Water Splitting on TiO2-Based Electrochemical Cells: A Small Cluster

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Water Splitting on TiO-Based Electrochemical Cells, a Small Cluster Study Fermin Rodriguez-Hernandez, Diana C. Tranca, Bartlomiej M. Szyja, Rutger A. van Santen, Aliezer Martínez Mesa, Llinersy Uranga-Pina, and Gotthard Seifert J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10894 • Publication Date (Web): 09 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Water Splitting on TiO2 -Based Electrochemical Cells, a Small Cluster Study F. Rodr´ıguez-Hernández1,3 , D. C. Tranca1 , B. Szyja2 , Rutger A. van Santen2 , A. Mart´ınez-Mesa3 , Ll. Uranga-Pi˜ na3 , and G. Seifert1 1

Physical Chemistry, Technische Universit¨ at Dresden, Mommsenstr. 13, Dresden 01062, Germany 2

Laboratory of Inorganic Materials Chemistry,

Schuit Institute of Catalysis, Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands and 3

Departamento de F´ısica Te´ orica, Universidad de La Habana, San L´ azaro y L, La Habana 10400, Cuba

The water splitting process on electrochemical cells is studied with focus on the energetics of the oxygen evolution reaction at the TiO2 -based anodes. New reaction mechanisms are proposed that lead to the decomposition of water molecules on TiO2 clusters. The oxygen evolution reaction at the anode is investigated using electronic structure calculations based on Density Functional Theory (DFT). Simulations are carried out for different cluster sizes (monomers and dimers). For each reaction path, the free energy profile is computed, at different biases, from the DFT energies as well as the entropic and the zero-point energy contributions. The mechanisms of the oxygen evolution reaction explored in the present work are found to be energetically more feasible than alternative reaction pathways considered in previous theoretical works based on cluster approximations of the surface of the photocatalyst. Finally, the representation of the surface of specific, commonly occurring, titanium dioxide crystals (e.g., rutile and anatase) within the small cluster approximation is able to reproduce qualitatively the rutile (110) outperforming of the anatase (001) surface.

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2 I.

INTRODUCTION

Molecular hydrogen is envisaged to play a significant role in clean energy generation in the future.1 The hydrogen technology based on fuel cells is a promising alternative to both the exhaustion of fossils based energy and the increase of the greenhouse gas emissions. There are two key technologies that need to be developed before the hydrogen fuel can effectively replace the traditional energy sources: the low-cost H2 production and the efficient storage of this gas under mild conditions (i.e. ambient temperature and pressure). There is a variety of chemical processes suitable for H2 production, ranging from the fossils-based processes and the electrolysis of water, to the employment of bio-gas, biomass and even the photosynthesis, in particular species of plants.2 All those processes have issues that hinder the use of the manufactured H2 as an energy carrier: some of them have very low efficiency while others are very expensive energetically. The pioneering work of Fujishima and Honda on the photocatalytic reaction over titanium dioxide was published in 1972.3 At that time, there was a great hope to obtain H2 from the process driven only by the solar energy. However, up to date, the low rate of the so-called hydrogen evolution reaction (HER) continues to be the main shortcoming of the production of hydrogen via water photoelectrolysis. Hydrogen is considered an energy carrier rather than an energy source, since hydrogen production in general, and particularly in electrochemical or photoelectrochemical cells (PEC), is characterized by energy losses. PEC and related devices are generally made of a semiconductor anode or photoanode (e.g., TiO2 ) and a metal cathode (e.g., Pt) immersed in an electrolyte. Two half-reactions characterize the water decomposition: the O2 evolution reaction (OER) at the anode and the H2 evolution reaction by recombination of H+ and e− at the cathode. The main source of the energy losses comes from the overpotentials of about 1 V at the anode surface.4 In the case of PEC, the photoanodes based on TiO2 are relatively cheap, chemically and biologically inert and very stable under illumination. TiO2 absorbs the UV radiation rather than the visible light, due to its band gap width (3 eV for the rutile structure and 3.2 eV for the anatase arrangement)5,6 , but the photoactivity of TiO2 can be extended from UV to the visible part of the solar spectrum by chemical doping7–13 , by changing the morphology of the solid, for example to nanotube arrays14,15 , or decorating the surface of titanium oxide with metal nano-particles(Pt, but also


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3 non-noble metals)16,17 . The accepted general mechanism of the hydrogen production process contains the following main steps: i) the creation of electron-hole pairs inside the anode by photoexcitation or the action of external bias: S → e− + S+ , where S stands for the surface of the anode and e− migrates to the cathode, and ii) the separation of the electrons and holes due to the driving force in the semiconductor-liquid junction and the reaction of the holes with water molecules or hydroxide ions from the electrolyte: S+ + H2 O → S-OH + H+ or S+ + OH− → S-OH. These processes have been extensively studied experimentally3,18,19 and theoretically5,6,19–22 . A commonly accepted theoretical description consists in the adsorption of two water molecules on the anode surface, followed by a reaction in which four electrons are transferred to the cathode in subsequent steps. At each step, the release of one H+ takes place.19,20 The reaction at the anode is energetically unfavorable and an external potential is needed to make the reaction thermodynamically allowed. Another possibility is to use solar energy for making the reaction to occur spontaneously. The anode surface can be considered as a catalyst for the water decomposition on the electrochemical cell and different studies consider a catalytic cycle in the description of this process.5,19,20,23 A cluster model of the surface presents several advantages in the description of the water decomposition on the electrodes, compared to the theoretical description of the surface. For these simplified models, electronic structure calculations more accurate than DFT-based methodologies (e.g., post Hartree-Fock methods) are affordable. A detailed inspection of the potential energy surface (PES) is tractable from the computational point of view, thereby allowing to extract information on the reaction mechanism. The atomistic description enables the identification of the rate-determining step as well as other relevant steps along the reaction path which exhibit large activation energies. This microscopic information could be benefical in the design of more efficient electrodes for electrochemical cells or PEC. Moreover, comparisons of the performance between calculations on extended surfaces and on small clusters within the same level of theory are useful in confirming the capability of the cluster model to reproduce the general trend of the energetics and the efficiency of the process. It provides insight on how to build a more realistic representation of the surface in the framework of the



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4 small cluster approximation. In the present work we address the theoretical modelling of the OER on TiO2 -based electrochemical cells employing small clusters models. At first, the reaction is studied on the clusters TiO2 and Ti2 O4 , motivated by previous works23,24 but assuming a different reaction mechanism, i.e., following the electrochemical scheme of Norskov et. al.20 The latter approach allows to estimate theoretically the overpotential of the process under standard thermodynamic conditions. The intermediate structures in the mechanisms proposed in Ref.23,24 motivate the study of the water splitting on Ti(OH)4 and Ti(OH)2 -O2 -Ti(OH)2 as more realistic representations of the surface of the anode. Likewise, the reaction is studied afterwards on the charged Ti(OH)− 4 cluster, and the differences to the neutral Ti(OH)4 are highlighted. The charged structure may be considered as a model of the situation in which the water decomposition occurs on a site where a trapped electronic state is localized. The influence of the cluster sizes on the water splitting is addressed via the analysis of the decomposition pathways on the structures Ti(OH)2 -O2 -Ti(OH)2 and Ti(OH)3 -O-Ti(OH)3 , containing two titanium atoms. The first of these dimeric models may be regarded as a simplified representation of the active Ti-sites on the rutile (110) surface, while the second one resembles the spatial arrangement of atoms in an anatase structure which was cut exposing the (001) surface (see Fig. 1). Although the methodology employed here to evaluate the overpotentials in different cluster models have been successfully used to account for experimental trends,25 the differences between the theoretical assumptions and the experimental conditions and the neglect of the activation barriers in the proposed scheme pose a significant challenge to the direct comparison between theoretical and experimental overpotentials .25 The goal of this study is to answer the following questions: Which cluster structure offers the most realistic representation of the surface of the anode for the description of the water splitting? How do the charged local sites influence the efficiency of the OER? Are the proposed models able to reproduce the trend of the variations of the overpotential due to the modification of the topology of the surface? The paper is organized as follows. In the section II, the methodology to compute the ab-initio energy of each structure, the variations of the free energy at each reaction step and the theoretical estimates of


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5 the overpotential is described. In section III, the main results of this work are presented and discussed. Finally, in section IV, a brief summary and some concluding remarks are presented.

