Rutile Band-Gap States Induced by Doping with Manganese in

Article pubs.acs.org/JPCC

Rutile Band-Gap States Induced by Doping with Manganese in Various Oxidation States Mazharul M. Islam* and Thomas Bredow Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Beringstrasse 4, 53115 Bonn, Germany

ABSTRACT: The effect of manganese doping on the electronic structure of titania in the rutile modification is investigated theoretically. The relative stability of the chemically accessible Mn oxidation states +I to +VII for MnTi defects is calculated in dependence of the spin state. For all MnTi oxidation states except +IV, additional lattice defects such as O and Ti vacancies were introduced to obtain charge neutrality. According to the calculated formation energies, Mn4+ is the most stable oxidation state for MnTi substitution in comparison with Mn3+ and Mn2+ doping. Depending on the Mn oxidation state, occupied and unoccupied states are created in the titania band gap. mixture of Mn2+ and Mn3+,26 or a mixture of Mn3+ and Mn4+,27−30 depending on the conditions of preparation. On the other hand, theoretical investigations came to the conclusion that MnTi doping in TiO2 mainly leads to the +IV Mn oxidation state.25,31−34 From experiment it is known that the Mn oxidation state as well as the photocatalytic properties of Ti1−xMnxO2 depend on the dopant concentration x. Xia et al.23 found that phases with x < 0.40 are stable. For these high concentrations the observed Mn oxidation state is +III. Feng et al.21 have found that the best photocatalytic performance is achieved for x = 0.03 with an oxidation state of +II. Other experimental studies concluded that the concentration of Mn is in the range of 2−6% for Mn2+ doping in TiO2 nanoparticles,18 3% for Mn3+,22 1−7% for a mixtures of Mn3+ and Mn4+ doping,27 up to 16.6% for a mixture of Mn2+/Mn3+ doping26 and 12% for a mixture of Mn3+ and Mn4+ doping.28 We report on a theoretical investigation of Ti-substitutional manganese doping in bulk rutile. Different Mn oxidation and spin states are considered for MnTi-type doping, and their relative stability is compared based on solid-state reaction energies. The induced changes in the electronic structures; i.e., generation of occupied and unoccupied band gap states and changes in the VBT and CBB positions are monitored.

1. INTRODUCTION The still increasing interest in titanium dioxide as basic material in photocatalytic, photoelectrocatalytic and photovoltaic devices is documented by the large number of recent reviews on this material.1−10 However, the application of titania in photocatalytic activities is hampered because of its large band gap (higher than 3 eV), which allows to use only a small fraction of the sunlight spectrum for light energy conversion. Consequently a large number of experimental and theoretical studies have focused on the reduction of the titania band gap by chemical modification. Transition elements, due to their particular d-electron configuration, may insert occupied and unoccupied states in the titania band gap. If these states are localized on the dopant atoms, it is possible that they act as recombination centers for electrons and holes formed after photoexcitation. However, transition-metal doping may also modify the absolute position of the conduction band bottom (CBB) or the valence band top (VBT) and may thus improve the photocatalytic activity of TiO2.11,12 For example, MTi doping with M = V,12 Ag,13 Ni,14,15 Cr,16,17 and Mn18−34 has been investigated so far. Here we focus on manganese doping in the rutile phase of titania. This phase, although being the ground-state modification under ambient conditions, has only recently come into focus for photochemical purposes.1 Previous experimental investigations suggest that the oxidation state of Mn doping in TiO2 varies from Mn2+,18−21 Mn3+22 to Mn4+,23−25 or is a © XXXX American Chemical Society

Received: January 2, 2015 Revised: February 22, 2015

A

DOI: 10.1021/acs.jpcc.5b00023 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

