First principles calculations of electronic and optical properties of Mo and C co-doped anatase TiO

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First principles calculations of electronic and optical properties of Mo and C co-doped anatase TiO

₂

H. X. Zhu^•J.-M. Liu

Received: 20 February 2014 / Accepted: 7 April 2014 / Published online: 24 April 2014 ÓSpringer-Verlag Berlin Heidelberg 2014

Abstract Using the first principles calculations, the electronic and optical properties of C, Mo and Mo-C-doped anatase TiO₂ are studied. For the Mo mono-doped TiO₂, the band gap reduces little, and the largest perturbation occurs at the CBM of TiO₂. C mono-doping suppresses the effective band gap, but the partially occupied subbands in the gap probably also serve as the recombination centers for electrons and holes. Therefore, the Mo-C co-doping is investigated for the charge compensation consideration.

We discuss six doped configurations and find that the total energy of the system is increased with increasing distance of C and Mo. It is found that co-doped configurations with C nearest to Mo possess the lowest total energy. Then, we focus on discussing three possible Mo-C adjacent co-doped configurations. The subbands mainly induced by C-2pstates in the band gap become fully occupied because the Mo atom contributes sufficient electrons to C anion for compensation. At the same time, the effective band gap is narrowed about 0.9 eV and the perturbation at the CBM occurred in Mo mono-doped TiO₂disappears, which means the band edges of doped system still straddle the redox potentials of water. Furthermore, the optical properties of the compensated Mo-C adjacent co-doped TiO₂ and pure TiO₂ are calculated. The optical absorption edges of the Mo-C co-doped TiO₂shift towards the visible light region.

1 Introduction

Titanium dioxide (TiO₂) is one of the most important semiconductor photocatalyst. It is the most suitable photocatalyst for degradation of environmental pollutants [1, 2] and directly splitting water or purifying water and air [3, 4] under sunlight irradiation due to its nontoxicity, low cost, strong catalytic activity, high chemical and thermal stability, etc. TiO₂ have three basic phases including brookite (Pbca), anatase(I4₁/amd) and rutile (P4₂/mnm) [5]. Especially, anatase phase TiO₂ has been widely researched and applied for its higher catalytic activity [6].

However, its wide band gap of Eg=3.2 eV means that TiO₂ can only absorb ultraviolet part of solar spectrum (*5 % of the solar energy), and the efficiency of TiO₂for using sunlight energy is rather low. To improve the efficiency of harvesting the solar light, the optimized band gap should be*2.0 eV, and realizing the visible light catalytic absorption of TiO2. So far, many theoretical and experimental works have been carried out to tailor the band gap of TiO₂[7–10], and try to reduce the band gap to produce more efficient absorption of sunlight.

For the spontaneous photoelectrochemical (PEC) water- splitting process, it need to utilize both the reducing and oxidation powers of TiO₂, The reducing power is decided by the position of conduction band minimum (CBM). The more closer the CBM to the vacuum level, the more stronger is the reducing capability, while the CBM energy of TiO₂ is only 0.3–0.4 eV higher hydrogen reduction potential. So, the effect is very small by adjusting the energy of CBM to reduce the band gap. The oxidation capability is measured by the VBM energy. More lower the VBM energy, more strong the oxidizing capability is. The VBM of TiO₂is about 1.6 eV below the oxidizing potential [11] for water splitting. Moreover, an ideal photocatalyst H. X. ZhuJ.-M. Liu (&)

Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

e-mail: shyzhhx13@163.com; liujm@nju.edu.cn H. X. Zhu

College of Physical Science and Electronic Techniques, Yancheng Normal University, Yancheng 224002, China DOI 10.1007/s00339-014-8433-0

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should have wide visible light PEC activity, and the band edges must straddle the redox potentials of water. Hence, it is a very effective method to reduce the band gap of TiO2

by raising its VBM energy.

The VBM of TiO₂mainly consists of oxygen 2p states, so it is a good method by doping those non-metallic elements S, B, C, and N [12–15] with the p-orbital energy higher than that of oxygen. The subbands induced by those doping atoms are located above the VBM, which suppress partially the effective band gap for electron transfer, and show remarkable improvement of the photocatalytic activity and optical absorption for visible light.

Particularly, the C doping has studied extensively. Since it is firstly found that the C-doped TiO₂ can promote the photocatalytic activity [16]. Soon after, more experimental and theoretical studies confirmed that C doping could induce the redshift of the optical absorption edge of TiO₂ [17–22]. However, a vital weakness for the mono-doping is related to the fact that the doping leads to the partial occupation of the localized mid-gap states [23], which unfortunately may create recombination centers for electron–hole pair, and thus reduce the catalysis efficiency because those recombination centers act as a trap for the light-induced charge carrier and then cut down charge carriers migrating to the surface during the photocatalysis [24, 25]. To overcome this negative effect, the most common and effective design scheme is the co-doping with transition-metal and non-metal, and the donor–

acceptor co-doping has been successfully applied [26–28].