II.

A.

METHODOLOGY

Model reaction pathways

We consider a standard two-electrode configuration of the electrochemical cell. The OER is initiated by the oxidation of a water molecule at the anode (Eq.1) and the H2 evolution can take place after the reduction of two H+ at the cathode (Eq.2).

H2 O →

1 O2 + 2H+ + 2e− 2

2H+ + 2e− → H2

E o = −1.23 V

E o = 0.00 V

(1)

(2)

The standard potentials of the reactions (Eq.1) and (Eq.2) show that the water splitting is not a spontaneous process.26 An external potential of 1.23 V is needed for the water decomposition to take place at standard conditions. The difference between the external potential required for the water splitting process and 1.23 V is known as the overpotential of the mechanism in a specific electrochemical or PEC. The OER on each of the considered clusters may be described by different reaction mechanisms in general, but they comprise a similar sequence of steps. As proposed in Ref.20 , the most relevant reaction steps can be summarized as follows:

A: H2 O + S → H2 O-S

(3)

B: OH-S → O-S + H+ + e−

(4)

C: H2 O + S → OH-S + H+ + e−

(5)



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6 D: O2 -S-H → S + O2 + H+ + e−

(6)

where S represents the substrate (cluster). Reaction A represents the adsorption of a water molecule on the cluster, and B is the injection of a H+ to the electrolyte while one electron migrates to the electrode. In step C, the decomposition of a water molecule occurs. After that, an OH− group is adsorbed on the surface while a H+ goes into the electrolyte and an electron is transferred to the cathode. The type D reactions proceed from an initial structure with an O2 molecule adsorbed on the surface. At the end of this step, the desorption of the O2 molecule, a proton and the electron transfer process are considered simultaneously. Reaction D represents the desorption of a preformed OOH group in an electron transfer process.20 Upon desorption, the attached OOH group is considered as a proton separated from the O2 molecule. The electron transfer and the proton dissociation is considered simultaneous, and therefore charge is maintained. The O2 desorption is considered to be induced by the extraction of a H+ , which is an electron-transfer process and its free energy barrier can be altered by the action of an external potential. Each step in the proposed reaction mechanism is modeled either as an electron-transfer process (e.g. reactions B, C, D) or as a non-electron-transfer step (reaction A). Sometimes, a combined process in which reactions C and D happen simultaneously is used. The equation H2 O + O2 -S → S-OH+O2 + H+ + e− represents one of such electron-transfer processes.

B.

Free energy calculations

The mechanism of the OER on each cluster is determined by the molecular energy landscape. For each of the reaction mechanisms, the optimized geometries of the intermediate structures and the corresponding zero point energies are calculated. The dependence of the free energy from the external potential U is considered within a simple heuristic model as proposed by Valdés et al.20 This quantity is used to get information about the overpotential needed for the OER to proceed according to every one of the proposed mechanisms. The expression ∆G = ∆E + ∆ZP E − T ∆S gives the variation of the intrinsic free energy (i.e., for a vanishing external potential) at every step of the reaction. The reaction energies (∆E) are obtained


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7 from electronic structure calculations based on DFT. The zero point energy corrections (∆ZP E) and the entropy changes (T ∆S) are computed based on the DFT calculations for vibrational frequency analysis and standard tables for gas-phase molecules26 . For the atoms and molecules adsorbed on the surface it is assumed that S = 0. Additionally, the study of the water decomposition on different molecular structures requires the calculation of the ground-state energies of the isolated molecules: H2 , O2 and H2 O. The electronic structure of the O2 molecule is not accurately described within DFT27–29 . Therefore, the O2 energies are computed according to Ref.20 The free energy change of the reaction H2 O → 1/2O2 + H2 is set at the experimental value of 2.46 eV, and computing the energies and zero-point corrections of the water and the H2 molecule by DFT based methods, it is possible to obtain an accurate estimate of the O2 zero-point energy. Without the external potential acting in the electrochemical cell, the water splitting process is not allowed from the energetic point of view. The action of external potentials can favor the process thermodynamically, as it makes the free energy profile down-hill along the reaction steps. To assess the influence of the external potential for the electrochemical step, a methodology based on the thermochemistry of the reaction was used.30 Following this method, every time an electron-transfer process takes place the free energy of the system is modified by ∆GU = 1/2H2 − eU, where H2 is the ground-state vibrational energy of a H2 molecule. At standard thermodynamic conditions (U = 0, pH = 0, p = 1 bar, T = 298 K), the free energy change of the reaction S-AH → S-A + H+ + e− is equal to the corresponding change in S-AH → S-A + 21 H2 .20 Choosing the standard hydrogen electrode (NHE) as reference potential results in the abovementioned variation ∆GU . The DFT calculations of the reaction energies are performed using an all electron approach at the B3LYP/TZV level of theory31–35 . All calculations were performed in the General Atomic and Molecular Electronic Structure System (GAMESS) package.36,37

III.

RESULTS AND DISCUSSION

The molecular configurations in the proposed mechanisms for the water decomposition on different clusters and the corresponding free energy profiles are shown in Fig.2 - Fig.7. The optimized structures



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8 and the energies of the intermediate steps show the details of the reaction mechanisms. For all the target systems, various processes are analyzed: the adsorption of two H2 O molecules, the splitting of the water into a H+ and an OH− , the attachment of the OH− group on the Ti active sites, the formation of the OOH− group, the formation and desorption of the O2 molecule, and finally the recovery of the initial cluster structure. The free energy is computed along every one of the proposed reaction paths. This quantity is employed to identify the rate-determining step in the reaction, thereby yielding the external potential required to make the free energy down-hill along the reaction coordinate. The cartesian coordinates of the final and the intermediate molecular configurations, their electronic energies, and the results of the frequency analysis are available in the Supplementary Material.

A.

Water splitting on TiO2 and on Ti2 O4 structures

Dixon et al.23,24 have proposed a mechanism of water splitting on small TiO2 clusters. In those studies, the cluster structures were used to simulate a catalytic nanoparticle in an aqueous media. Conversely to these preceeding studies23,24 , in the present work, TiO2 and Ti2 O4 are employed as models for the anode of an electrochemical cell and the OER is studied using an electrochemical approach. Both structures certainly constitute oversimplified models of the surface of the anode in the cell, mainly because the electronic structure of these configurations is far from that of the TiO2 surfaces. These simplified models for the anode of the electrochemical cells are compared with the model proposed in this work (see Section III B,III C,III D,III E). Motivated by the foregoing results23,24 , the first step in the reaction mechanisms is taken to be the formation of Ti(OH)4 and Ti(OH)2 -O2 -Ti(OH)2 , respectively, which is induced by the decomposition of two water molecules on the corresponding initial structures (i.e., TiO2 and Ti2 O4 ). The mechanism advances via a cascade of electron-transfer processes in which electrons flow from the new structures (that is, from Ti(OH)4 and Ti(OH)2 -O2 -Ti(OH)2 ) to the cathode, and protons are injected into the electrolyte at the same rate. The intermediate stable structures characterizing the process on TiO2 and its energy values in eV are shown in Fig.2a. The free energy profiles of this mechanism for different external potentials are depicted in Fig.2b. The decomposition of two water molecules on a TiO2 cluster produces the Ti(OH)4 structure


