Theoretical Study on Electronic Structure and Optical Performance of Nickel and Nitrogen Codoped Rutile Titanium Dioxide

1 Institute of Power Source & Ecomaterials Science, Hebei University of Technology, Tianjin 300130, China 2 Key Laboratory for Palygorskite Science and Applied Technology of Jiangsu Province, Huaiyin Institute of Technology, Huaian 223003, China 3 Key Laboratory of Special Functional Materials for Ecological Environment and Information, Hebei University of Technology, Ministry of Education, Tianjin 300130, China 4Qian’an College, Hebei United University, Hebei 064400, China


Introduction
Titanium dioxide has characteristics of strong catalytic activity, a long lifetime of photon-generated carrier, high chemical and thermal stability, and low cost; it has become one of the most extensively utilized ideal photocatalytic materials [1][2][3].Generally, titanium dioxide has three basic crystalline phases containing brookite, anatase, and rutile titanium dioxide.Anatase titanium dioxide has been widely studied, and rutile titanium dioxide as the most stable one should be further studied and applied.Unfortunately, rutile titanium dioxide has intrinsic wide band gap value of 3.0 eV, and it can be activated only under the ultraviolet radiation from sunlight with only a small portion of the solar energy, resulting in its quite low solar energy usage [4][5][6].Therefore, the high efficient usage of visible-light has become one of the most urgent purposes for the photocatalytic materials, and a large number of related theoretical and experimental studies have been performed to regulate the electronic structure and optical performance for titanium dioxide.
At present, many efforts have been made in enhancing the photocatalytic performance of titanium dioxide, including transition metal doping, nonmetal doping, noble metal loading, organic dye sensitizing, and semiconductor compounding [7][8][9][10][11].Among the above methods, ion doping has been regarded as one of the most effective ways.The previous studies have mostly focused on the single ion doping for titanium dioxide [12][13][14][15], but relatively few recent experimental works show that various ions codoping into titanium dioxide can enhance the optical absorption scope and photocatalytic activity.However, the above experimental ions codoping work has disadvantages of variable experimental conditions and sample fabrication methods, resulting in the difficulty in studying the ion doping effect and modification mechanism [16][17][18][19].Alternatively, the computer simulation could conquer the experimental work drawback and be applied to analyzing the ion doping effects and modification mechanism deeply.
In this paper, the density functional theory plane-wave ultrasoft pseudopotentials method within the first-principles framework has been applied to investigating the electronic structure and optical performance of different ions doping models, including nitrogen and/or nickel doping rutile titanium dioxide.The corresponding properties of pure rutile titanium dioxide are also calculated as a reference.Based on the above mentioned work, the effect of these ions on the electronic structure and optical performance of rutile titanium dioxide has been also illustrated.

Models and Computation Details
A 2 × 2 × 1 supercell containing twenty-four atoms for rutile titanium dioxide has been developed in the calculations.As shown in Figure 1, in nickel and nitrogen doped titanium dioxide model, one titanium atom and one oxygen atom were substituted by nickel and nitrogen atom, respectively.As a result, one supercell consisted of seven titanium atoms, fifteen oxygen atoms, one nickel atom, and one nitrogen atom; the atomic concentration of impurity was about 4.17% (atomic fraction) in total.The other models were developed using the almost identical way.
Ab initio calculations based on the density functional theory were performed with the Cambridge Serial Total Energy Package code in Materials Studio 5.5 provided from Accelrys Software Inc. [20,21].The ultrasoft pseudopotential was selected to depict the interaction between electrons and the ionic core.The electronic exchange-correlation energy was handled with Perdew-Burke-Ernzerhof (PBE) function in the generalized gradient approximation (GGA) framework.The energy cutoff for the plane-wave basis was 340 eV and Brillouin zone integrations were finished using a Monkhorst-Pack grid of 3×3×8 k-points [22,23].To obtain stable atomic configuration and accurate results comparable with experimental data, pure and various doped models were geometrically optimized by means of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.The convergence threshold for self-consistent tolerance was set to 1 × 10 −5 eV per atom and atomic relaxations were conducted until the residual forces were below 0.03 eV/ Å.The above parameters were suitable for getting well-converged total energy and geometry optimization results.After the geometry optimization, the band structure, density of states, and optical properties of the optimized supercells were calculated.For optical properties calculations, polycrystalline models and "scissors operators" were adapted.

