Size-dependent electronic structure of titanium-oxo-alkoxides: exploring quantum confinement at the smallest sizes

Abstract

The electronic structures of titanium-(oxo-)alkoxides with 1–18 Ti atoms are studied by UV spectroscopy, revealing size effects. These precise molecules act as the smallest titanium–oxygen systems for comparison with bulk and nanoparticulate TiO₂. The results show that at these ultrasmall sizes, with Ti/O cores of less than 1.5 nm, the energy gap is larger than bulk TiO₂ and increases significantly in the smallest compounds. Electrochemical studies supported by DFT calculations show that the greatest changes in electronic structure occur when moving from a complex with a single Ti atom to a dimeric species with two Ti sites. Constructive interaction of d-orbitals, combined with changes in coordination geometry, result in significantly different Ti-based LUMO energies in monomers, dimers and larger clusters, whilst the O-based HOMO energy level remains similar throughout. Size appears to be the dominating factor for LUMO position and energy gap despite the different connectivities, shapes and surface chemistries in these molecular clusters, which differ from bulk TiO₂. These results link materials chemistry with small inorganic molecules and show that (quantum) size effects remain applicable to the smallest systems. This understanding is important for the rational design of semiconductor materials with optimised properties.

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Introduction

Semiconducting metal oxides, such as titanium dioxide (TiO₂), are important photoactive functional materials used in photocatalytic processes, including as self-cleaning or antibacterial surfaces.^1–5 Thin films of TiO₂ are also important as protective layers and electron transport layers in electronic devices.^6,7 The electronic structure of bulk TiO₂ comprises of a filled (O 2p-based) valence band and an empty (Ti 3d(t_2g)-based) conduction band. The electronic structure of metal oxides becomes modified as particle sizes become very small due to the quantum confinement effect. At small sizes the electronic structure, built from overlap of the constituent atomic orbitals, ceases to be a continuum of energy states, and discrete energy levels are instead found. As the radius of a crystalline particle drops below that of the material's exciton Bohr radius the valence and conduction bands become narrower resulting in an increase in the ‘band gap’. Ultimately, on reaching molecular sizes these discrete energy levels represent the various molecular orbitals delocalised over the structure.

Quantum confinement is best known in quantum dot materials, such as CdSe nanoparticles, which exhibit size-dependent luminescence wavelengths, and the importance of this effect is recognised by the 2023 Nobel Prize in Chemistry for Bawendi, Brus and Ekimov.^8–10 TiO₂ has a wide band gap; reported as 3.00–3.03 (3.20) eV for rutile and 3.15–3.20 (3.42) eV for anatase, by measurement of the indirect (or direct) optical gap^11,12 (note that exact values may vary depending on experimental measurement method),¹² and a small exciton Bohr radius, estimated to be ∼0.8 nm for anatase.¹³ Quantum size effects in TiO₂ are only predicted for particle sizes with diameters <2 nm (Fig. 1a).^14–17 Even the band gaps of ultrasmall (1.5 nm–3 nm) anatase nanoparticles were shown to have negligible deviation from bulk values.^13,18 In contrast, 3.6 nm rutile nanoparticles have been reported to show a small blue shift compared to the bulk energy gap (3.38 eV vs. 3.2 eV, by direct transition).¹¹ Extended (NH₄/H)_4xTi_(1−x)O₂ nanosheets (0.7 nm thick) are also reported to have energy gaps of ∼3.8 eV,¹⁹ whilst nanofilaments (0.6 × 1.0 nm cross section) have even higher energy gaps of ∼4.0 eV (indirect transition).²⁰ The band gap of sub-monolayer TiO_x deposited on silica is shown to increase with decreasing coverage, as smaller TiO_x species become dominant.⁵ Ultrasmall TiO₂ particles produced using dendrimer templates, are reported to show size dependent band gaps ranging from 3.35–3.79 eV as the particle diameter decreased from 1.7 nm to around 1 nm in size.¹⁴ It is important to note that at these sizes (<100 Ti atoms), the species may be better described as a molecule, in which the surface plays a significant role. Structural distortion may occur due to the tiny size and influence of (bridging) surface ligands. This distortion may lead to changes in coordination geometry, covalency and/or Ti⋯Ti distances that may compete with intrinsic size effects.

Fig. 1 (a) Band gap prediction for TiO₂ particles based on quantum confinement effects using the effective mass approximation (EMA). Values from the Nosaka equation (similar to Brus equation), with a μ′ value of 1.63m₀.¹⁴ Note that a single TiO₆ octahedron has a size of ∼0.4 nm. N.B. the EMA is considered to overestimate energy gap at very small sizes. (b) Depiction of the density of states of the conduction bands of wide band gap oxide semiconductors that are constructed from different types of orbitals, and the response of the CBM with quantum confinement effects.