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9 in an exothermic process (5.04 eV).23,24 The proposed mechanism continues with the extraction of one H+ from the structure while an e− is transferred to the cathode. The formation of an O2 molecule is observed after the extraction of a second H+ . The next step is a type D reaction which consists of the desorption of the O2 molecule together with a proton from the cluster. This is the limiting step of the reaction, i.e., the one exhibiting the highest energy barrier (4.66 eV, see the curve labeled as U = 0.00 V in Fig.2b). After that, the last proton is extracted from the cluster and the TiO2 structure is recovered. Taking into account the entropic and the zero-point energy contributions, the free energy of each of the structures displayed in Fig.2a is evaluated. From the free energy profiles plotted in Fig.2b, it can be seen that the complete process is not favorable from the thermodynamic point of view in absence of an external force to drive the reaction (or in the dark, if the case of the water splitting on a PEC is considered). The mechanism remains energetically forbidden even if a potential bias amounting to electrochemical standard potential of the water splitting reaction (U = 1.23 V, Fig.2b) is applied. As in every reaction mechanism proposed in this work, a nonzero overpotential is necessary. For the TiO2 cluster structure, an external potential of 4.66 V is required for the OER to become thermodynamically favorable, the corresponding theoretical overpotential is 3.43 V. This value of the overpotential is much larger than the results of previous calculations (1.31 V for the anatase (001) surface6 and 0.78 V for the rutile (110) surface20 ) and the available experimental data (around 1 V4,6,20,25 for the water decomposition under standard thermodynamic conditions). These differences point to the dissimilarities in the electronic structures of the minimal TiO2 cluster and the extended titanium dioxide substrate. With the aim of studying the water decomposition on the TiO2 surface, the simplest cluster model involving at least two titanium centers is Ti2 O4 . The stable structures tracing the oxygen evolution on Ti2 O4 and their molecular energies in eV are shown in Fig.3a. The free energy profiles corresponding to different external potentials are presented in Fig.3b. The formation of Ti(OH)2 -O2 -Ti(OH)2 takes place after the decomposition of two water molecules on Ti2 O4 , and the binding energy of the complex is 5.22 eV.24 The extraction of a proton leads to the formation of an O2 molecule in the cluster (Fig.3a: structure-3). In the next step, the desorption of the O2 molecule occurs together with the dissociation of a second proton giving rise to the fourth structure in Fig.3a. The process goes on by means of the



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10 extraction of the two remaining protons, which completes the catalytic cycle. The limiting step is the formation of the O2 molecule, which demands to overcome a free energy barrier of 4.99 eV (U = 0.00 V, Fig.3b). Hence, an external potential of 4.99 V will supply the necessary energy to make the free energy landscape down-hill along the reaction path and the process thermodynamically allowed. The overpotential for the proposed mechanism is 3.76 V, which is even higher than the corresponding one for the water splitting on the TiO2 cluster (3.43 V). The comparison between the two pathways (Fig.2a and Fig.3a) shows that the limiting step is similar in both cases, and it relates to the O2 desorption process. Indeed, according to the free energy profiles plotted in Fig.2b and Fig.3b, the activation energies for these processes are nearly the same: 4.66 eV and 4.61 eV, respectively. The difference in the performance depending on the cluster model comes from the more extensive structural modification, that takes place preceding the release of the oxygen molecule in the case of the Ti2 O4 model. After the first H+ is extracted (Fig.3a, structure 3), striking changes of the molecular geometry occur with respect to structure 2 (i.e., bond breaking and formation), leading to the emergence of an O2 molecule. Because of this rearrangement of atomic positions, the present mechanism is thermodynamically less favorable than the previous one concerning the TiO2 cluster (i.e., it will require to overcome a somewhat higher energy barrier). For TiO2 and Ti2 (OH)4 cluster models, the coordination numbers are 2 and 4, respectively and the oxidation state for Ti is +4. These clusters are undercoordinated and adding water will lead to a more stable structure than the initial one. Thus, the system benefits from the hydration and the recovery of the initial state is costly. During the reaction mechanism of the water splitting, the coordination number changes from +2 to +3 or +4, which leads respectively to a change in the oxidation state of the system. In the proposed mechanisms, based on TiO2 and Ti2 O4 , the computed overpotentials exceed 3.4 V, while previous experimental and theoretical studies on extended surfaces report values around 1 V.4,6,20,25 The discrepancies between the values of the overpotential obtained presented until now and the reference data indicate that more investigation should be done to achieve better results compared with the experimental data. In the next sections more reliable models for representing the titanium oxide surface will be presented.


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11 B.

Water splitting on neutral Ti(OH)4 clusters

The top views of two different titanium dioxide surface morphologies commonly used as cathodes in electrochemical or PEC are shown in Fig.1. The diagrams reproduce the geometric arrangement of atoms in the rutile (110), Fig.1a and the anatase (001), Fig.1b, surfaces. The structures are obtained from a truncated rutile or anatase TiO2 crystal. Although the Ti atoms in the bulk semiconductor are 6-fold coordinated, the 5-fold coordinated atoms located on the outer plane have been identified as the active sites for the surface chemical reactions. These 5-fold coordinated Ti atoms are highlighted in Figs.1a and Fig.1b. The active Ti-sites on both model surfaces have four O atoms as nearest neighbors (1.93 ˚ A) and an additional O as second nearest neighbor (1.98 ˚ A).38 This suggests that a simple cluster structure (TiO4 ) might be used to represent the active sites on the semiconducting surfaces, by considering only a Ti atom linked to its nearest neighbors (i.e., the fourth closest O atoms). In this direction, we consider in this section the case of Ti(OH)4 as a cluster model for the description of the water splitting process. Actually, this structure goes one step further, since four H atoms have been considered in addition to the TiO4 complex. This modification saturates the TiO4 structure and in such a way the cluster model approaches the bonding situation of the surface. The electronic structure of Ti(OH)4 has been studied before as a model representation of specific sites in TiO2 surfaces.39 Moreover, the Ti(OH)4 is obtained as a product from an exothermic (5.04 eV) process after the decomposition of two water molecules on TiO2 (see structure 2 in Fig.2a).23,24 These facts point to the decomposition of two additional water molecules on Ti(OH)4 rather than on TiO2 as a more favorable mechanism from the thermodynamic point of view. For the study of the water splitting on Ti(OH)4 , a reaction mechanism in which two water molecules are adsorbed on the cluster and four H+ are removed in separate electron-transfer steps has been proposed. One O2 molecule and four H+ injected into the electrolyte are obtained as products of the reaction mechanism. The stable structures arising from the different phases in the proposed mechanism for the water splitting on Ti(OH)4 , together with the corresponding energy values in eV, are presented in Fig.4a. The free energy profiles along this path, for different external potentials, are plotted in Fig.4b. The adsorption of one water molecule on Ti(OH)4 leads to the formation of the structure labeled as Γ, and it causes