For co-doping combinations, there have two doped modes [29]: non-compensated model and compensated model.

For non-compensated co-doping, the positions of cation and anion are arbitrary. For compensated model, anion is bonded to cation, and the configuration usually has the lowest total energy [30,31].

Molybdenum (Mo) doped in TiO₂can effectively shift the absorption edge of TiO₂ towards visible light region [32]. Because the size of cation Mo is similar to cation Ti, Mo is easy to substitute Ti sites and results in stable doped system [33, 34]. Although Mo mono-doping TiO₂ can improve the absorption of visible light, the largest perturbation occurs at the CBM of TiO₂, which damages the reduction the pure of TiO₂. Moreover, the band gap of Mo- doped TiO₂ was only reduced about 0.22 eV compared with that of the pure TiO₂ [34]. While C doping can effectively narrow the band gap of TiO₂, because the C-2p states introduce three isolated states above the valence band [35]. For Mo-C co-doped TiO₂, Mo cation can provide two electrons for compensation, the recombination centers generated in the C mono-doped TiO₂ can be effectively annihilated, which will enhance the photocatalytic activity and visible light radiation, and the band edges of doped system still straddle the redox potentials of water.

According to the analysis above, the Mo and C co- doping may be a good scheme for improving the photocatalytic activity of TiO2. Although some works [11] ever proposed the scheme of Mo- and C-doped TiO₂ study, detailed theoretical study of the electronic structures of the Mo-C co-doped anatase TiO2is still lacking. In particular, specific calculations on the optical properties and electronic structures of different co-doped configurations are still non-available. In this paper, we investigate the electronic structures and optical properties of the C and Mo co- doped anatase TiO₂from the density functional theory, and focus on discussing three non-equivalent Mo-C adjacent co-doped configurations. For comparison, we also study the electronic of the C, Mo and Mo-C-doped anatase TiO₂in detail, at the same time, for the Mo-C co-doped TiO₂, we discuss six doped configurations: three adjacent co-doped configurations and three non-adjacent co-doped configurations, Furthermore, the optical properties of the Mo-C adjacent co-doped TiO₂and pure TiO₂are calculated.

2 Models and computation details

The first principles calculations are performed using the generalized gradient approximation (GGA) Perdew-Becke- Erzenhof (PBE) function [36] based on the density functional theory (DFT) with the Vienna ab initio simulation package (VASP5.2) code [37, 38]. The projector aug- mented wave (PAW) pseudopotential [39] is utilized for the interaction of valence electrons with ionic core, and the plane-wave basis sets are generated using cut-off energy of 450 eV. The Monkhorst–Pack methodkpoint grid is set to 5 95 95 for the Brillouin Zone [40]. For the structure optimization, the energy convergence threshold is set to 1.0910^-6eV/atom. We relax the pure and doped system, including the lattice constants and atomic position, until the Hellmann–Feynman force acting on each atom is reduced down to 1.0 meV/A˚ .

For absorption spectra, it is calculated by GGA and the scissor approximation correction [12]. Furthermore, we also calculate some electronic structure and optical properties using the GGA?U to test the effect of Hubbard U on the electronic structure of doped anatase TiO₂. As we know that the standard DFT often underestimates the band gap of transition-metal oxides significantly [41,42], due to its inaccuracy in dealing with the exchange correlation function ofd electron [43,44]. The GGA?U method, a simple and effective method to account for strongly cor- related interaction, which the Hubbard Uparameter introduced by Dudarev et al. [45], is applied to consider the non-local effect due to the Coulomb interaction. Here, we choose theU=5.8 eV for the Ti-3delectrons [46,47] and 4.0 eV for the Mo-4d electrons [48], and calculate the

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electronic structure and optical properties of the pure and compensated co-doped system.