2. COMPUTATIONAL METHOD In order to avoid the well-known problems of standard densityfunctional theory (DFT) at generalized-gradient approximation (GGA) level for the prediction of fundamental and optical band gaps for solids, 35 we employed the hybrid method PW1PW36−38 for the present study. This approach has shown reasonable agreement with experimental results for structural, thermodynamic and electronic properties for main group and transition metal oxides before.12,39 The crystallineorbital program package CRYSTAL0940 was used throughout. We have used atomic basis sets optimized for solid-state calculations in previous studies: 86-411G31d (20s12p4d/ 5s4p2d) for Ti and 8-411G1d (14s6p1d/4s3p1d) for O.12,39 An 86-411G41d (20s12p5d/5s4p2d) basis was used for Mn, as obtained previously for MnO.41 In order to model the experimental Mn concentrations as close as possible, we have used a Ti16O32 supercell for the study of MnTi substitution. Previous calculations of Ti2O4, Ti16O32, Ti32O64, and Ti54O108 supercells showed that defect formation energies are converged with a Ti16O32 supercell for transitionmetal-doped TiO2.12 The density of states projected onto the orbitals of Mn, Ti, and O (PDOS) was calculated using a Mulliken population analysis of the crystalline orbitals and a Fourier−Legendre technique42 with an 8 × 8 × 8 Monkhorst− Pack grid.43

respectively. Ferro- and antiferromagnetic coupling of the unpaired electrons of the two atoms per cell were taken into account using the broken-symmetry approximation to DFT. The 5Mn state with antiferromagnetic coupling was most stable (see Table 1). The stability of different VO configurations with Table 1. Calculated Spin States and Relative Energy (kJ/ mol) for Different Oxidation States Obtained for the Most Stable Structures Using a Ti16O32 Supercell type of doping Mn+ doping + O vacancy

Mn2+ doping + O vacancy

Mn3+ doping + O vacancy

Mn4+ doping Mn5+ doping + Ti and O vacancies

Mn6+ doping + Ti vacancy

3. RESULTS AND DISCUSSION 3.1. Stability of Mn Oxidation States in Ti1−xMnxO2. Mn has a [Ar]3d54s2 electronic configuration in the ground state. In solids it can adopt a large variety of oxidation states: +VII (3d04s0), +VI (3d14s0), +V (3d24s0), +IV (3d34s0), +III (3d44s0), +II (3d54s0) and +I (3d54s1), which can be distinguished, e.g., by the color of the compounds.44 The permanganate ion, MnO4−, contains the highest oxidation state (+VII) of manganese and is intensely colored (purple to black). Manganese also exists in the +VI state as in the manganate ion, MnO42− (green). The +V oxidation state is observed in potassium hypomanganate, K3MnO4, which is bright blue salt. Manganese has a +IV oxidation state in manganese dioxide, MnO2, which is a fairly stable black solid. The +III oxidation state is observed in manganese trifluoride, MnF3, which is a red solid. The +II oxidation state is very common in compounds including manganese sulfate and manganese chloride. Such compounds are usually pale-pink or yellow-green in color, and some exhibit fluorescence. Finally, the +I oxidation state can exist in organic complexes such as Methylcyclopentadienyl manganese tricarbonyl (MMT) C9H7MnO3. In this theoretical study of Mn doping in bulk rutile, we have employed a Ti16O32 supercell where the doping concentration was set to 12.5% for Mn+, Mn3+, Mn5+, Mn6+, and Mn7+, and 6.2% for Mn2+ and Mn4+. This is in the range of experimentally reported Mn concentrations.18,26−28 As initial step, full relaxation of lattice parameters and atomic positions was performed for each oxidation state taking into account different spin configurations. 3.1.1. Mn+ Doping. Two MnTi‴ defects (using Kröger−Vink notationKV) were created at first-nearest neighbor (1-NN) sites in the Ti16O32 supercell. It was assumed that this is the most stable Mn−Mn configuration due to the decreased electrostatic repulsion between the Mn+ cations. The excess charge (formally −6) was counterbalanced by three oxygen vacancies VO••. We considered 1Mn, 3Mn, and 5Mn local spin states,