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12 the decrease of the molecular energy of the system (Γ-structure in Fig.4a). According to the free energy variation, the Γ-structure is disadvantageous (Fig.4b). Since this is a reaction of type A (Eq.3) there is no electron-transfer happening, so the free energy change accompanying the water adsorption will be the same for all the external potentials. In order to be able to steer the reaction with the voltage applied to the electrochemical cell, an alternative mechanism needs to be considered. Here, we examine the direct transition from structure 1 to structure 2 (Fig.4a). The latter is a reaction of type C (i.e., a water molecule is decomposed into an OH− and a H+ and the OH− is adsorbed on the cluster, see Eq.5). In the structure Ti(OH)5 , the distances between the Ti and the oxygen atoms are between 1.83 ˚ A and 2.11 ˚ A. The value of 2.11 ˚ A shows that this is a weak connection between the Ti and the oxygen atom. As it can be seen from the Fig.4b, a high amount of energy is required for this structure to be constructed. The high number of coordinations show also that this structure is not stable. Using the same argument, the adsorption of a second water molecule (designated as ∆-structure in both Fig.4a and Fig.4b) is not included in the proposed mechanism, and a direct transition from structure 4 to structure 5 (Fig.4a) is preferred. This transition corresponds to the simultaneous occurrence of two of the abovementioned typical reactions. It can be regarded as the decomposition of a water molecule in a reaction of type C (Eq.5) together with a reaction in which the O2 molecule is desorbed (type D, Eq.6). Since both reactions occur at the same time, only one electron is transferred to the electrode during this phase. With these assumptions, the mechanism of the water decomposition on Ti(OH)4 becomes a fourstep process, each of them involving an electron transfer to the electrode. Using the previously introduced classification, the process consists in one reaction type C, two reactions of type B and a combined step which merges one reaction of type C and one of type D. Consequently, after the decomposition of a water molecule and the formation of the Ti(OH)5 complex (structure 2 in Fig.4a), one H+ is extracted from the structure. At this point, the formation of an OOH− group takes place (structure 3) in Fig.4a and the O2 molecule is formed, as it can be seen (structure 4) in Fig.4a. The O2 molecule is released in the following consecutive steps: the extraction of the next H+ in the corresponding reaction of type B (Eq.4), in which a H+ is injected to the electrolyte while an electron is transferred to the electrode, and the combined process which leads to the direct transition


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13 from structure 4 to structure 5 (Fig.4a). The determining step of the process is the decomposition of the first water molecule and the adsorption of the OH− group on the cluster, the largest energy barrier is 2.73 eV (see the curve corresponding to U = 0.0 V in Fig.4b). If an external potential of 2.73 V is exerted on the electrochemical cell, it provides the necessary energy to overcome the highest energy barrier, making the free energy profile down-hill along the reaction steps (curve marked as U = 2.73 V in Fig.4b). The corresponding value of the overpotential is 1.50 V. It is striking that considering Ti(OH)4 as a cluster model of the surface results in a substantial reduction of the theoretically predicted value of the overpotential, compared to those obtained for TiO2 (3.43 V) and Ti2 O4 (3.76 V). The comparison between the value of the overpotential corresponding to the reaction mechanism depicted in Fig.4a and previously reported results, indicates that the Ti(OH)4 cluster gives a more realistic representation of the overpotential of the surface of the anode than the TiO2 and Ti2 O4 structures, at least for the simulation of the water splitting on TiO2 substrates. In the following, we study the water splitting process on a charged local site on the anode, employing the Ti(OH)4 cluster to approximate the interaction sites on the surface.

C.

Water splitting on Ti(OH)− 4

The influence of an extra electron on the water splitting on the Ti(OH)4 structure is considered in this subsection. The charged structure simulates the influence, on the decomposition process, of an electron “trapped” in a local site at the surface. The Ti(OH)− 4 is used as a simplistic model for such trapping sites on the surface of the anode. The structures of stable molecular configurations along the water splitting reaction path and their energy values in eV are shown in Fig.5a. The free energy profiles for the proposed mechanism, in presence of different external potentials are given in Fig.5b. The mechanism initiates with the adsorption of a water molecule on Ti(OH)− 4 (structure 2 in Fig.5a). + It continues with the formation of a Ti(OH)− (structure 3, 5 structure due to the extraction of a H

Fig.5a). Extracting two additional protons in subsequent steps leads to the formation of the intermediate structures Ti(OH)4 O (d(Ti...O) = 1.88 ˚ A) and Ti(OH)3 O2 (structures 4 and 5 in Fig.5a). In the latter



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14 of these molecular configurations, an oxygen molecule is already preformed. Opposite to the reaction on neutral Ti(OH)4 , the adsorption of the first water molecule is favorable regarding the molecular energy and the free energy variations. The adsorption of a second water molecule is accompanied by a downward shift of both the electronic energy and the free energy (structure 6, Fig.5a). The last step is a reaction of type D (Eq.6), involving the desorption of an O2 molecule together with a H+ ion (structure 7, Fig.5a). In fact, this step is again the one determining the overall reaction rate: its activation energy is 3.49 eV (for a vanishing external electric field). As a consequence, applying an external bias of 3.49 V to the electrochemical cell causes the free energy to decrease monotonically along the reaction path and the decomposition can take place (U = 3.49 V, Fig.5b).

The overpotential is 2.26 V for the proposed reaction mechanism. This value is larger than the overpotential for the corresponding neutral cluster (1.50 V), but it is still smaller than those obtained for the TiO2 and the Ti2 O4 models. These results indicate that the electron trapped states do not increase the efficiency of the water decomposition process.

Alternatively, the investigation of the electrolysis on the Ti(OH)− 4 cluster gives some insight into the photocatalytic water splitting on dye-sensitized TiO2 surfaces. Due to the electron-injection process from the dye into the titanium dioxide, charged sites may appear on the surface. The dye-sensitization of the surface of the anode often leads to the improvement of the efficiency of the PEC.40–42 Therefore, the larger overpotential obtained for the Ti(OH)− 4 cluster (i.e., in presence of localized charges) compared to the neutral Ti(OH)4 model suggests that:

(a) there is a marked influence, on the performance of the PEC, of the delocalized character of the excess electron density in sensitized TiO2 surfaces (the electron is injected in the conduction band of the semiconductor),

(b) in the case of dye-sensitized PEC, the water splitting process might occur directly on the sensitizer rather than on the surface of the anode. In this case, the TiO2 surface only influences the electron transport properties of the electrochemical cell.


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15 D.

Water splitting on Ti(OH)2 -O2 -Ti(OH)2

The Ti(OH)4 cluster model was introduced as a local representation of the active sites on the TiO2 surfaces for the water splitting reaction in an electrochemical cell. Although it resembles the bonding of Ti-active sites to its nearest oxygen neighbors, considering several adjacent water adsorption sites is a natural way to progressively cover the gap between the minimal cluster representation and the extended surface. To this purpose, in the present subsection, we address the modelling of the water splitting process on the cluster Ti(OH)2 -O2 -Ti(OH)2 . This structure can be seen as a direct extension of the Ti(OH)4 model, including two Ti-active sites on the rutile (110) surface (the latter are indicated by the white and the light blue areas in Fig.1a , which are delimited by the dashed lines). In analogy with the treatment described in subsection B, the influence of the second neighboring oxygen atom (standing at 1.98 ˚ A from the 5-fold coordinated titanium on each site) on the water splitting is neglected, while one H atom is attached to each of the four external oxygen atoms (i.e., those not connected to the two Ti centers) to emulate the electronic structure of the surface within this simplistic cluster representation. Moreover, the Ti(OH)2 -O2 -Ti(OH)2 structure may be obtained as a result of a highly exothermic process (5.22 eV), namely the decomposition of two water molecules on Ti2 O4 (see structure 2 in Fig.3a).23 Due to this large formation energy, it is expected that the decomposition of two water molecules on Ti(OH)2 -O2 -Ti(OH)2 will be a much more energetically favorable process than the desorption of an O2 molecule and the extraction of four protons from Ti(OH)2 -O2 -Ti(OH)2 , as proposed in Fig.3a. The intermediate molecular structures representing the main steps of the H2 O splitting on Ti(OH)2 -O2 -Ti(OH)2 and their molecular energies in eV are shown in Fig.6a. The corresponding free energy profiles, computed for different external potentials, are depicted in Fig.6b. The proposed mechanism begins with the exothermic adsorption of a water molecule and its subsequent decomposition into an OH− group on the titanium site and the injection of a H+ ion into the electrolyte. A second H+ is extracted, and the recombination of two oxygen atoms takes place. Because of the high energetic cost associated to the extraction of the preformed O2 molecule, the adsorption of the second water molecule is considered as the next step. The H2 O is decomposed in one OH− linked to one of the Ti-sites and one H+ which is bonded to the oxygen lying between the titanium atoms. The next proposed step is an electron-transfer



