3S/SMD. ∆ZPE. (aq). a. B3LYP/LANL08/PCM_SP. ∆EDFT 3+. d. [RuIII(OH)(tpy)(SQ)]+(aq) + e- → [RuIII(OH)(tpy)(Cat)]0(aq) B3LYP/LANL08/PCMa. 115.43. 1.32. 0.99. -24.09. b. 115.43. 1.32. 0.99. -22.10. B3LYP/LANL08/SMD_SPc. 115.43. 1.32. 0.99. -24.22. 126.88. 1.90. 2.59. -25.30. B3LYP/LANL08/PCM_SP. M11L/MG3S/SMD a. d. Calculation 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.. 29.

(39) (a). (b). Figure 10. Pourbaix diagram for the Ru(OH2)(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. 30.

(40) Chapter 4. Conclusion. In summary, we have used mononuclear Ru-based water oxidation catalysts of Ru(OH2)(tpy)(tBu2Qn), Ru(OH2)(tpy)(Bpm), and Ru(OH2)(tpy)(Bpy) (tBu2Q = 3,5-di-tert-butyl-2,2-benzoquinone,. tpy. =. 2,2′:6′,2″-terpyridine,. Bpm. =. 2,2′-bipyrimidine, bpy = 2,2'-Bipyridine) to calculate pKa and standard reduction potential (Eo). Compared with the standard reduction potential, the reduction potential obtained from the SMD system is better than that acquired from the PCM system and is closer to experimental values. The Pourbaix diagram of Ru(OH2)(tpy)(tBu2Qn), Ru(OH2)(tpy)(Bpm), and Ru(OH2)(tpy)(Bpy) in the SMD system yielded the same result: the reduction potentials decreased. In particular, the pH-dependent [RuIV=O]/[RuV=O] couples potential decreased considerably. In a high oxidation state, we find that the pH-dependent [RuIV=O]/[RuV=O] couples potential is not influenced by any ligand because of the reaction on the metal center in high oxidation state. The pKa values are not good in the SMD system. Ru(OH2)(tpy)(tBu2Qn) has a new intermediate complex [RuIII(3αO·-)(tpy)(βSQ)]+ that can undergo radical-radical coupling to form an O−O bond then produce oxygen. Finally, we find that M11-L/MG3S is better than B3LYP/LANL08 and shows good performance. Truhlar’s method is a convenient way to calculate pKa and oxidation potential, and the calculated values are close to experimental values.. 31.

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