Theoretical Investigation of Water Oxidation Processes on Small

Article pubs.acs.org/JPCA

Theoretical Investigation of Water Oxidation Processes on Small MnxTi2−xO4 (x = 0−2) Complexes Choongkeun Lee and Christine M. Aikens* Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, United States S Supporting Information *

ABSTRACT: Understanding the water oxidation process on small metal oxide complexes is fundamental for developing photocatalysts for solar fuel production. Titanium oxide and manganese oxide complexes have high potential as components of a cheap, nontoxic, and stable photocatalyst. In this theoretical work, the water oxidation process on MnxTi2−xO4 (x = 0−2) clusters is investigated at the BP86 level of theory using two water molecules and fully saturated systems. In the oxidation cycle using two water molecules, Mn reduces the reaction energy; however, Mn does not reduce the reaction energy on the fully saturated system. When two water molecules are used, the highest reaction energy in the water oxidation cycle is lower than 3 eV, but the highest reaction energy is higher than 3 eV on fully saturated systems except for the pure titanium oxide complex which has a highest reaction energy of 2.56 eV. Dehydrogenation processes in the water oxidation cycle require higher energy than the O−O formation or water adsorption processes. The overall dehydrogenation energy is usually smaller on complexes including at least one Mn atom and it is smallest on the Mn2O4 complex that has two water molecules. Considering the highest reaction energy in the overall water oxidation cycle, water oxidation at the manganese atom of MnTiO4 hydrated with two water molecules is the most favorable in energy.

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INTRODUCTION Efforts toward developing an alternative energy source to replace fossil based fuels have been undertaken for the past few decades because fossil based fuels are a limited resource and are a cause of environmental pollution. One approach for developing clean energy is in the use of hydrogen, because hydrogen produces only water after oxidation.1−4 Hydrogen is a fuel that can be stored and transported, so it has certain advantages over other alternative energy sources such as photovoltaics. Hydrogen can be obtained from water via a water oxidation reaction, eq 1, which is an endoergic chemical reaction. 2H 2O → 2H 2 + O2

(E0 = − 1.23 V)

Among various materials considered, the TiO2 complex has a great potential for inexpensive and clean solar energy conversion.9−11 Many challenges remain to develop photocatalysts using TiO2 due to a high overpotential and band gap.13 The overpotential for water oxidation strongly depends on the size and structure of the metal oxide catalyst. Recent theoretical work of water oxidation on a small Ti2O4 cluster showed that the overall reaction is downhill with an external potential of 3.2 V.14 This result on a small complex is different from the overpotential of 2.2 V on the bulk rutile TiO2(110) surface.9,15 The overpotential of molecular oxygen evolution is also different. The overpotential is 0.5 eV on the outside of a TiO2 nanotube, but it is 1.0 eV on the inside of a TiO2 nanotube.16 On TiO2 anatase(101) and rutile(110) surfaces, the first dehydrogenation step requires the highest overpotential but it does not strongly depend on the local surface structure; the overpotential of the dehydrogenation step can be reduced by doping.17 According to theoretical work modeling water oxidation on a Mn dimer model catalyst, the dehydrogenation step is the reaction step requiring the highest overpotential.13 The essential process of water oxidation on photocatalysts is the photogeneration of electron−hole pairs. There is a challenge to harvest electron−hole pairs effectively in titanium oxide because of its high band gap (3.0 eV for rutile and 3.2 eV for anatase).18−21 This energy is in the ultraviolet region, accounting for less than 5% of the full solar spectrum. Many dopants, including 3d transition metals, are being used to reduce the band

(1)

Current systems used for water oxidation require high overpotentials. After the first report of photoelectrochemical hydrogen evolution using titanium dioxide, many photocatalysts, including metal oxides and semiconductors, have been investigated both theoretically and experimentally.1−12 Mn, Fe, Co, Ni, Ru, Ir, and Ti containing compounds are frequently used for solar fuel production.6 A nanorod shaped TiO2 complex showed higher efficiency for water oxidation than the spherical shaped complex type because of a decreased probability of electron−hole recombination.7 Decreasing the overpotential for hydrogen evolution as well as reducing the recombination of the generated hole and electron are challenges in the development of high efficiency photocatalysts. According to previous theoretical work on water oxidation, RuO2 and IrO2 showed overpotentials, 0.37 and 0.56 eV, respectively, lower than TiO2.9 In spite of the low overpotentials of Ru and Ir oxides, challenges to develop photocatalysts using nontoxic and abundant materials still remain. © XXXX American Chemical Society

Special Issue: A. W. Castleman, Jr. Festschrift Received: January 28, 2014 Revised: March 25, 2014

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dx.doi.org/10.1021/jp501002x | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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gap.2,7,11,12,18 The doping materials usually generate a new band between the conduction and valence bands of the TiO2 complex. Our previous work described the Mn doping effect on the HOMO−LUMO band gap and structural changes of various TiO2 complexes.18 The band gap was significantly decreased by Mn doping, but it was not decreased proportionally to the number of doped Mn, unlike the bulk system.18 The aim of this research is to study the Mn doping effect on water oxidation on a small TiO2 complex. The water oxidation reaction on the MnxTi2−xO4 (x = 0−2) complex is investigated with two water molecules, which is the minimum number of water molecules necessary to complete the water oxidation cycle. The water oxidation cycle consists of two water adsorption steps, four dehydrogenation processes, and molecular oxygen generation. Our study shows that the water adsorption process is usually exothermic and the dehydrogenation and molecular oxygen generation processes are endothermic. In the water oxidation study using two water molecules, Mn doping reduces the reaction energy, so reaction energies at the Mn atom are usually smaller than those at Ti atom. We also examine the water oxidation on the fully saturated (six water molecules) MnxTi2−xO4 (x = 0−2) complex. In the study on the fully saturated system, the energy diagram of the Mn doped system is found to be quite different from that of pure Ti2O4. In the two water molecules system, the molecular oxygen generation step requires less energy than the reaction energy required in saturated system.

ΔEO2 = E(MO·O) − E(M) − E(O2 )

where ΔEads, ΔEdis, and ΔEW are water adsorption, water dissociation, and overall water reaction energies, respectively, and MO represents metal oxide. ΔEH and ΔEO2 are dehydrogenation and molecular oxygen generation energies, respectively.

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RESULTS AND DISCUSSION I. Water Oxidation Process with Two Water Molecules. We study the water oxidation process on MnxTi2−xO4 (x = 0−2) complexes. There are four possible pathways, as shown in Scheme 1. For the water dissociation process, only dissociation to a terminal oxygen is considered in this study because this process leads to a more stable isomer than dissociation to a bridging oxygen, according to our previous work.30 In path 1, hydrogen is removed after adsorption and dissociation of two water molecules, and then molecular oxygen, O2, is evolved. In path 2, molecular oxygen is evolved after two hydrogen atoms are removed from the first water molecule, followed by adsorption of the second water molecule. Paths 3 and 4 have the same initial steps as path 2 in which two hydrogen atoms are removed from the first adsorbed water, followed by evolution of molecular oxygen after the second water molecule adsorbs on a metal atom. These two pathways are distinguished by the location of the adsorption of the second water molecule. In path 3, the second water adsorbs at a different metal atom from the first adsorption. In path 4, the water adsorbs at the same metal atom as the first adsorption. The reaction energies through the lowest energy pathway are shown in Tables 1−4 for all processes and all isomers are shown in the Supporting Information. The water oxidation cycle consists of three basic processes. The first process involves adsorption and dissociation of two water molecules, which are denoted W1 and W2. Dissociation is considered after water adsorption because the activation energy for dissociation is not high and dissociative water adsorption on metal oxide complexes is frequently reported.30−33 The second process is the removal of four hydrogen atoms; these steps are denoted H1, H2, H3, and H4. This dehydrogenation process may have two subprocesses: proton ion removal (deprotonation, -H+) and electron removal (oxidation, -e−). There are three possible pathways for the dehydrogenation process, as shown in Scheme 2. One is a deprotonation dominant pathway, denoted P, in which one proton ion is removed from the complex, followed by oxidation. A second process is an oxidation dominant pathway, denoted Ox, in which the deprotonation process happens following the oxidation process. In addition, proton-coupled electron transfer (PCET) or hydrogen atom transfer (HAT) may alternatively occur. The third basic process is the molecular oxygen evolving process, which is denoted X. The four pathways mentioned in the above paragraph combine each of these processes but in a different order. The circled numbers in Tables 1−4 represent the order in which these processes occur for a given pathway. Lowest energy isomers are shown in the figures. A. Water Oxidation Process on the Pure Ti2O4 Complex. The water oxidation process on pure Ti2O4 is studied first. All reaction energies are shown in Table 1 and the lowest energy structures are shown in Figures 2−5. The adsorption and dissociation energies of the first water molecule, W1, are −1.15 and −1.18 eV, respectively, which leads to structure 1. This process is same for all four pathways. 1. Path 1. The second water W2 adsorption and dissociation process energies (leading to structure 2) are −1.18 and −1.21 eV,