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16 process, which involves the desorption of the O2 molecule together with the extraction of a proton. Finally the last proton is extracted and the catalytic cycle is completed. The structures Γ, ∆ and Λ in Fig.6a represent alternative reaction paths which do not entail electron-transfer processes (e.g., water adsorption) and they are found to be unfavorable according to the free energy variations (U = 0.0 V, Fig.6b). Thus, the reaction is assumed to occur via the direct transition from structure 1 to structure 2 in Fig.6a. This is a reaction of type C (Eq.5), whereas the transition from structure 3 to structure 4 is a combined process comprising one reaction of type C and one of type D (Eqs.5 and 6). In this case, the reaction rate is determined by the extraction of the last H+ and a barrier of 2.86 eV in the free energy profile is associated with this step. The theoretical estimate of the overpotential is 1.63 V. This value is considerably smaller than the corresponding one obtained in the subsection A for the Ti2 O4 dimeric structure (3.76 V) following the model suggested in Ref.24 As it was mentioned above, the formation of Ti(OH)2 -O2 -Ti(OH)2 after the decomposition of two water molecules on Ti2 O4 is an exothermic process (5.22 eV). In the Ti2 O4 model of the surface, the assumption of a cyclic mechanism requires the reorganization of the Ti(OH)2 -O2 -Ti(OH)2 until the initial structure is recovered. On the other hand, for the present cluster, the exothermic processes in the reaction mechanism are characterized by smaller energy variations (less than 2 eV) and rearranging the Ti(OH)2 -O2 -Ti(OH)2 structure, after the decomposition of the first and second water molecules, requires overcoming lower energy barriers. Furthermore, in the present mechanism, the overpotential is quite similar to the value calculated for the monomer (1.50 V).

E.

Water splitting on Ti(OH)3 -O-Ti(OH)3

The Ti(OH)3 -O-Ti(OH)3 is a different dimer model (i.e., it has two titanium centers) of the surface of the TiO2 anode. It constitutes a natural extension of the Ti(OH)4 cluster to enclose two Ti centers. It results from the bridging of two Ti(OH)4 clusters mimicking the topology of the anatase (001) surface. The analogy is based on the same assumptions as before: only the Ti centers and their first neighboring O atoms are taken into account, while H atoms are attached to the external oxygens. The white and light blue areas (limited by the dashed rectangles) in Fig.1b highlight the surface cut modeled in this


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17 way. It is worth to notice that opposite to the previous system, in the present case there is only one oxygen-bridge in the structure. Moreover, the electronic structure of two spatial isomers of the present system has been studied previously (Ref.39 ) to represent the bonding situation of different local sites in the TiO2 surface.

The stable molecular configurations, indicative of the reaction mechanism on the present cluster model are displayed in Fig.7a, together with the corresponding energy values in eV. The free energy profiles resulting from adding entropic and vibrational energy contributions for different external potentials are depicted in Fig.7b.

The adsorption of the first water molecule is an exothermic reaction (0.34 eV) (Fig.7a: Γ-structure), while a parallel increase of the free energy in the process is observed. A reaction of type C (Eq.5) is proposed as the following step, during which the system evolves from structure 1 to structure 2 in Fig.7a. In the next two steps, an OOH− group is formed and the corresponding H+ gets extracted, yielding an O2 molecule adsorbed on the cluster. The proposed pathway continues with a combined process similar to the one discussed in the previous subsection: one reaction of type C and one of type D (Eqs.5 and 6) take place at the same time, and the O2 molecule is desorbed from the cluster together with a proton. For this path, the most energy-consuming step is the formation of the OOH− group and a barrier of 4.76 eV has to be overcome for the reaction to proceed this way (see the curve for the external voltage U = 4.76 V in Fig.7b). The value of the overpotential (3.53 V) is qualitatively different to the one obtained for the neutral Ti(OH)4 , and it is similar to the results obtained for the TiO2 and the Ti2 O4 models.

The deviations in the reaction mechanisms on Ti(OH)3 -O-Ti(OH)3 and Ti(OH)2 -O2 -Ti(OH)2 represent, within the framework of the small cluster model, the differences between the water splitting process on the TiO2 anatase (001) and rutile (110) surfaces. Albeit the model calculations presented here are not able to reproduce quantitatively the overpotentials observed experimentally,4 nor the results of previous theoretical studies on extended surfaces6,20 , the proposed reaction mechanisms are able to account for the observed trends of the overpotentials for the two representative crystallographic structures of titanium dioxide.



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18 F.

Entropic contributions and normal mode analysis

As it was mentioned in the methodology, the energy variations for the different reaction pathways used to represent the mechanisms of the water splitting on small cluster models were augmented with entropic contributions in order to describe the evolution of the free energy along the reaction coordinate. The entropic contribution to the free energy, at standard thermodynamic conditions, is modeled as the energy shifts due to the adsorption or desorption of the fragments (H+ , H2 O, and O2 ) on the cluster structure. These entropic variations were computed in the gas phase approximation and only the translational and rotational degrees of freedom of the molecules were considered. For example, the desorption of a H2 molecule causes the increase of the entropy and corresponding changes in the free energy amounting to 0.36 eV and 0.04 eV respectively, associated with the translational and rotational degrees of freedom of the released molecule, respectively. In the case of H2 O, the translation and rotation of the desorbed molecule contributes in 0.45 eV and 0.15 eV to the variation of the free energy. For the O2 gas, the experimental value of 0.63 eV is reported in standard tables (Ref.26 ) for the total contribution. The translational degrees of freedom are considered to be activated for all finite temperatures. Moreover, the characteristic temperatures for the activation of the vibrational (T vib ) and the rotational (T rot ) degrees of freedom in the gas phase - obtained from ab initio calculations, and experimental data (in the case of the O2 molecule) [Ref.43 ]- imply that only the translational and rotational degrees of freedom are activated at room temperature: T rot (H2 ) = 87.69 K, T vib (H2 ) = 6325 K; T rot (H2 O) = 41.16 K, T vib (H2 O) = 2408 K and T rot (O2 ) = 2.070 K, T vib (O2 ) = 2230 K. Table I shows the change in the overpotential for every reaction mechanism upon addition of the entropic contributions to the free energy, at standard ambient temperature and pressure. The overpotential obtained by neglecting this contribution (i.e., the 0 K overpotential) is just the voltage corresponding to the highest energy barrier in the molecular energy profile along the reaction path. It can be noticed, that the overpotential generally decreases when entropic effects are considered. This result is consistent with the qualitative understanding of activated processes: increasing thermal energy favors the occurrence of the reaction. On the other hand, the overpotential of the reaction initiated on the Ti(OH)4 cluster increases at normal thermodynamic conditions. It is worth to notice that at 0 K the adsorption of the


