The Influence of Halides in Polyoxotitanate Cages; Dipole Moment, Splitting and Expansion of d-orbitals and Electron-Electron Repulsion †

Metal-doped polyoxotitanate (M-POT) cages have been shown to be efficient single-source precursors to metal-doped titania [TiO 2 (M)] (state-of-the-art photocatalytic materials) as well as molecular models for the behaviour of dopant metal ions in bulk titania. Here we report the influence halide ions have on the optical and electronic properties of a series of halide-only, and cobalt halide- ‘ doped ’ POT cages. In this combined experimental and computational study we show that halide ions can have several effects on the band gaps of halide-containing POT cages, influencing the dipole moment (hole-electron separation) and the structure of the valance band edge. Overall, the band gap behaviour stems from the effects of increasing orbital energy moving from F to I down Group 17, as well as crystal-field splitting of the d-orbitals, the potential effects of the Nephelauxetic influence of the halides and electron-electron repulsion. The influence of halides on the electronic structures of polyoxotitanate cages is explored in this experimental and theoretical study. This shows that coherence of the HOMO-LUMO transition with the dipole moment, crystal-field splitting, the Nephelauxetic influence of the halides and electron-electron repulsion can all play a role in reducing band gap.


Introduction
Metal-'doped' polyoxotitanate (M-POT) cages of the form [TixOy(OR)zMnXm] (R = Et or i Pr, M = transition metal or lanthanide and X = halide) have been of great interest in recent years as single-source precursors to metal-doped TiO2 [TiO2(M)]. [1][2][3][4][5][6][7][8][9][10][11] In undoped TiO2 (a high band gap semiconductor), excitation leads to the promotion of an electron from the valence band [predominately O(-p)] to the conduction band [predominately Ti (-d)]. [12][13][14][15] The introduction of a metal dopant into TiO2 can improve the quantum efficiency of this process and the ability to harness a broader range of solar energy in two ways. Firstly, if the metal is inhomogenously dispersed within the titania it will induce a dipole within the bulk material, which promotes hole-electron separation. 16 Secondly, the low-lying dorbitals of the dopant metal (M) can mix with the orbitals at the band gap edge, raising the energy of the valence band and decreasing the band gap of [TiO2(M)] compared to TiO2 (from ca. 3.2 eV to ca. 2.7 eV). These effects have led to extensive applications of [TiO2(M)] in, for example, the photocatalytic destruction of pollutants and water splitting. 1-10,17- 22 We have shown that POT/M-POT cages can be used as atom-efficient, low-temperature single-source materials to [TiO2(M)], which can deliver the same M : Ti ratio from the M-POT to [TiO2(M)]. 20,23,24 A further key focus of interest in M-POTs is their potential structural and electronic relationship to bulk [TiO2(M)]. It is for this reason that the cages have typically been referred to as 'doped', when heterobimetallic cluster might have been considered more conventional. In order to be able to draw comparisons to the literature, we will continue with the naming scheme of 'doped' polyoxotitanate cage. The TixOy cores of M-POTs can be seen as nano-or sub-nano sized fragments of bulk TiO2, which are encapsulated in a stabilising ligand periphery. Important issues in this respect are the extent of quantum confinement in M-POTs compared to TiO2 and the relationship between structure and size of the M-POTs and their HOMO-LUMO/band gaps. This last issue is a contentious one. However, we have considered the band gap of the M-POT cages to correspond to the principle, predominantly O(-p)→Ti(-d) charge-transfer transition within the TixOy fragments of these species, by analogy with the electronic structures of bulk TiO2 and [TiO2(M)]. It is important in this regard to separate the spectroscopic effects of this transition from, for example, localised transitions like d-d transitions of dopant transition metal ions, which may otherwise lead to large errors in the determination of band gaps in M-POTs.