Mn7+ doping + Ti and O vacancies

spin state

relative energy

singlet triplet quintet doublet quartet sextet octet singlet triplet quintet doublet quartet singlet triplet quintet singlet triplet singlet triplet

573 211 0 100 0 44 273 424 0 23 190 0 251 94 0 63 0 0 139

average MnTi−VO distances of 1.95 Å, 1.98 Å, 3.48 and 3.58 Å (according to the unrelaxed atomic positions of the rutile bulk), see Figure 1a, was calculated. The configuration with the smallest Mn−VO distance, 1.95 Å, is energetically favored in all cases (Figure 1b). Structural relaxation of the defective supercells occurs mainly in the first- (1-NN) and second-nearest neighbor (2-NN) shells around MnTi. Two 1-NN O atoms moved apart from MnTi, thereby increasing their distance from 1.95 to1.67 Å. The 2-NN Mn−O distances were only slightly affected; they increased from 1.98 to 2.07 Å. All other distances changed by less than 2%, indicating that the lattice deformation after Mn+ doping is rather short-ranged. 3.1.2. Mn2+ Doping. The substitution of one Ti4+ by one Mn2+ will produce a MnTi″ point defect with a formal charge of −2 which can be compensated by an oxygen vacancy VO••. The possible spin states are 2Mn (s0d5 low-spin), 4Mn (intermediate) or 6Mn (s0d5 high-spin) in such case. The relative position of the two defects, MnTi and VO, was varied from 1NN to 4-NN, corresponding to Mn−VO distances of 1.95, 1.98, 3.48, and 3.58 Å as shown in Figure 2a. The relative stability of these structures is depicted in Figure 2b. For all considered spin states the 1-NN configuration is energetically preferred. The most stable spin state is 4Mn. Rather similar to the relaxed structure of the MnTi‴ defect, only the two 1-NN O atoms decreased their distance to the defect site, from 1.95 Å in the perfect rutile lattice to 1.67 Å. All other distances to the MnTi″ site did not change significantly. Therefore, the structural distortion due to the substitution of Ti4+ by Mn2+ is short-ranged. The local environment of the MnTi″ site with 1-NN VO changes from quasi-quadraticpyramidal to an irregular shape. B


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Figure 1. Doping of Mn+ accompanied by an O vacancy, (a) The local structure which shows the location of two Mn+ dopants at 2.97 Å (green disks) and oxygen vacancies in four different Mn−O distances (Mn−O = 1.95 Å (light blue disks), 1.98 Å (dark gray disks), 3.48 Å (pink disks) and 3.57 Å (yellow disks) respectively). (b) Plot of relative energy of various structures (as obtained for different oxygen vacancy locations and various spin states) versus the distance of Mn−O vacancy.

Figure 2. Doping of Mn2+ accompanied by an O vacancy. (a) The local structure which shows the location of O vacancies in four different Mn−O distances (Mn−O = 1.95 (light blue disks), 1.98 (dark gray disks), 3.48 (pink disks), and 3.57 Å (yellow disks) respectively). (b) Plot of relative energy of various structures (as obtained for different oxygen vacancy locations and various spin states) versus the distance of Mn−O vacancy.

Figure 3. Doping of Mn3+ accompanied by an O vacancy. (a) The local structure which shows the location of two Mn3+ dopants at 2.98 Å and O vacancies in four different Mn−O distances (Mn−O= 1.95 (light blue disks), 1.98 (dark gray disks), 3.48 (pink disks), and 3.57 Å (yellow disks) respectively). (b) Plot of relative energy of various structures (as obtained for different oxygen vacancy locations and various spin states) versus the distance of Mn−O vacancy.