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19 first water molecule in the mechanism (Γ-structure in Fig.4a) is more relevant. Indeed, going from the Γ-structure to structure 2 in Fig.4a becomes the rate-determining step (i.e, the energy barrier associated with this step is higher than that of the direct transition from structure 1 to structure 2 in Fig.4a). Nevertheless, the entropic change in the reaction mechanism at standard ambient temperature and pressure is negative, and the collective effect results in the enhancement of the overpotential. The entropic effects on the overpotentials for the reactions taking place on the TiO2 and Ti(OH)− 4 clusters are similar. An analogous behavior is found for the systems Ti(OH)2 -O2 -Ti(OH)2 and Ti(OH)3 O-Ti(OH)3 . The reason for these similarities is that each pair of cluster models share the same ratelimiting step: the release of O2 +H+ in the first case, and the H+ desorption in the latter (dimeric) models. The entropic contribution for each of these processes is the same. For instance, the H+ contribution (0.20 eV) is one half of that of H2 (0.36 eV + 0.04 eV). Likewise, in the case of Ti2 O4 , the free energy variation due to the entropic contributions does not match any of the other values listed in table I because of the distinct rate-determining step in the proposed reaction mechanism. The vibrational density of states (VDOS) of every structure on the reaction path of the water splitting on Ti(OH)4 is shown in Fig.8. Each VDOS has been computed by substituting the δ-like contributions of each of the vibrational eigenfrequencies ωk , obtained from the ab-initio calculations, by finite spread distributions centred at each value ωk . Fixed-variance normal distributions are thus employed to compute the contribution of each normal mode (see the supplementary material for more details about the Gaussian functions). The whole frequency domain is divided in three sub-intervals: the low frequency region (LFR) from 0 to 1000 cm−1 , the middle frequency region (MFR) from 1000 to 3500 cm−1 and the high frequency region (HFR) from 3500 to 4500 cm−1 . The VDOS of Ti(OH)4 is shown in Fig.8a. It presents a welldefined peak structure in the LFR, no relevant modes appear in the MFR and one additional peak is located in the HFR. The participation of each atom in the computed normal modes is evaluated from the projections of the corresponding eigenvectors along the different atomic displacements. This analysis leads to the conclusion that the structure of the VDOS in the LFR is characterized by collective motions of the cluster atoms. It is worth to notice that the VDOS of both anatase and rutile TiO2 extend from 0 cm−1 to almost 900 cm−1 .44 On the other hand, the structure of the spectrum in the HFR is consist of



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20 more localized oscillations: for example, in the present case, the band in the HFR is composed by four (almost degenerated) individual H-stretching modes. The adsorption of the first water molecule increases the number of normal modes, and most of the new vibrational frequencies contribute to the population in the LFR, Fig.8b. The three normal modes of the water molecule in the gas phase are noticeable in the VDOS structure: the bending mode νB (1735 cm−1 ), the symmetric stretching νSS (3713 cm−1 ) and the asymmetric stretching (3789 cm−1 ). The latter overlaps with the O-H stretchings of the structure. In Fig.8c the structure of the VDOS for Ti(OH)5 is shown. In addition to the collective modes (in the LFR) and the H-stretchings (in the HFR), the appearance of a small shoulder in the inner tail of the HFR-band can be observed. This shoulder represents a slightly weaker H-stretching in the cluster (the corresponding OH bond distance is 0.974 ˚ A, while the other OH separations are between 0.961 and 0.967 ˚ A). Furthermore, the panel d) in Fig.8 corresponds to the Ti(OH)3 OOH structure. Compared to the Ti(OH)5 , three new peaks appear in the VDOS: the O-OH (894 cm−1 ) mode, which represents the O-O stretching motion; the bent OO-H mode (1337 cm−1 ), which is associated with the H-bending motion in the OOH group and the aligned OO-H mode (3667 cm−1 ) corresponding to the H-stretching mode in the OOH group. These values are in good agreement with previous results (Ref.45 ) for similar modes in the H2 O2 molecule: 890 cm−1 for the O-O stretching, 1295 cm−1 for the symmetric H-bending and 3610 cm−1 for the H-stretching. The VDOS of Ti(OH)3 O2 is shown in Fig. 8e. The structure of the VDOS shows that the normal modes related with the H atom in the OOH group (i.e., the bent and aligned OO-H modes in Fig.8 d)) are no longer present in the spectrum. The frequency of the normal modes associated with the preformed O2 molecule (1197 cm−1 , labeled as O-O in Fig. 8 e)) is shifted with respect to the O-OH peak in Fig. 8 d). Conversely to the latter oscillation mode (O-OH in Fig. 8 d)), the O-O band in Fig. 8 e) corresponds to a normal mode which combines torsional and stretching motions of the O2 molecule linked to the Ti atom. This conclusion was verified through the analysis of the eigenvectors associated to this eigenfrequency, and it was further supported by the visualization of the atomic motions employing the Visual Molecular Dynamics (VMD) package.46 In the partial vibrational density of state (PVDOS) for every atom of the


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21 structure Ti(OH)3 O2 (Supplementary Material), it is shown that the O-O peak in Fig. 8 e) is composed by contributions coming from the oxygen atoms in the preformed O2 molecule. The modification of the VDOS upon adsorption of the second water molecule is shown in Fig. 8 f). In this case, the VDOS exhibits the peaks corresponding to the water molecule (νB and νSS ), and an O-O mode (1212 cm−1 ) whose frequency is very close to that of the O-O peak in Fig. 8 e). Interestingly, despite the similarities between these two frequencies (1197 cm−1 and 1212 cm−1 , the relative deviation is bellow 2% of the average of these two values), the visualization of the corresponding motions with the VMD package reveals that the O-O peak in the Ti(OH)3 O2 -H2 O structure is a purely stretching mode of the O2 molecule, while it corresponds to a combined motion in the Ti(OH)3 O2 cluster. The change in the nature of the O-O mode at this step, because of the adsorption of the water molecule, motivates the assumption of the H2 O adsorption as a more favorable way to continue the reaction among the other possible paths (e.g., the desorption of O2 from the Ti(OH)3 O2 structure).

IV.

CONCLUSIONS

In the present work, different mechanisms of the water splitting reaction on small cluster representations of TiO2 surfaces were investigated, and the relative advantages of several cluster models to simulate the main features of the process on the actual substrates were addressed. The energetics of the water decomposition pathways was described within the framework of the Density Functional Theory. The use of this level of theory allows the comparison of the results obtained in this work with previous studies of the same process on extended surfaces. The different molecular systems were considered to mimic the surface of the anode of a TiO2 -based electrochemical cell. This enabled the study of the properties of the cluster approximations and the influence of various structural features on the water splitting reaction (e.g., charged structure or different surface topologies). The electronic structure calculations provide a detailed picture of the water splitting process via the optimized geometries for every intermediate step, and the energy required for the system to move along the reaction path. Based on the DFT energies, we identified the rate-determining step for every reaction mechanism. In each case, applying the external potential needed to overcome the largest energy



