**DFT-based Theoretical Simulations for Photocatalytic Applications Using TiO2**

Yeliz Gurdal and Marcella Iannuzzi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68976

#### **Abstract**

TiO2 has been shown to be a potential candidate for photoinitiated processes, such as dye sensitized solar cells and water splitting in production of H<sup>2</sup> . The large band gap of TiO<sup>2</sup> can be reduced by functionalizing the oxide by adsorbing dye molecules and/or water reduc‐ tion/oxidation catalysts, by metal/nonmetal doping, and by mixing with another oxide. Due to these methods, several different TiO<sup>2</sup> ‐based complexes can be constructed having differ‐ ent geometries, electronic structures, and optical characteristics. It is practically impossible to test the photocatalytic activity of all possible TiO<sup>2</sup> ‐based complexes using only experi‐ mental techniques. Instead, density functional theory (DFT)‐based theoretical simulations can easily guide experimental studies by screening materials and providing insights into the photoactivity of the complexes. The aim of this chapter is to provide an outlook for cur‐ rent research on DFT‐based simulations of TiO<sup>2</sup> complexes for dye sensitized solar cells and water splitting applications and to address challenges of theoretical simulations.

**Keywords:** density functional theory, ab‐initio molecular dynamics, photocatalyst, TiO<sup>2</sup> , dye sensitized solar cells, water splitting

## **1. Introduction**

Emergent technologies and the demand for alternative energy sources, which do not produce greenhouse gases as a byproduct lead to a growing awareness in using those renewable sources already provided by nature, such as sunlight. The ideal goal is to emulate the photochemical process with which the plants convert H<sup>2</sup> O and CO2 into O2 and carbohydrates by absorbing photons in the energy range between 3.3 and 1.5 eV (visible spectrum). Scientists then aim at designing new catalysts that can employ the easily available sunlight and convert it into chemical energy, without depending on the activation energy generated by traditional fuels.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In 1938, for the first time, Goodeve and Kitchener [1] demonstrated the photocatalytic activity of the TiO2 surface, which can produce oxygen by absorbing UV light thus leading to the pho‐ tobleaching of dyes. This study has initiated many others toward discovering photocatalytic reactions that can be catalyzed by TiO2 . The success of this material is also justified by its high stability, low cost, no side effects on humans and environment, and ease in large‐scale usage. In spite of the promising properties of TiO<sup>2</sup> , the photocatalytic activity of the bare surface is not optimal, due to the too large energy gap [2]. This limits the photons' absorption and induces the fast recombination of the photogenerated carriers [3]. While these drawbacks sig‐ nificantly hinder the effective application of the pristine material, several possible solutions have been envisioned by considering surface modifications, such as composite semiconduc‐ tor coupling, metal/nonmetal doping, and functionalization by means of different types of adsorbates [4]. For instance, Zn‐porphyrin adsorbed on the TiO<sup>2</sup> surface reduces the threshold for the photons' absorption, and by allowing the fast electron injection toward the substrate, slows down the charge recombination process [5].

Among many photocatalytic applications of functionalized TiO<sup>2</sup> surface, water splitting for H2 production and dye sensitized solar cells (DSSCs) are among the most widely studied top‐ ics. Although the increasing number of promising studies is going to build photocatalytically efficient and robust several TiO<sup>2</sup> ‐based materials, in this field, the support of the theoretical approach to explore the properties of possible candidate materials is essential. The investiga‐ tion of proper atomistic models of the systems of interest, possibly including the electronic structure characterization and reproducing the relevant processes, can significantly help the screening of materials. In particular, it is necessary to understand the nature of the adsor‐ bate‐substrate interaction, and providing insights into the photoactivity prior to extensive experimental efforts. The aim of this chapter is to review the current progress and challenges in density functional theory (DFT)‐based simulations of functionalized TiO<sup>2</sup> surfaces, includ‐ ing rutile, anatase, and TiO<sup>2</sup> nanoparticles, with respect to the applications in photocatalytic water splitting and DSSCs.

## **2. Overview on density functional theory**

DFT is developed by Hohenberg, Kohn, and Sham [6, 7] in 1964 as a minimization problem of the ground state energy as a function of electron density. The approach is to solve any fully interacting problem by mapping it to a noninteracting problem introducing exchange‐correla‐ tion functional, see Eq. (1).

$$E = T\_s \left[ \left\{ \rho(r) \right\} \right] + \left\{ \left\{ \rho(r) \right\} \right\} v\_{\rm{out}}(r) \left\{ \rho(r) \right\} dr + E\_{\rm{xc}} \left[ \left\{ \rho(r) \right\} \right] \tag{1}$$

where *Ts* [*ρ*(*r*)] is the kinetic energy of the noninteracting system, *J*[*ρ*(*r*)] is the classical Coulomb repulsion energy, ∫ *v*ext(*r* ) *ρ*(*r* ) *dr* is the interaction of the external potential acting on the elec‐ trons, and *E* xc [*ρ*(*r*)] term is the exchange and correlational energy. All of these terms are called functionals and they depend on the electron density *ρ*(*r* ), i.e., the number of electrons per unit volume.

xc

Electron density can be expressed in many ways [8]; however, Gaussian and plane wave for‐ malism is shown to be significantly efficient for the description of the orbitals [9]. A localized Gaussian basis set positioned at each atom is used to expand the Kohn‐Sham orbitals and an auxiliary plane wave basis set is used to describe the electron density, thus improving the computational performance in the calculation of the Coulomb interactions. This scheme is shown to be a suitable choice for large‐scale DFT simulations [10, 11].