In the related semiconductor ZnO, studies of quantum size effects reveal that the main change in electronic structure is an elevation of the conduction band minimum (CBM), with the valence band maximum (VBM) less effected. In ZnO the conduction band is constructed from diffuse 4s orbitals with good overlap and is, therefore, a wide band, highly susceptible to quantum size effects (Fig. 1b).^21–23 In contrast, in CeO₂, the contracted 4f orbitals are the frontier unoccupied electronic states, and these create a narrow set of energy states which are barely effected by size effects.²⁴ The 3d orbitals of TiO₂ sit between these extremes,²⁵ and therefore, some change in CBM position is expected for TiO₂, but only at very small particles sizes.

Molecular chemistry reveals that at <2 nm Ti/O structures adopt different shapes and Ti–O coordination arrangements, showing structural distortion relative to bulk TiO₂ structures. Molecular titanium-oxo clusters, which have a surface stabilised by organic ligands, fall in this size range, and many have been reported with Ti/O cores ranging from 0.5–1.5 nm in size.^17,26–28 However, in these cluster molecules the repeating structure found in rutile or anatase is not typically observed, as at these very small sizes the surface environment dictates coordination geometries and overall structure. Despite changes in structure, <1 nm Ti-oxo clusters are capable of photoexcited charge separation under UV light, and can perform photocatalysis.^29–32 These clusters are closely related to the secondary building blocks in (photoactive) titanium-based MOFs.^33–37 This report investigates to what extent the quantum confinement effect can be extended to understand and predict the electronic structures of a range of Ti-(oxo-)alkoxides with Ti/O core sizes from 0.3–1.3 nm, even if the Ti–O connectivity differs from the parent structure.³⁸

Titanium tetra-alkoxides (e.g. [{Ti(OⁱPr)₄}_n]) are commonly used precursors for a wide range of compounds and materials, including the formation of TiO₂. Bulky titanium alkoxides such as [Ti(OAd)₄] (Ad = 1-adamantoxide) (Fig. 2) are mononuclear tetrahedral complexes in the solid-state, as confirmed by X-ray crystallography.^39–41 Less bulky alkoxides may crystallise as dimers (neopentoxide, ONp) or tetramers (ethoxide, methoxide), with five or six coordinate Ti centres respectively.^42,43 However, in solution lower degrees of oligomerisation are expected, with the monomeric form dominant for titanium tetra-neopentoxide, isopropoxide and tert-butoxide, and the trimeric form dominant for titanium ethoxide (Table S1).^42,44 The partial hydrolysis of titanium-alkoxides to form titanium-oxo-alkoxide clusters was extensively studied by Mosset, Klemperer, Day and Sanchez during the 1990s. Changing the degree of hydrolysis, temperature and reaction pressure can generate Ti-oxo-alkoxides of different sizes, which can be isolated by crystallisation (Fig. 2).^45–51 It is important to note that the smallest clusters such as [Ti₃O(OⁱPr)₉(OMe)] (Ti₃) form an equilibrium with higher nuclearity clusters and [Ti(OⁱPr)₄] when in solution.⁴⁵

Fig. 2 Crystal structures of [Ti(OAd)₄] and Ti-oxo-alkoxide clusters displayed to scale. Ellipsoids at 50% probability, C atoms displayed as capped sticks and hydrogen atoms omitted for clarity. Ti = lilac, O = red, C = grey.

A host of different structures, including a large Ti₅₂ cluster, can also be prepared by introducing extra organic ligands such as carboxylates or sulphates.^17,26,27,52 These additional ligands may have a significant influence upon electronic structure and can be used for ‘band gap engineering’, significant changes are noted for cases in which a dye ligand inserts energy levels within the Ti/O based HOMO–LUMO gap.^53,54 Therefore, the simple set of Ti-oxo-alkoxides, without extra surface ligands, are of particular interest for a systematic study of energy gaps versus size/nucleation.

The energy gaps of some Ti-oxo-alkoxide clusters have been previously reported using UV/visible spectroscopy to determine absorption onset, for example, [Ti₁₇O₂₄(OⁱPr)₂₀] (Ti₁₇) has a Ti/O spherical core diameter of 1.2 nm and a HOMO–LUMO gap reported as 3.36 (4.26) eV using Tauc's method to analyse the solution UV spectrum (in CH₂Cl₂) with a forbidden indirect transition (exponent n = 3, [Ti] = 9 mM) (or allowed direct transition (exponent n = 1/2, [Ti] = 0.04 mM) respectively),⁵⁵ however, a different value of 3.8 eV was reported using linear extrapolation of the absorption edge from diffuse reflectance UV spectroscopy (DRS) of a powder.^56,57 Both methods indicate a blue-shift of the energy gap from that of bulk TiO₂.