We simulate the Mo, C and Mo-C-doped anatase TiO₂ using a 292 91 TiO2 supercell containing 48 atoms, which is commonly supercell size used for doping [28,49, 50]. For the Mo mono-doping, one Mo atom substitutes for one Ti, denoted as TiO₂@Mo. Similarly, for the C doping, one C atom substitutes for one O atom,denoted as TiO₂@C. For the Mo-C co-doping, one O atom and one Ti atom are replaced by one C atom and one Mo atom, respectively. For direct compensated adjacent co-doping, Mo atom should bond to C atom because the doped anion and cation can form a strong bond by a direct charge transfer, which generally possesses the lowest total energy [30, 31]. First, we use a Mo atom to substitute for a Ti atom, and the Mo atom will locate at the center of oxygen octahedral, which four equatorial oxygen ions have two non-equivalent positions, and two apical oxygen ions are equivalent to each other. In other words, compared with Mo atoms, six oxygen atoms have three non-equivalent positions, while the C atom should substitute for one oxygen position of the oxygen octahedral, so direct compensated Mo-C adjacent co-doped anatase TiO2has three non-equivalent co-doped configurations denoted as TiO₂@Mo-CI, TiO₂@Mo-CII and TiO₂@Mo-CIII, and the Schematics are shown in Fig.1a–c, respectively. TiO2@ Mo-CI and TiO₂@Mo-CII are C replacing two non- equivalent equatorial oxygen positions, respectively, and TiO2@Mo-CIII is the C replacing one non-equivalent apical oxygen position. For Mo-C non-adjacent co-doped system, it has many different co-doped configurations; we

choose three configurations (the Schematics are shown in Fig.1e–f denoted as TiO₂@Mo-CIV, TiO₂@Mo-CV and TiO₂@Mo-CVI) to calculate the total energy and compare with adjacent co-doped model.

To compare the stability of different Mo-C co-doped configurations, we calculate the total energy of the six kinds of co-doped configurations and analyze the change trend of the total energy of the six configurations. The relationship curves of the energy change with the distance of Mo and C are shown in Fig.2, and the letters a–f Fig. 1 Schematic of

configurations of 29291 supercell of anatase TiO₂doped by one C atom and one Mo atoms,a–care three kinds of Mo-C adjacent co-doped configurations;d–f are three kinds of Mo-C non-adjacent co- doped configurations

Fig. 2 The relationship curves of the energy change with the distance of Mo and C. Theletters a–fmarked out in Figure represent the doping configurations (a)–(f) in Fig.1, respectively. Thered line is the curve of energy changing with the configurations,and theblue lineis the curve of energy changing with the distance between Mo and O

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marked out in Figure represent the different doping configurations a–f in Fig.1, respectively. The red line is the curve of energy changing with the configurations, and the blue line is the curve of energy changing with the distance between Mo and O. We find that the total energy of the co-doped systems increases with the increasing distance of C and Mo. The energy of non-adjacent configurations is all larger than adjacent model, and the adjacent co- doped configurations (a) with C nearest to Mo possess the lowest total energy, which confirms that compensated adjacent co-doping configuration possesses the lowest total energy.

3 Results and discussion

3.1 Optimized geometry structure

The optimized lattice parameters of pure anatase TiO₂are a=b=3.803 A˚ and c=9.663 A˚ , agreement with the earlier experimental and theoretical works [51,52], which confirm that our structural optimization method is reason- able. The lattice constants of different doping system are shown in Table1, from the table, we find the lattice con- stant changed slightly with different doping system.

Although the lattice parameter variation is very small, large structural aberrations may still exist. In order to further observe the internal distortion of lattice structure we compared the inward atomic position changes of different doping, and found that internal structure of TiO₂@Mo-CI and TiO2@ Mo-CII changes similar to each other. Here, we will analyze the internal structural difference of two typical compensated adjacent co-doping configurations: TiO₂@ Mo-CI and TiO₂@Mo-CIII. The calculated bond lengths of the two models are summarized in data. Moreover, the optimized atomic positions and the bonds on the (100) plane are plotted in Fig.3, and the sign digit marked out in the diagram is the corresponding bond length. At the same time, the corresponding parts of the pure model are also presented in Fig.3a as a reference for comparison. It is seen that the local lattice of TiO₂@Mo-CI shown in Fig. 3b is seriously distorted. The C-Mo bond length (1.758 A˚ ) of TiO₂@Mo-CI is about 0.2 A˚ shorter than the Ti–O ones (1.946 A˚ ) of pure system, and the Mo–O bond length (2.222 A˚ ) along the [010] direction is longer than the Ti–O ones (1.946 A˚ ) of pure system. At the same time, Mo atom moves up along the [001] direction, and the distance between Mo and up O atom decreases about 0.1 A˚ , the distance between Mo and down O atom enlarges about 0.13 A˚ . For the TiO2@Mo-CIII, the local lattice is also slightly distorted as shown in Fig.3c. That Mo atom mainly moves up along the [001] direction is relatively large. The C-Mo bond length is about 1.804 A˚ . All those

changes in the lattice structure may affect the electronic structure of system.