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CALCULATION METHOD Geometry optimizations are performed with the Amsterdam Density Functional (ADF) package.22 All calculations are performed using the BP86 functional and the ATZP (augmented polarized triple-ζ) Slater orbital basis set.23−29 The water oxidation process is studied using Ti2O4, MnTiO4, and Mn2O4 systems. Metal complexes with two and six water molecules adsorbed are considered; these are partially and fully saturated, respectively.30 In the two water molecule system, all adsorbed water molecules are dissociated in the initial structure, but molecular water adsorption is observed in the fully saturated system. All initial structures are shown in Figure 1. In these

Figure 1. Initial structures of (a) Ti2O4, (b) MnTiO4, and (c) Mn2O4.

structures, the oxidation state of the Mn atom is set at 4+, because the oxidation state of Ti is also 4+. Unrestricted BP86 calculations are performed for the optimization of the initial MnTiO4 and Mn2O4 complexes; their multiplicities are quartet and septet, respectively.30 Restricted BP86 calculations are performed for Ti2O4 in its ground state; unrestricted calculations are employed for higher multiplicities. The reaction energies are calculated as follows: ΔEads = E(MO·OH 2) − E(MO) − E(H 2O)

(1)

ΔEdis = E(MOH ·OH) − E(MO·OH 2)

(2)

ΔE W = ΔEads + ΔEdis

(3)

ΔE H = E(MOH) − E(MO) − E(H 2)/2

(4)

(5)

B



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Scheme 1. Reaction Pathways of Water Oxidation of the MnxTi2−xO4 (x = 0−2) Complex

eV for -H+ and -e−, respectively, and 6.46 and −4.8 eV for -e− and -H+ through Ox, respectively. The reaction energy of -H+ in P is smaller than that in the first dehydrogenation process, but the oxidation energy in Ox is larger. The overall reaction energy of dehydrogenation is 1.66 eV, which is much smaller than that in the first dehydrogenation. The second dehydrogenation process, H2, leads to structure 4 (Figure 3), which has a singlet spin multiplicity and neutral charge. A triplet spin state is also possible when only the oxidation state of the metal atoms is considered, but the triplet state structure (4′) is less stable in energy by 1.22 eV compared to the singlet (4). Two electron configurations are possible for this system when two electrons are removed from the Ti atoms, nominally [p6, p4] and [p5, p5]; both of the configurations are possible for the triplet. Considering multipole derived charge (MDC) distributions of both structures, 4 and 4′, the former

respectively, which are similar to the W1 process (Figure 2). The first dehydrogenation process, H1, leads to structure 3 (Figure 3), in which the spin multiplicity is a doublet and the total charge is neutral. Only one electron configuration for the two titanium atoms is possible: [Ne]3s23p6 and [Ne]3s23p5 for Ti(IV) and Ti(V), respectively, which is denoted in this work by [p6, p5]. The overall reaction energy for dehydrogenation to 3 is 2.95 eV. The reaction energies through P are 1.71 and 1.26 eV for -H+ and -e−, respectively, and they are 6.38 (-e−) and −3.43 (-H+) eV through Ox. The oxidation step is highly endothermic if it occurs before loss of a proton ion. The system is likely to undergo proton transfer before electron transfer or alternately hydrogen atom or proton-coupled electron transfer. Two intermediate structures in the H2 process have doublet and triplet spin states; these are the reduced and oxidized forms of structure 3. The reaction energies through P are 1.08 and 0.58 C



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Table 1. Reaction Energies of Water Oxidation Cycle on the Ti2O4 Complex W1 ads path 1

path 2

path 3

path 4

W2 diss

ads

H1 diss

①−2.33 −1.15 −1.18

②−2.39 −1.18 −1.21

①−2.33 −1.15 −1.18

⑤−0.90

①−2.33 −1.15 −1.18

④−2.41 −1.21 −1.20

①−2.33 −1.15 −1.18

④−1.34

H2

H3

H4

-H+

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-H+

③2.95 1.71 6.38 1.82 6.15 1.82 6.15 1.82 6.15

1.24 −3.43 ②2.96 1.14 −3.19 ②2.96 1.14 −3.19 ②2.96 1.14 −3.19

④1.66 1.08 6.46 2.06 6.55 2.06 6.55 2.06 6.55

0.58 −4.80 ③1.67 −0.39 −4.88 ③1.67 −0.39 −4.88 ③1.67 −0.39 −4.88

⑤2.22 1.41 0.81 5.06 −2.84 ⑥−1.57 0.21 −1.78 2.12 −3.69 ⑤2.22 1.41 0.81 5.06 −2.84 ⑤1.05 1.23 −0.18 5.51 −4.46

⑥2.48 1.59 6.09 1.88 3.41 1.59 6.09 1.40 5.49

0.89 −3.61 ⑦0.34 −1.54 −3.07 ⑥2.48 0.89 −3.61 ⑥2.58 1.18 −2.91

O2

ΔEmax

⑦0.36

2.95

④4.78

4.78

⑦0.36

2.96

⑦0.36

2.96

respectively), the O−O distance significantly shortens, but the O−Ti bond is elongated. The singlet has stronger O−O and weaker O−Ti bonds. During this process, a peroxo group (O22−) is created and its electron configuration is [σ2s2σ*2s2, σ2p2, π2px2π2py2, π*2px2π*2py2, σ*2p2], but as mentioned above, two electrons from [σ*2p2] move and fill up the p-orbital of Ti, so it becomes [σ2s2σ*2s2, σ2p2, π2px2π2py2, π*2px2π*2py2, σ*2p0]. The dehydrogenation reaction energy to create structure 5 from 4 in Figure 3 is 2.22 eV. In 5, the O−O and O−Ti bond lengths are 1.35 and 2.04 Å, respectively, which are shortened O−O but lengthened O−Ti bond lengths compared to those for structure 3. The spin multiplicity of 5 is a doublet in which the [p6, p5] electron configuration is possible. A quartet spin multiplicity [p6, p3] or [p5, p4] is also possible, but it leads to structure 5′, which is higher in energy by 1.93 eV and has no O− O bond, like in structure 4′. In structure 5′, the bond distances of O−O and O−Ti are 2.63 and 1.77 Å, respectively, which are much longer and shorter than O−O and O−Ti of structure 5, respectively. When two electrons go back to oxygen, the O−O bond interaction gets weaker and the O−Ti interaction is stronger. The reaction energies are 1.41 (-H+) and 0.81 (-e−) eV for P and 5.06 (-e−) and −2.84 (-H+) for Ox, respectively. Structure 6 is formed from structure 5 by dehydrogenation (Figure 3). The reaction energy of the dehydrogenation process is 2.48 eV. Of the possible spin multiplicities, the singlet state gives the most stable structure, 6, in which all terminal oxygen atoms form O−O bonds to the adjacent oxygen atom, as shown in Figure 3. As mentioned above, when an O−O bond forms, two electrons (four in total in structure 6) move to the empty porbitals of Ti atoms, so that the p-orbitals of Ti atoms are fully occupied. The reaction energies are 1.59 (-H+) and 0.89 (-e−) eV for P and 6.09 (5″, -e−) and −3.61 (-H+) for Ox, respectively. Structure 5″ is a triplet oxidation structure of 5, in which one set