There are many structural and electronic analogies between the electronic behaviour of M-POTs and bulk [TiO2(M)]. For example, in a recent structural and quantum mechanical study of a series of related Co II -'doped' POTs we showed that one potentially important effect in reducing the band gap of M-POTs is that of dipole moment, an effect which is directly analogous to that found in bulk [TiO2(M)]. 16 Thus, if the direction of the dipole moment is coincident with change in electron density for the HOMO-LUMO transition, a significant band gap reduction is expected. 16,[25][26][27][28] This conclusion has recently been challenged by Coppens and Zheng in respect to the experimental band gaps found in [Ti11O14(O i Pr)17(MX)] (M = Mn, Fe; X = Cl, Br or I). 26 However, 29 reassessment of their spectroscopic data (ignoring the spurious effect of localised d-d transitions) supports our conclusions concerning the influence of dipole moment on band gap. 26 In addition to the metal ion, halogen doping can also reduce the band gap of TiO2 and enhance its photocatalytic activity. 30 However, very few POT cages have been reported that model anion encapsulation in bulk TiO2. 30,31 A striking example is seen in the anion [(BrCo)6Ti15O24(O i Pr)18Br] -, in which a spherical POT 'traps' a bromide anion at the center. 9 In this experimental and computational paper we explore the electronic effects of halide inclusion in three series of halide  32,33 These studies stress the important relationship between dipole moment and band gap and also reveal that the halide ions in these species can make a number of other contributions to the band gap behaviour.

Halide-'Doped' POT Cages
The focus of this current work was on the effects of halide ions on the band gaps of 'undoped' polyoxotitanate (POT) and metal-'doped' polyoxotitanate cages (M-POT).  4 with WCl6 in i PrOH at 150 °C. The synthetic difficulties involved with other tungsten hexahalides, WX6 (X = F, Br, I) meant that this synthetic route could not be extended to the isostructural cages 1-X. 34 The cage 1-Cl is obtained in 14 % crystalline yield and was characterised by elemental analysis, IR spectroscopy, 1 H NMR spectroscopy and single-crystal X-ray crystallography. The structure of 1-Cl (Figure 1 In order to investigate the influence of the halide on the POT cage, a related Ti3-cage [Ti3O(O i Pr)9(OMe)] (1) was prepared from the reaction of Ti(O i Pr)4, water and methanol in 2propanol. 35 The 'undoped' [Ti3O(O i Pr)10] cage was not investigated as part of this study due to the low stability of this oxoalkoxide, probably due to steric effects and its low degree of condensation. 35 The cage compound 1-Cl is of special interest in being a rare example of a halide-containing POT cage, providing the opportunity to study the effects of halide-'doping' in this situation, in the absence of the effects of the orbital contributions by a dopant metal ion.
The diffuse reflectance UV-vis spectra of crystalline 1 and 1-Cl are shown in Figure 2, with the band gaps determined by the Direct Extrapolation (DE) method of 3.74 ± 0.12 eV for 1 and 3.22 ± 0.17 eV for 1-Cl. For this method, the Kubelka-Munk function is plotted against the energy of the photons and from the direct extrapolation of the absorption edge data to the energy axis the band gap can be determined. The error in the band gap, which is often ignored by authors, was derived from propagating the errors of regression. [36][37][38] It is clear that the 'undoped' cage 1 exhibits a larger band gap than the Cl-'doped' counterpart 1-Cl.  Please do not adjust margins DFT calculations were carried out to predict the influence of the halide on the band gaps of the whole series 1-X (X = F, Cl, Br, I). For these calculations the B3LYP functional [39][40][41] in conjunction with the 6-31g** basis set 42,43 (6-311g** for iodine 44 ), were used. Initial geometry optimisations of the four structures show good agreement with the structural features observed experimentally for 1-Cl, with the change in the halide ions having no effect on the overall arrangement adopted. The band gaps extracted from DOS calculations for the halide-POT cages are in the order 1-F (5.49 eV) > 1-Cl (5.41 eV) > 1-Br (5.11 eV) > 1-I (4.18 eV) (ESI Table S9). Comparison with the experimentally-determined value for 1 (3.74 ± 0.12 eV) and 1-Cl (3.22 ± 0.17 eV) shows that the calculated values vastly overestimate the band gap. However, band gaps obtained from TD-DFT calculations (first singlet excitation energy with oscillator strength ≥ 0) agree much better with the experimentally-obtained value: 1-F (4.42 eV) > 1-Cl (4.39 eV) > 1-Br (4.14 eV) > 1-I (3.36 eV) (ESI Table S10). Although, the two computational methods show different absolute values of the band gap, the significant point is the overall trend of a decrease in band gap with increasing halide size. 45 The calculated UV-vis spectra are provided in ESI Figure S1.