3.2 Electronic structures

The calculated total density of states (TDOS) of TiO₂@Mo, TiO₂@C, TiO₂@Mo-CI, TiO₂@Mo-CII, TiO₂@Mo-CIII and TiO₂@Mo-CIV are shown in Fig.4, and the dash red line is TDOS of the pure TiO₂for comparison. For the pure TiO₂, the conduction bands are predominantly of the Ti- 3dcharacter, while the valence bands mainly consist of the O-2pstate, and the Fermi level (EF) located at the VBM. In the case of TiO₂@Mo, the Mo substituting on the Ti site acts as the n-type doping and the E_F located near CBM,which consistent with recent theoretical result [32].

For Mo mono-doping, the band gap reduces little and the large perturbation occurs at the CBM compared to pure TiO2, which means that the Mo mono-doping may damage the reduction potential of CBM of the pure TiO₂. In the case of TiO₂@C, shown in Fig.4b, the C dopant forms p-type doping in TiO2which consistent with recent theoretical result [23]. Because C atom has higher atomic p-orbital energy than that of O atom, three isolated levels introduced by carbon atom are above the VBM of the pure TiO₂, which sharply reduces the effective band gap of TiO₂@C for electron transfer. The gap states mainly consist ofC-2p_x, C-2p_y,C-2p_zorbits, respectively, somewhat coupled with the adjacentO-2p, and slightly affect the VB and CB edges of the pure TiO₂. While, due to a carbon atom having two 2p electrons less than that of an oxygen atom, some gap states are partially occupied, which is easy to create oxygen vacancies and form recombination centers for electrons and holes, and these recombination centers will reduce the catalytic efficiency. For Mo-C compensated adjacent co-doped TiO₂, there have three doped configurations. The TDOS are shown in Fig.4c–f, respectively, we found that the CMB edge of co-doping system is slightly affected, and the perturbation at the CBM occurred in Mo Table 1 The optimized structure parameters of pure TiO2 and the doped models

a(A˚ ) b(A˚ ) c(A˚ )

Pure 3.803 3.804 9.663

TiO₂@Mo 3.818 3.818 9.639

TiO₂@C 3.842 3.788 9.664

TiO₂@Mo-CI 3.793 3.856 9.654

TiO₂@Mo-CII 3.861 3.792 9.652

TiO₂@Mo-CIII 3.796 3.838 9.672

TiO₂@Mo-CIV (d) 3.840 3.815 9.654

TiO₂@Mo-CV 3.852 3.802 9.650

TiO₂@Mo-CVI 3.845 3.807 9.659

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mono-doped TiO₂ disappears, that is to say, Mo-C compensated co-doped TiO₂ will keep the reduction potential of pure TiO₂. At the same time, the gap states induced by the C-2pstates coupled with the adjacentTi-4d, Mo-4d, O- 2pare located above the VBM of the pure TiO₂, and the effective band gap decreases about 0.9 eV as compared with pure system. Moreover, the band gap levels are all below the Fermi level after co-doping, which means that these subbands become entirely occupied and cannot act as traps for electron–hole pairs because double donor pro- vided by Mo atom could totally compensate the double acceptor C, which will certainly improve the visible light photocatalytic ability of the co-doped model. It is obvious that the compensated adjacent co-doping with Mo- and C-doped overcome the shortcomings of unoccupied C-2p gap states of C mono-doped TiO₂ and the large perturbation at the CBM caused by Mo-4d states of Mo mono-doped TiO₂, which will effectively enhance visible light photocatalytic activities and still can retain the redox activity of TiO2because the band edges of co-doped system still straddle the redox potentials of water [11].

Compared to the TDOS of the three compensated adjacent co-doped configurations, the TDOS near CBM are similar in shape, and the gap states of TiO₂@Mo-CI are also close to that of TiO₂@Mo-CII in appearance. Because the pre- sence of doping breaks the crystal field of oxygen octahedral, lowering the degeneration, and C-2pstate splits into C-2p_x, C-2p_y,C-2p_zorbits somewhat coupling with theO- 2p forming three gap states lying above VBM, respectively. For the TiO₂@Mo-CIII, the C atom substitutes for one of two apical oxygen of oxygen octahedral. The break of crystal field of oxygen octahedral is smaller than that of C atom substitute for one of four equatorial oxygen of oxygen octahedral. So C-2p state only partially split. For the compensated non-adjacent co-doping, the TDOS shown in Fig.4f, the gap states mainly induced byC-2porbit are totally occupied, but the serious perturbation mainly introduced by Mo-5dstate appears below the CBM, which obviously do not accord with the important design princi- ple that the band edges of doped system must still straddle the redox potentials of water. It is confirmed that Mo-C compensated adjacent co-doped TiO2 will enhance the

visible light photocatalytic activity because of introducing impurity states above the VBM and still keeping the redox activity of TiO₂.