Scheme 2. Detailed Subprocess of Dehydrogenation, in Which Blue and Red Arrows Mean Deprotonation and Oxidation Processes, Respectivelya

a

P and Ox mean deprotonation and oxidation dominant processes, respectively. PCET is proton-coupled electron transfer and HAT is hydrogen atom transfer.

configuration appears to be more favorable, which may suggest why the singlet is more stable than the triplet. The charges of Ti at the left-hand side in 4 and 4′ in Figure 3 are reduced to about 3.2 and 3.6, respectively, from 5.6 of 2, but the charges of Ti at the right-hand side are increased to 6.4 and 6.2 of 4 and 4′, respectively. Charges of oxygens for the bridging oxo group, terminal OH groups, and O−O of 4 are −2.8, −1.7, and −0.5, respectively, which are similar to −2.6, −2.0, and −0.8 of 4′, respectively. The first two values do not change much from −2.5 and −1.9 in 2, but the third is quite increased from −1.9. It shows that the O−O moiety is more positive in 4 than in 4′. This suggests a change in binding between the two structures. A terminal oxo oxygen (O) has a formal −2 charge; creation of a peroxo group (O22−) from two oxo groups leads to a return of two electrons to the metal atoms. The bond lengths of O−O and O−Ti are 1.48 and 1.83 Å, respectively, in structure 4. Compared to the corresponding distances in 4′ (2.50 and 1.78 Å,

Figure 2. Water adsorption and dissociation on the Ti2O4 complex. Relative energies are in electrovolts. D



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Figure 3. Water oxidation process path 1 on the Ti2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

Figure 4. Water oxidation process path 2 on the Ti2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

of terminal oxygens have a bond. A singlet isomer (not shown) of 5″ is possible in which both sets of oxygen atoms form a bond, but it is less stable than the triplet structure (5″) by 0.56 eV. Two more isomers of 6 exist, which are triplet (6′) and quintet (6″) structures, but they are higher in energy by 0.06 and 5.28 eV than 6. In the triplet, two terminal oxygens at one side form an O−O bond, but they do not form a bond at the other side. All terminal

oxygens in the quintet exist as separate oxo groups without forming a bond. The reaction energy to generate molecular oxygen is 0.36 eV when the starting structure is considered to be the product. Unfortunately, when O−O forms a double bond and molecular oxygen is generated from 6, it can lead to quite a different structure (0′) from the starting structure, as shown in Scheme 1 and Figure 3. Structure 0′ is much less stable in energy by 4.34 eV E



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Figure 5. Water oxidation processes paths 3 and 4 on the Ti2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

that for path 1. It may not be easy to form a coordinate bond between water and Ti atom because the Ti atom is electron rich. In 10, the oxygen in the adsorbed water is located in almost the same plane as Ti and the bridging oxygen atoms. The last two processes, H3 and H4, lead to structures 11 and 0, with reaction energies of −1.57 and +0.43 eV. In H3, the reaction energies of -H+ and -e− for P are +0.21 and −1.78 eV, respectively. The former energy is much smaller compared to all of the previous deprotonation energies in the deprotonation dominant pathways; in addition, the oxidation energy is exothermic. The reaction energies of -e− and -H+ for Ox are +2.12 and −3.69 eV, respectively. The oxidation energy of Ox is quite small compared to other values such as H3 in path 1 of about 5 eV. In H4, the reaction energies of -H+ and -e− for P are +1.88 and −1.54 eV, respectively, and the energies of -e− and -H+ for Ox are +3.41 and −3.07 eV, respectively. The oxidation energies in H3 and H4 are much smaller compared to those in path 1. The possible electron configuration of 10 is [p6d1, p6d1 or p6d2, p6d0] in which the oxidation state of Ti atoms is same as that of 9. Unlike path I, two electrons occupy Ti d-orbitals. The lower dehydrogenation energy may be due to electron removal from a d-orbital. 3. Path 3. The W1, H1, and H2 processes are the same as path 2 leading up to structure 8. From 8, water adsorption process W2 could lead to an intermediate in which the water adsorbs at the other Ti atom rather than the one the first water adsorbed to; this process is exothermic by −1.21 eV (Figure 5). The dissociation process leads to structure 4 with a dissociation energy of −1.20 eV; further processes would follow path 1. The singlet spin multiplicity does not change during this dissociation process. 4. Path 4. Like path 3, W2 happens after reaching structure 8. In W2, leading to 12, the second water adsorbs at the same Ti atom that adsorbed the first water molecule (which is different from path 3) with a reaction energy of −1.34 eV (Figure 5). The water dissociation process occurs simultaneously with the adsorption process. The reaction energy is smaller than the overall reaction energy of adsorption and dissociation in path 3. The overall reaction energies of H3 and H4 are 1.05 and 2.58 eV, respectively, which lead to structures 13 and 14, respectively.

than the starting structure 0. It is not clear how this system would return to the starting structure in a catalytic cycle. Formation of triplet molecular oxygen from a singlet titanium complex is not ideal, as the product titanium complex would then be in a triplet state; formation of molecular oxygen from a triplet titanium complex is preferred. In addition, the oxygen atoms must rearrange to regenerate the starting complex. During this process, the electron configuration of the peroxo group (O22−) on the titanium complex is [σ2s2σ*2s2, σ2p2, π2px2π2py2, π*2px2π*2py2, σ*2p0] because two electrons move to a p-orbital of a Ti atom in structure 4, as mentioned above. When molecular oxygen is generated, two more electrons, one at [π*2px] and another one at [π*2py], move and occupy a p-orbital of Ti. 2. Path 2. In this pathway, dehydrogenation from the first adsorbed water occurs before the second water adsorbs, as shown in Figure 4. The reaction energies of H1 (leading to 7) and H2 (leading to 8) are 2.96 and 1.67 eV, respectively. The energies are almost the same as those in path 1. In the first dehydrogenation, the reaction energies are 1.82 (-H+) and 1.14 (-e−) eV for P and +6.15 (-e−) and −3.19 (-H+) for Ox, respectively. The reaction energies of H2 are +2.06 (-H+) and −0.39 (-e−) eV for P and +6.55 (-e−) and −4.88 (-H+) for Ox, respectively. Again, the Ox pathway is unlikely to occur because of the large endothermicity of the electron removal. The P pathway is possible, but HAT or PCET is likely in this case so as to reduce the magnitude of the endothermic step. The spin multiplicities of structure 7 and 8 are doublet and singlet, respectively. In the case of 8, a triplet (8′) is also possible, but this structure is higher in energy by 1.08 eV and the O−O bond has not been formed. In path 2, molecular oxygen is generated after H1 and H2. This process (leading to 9) requires 4.78 eV, which is much larger than in path 1. This step is likely highly endothermic because it leads to a very low coordinated titanium atom. When the OO double bond forms, two electrons move to Ti atoms and the two Ti atoms have similar MDC values of about 2.0. The spin multiplicity of 9 is a triplet in which the oxidation states of the two Ti atoms are Ti(III), Ti(III). The next process is the second water molecule adsorption, W2, which leads to structure 10. The reaction energy is −0.90 eV, which is much smaller compared to F



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Figure 6. Water adsorption and dissociation on the MnTiO4 complex. Relative energies are in electronvolts.