Results and Discussions
After the geometry optimization, the lattice parameters of the pure rutile titanium dioxide supercell are obtained as follows:  = 9.32939 Å,  = 9.32939 Å, and  = 2.966985 Å.The above lattice parameters are in good agreement with the experimental results [24,25], which reflects that the chosen calculation methods are reasonable, and the authentic results could be obtained.Aiming at conveniently comparing the electronic structures of different ions doping models, the same k-points mesh is set to sample the first Brillouin zone for all models.The calculated band gap of pure rutile titanium dioxide is 1.87 eV at G (gamma point) shown in Figure 2; however, the value is much lower than 3.0 eV as the experimental value.The reason for the above phenomenon is that the discontinuity in the exchange-correlation potential is not taken into account within the framework of density functional theory, and the calculated band gap value is often lower than the experimental value [26,27].The calculated band structures of Ni-doped, N-doped, and Ni + N-codoped rutile titanium dioxide are shown in Figure 2, respectively.
From Figure 2, we can see that the energy levels decline and are split due to the reduction of crystal symmetry degree and destruction of periodic potential field by means of doping.As a result, the valence band top and conduction band bottom of rutile titanium dioxide are both removed towards low energy.Meanwhile, the new energy levels between valence band and conduction band are introduced by electrons of impurity atoms, thus the band gap values of the doped system are all decreased.Specifically, the band gap decreases of Ni-doped, N-doped, and Ni + N-codoped rutile titanium dioxide doped system are 0.08, 0.11, and 0.44 eV, respectively.For Ni-doped rutile titanium dioxide, isolated impurity energy levels are mainly located in the middle of band gap.The above impurity energy levels overlap with valence band maximum or conduction band minimum of rutile titanium dioxide fully.For N-doped rutile titanium dioxide, the impurity energy levels mainly located above the valence band are acceptor states.These states lead to the decrease of band gap and photoelectron transition energy.For N + Ni-codoped rutile titanium dioxide, the energy levels splitting becomes more apparent due to the further decrease of crystal symmetry degree, and more impurity energy levels are developed in the band gap of rutile titanium dioxide.Compared with the single N-or Ni-doped rutile titanium dioxide, the overlapping between impurity energy levels and valence band maximum or conduction band minimum is more apparent.Nickel and nitrogen codoping can adjust the band structure of rutile titanium dioxide, and impurity energy levels are developed in the band gap of rutile titanium dioxide.As a result, the band gap of doped system is decreased effectively, and the separation of electronhole pairs becomes more desirable, which has significant influence on increasing the catalytic activity and visible-light absorption of rutile titanium dioxide [28,29].
The calculated total density of states and partial density of states of doped models are shown in Figure 3, in order to analyze the origin of the band gap change and the variation of electronic structures caused by doping.Specifically, Figure 3(a) shows the total density of states of all the models; Figures 3(b)-3(e) represent the calculated partial density of states of different doped models, and the vertical dot line at 0 eV is Fermi level.
From Figure 3, it can be seen that valence band and conduction band are mainly composed of O-2p states and Ti-3d states in all rutile titanium dioxide modles.For the pure rutile titanium dioxide, the conduction band is primarily provided by the Ti-3d states, and the valence band is primarily given by the O-2p and partial Ti-3d states.The obtained electronic structures described in the present work are consistent with the results of other theoretical methods [30].For Ni-doped rutile titanium dioxide, the impurity states are in the middle of band gap, which are composed of O-2p and N-3d states.These states service as a "ladder" through which the electrons in the valence band can be excited to them and then excited to the conduction band.For N-doped rutile titanium dioxide, the valence band around Fermi level is composed by electrons in both the O-2p and N-2p orbit, and it is mainly composed by electrons in the O-2p orbit for pure rutile titanium dioxide.In addition, the valence band around Fermi level is wider than that of pure rutile titanium dioxide, and the valence band top has been shifted up.On the other hand, the conduction band width around Fermi level is approximate to that of pure rutile titanium dioxide, and the conduction band bottom has been shifted down.As a result, the band gap of the N-doped rutile titanium dioxide is decreased, which is consistent with the band structure calculated result.For nickel and nitrogen codoped titanium dioxide, the valence band is mainly developed by O-2p states hybridization with N-2p states.The impurity energy levels developed by N-2p states overlapped with valence band maximum are situated on the valence band maximum, and the impurity energy levels developed by Ni-3d states are situated on the top of valence band, resulting in the decrease of charge carriers recombination rate and photocatalytic activity improvement of titanium dioxide [31][32][33].Meanwhile, the electrons in the valence band can be excited to them and then excited to the conduction band subsequently by visible-light absorption, which is caused by the above impurity energy levels in the band gap.Therefore, these impurity energy levels have advantages on extending the sensitive light wavelength towards visible-light region.The calculated optical absorption spectra of different doped titanium dioxide models between 200 and 700 nm are shown in Figure 4, in order to investigate the doping effect on the optical performance of rutile titanium dioxide.For all calculations, the scissors operator is chosen as 1.13 eV based on the difference between the experimental and calculated band gap, which could make the obtained results consistent with experimental values.
From Figure 4, it can be seen that the fundamental absorption edges red-shift toward visible-light region after nitrogen or nickel doping.The above phenomenon is more apparent for nitrogen and nickel codoped rutile titanium dioxide than that of nitrogen or nickel single doped rutile titanium dioxide.Therefore, the optical absorption curves of nickel and nitrogen codoped rutile titanium dioxide indicate the highest photoresponse for visible-light, which is consistent with the conclusions obtained from the electronic structure analysis.