To further explore the Mo-C adjacent co-doped system, the calculated band structures of pure TiO₂ and three compensated adjacent co-doped system are plotted in Fig.5. The pure anatase TiO₂ is a direct band gap semiconductor, with the calculated band gap of 2.04 eV, Fig. 3 Optimized (100) plane

atomic structures of pure (a), TiO₂@Mo-CI (b) and

TiO₂@Mo-CIII (c). The atomic bond lengths are numerically labeled

(a)

(b)

(c)

(d)

(e)

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Fig. 4 The calculated TDOS for pure TiO₂(red) compared with doped system (blue) for the TiO2 of TiO₂@Mo (a), TiO₂@C (b), TiO₂@Mo-CI (c), TiO₂@Mo-CII (d). TiO₂@Mo-CIII (e) and TiO₂@Mo-CIV (f). Thedashed linesrepresent the highest occupied levels in the doped TiO₂

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which is similar to previous theoretical work [13,53]. But our result is still underestimated compared with the experimental band gap of 3.2 eV [54] due to the well- known limitation of the generalized gradient approximation (GGA). The calculated band structures of TiO₂@Mo- CI and TiO₂@Mo-CII are shown in Fig.5b, c, respectively. The band structures of the two doped types are similar to each other. The E_F is above the gap states and all gap states are fully occupied by electrons. At the same time, these subbands suppress the effective band gap about 0.7 eV and obviously improve visible light photo- activity. Figure5b is the band diagram of TiO₂@Mo-CIII.

We find that the E_F is still above the gap states, and the effective band gap is suppressed about 0.91 eV, which will perfectly improve the catalytic performance of the system.

To further understand the electronic structure of the compensated adjacent co-doped system, the calculated electron density and charge density differences are plotted in Fig.6. Because charge density difference properties of TiO₂@Mo-CI and TiO₂@Mo-CII are similar to each other, we choose to show the electron density of TiO₂@Mo-CI in Fig.5. Figure5a is the electron density of pure system calculated for comparison, and Fig.5b, c is the electron density of TiO2@Mo-CI and TiO2@Mo- CIII, respectively. By comparing Fig.5a, b, c, it is found that the electron density in the region between the C and Mo is larger than that between the O and Ti of pure

system, which means that the covalent bonding in Mo-C group is stronger than that in Ti–O group. See Fig.5b, the electron density in the region between Mo and the top O along the [001] direction is larger than that of Ti–O of pure system, and the electron density in the region between Mo and the right O along the [010] direction is smaller than that of Ti–O of pure system. For TiO₂@Mo- CIII system shown in Fig. 5c, the electron density in the region of Mo and O along the [010] direction is also larger than that of Ti–O of pure system. The charge density difference of pure TiO₂, TiO₂@Mo-CI and TiO₂@Mo-CII is shown in Fig.5d–f, respectively, we found that the electron density difference in C region is larger than that in O region of pure system, which implies that C accepted more electron numbers in the Mo-C co- doped system than those O in the pure system. The electron density difference in Mo region reduces largely near the C atom, which also means that the Mo in co- doped system donated more electrons than the Ti. More- over, due to the repulsion of C ion, Mo ion is polarized along the Mo-C-direction, which is in agreement with literature [47,55]. At the same time, other ions around the Mo also have different degree polarization. All above maybe come into being an effective polarization field in the Mo-C co-doped anatase TiO2, which will promote the separation of electrons and holes excited by photo and improve the catalytic performance of the co-doped system [56, 57].

(a) (b)

(c) (d)

Fig. 5 The calculated band structures along the high symmetry linesof the Brillouin zone for a supercell of pure system (a), TiO₂@Mo-CI (b), TiO₂@Mo-CII (c), and TiO₂@Mo-CIII (d). Thered dashed linesrepresent the Fermi level

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3.3 Optical properties

The electrons can transfer from the occupied states to the unoccupied states, and the transferring process is accom- panying by the emission and absorption of phonons, so the excited spectra can be considered as a joint density of states between the conduction band and valence band. Using the linear response method, the macro-optical response function of material may be described by the complex dielectric function [58]. The optical properties are essentially measured by the dielectric function, which consist of two parts of the real and imaginary parts expressed as e(x)= e₁(x)?ie₂(x). It is mainly related with the band structure of material. The imaginary part e2(x) can be calculated from the momentum matrix elements between the occupied and unoccupied wave functions. The imaginary part of the dielectric functione2(x) can be written as follow

e₂ðhxÞ ¼2pe² Xe₀

X

c;v;k

w^c_kj jwur^ ^v_k

²dE_kE_khx

ð1Þ wherecandvrepresent the conduction band and valence band, respectively, u is the vector of defining the polarization of the electric field,kis the reciprocal lattice vector;

andxis the frequency of photon. The real parte₁(x)can be calculated from the imaginary part e2(x) by the Kra- mer–Kronig relationship [59]. The optical constants can be evaluated from the real and imaginary parts of the dielectric function, in which the optical absorption spectra can be evaluated using the following expression [29]

aðxÞ ¼ 2½

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e²₁ðxÞ þe²₂ðxÞ q

e₁ðxÞ

¹₂

ð2Þ As the optical absorption spectrum can provide a com- parative information on the optical properties of materials