3.1.3. Mn3+ Doping. For the formation of a MnTi′ defect we reconsidered our previously utilized models for Al3+39 and V3+12 doping in rutile TiO2. Formally the two closest Ti4+ ions (1-NN distance of 2.98 Å) were substituted by two Mn3+ ions and

additionally an oxygen vacancy VO•• was introduced to obtain charge neutrality. Four defect configurations were considered here. The average MnTi−VO distance was 1.95 (1-NN), 1.98 (2NN), 3.48 (3-NN), and 3.58 Å (4-NN), see Figure 3a. The C


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Figure 4. (a) Doping of Mn4+ (green, blue and red disks represent Mn, Ti, and O respectively). (b) Mn5+ doping in combination with Ti and O vacancies. (b) Local structure which shows the location of two Mn5+ dopants at 2.98 Å (green disks), one Ti vacancy located at Ti−Mn = 3.57 Å (light gray disks), and O vacancies in four different Mn−O distances (Mn−O = 1.95 (light blue disks), 1.98 (dark gray disks), 3.48 (pink disks), and 3.57 Å (yellow disks) respectively). Plot of relative energy of various structures (as obtained for different oxygen vacancy locations and various spin states) versus the distance of Mn−O vacancy.

Figure 5. (a) Local structure showing Mn6+ doping in combination with Ti vacancy (green, blue, red and dark gray disks represent Mn, Ti, O, and Ti vacancy respectively). (b) Doping of Mn7+ accompanied by Ti and O vacancies. (a) Local structure which shows the location of two Mn7+ dopants at 2.98 Å (green disks), two Ti vacancies located at Ti−Mn = 2.98 and 3.57 Å (light gray disks) and oxygen vacancies in four Mn−O distances (Mn−O = 1.95 (light blue disks), 1.98 (dark gray disks), 3.48 (pink disks), and 3.57 Å (yellow disks) respectively). Plot of relative energy of various structures (as obtained for different oxygen vacancy locations and various spin states) versus the distance of Mn−O vacancy.

3.1.5. Mn5+ Doping. Two 1-NN Ti4+ ions were substituted by two Mn5+ ions thus forming 2 MnTi• defects. We selected a defect configuration where the formal charge (+2) was counterbalanced by VTi⁗ and VO••. Singlet and triplet local spin states were considered for Mn5+ with a s0d2 configuration, leading to overall cell multiplicities of zero, two, and four, if ferro- and antiferromagnetic coupling is taken into account. The positions of both titanium and oxygen vacancies relative to the two MnTi• defects were varied. In Figure 4b, the relative energy of selected defect configurations is shown. VTi⁗ is located far from the Mn atom (Mn−VTi = 3.57 Å). The oxygen vacancy can be located at Mn−O distance of 1.95, 1.98, 3.48, 3.58, and 4.58 Å. The relative stability of the corresponding structures is compared in Figure 4c. The most stable overall spin state is the quintet. The defect configuration with Mn−VTi = 3.57 Å and Mn−VO = 1.98 Å is the ground state for all considered multiplicities. In contrast to the cases described above, Ti-substitutional Mn5+ doping gives rise to significant changes of the atomic positions near the defect sites. One of the 1-NN O atoms moves away from the MnTi site by 0.20 Å, the other three 1-NN O atoms move inward by 0.05 Å. The changes of the distances of other 1-NN to 4-NN atoms range between −4.0% and +1.2%.