Table 2. Reaction Energies of Water Oxidation Cycle at Ti in the MnTiO4 Complex W1 ads

W2 diss

ads

H1 diss

-H

+

-e− ①−2.37 −1.22 −1.15

②−1.35 −0.66 −0.69

path 2

①-2.37 −1.22 −1.15

⑤−1.02

path 3

①-2.37 −1.22 −1.15

④−1.38 −0.87 −0.51

path 4

①-2.37 −1.22 −1.15

④−1.25

path 1

H2 -e

−

-H+

③0.94 −0.62 −3.92 ②1.73 1.47 0.26 5.25 −3.52 ②1.73 1.47 0.26 5.25 −3.52 ②1.73 1.47 0.26 5.25 −3.52 1.56 4.86

-H

+

H3 -e

-e−

−

-H+ ④1.96

1.45 5.29

0.51 −3.33 ③2.74 1.87 0.87 6.57 −3.83 ③2.74 1.87 0.87 6.57 −3.83 ③2.74 1.87 0.87 6.57 −3.83

-H

+

-e−

H4 -e

−

-H+

⑤1.04 0.17 0.87 6.17 −5.13 ⑥−1.00 0.13 −1.13 3.34 −4.34 ⑤1.20 0.35 0.85 6.34 −5.14 ⑤1.05 0.87 0.18 5.40 −3.83

-H

+

-e−

-e

O2

ΔEmax

⑦2.17

2.56

④4.13

4.13

⑦2.17

2.74

⑦1.48

2.74

−

-H+

⑥2.56 1.60 0.96 7.11 −4.55 ⑦0.74 3.56 −2.82 4.28 −3.54 ⑥0.86 −0.10 0.96 6.46 −5.60 ⑥1.57 1.17 0.40 5.40 −3.83

Figure 7. Water oxidation process path 1 at Ti of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

The reaction energies of subprocesses of -H+ and -e− for P are +1.23 and −0.18 eV respectively, and -e− and -H+ for Ox are +5.51 and −4.46 eV, respectively, in H3. In H4, reaction energies of -H+ and -e− for P are 1.40 and 1.18 eV respectively, and -e− and -H+ for Ox are +5.49 and −2.91 eV, respectively. In path 4, O O formation requires 0.36 eV. Unlike the other pathways (paths

1, 2, and 3), path 4 leads to direct formation of the initial structure 0 from triplet 14 without oxygen rearrangement. On Ti2O4, the step in the water oxidation cycle requiring the highest energy is the first dehydrogenation process, which is approximately 2.95 eV for the most endothermic step, but in path 2, OO formation is the most endothermic step. The OO formation step typically requires less than 1 eV except in path 2 in G



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Figure 8. Water oxidation process path 2 at Ti of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

reaction energies of +4.86 and −3.92 eV for -e− and -H+; because this process continues to be unlikely, it will not be further discussed in this section. The overall H1 reaction energy is 0.94 eV, which is much smaller than 2.95 eV of the Ti2O4 complex, but the overall energy of H2 is 1.96 eV, which is larger than 1.66 eV of the pure Ti2O4 complex. The reason is not clear, but it seems that the dehydrogenation reaction at the Mn site requires lower energy than that at the Ti site. The reaction energies of -H+ and -e− of P are 1.45 and 0.51 eV, respectively. H3 leads to structure 20, whose spin multiplicity is a singlet because the 3 electrons from d-orbitals of Mn atom are completely removed through this dehydrogenation process. A triplet isomer is possible similar to the pure Ti2O4 complex, but the triplet isomer (not shown) of 20 has almost the same structure as 20 and a slightly higher energy by 0.05 eV. To be a triplet state, the two terminal oxygen atoms at Mn site have to form a single bond and donate two electrons to dorbitals on the Mn atom, but 20 does not have single bond character between terminal oxygen atoms, as shown in Figure 7. The electron transfer process from oxygen to metal produces a more stable isomer in the Ti2O4 complex, but in this MnTiO4 complex, the electrons would occupy d-orbitals of the metal atom, which does not make this system particularly stable. A triplet isomer is the most stable in the deprotonated structure of 20. A singlet isomer (not shown) having a single O−O bond at the Ti site is higher in energy by 0.96 eV than the triplet. Structure 21 formed by H4 has a doublet spin state. As mentioned in path 1 of Ti2O4 complex, OO generation between terminal oxygens does not produce the starting structure 15. A doublet intermediate structure, 21′, in which the O−O bond forms between the two terminal oxygens at the Ti and the Mn atom may form. 21′ is less stable than 21 by 0.43 eV and the molecular oxygen generation energy from 21′ is 1.74 eV. The overall molecular oxygen generation energy is 2.17 eV, which is much larger compared to that of path 1 of Ti2O4 complex.

which it needs 4.78 eV. Of the two subprocesses in dehydrogenation, the oxidation-first process requires higher energy than the deprotonation-first pathway. When even numbers of hydrogen atoms are removed, the singlet state is generally more stable than the triplet state, because an O−O bond forms and two electrons fill the empty p-orbital on Ti atoms. The H1 and H2 dehydrogenation energies do not greatly differ whether a second water molecule is adsorbed or not. B. Water Oxidation Process at the Ti atom of the MnTiO4 Complex. In MnTiO4, oxygen evolution due to water oxidation can occur at either atom. This section focuses on oxygen evolution at the Ti atom. The spin multiplicity of the initial structure is a quartet, with electronic configurations of Mn(IV) and Ti(IV) of [Ne]3s23p63d3 and [Ne]3s23p6, respectively, which are denoted by [p6d3,p6]. The water adsorption and dissociation processes on this MnTiO4 complex are shown in Figure 6. The W1 process at Ti atom, leading to 16, is exothermic by −2.37 eV (−1.22 and −1.15 eV for adsorption and dissociation, respectively), which is similar to −2.33 eV of the Ti2O4 system. There are two possible ways for the second water to adsorb. The second water can adsorb at the Ti site, which is the same atom as the first, or it can adsorb at the Mn site. Our previous work shows that the former structure is less stable energetically than the latter one.30 Thus, the remaining steps in the water oxidation cycle are described with water adsorbed at the Mn site except in path 4. The reaction energies are shown in Table 2. 1. Path 1. The energy of W2 which leads to 17 is −1.35 eV (−0.69 and −0.66 eV for adsorption and dissociation, respectively). H1, leading to 18, and H2, leading to 19, processes are shown in Figure 7. The first dehydrogenation drives two isomers, 18 and 18′. In structures 18 and 18′, hydrogen is removed from the hydroxide on the Mn or Ti atom, respectively. The former is more stable than the latter by 0.95 eV. Its electron configuration is [p6d2, p6]. The energies of -H+ and -e− of the P process are +1.56 and −0.62 eV, respectively. The Ox process has H



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Figure 9. Water oxidation processes paths 3 and 4 at Ti of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

2. Path 2. In this pathway, H1 (leading to 22) and H2 (leading to 23) occur after W1 with energies of 1.73 and 2.74 eV (Figure 8). H1 is smaller but H2 is larger compared to these steps for the pure Ti2O4 complex. The subprocess energies of H1 are 1.47 and 0.26 eV for -H+ and -e− of P. In H2, the energies of -H+ and -e− for P are +1.87 and −0.87 eV. A HAT or PCET pathway here would require only 1.00 eV. In 23, the quartet state is slightly more stable than the doublet state by 0.07 eV, although the spin multiplicity of the oxidized form of 22 is a doublet (a quartet structure is possible, but it is less stable than the doublet by about 0.5 eV). The expected oxidation state and electron configuration of the metal atoms are MnVITiIV and [p6d1, p6], respectively. MDC values of Mn and Ti are about 0.2 and 4.0 and the charges of all oxygens are about −1, except Ot at the Mn atom, which has a charge of 0.1. Considering the charge distribution, electrons are concentrated at the Mn atom. It appears that two electrons from the oxygens transfer to the Mn atom similar to structure 8 in Figure 4, but the reason is not clear how electrons transfer from oxygen to metal without O−O formation. When the bond lengths between terminal oxygen and Ti atom in 8 and 8′ and 23 are compared, the electron transfer is quite different from that in 8. The Ti−O and O−O distances, respectively, are about 1.8 and 1.5 Å in 8, about 1.8 and 2.7 Å in 8′, and about 1.7 and 2.7 Å in 23. 8′ and 23 have similar bond lengths, but in 23 the Ti−O distance is slightly shortened. The O−O distance of 23 is slightly lengthened by about 1.5 Å from 8, which has a single O−O bond. No single bond character is evident between terminal oxygen atoms in 23. The Ti−O bond in 23 is shorter than 1.8 Å found in 8 and 8′. Structure 24 has a sextet state because a total of four electrons are transferred to d-orbitals of Mn when molecular oxygen is generated. The possible electron configuration of 24 is [p6d5, p6]. All atoms in 24 are on a single plane, as shown in Figure 8. The second water adsorption reaction, W2, is exothermic by −1.02 eV like in Ti2O4, which leads to structure 25. In 25, the water is