[29,60], here, we will calculate the absorption spectrum of doped system. Moreover, the calculated band gap is 2.04 eV, which is underestimated compared to experimental value of 3.2 eV, therefore, the scissor approximation [12, 58] of 1.16 eV is used to calculate the optical results to make it compatible with experimental data. The calculated optical absorption spectra as the function of photon energy for pure TiO2, TiO2@Mo-CI,TiO2@Mo-CII and TiO₂@Mo-CIII are shown in Fig.7. The energy range of visible light is marked out in Fig.7using green lines. It is found that the absorption edge of pure TiO₂ is mainly located in the region of ultraviolet light, which is in agreement with the experimental and theoretical data of the band gap [61]. These optical excitations of pure TiO₂ mainly arise from electrons transiting from the O-2pto Ti- 3d states. Optical absorption spectra illustrate that co- doped TiO₂has shifted the absorption edge towards visible light range, which means that adjacent co-doping achieved the expectant absorption edge redshift. Due to impurity states in the band gap induced by doping atoms, electrons shifting from gap states to CBM need less energy excita- tion of phonon, which cause visible light absorption. In comparison, the absorption edges of TiO₂@Mo-CI and TiO₂@Mo-CII are similar to each other because of the similar band structure. Moreover, the absorption coefficient of TiO₂@Mo-CIII is larger than that of TiO₂@Mo-CI and TiO₂@Mo-CII in the region of visible light on the whole. It indicated that Mo and C co-doped TiO₂in configuration III is in favor of improving the visible light absorbing, which mainly is due to the differences of the electronic structure of different configurations. The absorption spectra further prove that Mo-C compensated adjacent co-doped TiO₂is a feasible method to improve catalytic absorption of the visible light.

Fig. 6 Calculated electron density of pure (a), TiO₂@Mo- CI (b) and TiO₂@Mo-CIII (c), and the electron density difference of pure (d), TiO₂@Mo-CI (e), and TiO₂@Mo-CIII (f). Contours show the values in a slice of the (100) plane. The units are electrons A˚^-3. In panels (a), (b) and (c), Color fromblueto redrepresents electron density changes from low to high. In panels (d), (e) and (f), Colorred (blue) represents the electron density increased (decreased)

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3.4 The effect of HubbardU

We have studied the overall electronic and optical properties of the doped anatase TiO₂using GGA, which gives a good overall description, though the GGA often underestimates the band gap values of transition-metal oxides evidently. Here, we also study the electronic structure and optical properties of the pure and compensated co-doped system using GGA?U calculations and test the Hubbard effect on the electronic structure and optical of doped anatase TiO₂.

The TDOS of pure and compensated co-doped system are calculated using the GGA?U, the calculated band gap for pure anatase TiO₂ is 3.0 eV, which enlarges about 0.96 eV compared to the gap value obtained by GGA, and it is only 0.2 eV less than the experimental value of 3.2 eV.

It proves that GGA?U method can get more accurate band gap compared to GGA method. Comparing TDOS obtained from GGA and GGA?U, we found that the energy opens up mainly by elevating the CBM because of the incorporation of Hubbard U, and the difference of VBM shows ignorable, because the VBM of the co-doped TiO₂mainly consists of the oxygen 2pstates and the CBM mainly consists of the titanium 4d states. Other than that, the basic characteristics of TDOS have nearly no change from the GGA and GGA?U calculations, such as, the shape of gap states induced mainly by C doping atom is also similar to each other, which is consistent with exten- sive theoretical tests [43, 62]. It allows one to perform reliable study using GGA functional for simplicity.

We also calculate the optical properties of pure and compensated Mo-C co-doped system using GGA?U method. The obtained optical absorption coefficient curves as the function of photon energy for pure TiO₂, TiO₂@

Mo-CI, TiO₂@Mo-CII and TiO₂@Mo-CIII are shown in Fig.8. The absorption spectrum of pure anatase TiO2 is mainly located in the region of ultraviolet light, which is consistent with the result obtained by GGA? the scissor approximation. For the three co-doped configurations, all absorption spectra have visible light coverage, which show that Mo and C co-doped systems have good visible light photocatalytic activity. By comparing Figs. 7 and 8, it is found that both the optical absorption edges by two different methods extend up to the visible light range. That is to say, Mo and C co-doped anatase TiO₂ realize the expected visible light absorption both using GGA and GGA?Umethods.