following atomic spin states were considered for Mn3+ with assumed s0d4 configuration: 1Mn (t2g4 low-spin), 3Mn (t2g4 high-spin), and 5Mn (t2g3eg1 high-spin). As described above, ferro- and antiferromagnetic coupling between the two openshell Mn ions was considered. The relative stability of the defect configurations and spin states is presented in Figure 3b. The triplet state with ferromagnetic coupling is the most stable (see Table 1). For all three considered spin states, the 2-NN MnTi′-VO configuration is the most stable. The oxygen vacancy is bridging the two Mn atoms. Atomic displacements with respect to the perfect lattice are observed mainly for the 1-NN and 2-NN atoms, but are relatively small: four of the 1-NN Mn−O distances slightly decrease by 0.03 Å and two of the 2NN Mn−O distances increased by 0.03 Å. All other atoms do not relax significantly. 3.1.4. Mn4+ Doping. The substitution of one Ti4+ by one Mn4+ (s0d3) creates a neutral MnTi point defect as shown in Figure 4a and does therefore not require an additional oxygen vacancy. Mn4+ may have a low-spin doublet state (2Mn) or a high-spin quartet state (4Mn). In our calculations the quartet state was by far more stable (Table 1). Because of the similar ionic radii of Ti4+ and Mn4+ (Shannon radii for 6-fold coordination: 0.61 Å (Ti) and 0.53 Å (Mn), respectively45), there is almost no relaxation of the atomic positions. All calculated atomic displacements are below 0.01 Å. D


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The Journal of Physical Chemistry C 3.1.6. Mn6+ Doping. For this case we considered the substitution of three Ti4+ ions by two Mn6+ ions with s0d1 configuration, leading to 2MnTi•• + VTi⁗ as shown in Figure 5a. The ferro- and antiferromagnetic coupling between the Mn spins will produce overall singlet and triplet spin states for the unit cell, respectively. According to the results of the hybrid method (see Table 1), the triplet state is clearly the ground state. In this case a significant structural relaxation is observed. One 1-NN O atom moves 0.37 Å toward the MnTi•• sites. Other neighbor atoms change their distances to the defect site between −3.2% and +2.3%. 3.1.7. Mn7+ Doping. The substitution of four Ti4+ by two Mn7+ (s0d0) ions was modeled with a 2MnTi••• + 2 VTi⁗ + VO•• defect configuration as shown in Figure 5b. In this case there are no unpaired electrons and the ground state is a closed-shell singlet (Table 1). In the most stable defect configuration the MnTi−VTi distances are 2.98 and 3.57 Å, respectively, and the MnTi−VO distance is 1.98 Å. Structural relaxation is rather pronounced. Two 1-NN O atoms relax by 0.35 Å toward the Mn sites, and also the two other 1-NN Mn− O distances decrease by 0.11 Å. The 2-NN Mn−O distance reduces by 2.0%. Interestingly, the 3-NN Mn−Mn distance decreases by −9.4%. The 4-NN, 5-NN, and 6-NN atoms change their distances to the defect site between −3.1% and +2.2%. 3.2. Relative Stability. The relative stability of the abovediscussed defect structures with different Mn oxidation states is determined on the basis of the calculated formation energy (ΔE) of Ti1−xMnxO2 with respect to MnO2(s), TiO2(s), and O2(g). The total energies of MnO2(s), TiO2(s), and O2(g) are calculated after full optimization at PW1PW method. ΔE values for Mn+, Mn2+, Mn3+, Mn4+, Mn5+, Mn6+, and Mn7+ are calculated with eqs 1−7:

Ti nO2n + 2MnO2 = Ti n − 3Mn2O2n + 3TiO2 − O2 ΔE(Mn 6 +) = [E(Ti n − 3Mn2O2n) − O2 ] − [(n − 3) × E(TiO2 ) + 2 × E(MnO2 )]

(6)

Ti nO2n + 2MnO2 = Ti n − 4Mn2O2n − 1 + 4TiO2 − 3/2O2 ΔE(Mn 7 +) = [E(Ti n − 4Mn2O2n − 1) − 3/2 × O2 ] − [(n − 4) × E(TiO2 ) + 2 × E(MnO2 )] (7)