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22 barrier tends to flatten the free energy profile in the vicinity of the most energy-consuming step. The overpotential corresponding to each reaction mechanism was estimated employing a previously developed thermochemical methodology, which explicitly takes into account the applied external potential in the free energy calculations.19 Since the free energy landscape and the computed overpotentials depend on the chosen reaction path, other plausible pathways have been explored. Alternative mechanisms considered in previous studies (e.g., the binding of an additional H2 O molecule to specific molecular structures) were found to require a larger potential bias to steer the reaction. In most of the proposed mechanisms the inclusion of the entropic contribution to the free energy favors the reaction (i.e., it decreases the overpotential). The vibrational degrees of freedom in the gas phase of H+ , H2 O and O2 at standard conditions do not contribute to the entropy change of different intermediate structures. Taking the reaction mechanism of the water splitting on Ti(OH)4 as an example, it is shown that the VDOS of the intermediate structures reflects the main features of the water splitting process. Likewise, the information extracted from the normal modes analysis is a useful tool to grasp which structure is more suitable as the next step in the reaction mechanism. Specifically, the adsorption of a second water molecule on the Ti(OH)3 O2 cluster followed by the release of an oxygen molecule was found to be more favorable than the reverse process (i.e., the direct desorption of O2 from the Ti(OH)3 O2 cluster and the subsequent adsorption of a water molecule). The mechanism proposed for the water electrolysis on the Ti(OH)4 cluster significantly improves the agreement between the computed overpotential and the experimental and theoretical values reported for extended surfaces, with respect to similar reaction mechanisms taking place on TiO2 and Ti2 O4 clusters. Therefore, the Ti(OH)4 structure provides a more realistic representation of the surface of the anode, compared to the molecular structures suggested in previous works.23,24 On the other hand, the calculations performed for the Ti(OH)− 4 model show that the addition of localized charges does not favor the water decomposition. The cluster models can be considered as elementary building blocks which approximate the surface. They can be made progressively larger, eventually approaching the bulk surface. In this direction, we considered dimeric structures to represent different topologies of the semiconducting surface


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23 Ti(OH)2 -O2 -Ti(OH)2 , for rutile (110) and Ti(OH)3 -O-Ti(OH)3 , for anatase (001). For the first of these models, we obtained a similar value of the overpotential as for the Ti(OH)4 cluster, while it differs significantly from the overpotential for the oxygen-linked Ti(OH)3 dimer. The Ti(OH)2 -O2 -Ti(OH)2 and the Ti(OH)3 -O-Ti(OH)3 clusters provide reasonable representations of the spatial disposition of atoms in the neighborhood of the interaction sites on rutile and anatase surfaces. Although the corresponding overpotentials do not match the previous results reported for extended surfaces6,20 , these cluster models correctly predict the relatively larger feasibility of decomposing water molecules on rutile (110) surfaces compared to anatase (001) substrates. These results suggest the possibility to predict, within the small cluster approximation, the relative performance of different TiO2 -based surfaces for the catalytic splitting of water molecules.

V.

CORRESPONDING AUTHOR

E-mail: [email protected]

VI.

ACKNOWLEDGMENTS

F.R.H. thanks the International Max Plack Research School for Dynamical Processes in Atoms, Molecules and Solids, Dresden for support of this work.

VII.

SUPPORTING INFORMATION

The Supporting Information is available free of charge on the ACS Publications website. Details of the structure information, vibrational density of states (VDOS) and partial vibrational density of states (PVDOS) (PDF).

1

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Wang, T. H.; Fang, Z.; Gist, N. W.; Li, S.; Gole, J. L.; Dixon, D. A. Computational Study of the Hydrolysis Reactions of the Ground and First Excited Triplet States of Small TiO2 Nanoclusters. J. Phys. Chem. C 2011, 115, 9344-9360.

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Man, I. C. et. al. Universality in Oxygen Evolution Electrocatalysis on Oxide Surfaces. ChemCatChem 2011, 3, 1159-1165.

26

Atkins, P. W. Physical Chemistry, 6th ed. Oxford University Press: Oxford, U. K., 1998; pp 485, 925-927, 942.

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Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved Adsorption Energetics within Density-Functional Theory using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B 1999, 59, 7413-7421.

28

Perdew, J. D.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868.



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Zhang, Y.; Yang, W. Comment on Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1998, 80, 890.

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Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L. Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode. J. Phys. Chem. B 2004, 108, 17886-17892.

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Becke, A. D. Density-Functional Thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648-5652.

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Lee, C.; Yang, R. G.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789.

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Dunning, T. H. Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First-Row Atoms. J. Chem. Phys. 1971, 55, 716-723.

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Wachters, A. J. H. Gaussian Basis Set for Molecular Wavefunctions Containing Third-Row Atoms. J. Chem. Phys. 1970, 52, 1033-1036.

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Schmidt, M. W. et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347-1363.

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Gordon, M. S.; Schmidt, M. W. Theory and Applications of Computational Chemistry, the First Forty Years, Elsevier, Amsterdam, 2005, pp 1167-1189.

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Muscat, J.; Swamy V.; Harrison N. M. First-Principles Calculations of the Phase Stability of TiO2 . Phys. Rev. B 2002, 65, 224112 (15 pag.).

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Tsuchiya, T.; Whitten, J. L. Theoretical Study of the Molecular and Electronic Structures of TiO4 H4 , Ti2 O7 H6 , and Ti2 O6 H4 . J. Phys. Chem. C 2011, 115, 1635-1642.

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27 44

Shjaee, E.; Mohammadizadeh, M. R. First-Principles Elastic and Thermal Properties of TiO2 : a Phonon Approach. J. Phys.: Condens. Matter 2010, 22, 015401 (8 pag.).

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Dorofeeva, O. V.; Iorish, V. S; Novikov, V. P.; Neumann, D. V. NIST-JANAF Thermochemical Tables. II. Three Molecules Related to Atmospheric Chemistry: HNO3 , H2 SO4 , and H2 O2 . J. Phys. Chem. Ref. Data 2003, 32, 879-901.

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Humphrey, W., Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33-38.



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28

FIGURE CAPTIONS Fig.1 (a) Top view of the rutile TiO2 (110) surface. The oxygen atoms are represented by the red points and the Ti are the blue ones. It is also represented the active site on the surface which is studied by a small cluster considering only the firsts neighbours of one 5-fold coordinated Ti (white dashed square). The extension of the cluster model including the next Ti-active site is also drown (dashed rectangle including the light blue square) (b) Top view of the anatase TiO2 (001) surface. The white dashed square is the smaller cluster representation for the active sites on this surface while the rectangle including the light blue square is the representation when two Ti-centers are considered. Fig.2 (a) Water splitting on TiO2 : TiO2 + 2H2 O → TiO2 + 2H2 + O2 . The molecular energies are in eV. (b) Free energy profile of the water splitting mechanism on TiO2 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line), minimum external potential which makes the free energy of the process down-hill in the reaction steps: 4.66 V (blue line). The limiting step for this mechanism is shown. The corresponding overpotential is 3.43 V. Fig.3 (a) Water splitting on Ti2 O4 : Ti2 O4 + 2H2 O → Ti2 O4 + 2H2 + O2 . The molecular energies are in eV. (b) Free energy profile of the water splitting mechanism on TiO2 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line), minimum external potential which makes the free energy of the process down-hill in the reaction steps: 4.99 V (blue line). The limiting step for this mechanism is shown. The corresponding overpotential is 3.76 V. Fig.4 (a) Water splitting on Ti(OH)4 : Ti(OH)4 + 2H2 O → Ti(OH)4 + 2H2 + O2 . The molecular energies are in eV. The Γ and ∆ structures highlight the configurations which increase the free energy independently of the external potential. (b) Free energy profile of the water splitting mechanism on the neutral Ti(OH)4 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line),


Page 29 of 40

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29 minimum external potential which makes the free energy of the process down-hill in the reaction steps: 2.73 V (blue line). The Γ and ∆ marks represent the reaction steps with increasing free energies which can not be reduced by the external potential. The limiting step for this mechanism is shown. The corresponding overpotential is 1.5 V.

− − Fig.5 (a) Water splitting on Ti(OH)− 4 : Ti(OH)4 + 2H2 O → Ti(OH)4 + 2H2 + O2 . The molecular energies

are in eV. (b) Free energy profile of the water splitting mechanism on the electronically activated Ti(OH)− 4 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line), minimum external potential which makes the free energy of the process down-hill in the reaction steps: 3.49 V (blue line). The limiting step for this mechanism is shown. The corresponding overpotential is 2.26 V.