located slightly out of the plane of 24. The reaction H3 leads to a quintet 26 which is exothermic by −1.00 eV. The reaction energies of subprocess P are +0.13 and −1.13 eV for -H+ and -e−, respectively. Dehydrogenation process H4 returns the system to the starting quartet structure 15, with a reaction energy of 0.74 eV. The reaction energies of subprocess P are +3.56 and −2.82 eV for -H+ and -e−, respectively. Thus, HAT or PCET is more likely for this step. 3. Path 3. In this pathway, a second water adsorbs at the Mn atom in structure 23, which leads to structure 27 (Figure 9). The overall energy of W2 is −1.38 eV, whose subprocess reaction energies are −0.87 and −0.51 eV for adsorption and dissociation processes, respectively. Dehydrogenation processes H3 and H4 lead to structures 28 and 21. The following process, O2, is the same as that in path 1. The spin multiplicity is a quartet for 27, and a triplet in 28 and the oxidized structure of 27, but it is a doublet in the lowest energy deprotonated structure. The possible electron configuration of the deprotonated structure is [p6d1, p6] for this doublet state. The reason why the structure is more stable in the doublet state is not clear, because the structure does not change much and the bond length of Ti−O is almost the same in both 27 and its deprotonated structure. The distance between two terminal oxygen atoms is only slightly lengthened by about 0.1 Å and the bond length of Mn−O(H) is slightly shortened by about 0.15 Å by the deprotonation. The molecular oxygen generation energy is 2.17 eV which is much larger than that of path 3 for Ti2O4. 4. Path 4. The W2 process happens at the Ti site in this pathway. This process, leading to 29 (Figure 9), is dissociative adsorption. The adsorption energy is −1.25 eV, which is smaller than that in path 3. In 29, the adsorbed water forms an O−O bond with one of the terminal oxygen atoms. Dehydrogenation processes H3 and H4 lead to structures 30 and 31. The overall energies are 1.04 and 1.57 eV for H3 and H4. The former is I



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Table 3. Reaction Energies of Water Oxidation Cycle at Mn in the MnTiO4 Complex W1 ads path 1

path 2

path 3

path 4

W2 diss

ads

H1 diss

①−2.37 −1.22 −1.15

②−1.35 −0.66 −0.69

①−1.25 −0.71 −0.54

⑤−1.07

①−1.25 −0.71 −0.54

④−2.42 −1.28 −1.14

①−1.25 −0.71 −0.54

④−0.11

H2

H3

H4

-H+

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-H+

1.56 4.86 1.60 4.86 1.60 4.86 1.60 4.86

③0.94 −0.62 −3.92 ②0.89 −0.71 −3.97 ②0.89 −0.71 −3.97 ②0.89 −0.71 −3.97

④1.96 1.45 5.29 1.28 5.39 1.28 5.39 1.28 5.39

0.51 −3.33 ③0.95 −0.33 −4.44 ③0.95 −0.33 −4.44 ③0.95 −0.33 −4.44

⑤1.04 0.17 0.87 6.17 −5.13 ⑥−0.26 1.00 −1.26 3.45 −3.71 ⑤2.05 1.18 0.87 5.88 −3.83 ⑤2.11 1.41 0.70 5.41 −3.30

⑥2.75 1.60 7.11 2.08 5.03 1.60 7.11 1.27 5.43

1.15 −4.36 ⑦1.26 −0.81 −3.77 ⑥2.75 1.15 −4.36 ⑥1.32 0.05 −4.11

O2

ΔEmax

⑦1.98

2.75

④4.43

4.43

⑦1.98

2.75

⑦1.04

2.11

Figure 10. Water oxidation process path 1 at Mn of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

Figure 11. Water oxidation process path 2 at Mn of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

similar to that in path 3, but the latter is much higher. The molecular oxygen generation energy is 1.48 eV.

For the water oxidation cycle at Ti of MnTiO4, the highest energy process is a dehydrogenation process, except for OO J



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Figure 12. Water oxidation processes paths 3 and 4 at Mn of the MnTiO4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

33 has a higher energy than 16 by 1.12 eV. The reaction energies are −0.71 and −0.54 eV for adsorption and dissociation, respectively. The first dehydrogenation process, H1, leads to triplet 34 with an overall reaction energy of 0.89 eV. The energies of subprocess P are +1.60 and −0.71 eV for -H+ and -e−, respectively. The energy of H2 leading to doublet 35 is 0.95 eV. A quartet isomer, 35′, is possible, but it is less stable by about 1.8 eV than 35; however, it has an oxygen−oxygen bond unlike 35. The energies of H1 and H2 at the Mn site are smaller compared to those at the Ti site. The molecular oxygen generation process leads to sextet 36, in which the possible electron configuration is [p6d5, p6]. The reaction energy is 4.43 eV, which is larger than that at the Ti site but smaller than that on Ti2O4. It should be noted that a multiplicity change from double to sextet would not be allowed, so it is possible this pathway would actually proceed through higher energy structures such as 35′. The second water adsorption, W2, leads to sextet structure 37, which is more stable than 25 by 1.26 eV. The reaction energy of W2 is −1.07 eV. The third dehydrogenation process leading to quintet structure 38 is exothermic by −0.26 eV like path 2 on Ti2O4 and at the titanium atom of MnTiO4. The energies of subprocess P are +1.00 and −1.26 eV for -H+ and -e−, respectively. Structure 38 is changed into the initial structure, 15, by the fourth dehydrogenation process whose reaction energy is 1.27 eV. It is larger by about 0.5 eV compared to the energy for the related process at the Ti site. The subprocess reaction energies of H4 are +2.08 and −0.82 eV for -H+ and -e− of P, respectively. 3. Path 3. The processes leading to 35 from 15 (W1, H1, and H2) are the same as those of path 2. The W2 process leading to structure 39 (Figure 12) is exothermic by −2.42 eV, with energies of adsorption and dissociation of −1.28 and −1.14 eV, respectively. The third dehydrogenation, H3, leads to singlet 20; after this, the water oxidation process follows path 1. The reaction energy of H3 is 2.05 eV, which is larger than 1.04 eV, leading to 20 from 19 in path 1. The highest reaction energy is 2.75 eV at H4 as in path 1.

bond formation in path 2, which requires 4.13 eV. The highest dehydrogenation energy is 2.56 eV for path 1 and 2.74 eV for the others. The molecular oxygen generation energies are larger than 1 eV, which is quite different from the energy for the pure Ti2O4 complex of less than 1 eV for most pathways, although in path 2 the energy is smaller than that in Ti2O4 by 0.65 eV. Dehydrogenation on MnTiO4 is more favorable in energy than on Ti2O4 due to the lowered dehydrogenation energies, but O O bond formation on Ti2O4 is more favorable because it is less endothermic. C. Water Oxidation Process at the Mn atom of the MnTiO4 Complex. This section focuses on water oxidation at the Mn atom of MnTiO4. Reaction energies are shown in Table 3. The first water adsorption and dissociation at the Mn atom is the same as the process in the previous section. The other processes are described below. 1. Path 1. The first three dehydrogenation processes in this pathway are the same as path 1 in the previous section because the lowest reaction energy pathway is considered. The difference occurs at the fourth dehydrogenated structure, 32 (Figure 10) which does not include an O−O bond interaction at the Ti atom site unlike structure 21. Structure 32 is slightly less stable than structure 21 by about 0.2 eV. The fourth dehydrogenation energy is a little bit different from that at the Ti atom site, because it leads to this different structure. The overall energy is 2.75 eV, which is higher by 0.19 eV than the process at the Ti site. The expected intermediate structure is 21′ for forming an OO double bond, which is the same as for path 1 in the previous section. This intermediate structure has a higher energy than 32 by 0.24 eV, and the molecular oxygen generation energy is 1.74 eV. The overall reaction energy is 1.98 eV, which is smaller than that at the Ti atom site, but it is much higher than molecular oxygen generation on Ti2O4. 2. Path 2. In path 2, the first water adsorption and dissociation process, leading to 33, is different from that of path 1, because the process at the Mn atom site is considered (Figure 11). Structure K