The density of states (DOS) diagrams of 1-X are key to understanding the trend in decreasing band gap from X = F to X= I. They indicate that, as expected, the conduction bands (or LUMO) are predominantly made up of the Ti(-d) orbitals ( Figure  3, ESI Table S1-4). The valence band (or HOMO) is initially dominated by the O(-p) character for 1-F. However, moving from F, to Cl, to Br and then I, the orbital contribution to the HOMO from the halide ion increases from 2 % for 1-F to 35 % for 1-Cl also for 1-Br the HOMO is 63 % Br and for 1-I it is 91 % I ( Figure 3, ESI Table S1-S4). It is clear from these calculations that the increasing energy of the valance orbitals of the halide located at the band gap edge is the reason for the observed decrease in the band gap moving down Group 17. This is illustrated schematically in Figure 4. The C3 symmetry of the series 1-X suggests that the dipole moment lies along the C3 axes of the complexes, which was confirmed by DFT calculations. Calculation of the dipole moments shows that the iodine has a major influence in comparison to the other halides: 1-F (1.07 D) ≈ 1-Cl (0.90 D) ≈ 1-Br (0.84 D) << 1-I (3.28 D). The HOMO and LUMO of 1-X are shown in Figures 4e and f, respectively (for 1-Cl). The LUMO is centred around the Ti3O core, whilst the major contribution to the HOMO comes from the halide ion. Therefore, the HOMO-LUMO transition is in the same direction as the dipole moment, in line with our previous conclusions concerning the Please do not adjust margins Please do not adjust margins relationship between the effect of dipole moment on the reduction of band gap drawn from a Co II -'doped' series of M-POTs. 16,25 These findings are also in-line with the behaviour of halide-'doped' TiO2. 46,47 Halide Ions in Co II -POTs The Cl and Br cages for 2-X and 3-X have previously been reported. 50 The experimental UV-vis spectra of 2-X (X = Cl, Br) and 3-X (X = Cl, Br) have two major features, absorption edges in the 300 -400 nm region associated with the TixOy core and Co II d-d transitions ( 4 A2  4 T1) at 550 nm ( Figure 6, ESI Figure  S12). 51 Analysis of the TixOy cut-off reveals that the band gaps in 2-Cl (3.65 ± 0.09 eV) and 2-Br (3.57 ± 0.13 eV) are identical within experimental error. Unfortunately, the band gap of the 'undoped' counterpart 2 could not be obtained due to its low melting point. Again, in the case of 3-X the band gap values for 3-Cl (3.61 ± 0.06 eV) and 3-Br (3.57 ± 0.05 eV) are identical within experimental error [but less than for 'undoped' 3 (3.88 ± 0.13 eV)]. The seeming invariance of the band gap behaviour of the cages 2-X and 3-X with different halides cannot be explained by dipole moment alone. In order to give insight into the experimental band gaps, we turned to DFT calculations. Table 1 shows the calculated band gaps (Eg) for the two Co II -'doped' M-POT cages (2-X and 3-X) for both α and β spin states obtained from DOS calculations. In all cases Eg(β) is smaller than Eg(α). This can be explained by studying the DOS plots for the two families of cages. In this case, absolute numbers of the band gaps could not be obtained from the first singlet exited state from TD-DFT calculations due to the presence of d-d transitions.     Table  S21-S25). This same trend is seen for 2-X (ESI Table S11-S15). In conclusion, the computational results suggest that 2/3-F should have a smaller band gap than their Cl counterparts (for both Eg(α) and Eg(β), Table 1). This is quite surprising, since one would expect the heavier halide to contribute higher energy electronic states to the valence band, as was demonstrated by the behaviour of 1-X.
Overall, the predicted behaviour of these cages can be understood in terms of the effect of the halide ligands on the magnitude of the splitting of the d-orbitals () (i.e., the position in the Spectrochemical series), combined with the contribution of the halide orbitals to the valance band edge and its effect on the expansion of the d-orbitals (i.e., the Nephelauxetic effect). For Cl, Br and I, both the energy of the valance orbitals and their Nephelauxetic influence increases down going from Cl, to Br, to I. The reduction in band gap is a consequence mainly of the increased contribution of the valance orbitals of the halide at the valance band edge. For F, however, the reduction in the band gap predicted by calculations is primarily the result of the larger crystal-field splitting of the e and t2 orbitals, resulting in the t2 orbital making a larger contribution to the valance band edge (even though the valance orbitals of F are buried within the valance band). Calculations also suggest that an additional contribution to the lowering of the band gap in the case of F is that of the increased O(-p) orbital energy in the alpha channel, which is probably due to F(-p)/O(-p) orbital repulsion, which is greater for the more electron dense F than for the other halides. This results in an increase in the O(-p) orbital energy (i.e., the valence band energy). These conclusions are depicted schematically in Figure 8.