In 1938, for the first time, Goodeve and Kitchener [1] demonstrated the photocatalytic activity

tobleaching of dyes. This study has initiated many others toward discovering photocatalytic

stability, low cost, no side effects on humans and environment, and ease in large‐scale usage.

is not optimal, due to the too large energy gap [2]. This limits the photons' absorption and induces the fast recombination of the photogenerated carriers [3]. While these drawbacks sig‐ nificantly hinder the effective application of the pristine material, several possible solutions have been envisioned by considering surface modifications, such as composite semiconduc‐ tor coupling, metal/nonmetal doping, and functionalization by means of different types of

for the photons' absorption, and by allowing the fast electron injection toward the substrate,

 production and dye sensitized solar cells (DSSCs) are among the most widely studied top‐ ics. Although the increasing number of promising studies is going to build photocatalytically

approach to explore the properties of possible candidate materials is essential. The investiga‐ tion of proper atomistic models of the systems of interest, possibly including the electronic structure characterization and reproducing the relevant processes, can significantly help the screening of materials. In particular, it is necessary to understand the nature of the adsor‐ bate‐substrate interaction, and providing insights into the photoactivity prior to extensive experimental efforts. The aim of this chapter is to review the current progress and challenges

DFT is developed by Hohenberg, Kohn, and Sham [6, 7] in 1964 as a minimization problem of the ground state energy as a function of electron density. The approach is to solve any fully interacting problem by mapping it to a noninteracting problem introducing exchange‐correla‐

[*ρ*(*r*)] is the kinetic energy of the noninteracting system, *J*[*ρ*(*r*)] is the classical Coulomb

[*ρ*(*r*)] term is the exchange and correlational energy. All of these terms are called

repulsion energy, ∫ *v*ext(*r* ) *ρ*(*r* ) *dr* is the interaction of the external potential acting on the elec‐

functionals and they depend on the electron density *ρ*(*r* ), i.e., the number of electrons per unit

surface, which can produce oxygen by absorbing UV light thus leading to the pho‐

. The success of this material is also justified by its high

‐based materials, in this field, the support of the theoretical

nanoparticles, with respect to the applications in photocatalytic

 [ *ρ*(*r* ) ]+*J* [ *ρ*(*r* ) ]+∫ *v*ext(*r* ) *ρ*(*r* ) *dr* + *E*xc [ *ρ*(*r* ) ] (1)

, the photocatalytic activity of the bare surface

surface reduces the threshold

surface, water splitting for

surfaces, includ‐

of the TiO2

190 Titanium Dioxide

H2

reactions that can be catalyzed by TiO2

In spite of the promising properties of TiO<sup>2</sup>

slows down the charge recombination process [5].

**2. Overview on density functional theory**

efficient and robust several TiO<sup>2</sup>

ing rutile, anatase, and TiO<sup>2</sup>

water splitting and DSSCs.

tion functional, see Eq. (1).

*E* = *T*<sup>s</sup>

xc

where *Ts*

volume.

trons, and *E*

adsorbates [4]. For instance, Zn‐porphyrin adsorbed on the TiO<sup>2</sup>

Among many photocatalytic applications of functionalized TiO<sup>2</sup>

in density functional theory (DFT)‐based simulations of functionalized TiO<sup>2</sup>

Although the achievement in introducing electron density depends on the total energy instead of the electron wave function formalism and providing simple, universal, and self‐consistent‐ field description of the ground‐state electronic structure, any practical usage of DFT requires an accurate description to the exchange and correlational effects, *E* [*ρ*(*r*)], see Eq. (2).

$$E\_{\rm ac} \left[ \begin{smallmatrix} \rho(r) \end{smallmatrix} \right] \!\!\equiv \left( V\_{\alpha} \left[ \begin{smallmatrix} \rho(r) \end{smallmatrix} \right] \!\!\begin{smallmatrix} \rho(r) \end{smallmatrix} \right) \!\!\left( T \left[ \begin{smallmatrix} \rho(r) \end{smallmatrix} \right] \!\!\right) \!\!\left( T \left[ \begin{smallmatrix} \rho(r) \end{smallmatrix} \right] \!\!\right) \!\!\left( T \begin{smallmatrix} \rho(r) \end{smallmatrix} \right) \!\!\right) \tag{2}$$

where *T*[*ρ*(*r* )] is the kinetic energy of the interacting system and *V* ee [*ρ*(*r* )] is the nonclassical interaction between electrons. Although the exact analytic expression of the exchange‐cor‐ relation functional is not known, approximations to these terms have been demonstrated to be able capture most of the physical/chemical properties of many systems from the solid state to the liquid state.