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Table 4. Reaction Energies of Water Oxidation Cycle on THE Mn2O4 Complex W1 ads path 1

path 2

path 3

path 4

W2 diss

ads

H1 diss

①−1.33 −0.62 −0.71

②−1.13 −0.67 −0.46

①−1.33 −0.62 −0.71

⑤−0.74

①−1.33 −0.62 −0.71

④−1.22 −0.69 −0.53

①−1.33 −0.62 −0.71

④−0.18

H2

H3

H4

-H+

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-e−

-H+

-e−

-H+

-e−

-H+

-e−

-H+

1.38 4.74 1.11 5.47 1.11 5.47 1.11 5.47

③0.70 −0.68 −4.04 ②0.85 −0.26 −4.62 ②0.85 −0.26 −4.62 ②0.85 −0.26 −4.62

1.19 5.35 0.99 5.70 0.99 5.70 0.01 5.70

④0.90 −0.29 −4.45 ③0.91 −0.08 −4.79 ③0.91 −0.08 −4.79 ③0.91 0.90 −4.79

⑤0.86 0.83 0.03 5.41 −4.55 ⑥−0.35 0.50 −0.85 3.57 −3.92 ⑤0.79 0.76 0.03 5.66 −4.87 ⑤2.44 2.37 0.07 5.56 −3.12

⑥1.07 0.48 6.19 1.50 5.36 0.48 6.19 0.78 5.69

0.59 −5.12 ⑦1.34 −0.16 −4.02 ⑥1.07 0.59 −5.12 ⑥0.87 0.09 −4.82

O2

ΔEmax

⑦3.88

3.88

④4.27

4.27

⑦3.88

3.88

⑦1.39

2.44

Figure 13. Water adsorption and dissociation on the Mn2O4 complex. Relative energies are in electronvolts.

Figure 14. Water oxidation process path 1 on the Mn2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

4. Path 4. The W1, H1, and H2 processes are the same as those in path 2. The second water adsorption, W2, at the Mn atom leads to 40 in which the water molecule is only physically adsorbed, as shown in Figure 12. The reaction energy of W2 is −0.11 eV, which is smaller than that of W2 at the Ti site in path 3. The third dehydrogenation process, H3, leads to singlet structure 41, whose reaction energy is 2.11 eV. During the H3 process the

hydroxide binds to the Mn atom. The distance between oxygen and Mn is about 2.5 Å in 40 but about 1.9 Å in 41. The energies of the P subprocess of H3 are +1.41 and −0.70 for -H+ and -e−. In H4 leading to doublet 42, an O−O single bond forms. Two possible electron configurations are possible, [p5d0, p6] and [p6d1, p6]. In the latter case, two electrons transfer from O−O to the Mn atom. The reaction energy of H4 is 1.32 eV. The L



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Figure 15. Water oxidation process path 2 on the Mn2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

Figure 16. Water oxidation process paths 3 and 4 on the Mn2O4 complex. Relative energies are in electronvolts. The black arrows represent the overall reaction pathway, the blue arrows represent the deprotonation reactions, and the red arrows represent the oxidation reactions. Parenthetic numbers represent total charge and spin multiplicity.

molecular oxygen generation energy from structure 42 is 1.04 eV. The highest reaction energy process in path 4 is the third dehydrogenation process, which is smaller than the highest reaction energy of any other pathway at the Mn site. In the water oxidation process at the Mn atom site, many processes are same as those at the Ti atom site. The highest reaction energy process is dehydrogenation from the second adsorbed water molecule, except in path 2 in which it is the molecular oxygen generation process. Considering the highest

energy step, path 4 is the most favorable in energy, in which the highest energy step is 2.11 eV. The molecular oxygen generation energy is 1.04 eV, which is also smaller than this step in other pathways at Mn of MnTiO4. The potential issue with the feasibility of path 4 is the strength of the W2 interaction. D. Water Oxidation Process on the Mn2O4 Complex. The spin multiplicity of the initial structure, 43, is a septet and the oxidation state of Mn atom is 4+ to maintain the neutrality of the complex. Reaction energies for the water oxidation process on M



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pure Mn2O4 are shown in Table 4. The first water adsorption and dissociation process, W1, leading to 44 from 43 is the same in all four pathways. The overall energy is −1.33 eV; the adsorption and dissociation energies are −0.62 and −0.71 eV, respectively. 1. Path 1. The water adsorption and dissociation processes are shown in Figure 13. The energy for W2 is −1.13 eV in which the adsorption and dissociation energies are −0.67 and −0.46 eV, respectively. The adsorption energies in W1 and W2 are similar, but the dissociation energy in W1 is larger than that in W2. The first dehydrogenation process, H1, leads to sextet structure 46, with an overall reaction energy of 0.70 eV (Figure 14). The energies of the subprocesses are +1.38 and −0.68 eV for -H+ and -e− of P and +4.74 and −4.04 eV for -e− and -H+ of Ox, respectively. As before, HAT or PCET is likely for this case. The reaction energy of H2 leading to quintet 47 is 0.90 eV. Process H3 leads to quartet structure 48 with an overall reaction energy of 0.86 eV. The fully dehydrogenated structure 49, a triplet, occurs from process H4 with a reaction energy of 1.07 eV. Structure 49 does not show strong O−O bond interaction as observed in the related Ti2O4 complex, 6, in Figure 3. The possible electron configuration is [p6d1, p6d1], because the electron transfer from oxygen to Mn atom does not occur. To produce starting structure 43 after molecular oxygen generation, an intermediate structure 49′ is expected which is higher in energy by 1.98 eV. In 49′, an O−O bond forms between two terminal oxygens from different Mn atoms. The overall reaction energy of molecular oxygen generation is 3.88 eV. 2. Path 2. The W1 process is the same as that in path 1 described above. The H1 process leads to sextet structure 50 with an overall reaction energy of 0.85 eV. The second dehydrogenation process, H2, leads to quintet structure 51, with a reaction energy of 0.91 eV. The molecular oxygen generation process leads to nonet structure 52 with a reaction energy of 4.27 eV. Because the quintet to nonet conversion is not possible, this pathway would need to proceed via higher energy isomers. In 52, the electron configuration is [p6d4, p6d4] and the oxidation state of the Mn atoms is 3+. The W2 process leads to structure 53 and the reaction energy is −0.74 eV. The H3 process is an exothermic reaction like path 2 in Ti2O4 and MnTiO4. The dehydrogenation energy leading to octet structure 54 is −0.35 eV, with subprocess energies of +0.50 and −0.85 eV for -H+ and -e− of P, respectively. The fourth dehydrogenation process, H4, leads to the initial structure 43. The overall reaction energy is 1.34 eV, with subprocess energies of +1.50 and −0.16 eV for -H+ and -e− of P, respectively. In the P subprocesses of H3 and H4, the deprotonated structures are almost planar, as shown in Figure 15. 3. Path 3. The W1, H1, and H2 processes are the same as path 2. The second water adsorbs at the opposite Mn atom to the one where the first water adsorbed, and hydrogen dissociates to a terminal oxygen, which leads to quintet structure 55 (Figure 16). The reaction energies are −0.69 and −0.53 eV for adsorption and dissociation. The possible electron configuration is [p6d2, p6d2]. H3 leads to quartet structure 48 and the remaining processes are the same as those of path 1. The reaction energy of H3 is 0.79 eV with subprocess energies of 0.76 and 0.03 eV for -e− and -H+, respectively. 4. Path 4. Path 4 is different from path 3 in that the second water adsorbs at the same Mn atom where the first water adsorbed. The W2 process leads to structure 56. The reaction energy of the adsorption is −0.18 eV, which is smaller than that in path 3. Again, the water molecule is only weakly adsorbed. H3 leads to sextet structure 57, in which an O−O single bond forms.