Although the experimental errors involved do not allow us to discern the theoretically predicted trends in detail, the implication is that the similarity of the band gaps of the two series of compounds 2-Cl, 2-Br and 3-Cl, 3-Br observed experimentally results from the counterbalance of the effect of the contribution of the halide orbitals at the band gap edge (which is most significant for Cl, Br and I) versus greater crystal field splitting and increased O(-p) orbital energy (which is the greatest contribution for F).

Experimental
Materials and Synthesis: All chemicals were purchased from Sigma-Aldrich and used in their standard state. Anhydrous ethanol and isopropanol were prepared via distillation over Mg turnings. Autoclaves were loaded with reactants in a N2-filled glove box (Saffron, type α). Several of the Co-POT cages were synthesised according to the literature: 1, 35 2-Cl, 52 2-Br, 16

X-ray Crystallography:
Single crystal X-ray diffraction was carried out using a Nonius Kappa CCD (Mo-kα) (1-Cl). Data reduction was done using the HKL Denzo and Scalepack program. Structure solutions were obtained using the SHELXS-97 software 53 and structure refinement completed using the SHELXL-97 programme. 54 Details of the refinement are provided in the ESI Table S31. CCDC reference number 1499257 (1-Cl) can be obtained free of charge from The Cambridge Crystallographic Data Centre.
Spectroscopic Measurements: Elemental analysis for carbon and hydrogen was performed using an Exeter CE-440 Elemental Analyser. Samples were prepared in aluminium capsules in a N2filled glove box. Infrared (IR) spectroscopic measurements were performed on powdered samples using a Perkin Elmer Spectrum One FT-IR fitted with a diamond attenuated total reflectance system, which allowed for direct measurement of samples without the need for a nujol mull. UV-Vis measurements were made using a Varian Cary 50 UV-Vis spectrophotometer. The diffuse reflectance spectra were collected on powdered samples that were sandwiched between quartz plates and sealed with parafilm in a N2-filled glovebox. The Kubelka-Munk function F(R) was recorded over the range 250-800 nm. To determine the band gaps, the Kubelka-Munk function was plotted against the photon energy and the band gap was determined from direct extrapolation of the absorption edge to the energy axis. The errors were derived from propagating the errors of regression. [36][37][38] Theoretical Calculations: Geometry optimisations of the polyoxotitanate cages were carried out using the Gaussian-Programme package (Revision D.01). 55 The optimised structures were obtained employing the B3LYP 39-41 density functional. The 6-31g** 42,43 basis set (6-311g** 56 for iodine from the EMSL database 57,58 ) was used throughout the calculations of the Ti3cage series, whereas the 6-31g* 42,43 basis set (6-311g* 56 for iodine from the EMSL database 57,58 ) was used for the larger cobalt-'doped' POT cages. Time-dependent DFT (TD-DFT) calculations were carried out for the calculation of excited Please do not adjust margins Please do not adjust margins states. [59][60][61][62][63] For the generation of the DOS as well as the UV-vis spectra and the analysis of the data the programme suit GaussSum 64 was used. For the DOS calculation analysis of the iodine-containing cages (2-I and 3-I) with GaussSum, the output file of the Gaussian calculation (more precisely the alpha and beta occupied eigenvalues with λ ≥ 4000 eV) had to be modified/given an energy value. Usually, for the determination of the band gap of discrete molecules, the lowest UV-vis excitation energy (excitation energy of the first singlet excited state obtained from TD-DFT calculations) provides a reasonable approximation of the HOMO-LUMO gap. 65 However, in the case of clusters containing transition metals, which, can undergo d-d transitions, this first excitation energy cannot be used as the band gap approximation, since the band gap would be completely underestimated (e.g. 0.7 eV for 3-Cl). Therefore, the band gaps were obtained from density of state calculations.