Here n = 16 for the Ti16O32 supercell. The obtained values for ΔE (Table 2) indicate that the most stable oxidation state Table 2. Calculated Reaction Energy ΔE and Enthalpy ΔH (kJ/mol) According to Eqs 1−7 for Mn+, Mn2+, Mn3+, Mn4+, Mn5+, Mn6+, and Mn7+ Doping, Respectively oxidation state

spin state

ΔE

ΔH

Mn+ doping + O vac Mn2+ doping + O vac Mn3+ doping + O vac Mn4+ doping Mn5+ doping + Ti + O vac Mn6+ doping + Ti vac Mn7+ doping + Ti + O vac

quintet quartet triplet quartet quintet triplet singlet

964 348 328 19 499 900 1162

998 377 355 41 533 935 1195

for manganese doping is Mn4+ (ΔE = 19 kJ/mol). Mn3+ (ΔE = 328 kJ/mol) and Mn2+ (ΔE = 348 kJ/mol) doping are much more endothermic and may be feasible at low oxygen partial pressures. These findings are in line with the experiments showing that Mn4+,23−30 Mn3+22 and Mn2+18−21 occur in Ti1−xMnxO2 systems. According to our investigation, Mn5+ (ΔE = 499 kJ/mol), Mn+ (ΔE = 964 kJ/mol), Mn6+ (ΔE = 900 kJ/ mol) and Mn7+ (ΔE = 1162 kJ/mol) substitutions are less likely, and are also not observed in experiment. Effects of temperature and contributions from zero point energy on the calculated formation energies are explicitly taken into account by additional frequency calculations for the most stable defect configurations of each Mn oxidation state. After these corrections ΔH instead of ΔE in eqs 1 − 7 is obtained. In Table 2, the calculated ΔH300 K for Mn+, Mn2+, Mn3+, Mn4+, Mn5+, Mn6+ and Mn7+ doping are shown. The changes are not negligible, between 21 and 35 kJ/mol, but they do not alter the relative stability. 3.3. Electronic Properties. The effect of MnTi doping on the electronic properties of TiO2 was investigated by means of the projected density of states (PDOS) obtained with CRYSTAL-PW1PW method. The calculated electronic band gaps (Eg), the widths of the gap states (Wg), and the type of gap states for all doping states are given in Table 3. In all considered cases the calculated fundamental band gap of stoichiometric rutile, 3.54 eV,39 was reduced by Ti−Mn substitution because occupied or empty gap states have been formed which are mainly composed of Mn orbitals. Their nature strongly depends on the Mn oxidation state: occupied gap states appear in the case of Mn+, Mn2+, Mn3+, and Mn6+ doping, whereas empty states are found for Mn4+, Mn5+ and Mn7+ doping, if the most stable spin states and defect configurations are considered. The band gap of doped TiO2 is reduced to 1.18, 1.60, 2.14, 2.24, 0.56, 1.17, and 1.02 eV for Mn+, Mn2+, Mn3+, Mn4+, Mn5+, Mn6+, and Mn7+ doping, respectively. The calculated DOS of doped TiO2 are compared with undoped rutile in Figure 6. For

Ti nO2n + 2MnO2 = Ti n − 2Mn2O2n − 3 + 2TiO2 + 3/2O2 ΔE(Mn+) = [E(Ti n − 2Mn2O2n − 3) + 3/2 × E(O2 )] − [(n − 2) × E(TiO2 ) + 2 × E(MnO2 )] (1)

Ti nO2n + MnO2 = Ti n − 1MnO2n − 1 + TiO2 + 1/2O2 ΔE(Mn 2 +) = [E(Ti n − 1MnO2n − 1) + 1/2 × E(O2 )] − [(n − 1) × E(TiO2 ) + E(MnO2 )] (2)

Ti nO2n + 2MnO2 = Ti n − 2Mn2O2n − 1 + 2TiO2 + 1/2O2 ΔE(Mn 3 +) = [E(Ti n − 2Mn2O2n − 1) + 1/2 × E(O2 )] − [(n − 2) × E(TiO2 ) + 2 × E(MnO2 )] (3)