Fig.6 (a) Water splitting on Ti(OH)2 -O2 -Ti(OH)2 : Ti(OH)2 -O2 -Ti(OH)2 +2H2 O → Ti(OH)2 -O2 -Ti(OH)2 + 2H2 + O2 . The molecular energies are in eV. The Γ, ∆ and Λ structures highlight the configurations which increase the free energy independently of the external potential. (b) Free energy profile of the water splitting mechanism on Ti(OH)2 -O2 -Ti(OH)2 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line), minimum external potential which makes the free energy of the process down-hill in the reaction steps: 2.86 V (blue line). The Γ, ∆ and Λ marks represent the reaction steps with increasing free energies which can not be reduced by the external potential. The limiting step for this mechanism is shown. The corresponding overpotential is 1.63 V.

Fig.7 (a) Water splitting on Ti(OH)3 -O-Ti(OH)3 : Ti(OH)3 -O-Ti(OH)3 +2H2 O → Ti(OH)3 -O-Ti(OH)3 + 2H2 + O2 . The molecular energies are in eV. The Γ structure highlight the configuration which increase the free energy independently of the external potential. (b) Free energy profile of the water splitting mechanism on Ti(OH)3 -O-Ti(OH)3 at standard conditions under different external potentials. Zero external potential (red line), standard potential of the overall water splitting reaction: 1.23 V (green line), minimum external potential which makes the free energy of the



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Page 30 of 40

30 process down-hill in the reaction steps: 4.76 V (blue line). The Γ structure represents the reaction step with increasing free energy which can not be reduced by the external potential. The limiting step for this mechanism is shown. The corresponding overpotential is 3.53 V. Fig.8 Vibrational density of states (VDOS, in arbitrary units) of every intermediate structure for the water decomposition on Ti(OH)4 . The bending and the symmetric stretching modes of the water molecules are identified as νB (1735 cm−1 ) and νSS (3713 cm−1 ) respectively. In panel d) three modes corresponds to the OOH group: The O-O stretching, denoted as O-OH (894 cm−1 ); the H bending, identified by the bent OO-H (1337 cm−1 ) and the O-H stretching, marked by the aligned OO-H (3667 cm−1 ). The peaks designated as O-O corresponds to normal modes associated with the motion of the preformed O2 molecule: in panel e) it represents a combined stretching and torsional mode (1197 cm−1 ) while in panel f) it corresponds to a vibrational mode of the O2 structure (1212 cm−1 ).


Page 31 of 40

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31

TABLE CAPTIONS Table I Variation of the overpotential for every reaction mechanism upon inclusion of the entropic contributions due to adsorbed and desorbed fragments, at standard ambient temperature and pressure. In every case, if the entropic influence is not taken into account, the value of the overpotential (i.e., 0 K overpotentials) matches the highest energy barrier along the corresponding molecular energy profile.



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Page 32 of 40

32 TABLE I Cluster model

∆U (V)

TiO2

-0.83

Ti2 O4

-0.46

Ti(OH)4

0.22

Ti(OH)− 4

-0.83

Ti(OH)2 -O2 -Ti(OH)2

-0.20

Ti(OH)3 -O-Ti(OH)3

-0.20


Page 33 of 40

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33

(a)

(b)

FIG. 1



34 Hydrogen Oxygen Titanium

5.15 TiO2

4.64

6

5

0.00

−0.859

TiO2

−2.41

+ H

+ O2 +H

4

1

+ H

3 2H2O + H

−5.04 2

(a)

Water splitting on TiO2 5 U = 0.00 V U = 1.23 V U = 4.66 V

∆G = 4.66 eV

0

G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 40

-5

-10

1 -15

0

2 1

3 2

4

3 Reaction steps

6

5 4

(b)

FIG. 2


5

6

Page 35 of 40

35 Hydrogen Oxygen Titanium

5.41

5.15

4

0.00

−0.030

Ti 2 O4

3

1

2H2O

Ti 2 O4

4.58

+ H

6

5

+ H

5

6

+

O2 +H

+ H

−5.22 2

(a)

Water splitting on Ti2O4 5 ∆G = 4.61 eV ∆G = 4.99 eV

0

-5 G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


U = 0.00 V U = 1.23 V U = 4.99 V

-10

-15 1 -20

0

2 1

3 2

4

3 Reaction steps

4

(b)

FIG. 3


5

6


36

Hydrogen

∆

Oxygen

5.15

Titanium

Ti(OH) 4

3.91

5

4

3.02

+ H2O H

3

2.33

Γ

3.55

+ O2 + H

+ H

2

0.00 Ti(OH) 4

1

+ H

−0.177

H2O

(a)

Water splitting on Ti(OH)4 ∆

4

2 ∆G = 2.73 eV Γ

0 G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 40

U = 0.00 V U = 1.23 V U = 2.73 V ∆G = 0.42 eV ∆G = 0.24 eV

-2

-4

1

-6 0

3

2 1

2

5

4 3

4

Reaction steps

(b)

FIG. 4


5

Page 37 of 40

37

Hydrogen Oxygen

5.15

Titanium

Ti(OH) − 4

7

1.45 0.971 4

5 + H

0.00

H2O

+ O2 + H

0.826 6

Ti(OH) − 4

1

−0.691

+ H

2

H2O

−1.38

+ H

3

(a) -

Water splitting on Ti(OH) 4 5 U = 0.00 V U = 1.23 V U = 3.49 V

∆G = 3.49 eV

0 ∆G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-5

1 -10

0

2 1

3 2

4 3 4 Reaction steps

6

5 5

(b)

FIG. 5


7 6

7


38 ∆

Hydrogen

Λ

Oxygen

5.15

Ti(OH) 2−O2−Ti(OH)2

Titanium

5

3.92 3

3.59

+ H

2

2.09 + O2 + H

0.00

Ti(OH) 2−O2−Ti(OH)2

4

+ H

1 H2O

+ H

3.56

H2O

1.90

Γ

−0.246

(a)

Water splitting on Ti(OH)2-O2-Ti(OH)2 ∆ Λ ∆G = 2.86 eV

4

2

Γ

0 G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 40

U = 0.00 V U = 1.23 V U = 2.86 V ∆G(+H2O) = 0.36 eV ∆G(+H2O) = 0.27 eV ∆G(H+OH) = 0.23 eV

-2

-4

-6

1 0

2 1

3 2

4 3

5 4

Reaction steps

(b)

FIG. 6


5

Page 39 of 40

39 Hydrogen

OH

Oxygen Titanium

5.15

Ti(OH) 3−O−Ti(OH)3

5

4.19

+ O2 + H

4

Γ

+ H

2.84 3

0.00

Ti(OH) 3−O−Ti(OH)3

1

−0.344

H2O

+ H

−2.13

+ H

2

(a)

Water splitting on Ti(OH)3-O-Ti(OH)3 5

∆G = 4.76 eV

Γ 0

-5 G(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


U = 0.00 V U = 1.23 V U = 4.76 V ∆G(+H2O) = 0.26 eV

-10

-15

1 -20

0

3

2 1

2

4 3

5 4

Reaction steps

(b)

FIG. 7


5


40 a)

Ti(OH)4

b)

Ti(OH)4-H2O

νB VDOS(arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 40

c)

Ti(OH)5

d)

Ti(OH)3OOH

H O-OH

νSS

OO-H

OO

e)

Ti(OH)3O2 O-O

f)

0

500

1000

Ti(OH)3O2-H2O

νB

O-O

1500

2000 2500 -1 ω(cm )

3000

νSS

3500

4000

FIG. 8

O2 − TS

+

O2 + 2H2

Cluster Model Cluster + 2 H2O FIG. 9: Table of Contents (TOC) Image.


Water Splitting on TiO2-Based Electrochemical Cells: A Small Cluster

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