Conclusion
We have developed and calculated the supercells of pure rutile titanium dioxide, nitrogen, and/or nickel doping rutile titanium dioxide, using ab initio calculations with the planewave ultrasoft pseudopotentials method.On the basis of the above calculational results, the electronic structure and optical performance of the above various ions doping models have been also studied.The results indicate that the energy levels splitting becomes apparent for nitrogen and nickel codoped rutile titanium dioxide, and the overlapping between impurity energy levels and valence band maximum or conduction band minimum is more apparent than that of single ion doping.Nitrogen and nickel codoping is quite useful for the decrease of charge carriers recombination rate and energy gap, thus resulting in the great photocatalytic activity increase of rutile titanium dioxide.The optical absorption curves of nitrogen and nickel codoped rutile titanium dioxide indicate that the fundamental absorption edges red-shift toward visible-light region after nitrogen or nickel doping, especially for nitrogen and nickel codoped rutile titanium dioxide.Moreover, the highest photoresponse for visiblelight is consistent with the conclusions obtained from the electronic structure analysis.The above conclusions could give the theoretical advice for further developing of titanium dioxide photocatalyst and related experimental research.

Figure 1 :
Figure 1: Supercell model for Ni + N-codoped rutile titanium dioxide in the present work (red ball represents the O atom; white ball represents the Ti atom; blue ball represents the Ni atom; yellow ball represents the N atom).

Figure 3 :− 1 )Figure 4 :
Figure 3: (a) Calculated and comparison total density of states; calculated partial density of states of (b) pure rutile titanium dioxide, (c) Ni-doped rutile titanium dioxide, (d) N-doped rutile titanium dioxide, and (e) Ni + N-codoped rutile titanium dioxide.The dot line at zero point energy is Fermi level.