4 Conclusion

In summary, we have carefully studied the electronic structures of pure TiO₂, Mo-doped TiO₂, C-doped TiO₂, compensated Mo-C adjacent and non-adjacent co-doped TiO₂ systems using the DFT method with GGA and GGA?U functions. Mo doping at Ti position of TiO₂ creates Mo-4d states at the CBM of TiO₂, which perturb the reduction of CBM of TiO2. The C-2p states locating above VBM introduced by C mono-doping at O sites largely suppress the effective band gap while the partially occupied gap states may serve as the recombination centers for electrons and holes. In compensated Mo-C adjacent co- doped TiO₂, the effective band gap is narrowed about 0.9 eV and the perturbation at the CBM occurred in Mo mono-doped TiO₂ disappears. Moreover, due to the Mo atom donating enough electrons for compensation, the subbands mainly induced by C-2p states become fully occupied, which will help in improving the photocatalytic Fig. 8 Calculated optical absorption spectrum of pure TiO₂, TiO₂@Mo-CI, TiO₂@Mo-CII and TiO₂@Mo-CIII using GGA?U Fig. 7 Calculated optical absorption spectrum of pure TiO₂,

TiO₂@Mo-CI, TiO₂@Mo-CII and TiO₂@Mo-CIII using GGA

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activity of the co-doped TiO₂. In fact, the calculated optical absorption spectrum of the co-doped systems shows that the optical absorption edges extend up to the visible light region. All results show that Mo-C adjacent co-doping is conducive to create visible light photocatalysis, and still keep the natural redox performance of pure TiO2.

Acknowledgments This work was supported by the National 973 Projects of China (Grants No. 2011CB922101), the Natural Science Foundation of China (Grants No. 11234005 and No. 51332006), and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

References

1. A.L. Linsebigler, G. Lu, J.T. Yates, Chem. Rev.95, 735 (1995) 2. S. Klosek, D. Raftery, J. Phys. Chem. B105, 2815 (2001) 3. A. Fujishima, K. Honda, Nature (London)238, 37 (1972) 4. P. Wang, S.M. Zakeeruddin, J.E. Moser, M.K. Nazeeruddin, T.

Sekiguchi, M. Gra¨tzel, Nat. Mater.2, 402 (2003) 5. X.Q. Gong, A. Selloni, Phys. Rev. B76, 235307 (2007) 6. M. Xu, Y. Gao, E.M. Moreno, M. Kunst, M. Muhler, Y. Wang,

H. Idriss, C. Wo¨ll, Phys. Rev. Lett.106, 8302 (2011)

7. T. Ohno, T. Mitsui, M. Matsumura, Chem. Lett.32, 364 (2003) 8. M. Niu, W.J. Xu, X.H. Shao, D.J. Cheng, Appl. Phys. Lett.99,

203111 (2011)

9. R. Amadelli, L. Samiolo, M. Borsa, M. Bellardita, L. Palmisano, Catal. Today206, 19 (2013)

10. F. Lucassen, M. Koch-Mu¨ller, M. Taran, G. Franz, Am. Miner.

98, 7 (2013)

11. Y. Gai, J. Li, S.S. Li, J.B. Xia, S.H. Wei, Phys. Rev. Lett.102, 036402 (2009)

12. T. Umebayashi, T. Yamaki, S. Yamamoto, A. Miyashita, S. Ta- naka, J. Appl. Phys.93, 5156 (2003)

13. K. Yang, Y. Dai, B. Huang, Phys. Rev. B76, 195201 (2007) 14. H. Irie, Y. Watanabe, K. Hashimoto, Chem. Lett.32, 772 (2003) 15. R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Science

293, 269 (2001)

16. S.U.M. Khan, M. Al-Shahry, W.B. Ingler Jr, Science297, 2243 (2002)

17. J.H. Park, S. Kim, A.J. Bard, Nano Lett.6, 24 (2006)

18. M. Shen, Z. Wu, H. Huang, Y. Du, Z. Zou, P. Yang, Mater. Lett.

60, 693 (2006)

19. K. Yang, Y. Dai, B. Huang, M.-H. Whangbo, J. Phys. Chem. C 113, 2624 (2009)

20. H. Kamisaka, T. Adachi, K. Yamashita, J. Chem. Phys. 123, 084704 (2005)

21. Y. Choi, T. Umebayashi, M. Yoshikawa, J. Mater. Sci.39, 1837 (2004)

22. C.D. Valentin, G. Pacchioni, A. Selloni, Chem. Mater.17, 6656 (2005)

23. K. Yang, Y. Dai, B. Huang, M.-H. Whangbo, Appl. Phys. Lett.

93, 132507 (2008)

24. H. Irie, Y. Watanabe, K. Hashimoto, J. Phys. Chem. B107, 5483 (2003)

25. M. Batzill, E.H. Morales, U. Diebold, Phys. Rev. Lett. 96, 026103 (2006)

26. T. Yamamoto, T. Ohno, Phys. Rev. B85, 033104 (2012) 27. W.J. Yin, H.W. Tang, S.H. Wei, M.M. Al-Jassim, J. Turner, Y.F.