Ti nO2n + MnO2 = Ti n − 1MnO2n + TiO2 ΔE(Mn 4 +) = [E(Ti n − 1MnO2n)] − [(n − 1) × E(TiO2 ) + E(MnO2 )] (4)

Ti nO2n + 2MnO2 = Ti n − 3Mn2O2n − 1 + 3TiO2 − 1/2O2 ΔE(Mn 5 +) = [E(Ti n − 3Mn2O2n − 1) − 1/2 × O2 ] − [(n − 3) × E(TiO2 ) + 2 × E(MnO2 )] (5) E


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Table 3. Calculated Band Gap Eg, Width of the Gap States Wg (eV) and Type of the State for Mn+, Mn2+, Mn3+, Mn4+, Mn5+, Mn6+, and Mn7+ Doping, Respectively Mn+ doping + Ox vac Mn2+ doping + Ox vac Mn3+ doping + Ox vac Mn4+ doping Mn5+ doping + Ti + Ox vac Mn6+ doping + Ti vac Mn7+ doping + Ti + Ox vac undoped rutile

quintet quartet triplet quartet quintet triplet singlet

Eg (eV)

Wg (eV)

type of gap states

1.18 1.60 2.14 2.24 0.56 1.17 1.02 3.5439

0.50 0.35 0.47 0.40 0.35 0.30 0.30

occupied occupied occupied empty empty occupied empty

(Figure 6b). But there are also unoccupied Mn 3d orbitals located ∼2.7 eV above the VBT. The width of the occupied states (Wg) is 0.35 eV (Table 3). The rutile band gap was thereby reduced to 1.60 eV due to Mn2+ doping. Mn3+ doping creates occupied Mn 3d states ∼0.9 eV above the VBT (Figure 6c) which reduces the band gap to 2.14 eV. Ti4+ substitution by Mn4+ generates unoccupied defect peaks composed of Mn 3d states 0.9 eV below the CBB. The band gap decreases to 2.24 eV for Mn4+ doping (see Table 3). Thus, we observe contrasting behavior for Mn2+-, Mn3+-, and Mn4+-doped rutile in terms of the occupation of the band gap states, depending on the number of Mn d electrons. There are also unoccupied states near the CBB in Mn2+-doped rutile. Under illumination with visible light Mn2+ may therefore act as a center of an intraatomic excitation or de-excitation, in particular after reduction of the local symmetry which makes d−d-excitations dipole allowed. It may therefore act as an unwanted recombination center. For Mn4+ doping, there are only unoccupied defect states of manganese at the CBB, therefore optical excitations involving Mn 3d and O 2p orbitals from the VBT are still of interatomic nature. In all cases, the band gap has reduced significantly compared to undoped rutile and this may lead to an increased absorption of visible light. In this discussion the differences between fundamental and optical band gaps have to be considered as mentioned above. But the qualitative trends are expected to be correct. We have investigated atomic spin densities obtained from a Mulliken population analysis for all the considered oxidation states. It is observed that spin is mainly localized on Mn site in all cases, with complete localization for Mn4+ substitution. Our findings are in well accord with the available experiments. According to a UV−vis spectrometry study,50 the Mn doping creates intermediate bands (IB) within the band gap of rutile which reduces the optical band gap from 3.0 eV to 1.5−2.4 eV. The presence of oxygen vacancies along with the dopant reduces the band gap further compared to the less oxygen-deficient samples.50 According to our previous work39 and many other theoretical studies, an oxygen vacancy in rutile creates occupied defect levels below the CBB which reduces the band gap to approximately 1 eV. Also experimental investigations showed that the band gap due to the oxygen vacancy in rutile is about 1.2 eV.51,52 In the present study, only Mn2+ and Mn3+ doping in combination with oxygen vacancies introduces occupied states in the rutile band gap, whereas Mn4+ doping without oxygen vacancy creates unoccupied states in the band gap. The band gap for VO-associated doping is smaller (1.60 and 2.14 eV for Mn2+ and Mn3+ respectively) than that of Mn4+-doped rutile (2.24 eV). Experiments show that Mn doping in TiO2 nanoparticles reduces the effective band gap from 3.28 to 2.81 eV, 2.08 and 2.03 eV on incorporation of 2%,