It seems two electrons transfer from oxygen to a metal atom, so possible electron configurations are [p6d3, p6d2] or [p6d5, p6d0]. The reaction energy is 2.44 eV, with subprocess energies of 2.37 and 0.07 eV for -H+ and -e− of P, respectively. The fourth dehydrogenation process, H4, leads to quintet structure 58 with a reaction energy of 0.87 eV. The subprocess energies are 0.87 and 0.09 eV for -H+ and -e− of P, respectively. The molecular oxygen generation energy is 1.39 eV. In water oxidation on pure Mn2O4 complex, the highest reaction energy occurs during the molecular oxygen generation process, except in path 4 in which it is H3. The dehydrogenation energy is usually about 1 eV, except H3 of path 4 in which it is 2.44 eV. E. Summary of Water Oxidation on MnxTi2−xO4 (x = 0−2) Complexes. Energy diagrams of the pathway with the least endothermic highest-energy step for the four catalysts (Ti2O4, Mn, and Ti sites of MnTiO4 and Mn2O4) are shown in Figure 17.

Figure 17. Energy diagrams of the water oxidation process for the lowest energy step of each system with two water molecules (path 1 on Ti2O4 and at Ti of MnTiO4 and path 4 at Mn of MnTiO4 and on Mn2O4; reaction order is rearranged.). Arrow points are the largest reaction energies in the pathways.

The water oxidation process on Ti2O4 and at the titanium atom of MnTiO4 favors path 1, but it favors path 4 at the manganese atom of MnTiO4 and on Mn2O4. Inclusion of a Mn atom reduces the reaction energy, but it is not proportional to the number of Mn atoms. The reaction energies of water oxidation at the Mn atom of MnTiO4 and on Mn2O4 are similar. The oxidation at the Mn atom of the MnTiO4 complex has the lowest reaction energy step in all pathways, with a highest energy step of 2.11 eV for the H3 process. Path 2 usually shows low reaction energy for dehydrogenation processes, but the molecular oxygen generation process produces a less stable high spin complex so the process requires the highest reaction energy for OO bond formation. All deprotonation reactions in the Ox subprocess are exothermic, but the oxidation steps require very high energy. Because the oxidation is highly endothermic, this subprocess is unlikely to occur. Some oxidation processes in P are exothermic, but not greatly. Oxidation at the Mn atom in dehydrogenation processes requires lower energy than that at Ti atom, which is likely due to electrons in d-orbitals. When the overall dehydrogenation energies for the lowest reaction energy pathways are compared, a similar trend is observed to the highest reaction energy. It is the largest on Ti2O4 (9.31 eV) and the smallest on Mn2O4 (5.07 eV). The overall dehydrogenation energies are 6.50 and 5.26 eV at Ti and Mn atom of MnTiO4. The OO double bond formation at Mn atom requires higher energy than that at Ti atom. The reason is not clear, but it may be because electrons at oxygen can easily transfer to p-orbitals on Ti atoms when the O−O bond forms to N



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Figure 18. Water oxidation process on the fully saturated Ti2O4 complex. Relative energies are in electronvolts.

Figure 19. Water oxidation process on the fully saturated MnTiO4 complex. Relative energies are in electronvolts.

electron configuration of [p6, p6]. As shown in Figure 18, structure 59 has four undissociated water molecules and four hydroxyl groups. The two bridging oxygen atoms do not possess hydrogen because water dissociation to bridging oxygen is an endothermic process with a high energy step.30 The first dehydrogenation process leads to doublet structure 60, with a reaction energy of 2.56 eV, which is a little bit smaller than that of the two water molecule system on pure Ti2O4. The second dehydrogenation process leads to triplet structure 61. The reaction energy, 2.47 eV, is smaller than the first dehydrogenation. During the third dehydrogenation process leading to doublet structure 62, an O−O bond forms. The reaction energy is 1.09 eV, which is significantly decreased from the previous dehydrogenation energy. Considering the electron configuration of metal atoms to be [p6, p3] or [p5, p4], quartet isomers in which

reduce the system energy, but transferring electrons from oxygen to d-orbitals on Mn atoms does not greatly reduce the system energy. II. Water Oxidation Process with Metal Oxide Complexes Fully Saturated by Water Molecules. According to our previous work,30 MnxTi2−xO4 (x = 0−2) complexes can be saturated by six water molecules and produce stable complexes. The initial structures of these hydrated metal oxide complexes are obtained from our previous work.30 This study of the water oxidation process on fully saturated systems considers only the HAT/PCET process because this process is typically favored over the deprotonation and the oxidation dominant pathways, as shown above. 1. Water Oxidation Process on the Ti2O4 Complex. The spin multiplicity of the initial structure 59 is a singlet, with a possible O



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Figure 20. Water oxidation process on the fully saturated Mn2O4 complex. Relative energies are in electronvolts.

bridges are present between the two metals atoms. The spin densities of metal atoms are also similar, but the spin densities of oxygens of O−O are quite different in two isomers. The spin densities of Ti and Mn are about 0.1 and 2.4 in 68 and about 0.0 and 2.5 in 68′, respectively, and the spin densities of oxygens are −0.5 and −0.3 in 68, but they are 0 in 68′. According to charge and spin densities, it seems that the overall spin multiplicity of the system strongly depends on the spin density of oxygens. The two oxygens in 68 have an internuclear distance of 2.2 Å, but two oxygens in 68′ form a bond with a bond length of 1.5 Å. The third dehydrogenation processes from 68 and 68′ lead to triplet isomers 69 and 69′ with reaction energies of 0.49 and 0.68 eV, respectively. The structures are not changed much by the dehydrogenation, but the O−O bond length in 69 is shortened by about 0.7 Å. The fourth reaction steps leading to doublet 70 and quintet 70′ differ for the two isomers 69 and 69′, respectively. The fourth dehydrogenation occurs from 69 with a reaction energy of 2.01 eV, but molecular oxygen generation occurs from 69′ with reaction energy of 2.86 eV. The fifth reaction steps lead to same quartet structure 71 with reaction energies of 0.48 and 0.18 eV for a molecular oxygen generation from 70 and the fourth dehydrogenation from 70′. The molecular oxygen generation energies in both paths are endothermic in contrast to the exothermic oxygen generation process on Ti2O4. Water can adsorb at Mn (leading to 72) and at Ti (not shown) atoms. The former structure (72) is more stable by 1.12 eV than when water adsorbs at the Ti atom. The reaction energy is −1.75 eV and second water adsorption energy is −1.47 eV. 72′ and 72″ show the reorientation process of oxygen atoms in MnTiO4. Overall, the highest reaction energy is the second dehydrogenation process in which a hydrogen atom is removed from a water adsorbed at the Ti atom. When the highest reaction energy steps are compared, the pathway leading to quartet 68′ is more favorable in energy than through 68. The highest endothermic reaction step through 68′ is a molecular oxygen generation with energy of 2.86 eV, but for the pathway through 68 it is the H2 step with an energy of 3.27 eV. A smaller reaction energy is required when molecular oxygen is generated from the doublet

the O−O bond is not formed are possible, but the doublet state is more stable by more than 1.0 eV. As mentioned for path 1 on pure Ti2O4, it seems that two electrons fill p-orbitals on the Ti atom so that the electron configuration changes to [p6, p5], which is a doublet state. The fourth dehydrogenation process leads to triplet structure 63. The reaction energy leading to 63 is 1.02 eV. The molecular oxygen generation process leading to singlet structure 64 from 63 is an exothermic process by −1.43 eV, in which one hydroxyl group transfers to other Ti atom, as shown in Figure 18. A water molecule then adsorbs at a vacant Ti site which leads to singlet structure 65. The reaction energy is −0.22 eV. The second water adsorption energy is −0.54 eV. In the water oxidation process on fully saturated Ti2O4, the highest reaction energy process is the first dehydrogenation, similar to the system with only two water molecules, but the highest energy step only requires 2.56 eV, which is much smaller compared to the energy of the water oxidation on Ti2O4 with two water molecules. Thus, complete solvation of the cluster compound (which would be likely under water oxidation conditions) is favorable for the oxygen generation process. 2. Water Oxidation Process on the MnTiO4 Complex. The fully saturated initial MnTiO4 complex, 66, has a quartet state whose electron configuration is [p6d3, p6]. Unlike at saturated Ti2O4 complex, in 66, two bridging oxygen atoms have hydrogen and two undissociated water molecules are bound at Ti atom, as shown in Figure 19. The first dehydrogenation process leads to triplet structure 67, with a reaction energy of 1.92 eV, which is smaller than that in the saturated Ti2O4 complex but is larger than that on MnTiO4 with two water molecules. The second dehydrogenation process leads to two isomers of a doublet, 68, and a quartet, 68′, structures with reaction energies of 3.27 and 2.53 eV, respectively. According to MDC distribution, the Mn and Ti in 68 and 68′ have almost same charges: 1.3 and 3.0 in 68 and 1.5 and 2.8 in 68′, respectively. Although their charge distribution is almost the same, their structure and O−O bond formation reaction are quite different from each other. In 68, two hydroxyl oxygens at the Mn and Ti atoms react to form a hydroperoxide bridge connecting the two metal atoms, but in 68′, two oxygen atoms at the Ti atom react and three hydroxyl P