Yan, Phys. Rev. B82, 045106 (2010)

28. X.G. Ma, Y. Wu, Y.H. Lu, J. Xu, Y.J. Wang, Y.F. Zhu, J. Phys.

Chem. C115, 16963 (2011)

29. Y. Fang, D.J. Cheng, M. Niu, Y.J. Yi, W. Wu, Chem. Phys. Lett.

567, 34 (2013)

30. R. Long, N.J. English, Chem. Mater.22, 1616 (2010)

31. H. Liu, Z. Lu, L. Yue, J. Liu, Z. Gan, C. Shu, T. Zhang, J. Shi, R.

Xiong, Appl. Sur. Sci.257, 9355 (2011)

32. M. Khan, J.N. Xu, N. Chen, W.B. Cao, Phys. B407, 3610 (2012) 33. L.G. Devi, B.N. Murthy, S.G. Kumar, J. Mol. Catal. A Chem.

308, 174 (2009)

34. M.S. Jeon, W.S. Yoon, H. Joo, T.K. Lee, H. Lee, Appl. Surf. Sci.

165, 209 (2000)

35. S. Mohapatra, M. Misra, V. Mahajan, K. Raja, J. Catal.246, 362 (2007)

36. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett.77, 3865 (1996)

37. G. Kresse, J. Hafner, Phys. Rev. B47, R558 (1993) 38. G. Kresse, J. Furthmu¨ller, Phys. Rev. B54, 11169 (1996) 39. P.E. Blo¨chl, Phys. Rev. B50, 17953 (1994)

40. H.J. Monkhorst, J.D. Pack, Phys. Rev. B13, 5188 (1976) 41. M. Nolan, G.W. Watson, J. Chem. Phys.125, 14470 (2006) 42. D.O. Scanlon, B.J. Morgan, G.W. Watson, A. Walsh, Phys. Rev.

Lett.103, 096405 (2009)

43. X. Han, G. Shao, J. Phys. Chem. C115, 8274 (2011) 44. G. Shao, J. Phys. Chem. C112, 18677 (2008)

45. S.L. Dudarev, G.A. Botton, S.Y. Savarsov, C.J. Humphreys, A.P.

Sutton, Phys. Rev. B57, 1505 (1998)

46. R. Long, N.J. English, ChemPhysChem11, 2606 (2010) 47. H.X. Zhu, J.-M. Liu, Comput. Mater. Sci.85, 164 (2014) 48. S. Lutfalla, V. Shapovalov, A.T. Bell, J. Chem. Theory Comput.

7, 2218 (2011)

49. M. Khan, J.N. Xu, N. Chen, W.B. Cao, J. Alloys Compd.513, 539 (2012)

50. R.S. Zhang, Y. Liu, Q. Gao, F. Teng, C.L. Song, W. Wang, G.R.

Han, J. Alloys Compd.509, 9178 (2011)

51. J.K. Burdett, T. Hughbanks, G.J. Miller, J.W. Richardson, J.V.

Smith, J. Am. Chem. Soc.109, 3639 (1987)

52. R. Long, N.J. English, Chem. Phys. Lett.478, 175 (2009) 53. R. Asahi, Y. Taga, W. Mannstadt, A.J. Freeman, Phys. Rev. B61,

7459 (2000)

54. H. Tang, H. Berger, P.E. Schmid, F. Levy, G. Burri, Solid State Commun.23, 161 (1977)

55. W.J. Shi, S.J. Xiong, Phys. Rev. B84, 205210 (2011)

56. J. Sato, H. Kobayashi, Y. Inoue, J. Phys. Chem. B 107, 7970 (2003)

57. Y. Inoue, Energy Environ. Sci.2, 364 (2009)

58. X.H. Yu, C.S. Li, Y. Ling, T.A. Tang, Q. Wu, J.J. Kong, J. Alloys Compd.507, 33 (2010)

59. D.B. Melrose, R.J. Stoneham, J. Phys. A Math. Gen. 10, L17 (1977)

60. M. Li, J.Y. Zhang, D. Guo, Y. Zhang, Chem. Phys. Lett.

539–540, 175 (2012)

61. Z. Zhou, M. Li, L. Guo, J. Phys. Chem. Solids71, 1707 (2010) 62. G. Shao, J. Phys. Chem. C113, 6800 (2009)