Figure 6. Total density of states for (a) undoped rutile TiO2, (b) α and β electrons of Mn2+-doped Ti16O32 (c) α and β electrons of Mn3+doped Ti16O32, and (d) Mn4+-doped Ti16O32.

brevity, here we have compared the DOS of undoped rutile (Figure 6a) with those of Mn2+ (Figure 6b), Mn3+ (Figure 6c), and Mn4+ (Figure 6d) doped rutile only. In rutile TiO2,39 the VBT predominantly consists of oxygen 2p orbitals and the CBB of Ti 3d orbitals (Figure 6a). The calculated rutile electronic band gap, 3.54 eV, is within the range of experimental values, 3.3 ± 0.5 eV.46 It has to be noted that the fundamental band gap corresponds to the difference between VBT and CBB. It corresponds to the results of photoemission spectroscopy.47 In contrast the optical band gap is measured by UV−vis techniques. For rutile, the experimentally obtained optical band gap is around 3.0 eV.48,49 The two extra electrons incorporated by MnTi″ defects induce occupied Mn 3d gap states ∼0.8 eV above the VBT F


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The Journal of Physical Chemistry C 4% and 6% Mn2+, respectively.36 Mn3+ and Mn4+ dopants generate midgap electronic states, facilitating the transition of electrons from the valence band to higher electronic energy states available in the band gap.53 Similar effect was also observed for the transition metals adsorption on rutile TiO2 (110) surface.54

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4. SUMMARY AND CONCLUSIONS Stability and electronic structure of manganese-doped rutile TiO2 were studied theoretically at hybrid DFT level. All common Mn oxidation states are explored and the relative stability of all possible spin states was calculated. The most stable atomic spin states are 5Mn+, 4Mn2+, 3Mn3+ (ferromagnetic), 4Mn4+, 3Mn5+ (ferromagnetic), 2Mn6+ (ferromagnetic), and 1Mn7+ (diamagnetic). On the basis of the calculated reaction energy (ΔE) with respect to MnO2, TiO2 and O2 we conclude that +IV, +III and +II are the most likely oxidation states of Mn in rutile. Dopants generate midgap electronic states which reduce the fundamental band gap of rutile. This may enhance the absorbance of visible light of Mn-doped titania with respect to stoichiometric titania. The connection to photocatalytic activity, however, is not straightforward. If both occupied and unoccupied defect levels arise from the same Mn dopant atom, it may act as a trap for absorbed photons and even accelerate electron−hole recombination. Those dopants, e.g. Mn4+, that predominantly create unoccupied states below the CBB, will attract the electrons after absorption while the holes are still localized on the oxygen atoms. Thus, the oxidation process at the catalyst surface may be enhanced in this way. Full catalytic activity with respect to water splitting strongly depends on the coupling of the Mn gap states which will govern the electron mobility. The coupling in turn depends on the Mn concentration and distribution within the lattice. This has to be further studied in the future. But among the Mn species investigated here, Mn4+ is the most promising candidate for improved photocatalytic activity.

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AUTHOR INFORMATION

Corresponding Author

*(M.M.I.) E-mail: [email protected]. Telephone: +49-228-73-2254. Fax: +49-228-73- 9064. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.M.I. is grateful to Deutsche Forschungsgemeinschaft (DFG) for the postdoctorate funding of DFG-Forschergruppe 1277 molife “Mobilität von Li-Ionen in Festkörpern” project and to Prof. Andrea Gerson of the University of Mawson Institute, South Australia, for fruitful discussion.

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Rutile Band-Gap States Induced by Doping with Manganese in

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