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intermediate (70) in which two oxygen atoms are bound at different Mn atoms than when it is generated from the triplet (69′) in which both oxygen atoms are bound at same Mn atom. 3. Water Oxidation Process on the Mn2O4 Complex. The initial structure, 73, which is fully saturated by six water molecules is obtained from our previous work.30 In this structure one bridging oxygen has a hydrogen atom, but the other does not. Three water molecules remain in undissociated form: one at the left-hand side Mn and the other two at the right-hand side Mn atom, as shown in Figure 20. The spin multiplicity of the initial structure is a septet and the possible electron configuration is [p6d3, p6d3]. The first hydrogenation process leads to sextet structure 74 with a reaction energy of 2.10 eV. The reaction energy is larger than that of H1 on the MnTiO4 saturated system and is also larger than that of H1 of MnTiO4 and Mn2O4 with two water molecules. The second dehydrogenation reaction energy is 0.28 eV, which is smaller than any other dehydrogenation energy in this study. H2 leads to quintet structure 75, whose possible electron configuration is [p6d2, p6d2] or [p6d3, p6d1]. In H1 and H2, hydrogen atoms are preferentially removed from molecular adsorbed water molecules. H3 leads to sextet 76 in which an O−O bond forms; this reaction energy is 2.79 eV, which is the largest energy of the four dehydrogenation processes. Possible electron configurations are [p6d3, p6d2] or [p6d5, p6d0]. Two electrons transfer to d-orbitals of Mn atoms. A quartet structure (not shown) having [p6d2, p6d1] or [p6d3, p6d0] configuration is also possible, but in the optimized structure the backbone is broken and it is more than 4 eV higher in energy. The 0.96 eV reaction energy of H4 is smaller than that of H3 and leads to quintet 77. A molecular oxygen generation process leads to septet 78 with a reaction energy of 4.55 eV. In 78, adsorbed water molecules have rearranged their positions. When molecular oxygen is generated, two vacant coordination sites occur at vertical position of Mn atoms. Then, two hydroxyl groups in equatorial positions replace these vacancies. W1 and W2 reaction energies are −1.26 and −4.47 eV, respectively. The molecular oxygen generation process requires the largest reaction energy in this cycle which is similar to the process on Mn2O4 with two water molecules. This reaction energy, 4.55 eV, is also much larger than the largest reaction energies of Ti2O4 and MnTiO4 with six water molecules. The reason why molecular oxygen generation on Mn2O4 requires a much higher energy is not clear. This may be due to the coordination number of the Mn atoms: the octahedral coordination of Mn atom is broken by the molecular oxygen generation. In our previous work, when the coordination number of Mn atom becomes 6, the water adsorption energy is much larger than the other adsorption energies.30 Similarly, when both coordination numbers of the Mn atoms in 77 changes to 5 due to molecular oxygen generation, the reaction requires high energy, but when water molecules reoccupy the sixth coordination sites of each Mn atom (79 → 73), the reaction is highly exothermic in energy. An energy diagram of water oxidation on small MnxTi2−xO4 (x = 0−2) complexes hydrated by six water molecules is shown in Figure 21. The highest reaction energy is not decreased for Mncontaining systems unlike the complexes hydrated by two water molecules. The first and second dehydrogenation processes require higher reaction energies on Ti2O4 and MnTiO4, but the first and third dehydrogenation processes are higher in energy on the Mn2O4 complex. In the first two dehydrogenation processes, hydrogens from molecular water are removed rather than hydrogen from hydroxyl groups. The overall dehydrogenation energy is largest on the MnTiO4 complex (7.69 eV) compared to

Figure 21. Energy diagrams of the water oxidation process for the lowest energy step of each system with six water molecules. Arrow points are the largest reaction energies in the pathways.

6.13 eV on Mn2O4 and 7.14 eV on Ti2O4. On Ti2O4, the molecular oxygen generation process is exothermic, but it is endothermic on the others. It is likely exothermic on Ti2O4 because this regenerates the singlet [p6, p6] state. The energy of the water adsorption reactions on Ti2O4 is smaller than that of the others. The highest reaction energy on Ti2O4 is 2.56 eV, which is smaller than 2.95 eV for the complex hydrated by two water molecules. However, on the fully saturated MnTiO4 and Mn2O4 complexes, the highest energies, 2.86 and 4.55 eV, are much larger than 2.11 and 2.44 eV for the two water systems. Because the complexes are likely to be fully saturated in aqueous solution, this demonstrates that consideration of saturated clusters is necessary for accurate predictions of reaction energies. During the O−O bond generation step, two oxygens attached at the same Ti atom form a bond on Ti2O4, but oxygens attached at different metal atoms form a bond on Mn2O4. On MnTiO4, both O−O formation structures (at the Ti atom or bridging the Mn and the Ti atoms) are possible, but generation of O−O exclusively at the Ti atom has a lower reaction energy than when it bridges between the Mn and Ti atoms.

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CONCLUSIONS Water oxidation processes are studied on small MnxTi2−xO4 (x = 0−2) complexes with two water molecules and a fully saturated system with six waters. The two water molecules are the minimum required for catalytic water oxidation. In the two water molecules system, path 4 at the Mn atom of the MnTiO4 complex is most favorable in energy for water oxidation with a highest reaction energy step of 2.11 eV, but the overall dehydrogenation energy is smaller on Mn2O4. Path 2 does not occur favorably because the molecular oxygen generation process requires a high energy and generates a less stable high spin complex. The hydrogen removal process requires high energy. The molecular oxygen generation process is the lowest on the pure Ti2O4 complex, but hydrogen removal requires a higher energy for this system. In the fully saturated systems, the highest reaction energy on Ti2O4 is smaller than those on MnTiO4 and Mn2O4, but the overall dehydrogenation energy is smallest on Mn2O4. The molecular oxygen generation step on Ti2O4 is exothermic, but it is endothermic on the complexes that include one or more Mn atoms. In the reaction on Mn2O4, the O2 process requires a huge reaction energy compared to the other reactions. The reason is not clear, but it may be due to the coordination numbers of the Mn atoms, which drop from 6 to 5 in this process. On Ti2O4, the O−O bond forms between two oxygens on the same Ti atom, Q



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but it forms between two different metal atoms for MnTiO4 and Mn2O4. Compared to the energy of the two water molecules system, the highest reaction energy of the fully saturated system is smallest on Ti2O4, but it is larger on MnTiO4 and Mn2O4. The overall dehydrogenation energy is smaller on Ti2O4, but it is larger on the others, similar to the highest reaction energy. The water oxidation reaction on the MnTiO4 complex using two water molecules is the most favorable in energy, if the highest energy reaction energy step is considered.

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ASSOCIATED CONTENT

S Supporting Information *

All isomers in the water oxidation process on small MnxTi2−xO4 (x = 0−2) complexes and their energies. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. CHE-0955515. C.M.A. also thanks the Alfred P. Sloan Foundation for a Sloan Research Fellowship (2011−2013) and the Camille and Henry Dreyfus Foundation for a Camille Dreyfus Teacher-Scholar Award (2011−2016).

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Theoretical Investigation of Water Oxidation Processes on Small

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