Many methods have been proposed to calculate exchange‐correlation contribution to the total energy [12]. One of the most commonly used ones is the generalized gradient approximation (GGA), where the exchange and correlation energy depends on both electron density and its gradient [13]. This method includes semiempirical functionals that consist of one or more parameters fitted to experimentally observed quantities. Perdew‐Burke‐Ernzerhof (PBE) [14] and Becke exchange/Lee‐Yang‐Parr correlation (BLYP) [15] are the most popular semiempiri‐ cal functionals. These functionals are successfully applied to many systems from metals to 2D self‐assemblies [16]. However, it is shown that they fail to reproduce some of the experimen‐ tally observed properties of oxides accurately, due to the incorrect description of electronic localization by standard DFT [17]. The problem is the incomplete cancellation of the Coulomb self‐interaction in GGA functionals, which leads to stabilization of electron delocalization [18]. For instance, PBE density functional is shown to be quite good to capture structural properties of both bulk phase and the surface of TiO<sup>2</sup> ; however, band gap of bulk TiO<sup>2</sup> is pre‐ dicted as 1.74 eV [19] which significantly underestimates the experimentally measured band gap of 3.2 eV [20]. Therefore, for electronic structure analysis and band alignment of oxides one should go beyond GGA [21].

One of the commonly applied methods to overcome the failure of GGA is to use hybrid den‐ sity functionals that mix exact exchange from Hartree‐Fock exchange [22] and correlation from GGA. Applying hybrid functionals removes some of the self‐interaction error and favors localized electronic states by reducing the barrier to the localization [23]. Including orbital analogue of exchange formalism in hybrid functionals often improves the accuracy of the simulations; however, computational cost increases by at least an order of magnitude with respect to the pure GGA formalism. The most popular hybrid functionals are, e.g., HSE06 [24] and PBE0 [25]. The band gap of the bulk TiO<sup>2</sup> is calculated to be 4.21 eV [26] and 3.35 eV [21] by PBE0 and HSE06, respectively. Although larger band gaps are obtained for semiconduc‐ tors using hybrid functionals, one should carefully choose the exchange‐correlation formal‐ ism since significantly larger band gaps can also be obtained, e.g., PBE0.

For most of the photocatalytic applications of TiO<sup>2</sup> , a photosensitizer or an active catalyst is adsorbed on the surface in which case both chemical and physical interactions play a role on the adsorption geometry or stability of the complex. For instance, it is shown that cis/trans coordination of the ligand with respect to anchoring group adsorbed on anatase TiO<sup>2</sup> (110) surface affects binding mode of the dye which likely arises due to the dispersion interactions [27]. It is well known that the exchange‐correlational functionals suffer for a poor descrip‐ tion of dispersion interactions or van der Waals interactions. To increase the accuracy of the simulations the missing dispersion interactions can also be incorporated into DFT. One way is to add dispersion energy correction term, Grimme‐D3 [28], which calculates pairwise inter‐ actions between atomic species and shows usual 1/r<sup>6</sup> asymptotic behavior, on top of the total energy obtained by DFT.

Using DFT, one can optimize structures, determine the most stable adsorption geometries, calculate corresponding adsorption and interaction energies, and extract electronic proper‐ ties. Electronic structure can be analyzed by calculating projected density of states, which also provides energy band gaps, schematic representation of molecular orbitals, charge distribution maps, and charge density difference maps. On the other hand, the exploration of the conforma‐ tional space at finite temperature is obtained by running ab‐initio molecular dynamics simula‐ tions (AIMD) [29] through the generation of trajectories of several picoseconds. Phase‐space trajectories are generated via numerical integration of equations of motion. Due to the advances in the electronic structure calculations, forces can be derived directly from the electrons without any empirical parameters. Within the Born‐Oppenheimer approximation [30], electrons are fully decoupled from the nuclear motion at each MD step. Nuclei is subsequently propagated accord‐ ing to the forces obtained from the electronic structure calculation from timestep to timestep.

Although there are significant contributions to the modeling of materials/devices using many simulation methods, such as time‐dependent density functional theory (TD‐DFT) [31] or quantum mechanics‐molecular mechanics (QM/MM) [32], it is beyond the scope of this chap‐ ter to give a complete overview of all studies with different simulation techniques. Therefore, the following sections will focus on theoretical simulations of DSSC and water splitting using DFT, sometime in combination with AIMD.