It can be challenging to make direct comparisons between studies due to the different spectroscopic methodologies and analyses conducted across different studies (SI note 1).⁵⁸ In this paper we compare the absorption spectra of a range of differently sized Ti-(oxo-)alkoxides using consistent experimental techniques, to qualitatively show size-related absorption shifts.

Results & discussion

Electronic absorption spectroscopy

Solution phase UV spectroscopy was conducted on Ti-alkoxides and Ti-oxo-alkoxides at (consistent) high concentrations ([Ti] = 35 mM) in pentane solvent to most accurately determine changes in indirect absorption onset. Solid-state DRS spectra were also collected for comparison.

To benchmark our data against the literature, the solid-state UV spectrum of bulk anatase and rutile was collected, Tauc's analysis was conducted using n = 2 (or ½) for indirect (and direct) transitions (note direct values are given in italics throughout the discussion). In our hands, the band gap is calculated as 3.1 (3.3) eV for anatase and 2.9 (3.1) eV for rutile (Fig. 3c, S2). The absorption spectrum of Ti₁₇ was collected in solution (in duplicate) and in the solid-state and analysed by Tauc's method. To compare with different methodologies of determining absorption onset methods to estimate indirect and direct transitions were both used (see experimental methods). Indirect absorption of solution data ([Ti] = 35 mM, exponent n = 3)⁵⁵ gave an onset value of 3.6 ± 0.1 eV (literature 3.4 eV),⁵⁵ whilst DRS data gave a lower value of ∼3.2 eV. The direct absorption value from low concentration solution data ([Ti] = 0.11 mM, exponent n = 1/2) was 4.3 ± 0.1 eV (literature 4.3 eV)⁵⁵ but from solid-state data gave 3.5 ± 0.1 eV. The difference between solution and solid-state data is greater than observed for some other Ti-oxo clusters, e.g. only a minor red-shift (<0.1 eV) was previously determined by our research team when comparing solid-state and concentrated solution data, for [Ti₄O₄(OⁱPr)₄(O₂PPh₂)₆].³¹ However differences between the solid-state and solution spectra of other metal alkoxide species have been previously reported,²⁴ and perhaps represents the ability of these structures to adjust to surrounding environment. To ensure that the red-shift in the solid spectrum was not due to trace hydrolysis under air, the measurement was repeated in a quartz cuvette sealed within the glovebox with vacuum grease, and this gave a very similar spectrum (which did not change over several days). Comparison of absorption onset values is difficult due to the different ways of calculating them, and differences between solution and solid-state data (Fig. S2), noting the linear absorption scale for solution data, but closer to logarithmic scale for diffuse reflectance data (which emphasizes low intensity features). Therefore, best comparisons are made by collecting absorption spectra under consistent conditions and comparing the spectra themselves.

Fig. 3 Solution (a, 35 mM; b, 0.11 mM) and solid-state DRS (c) absorption spectra of titanium tetra-alkoxides.

Titanium alkoxides [{Ti(OR)₄}_n] with differing structures (e.g. monomers, trimers, tetramers, Table S1, Fig. S3–S6)^44,59 were examined to consider the smallest possible Ti/O systems. ¹H DOSY NMR spectroscopy was used to investigate the degree of oligomerisation in the soluble compounds in d⁸-toluene (Fig. S7–S9). Both [Ti(O^tBu)₄] (29 mM) and [Ti(OⁱPr)₄] (35 mM or 1.8 mM) diffuse at similar rates to the solvent, indicating small monomeric molecules dominate with predicted hydrodynamic diameters of 0.67 nm and 0.60 nm respectively (comparable to ∼0.75 nm estimated from crystal structure of [Ti(OAd)₄]).^42,59 In contrast, samples of [{Ti(OEt)₄}_n] ([Ti] = 35 mM) diffuse more slowly through solution with an estimated diameter of 0.93 nm (N.B. the trimer is expected to be dominant at this concentration, with an expected diameter of ∼0.9 nm).^43,44 Despite the similar aliphatic groups on these titanium alkoxides (R = Et, ⁱPr, ^tBu, Ad), significant changes are observed in the absorption spectra, which track with the degree of oligomerisation (Fig. 3). Upon oligomerisation, an increasing number of Ti and O atoms contribute to the electronic structure of the molecule, and, the coordination geometry at Ti also changes from tetrahedral, to trigonal bipyramidal (on dimerization) and then to octahedral in larger oligomers. Monomeric [Ti(OAd)₄] and [Ti(O^tBu)₄] absorb only from deep in the UV at 4.3 (4.8) and 4.2 (4.9) eV (Fig. 3a and b, S10–S13, [Ti] = 35–1.75 mM (0.1 mM)). The initial absorbance maxima for [Ti(O^tBu)₄] at 228 nm is consistent with studies of isolated tetrahedrally coordinated Ti sites in mesoporous silica.^60,61 A 35 mM solution of [{Ti(OⁱPr)₄}_n], which may contain dimers, absorbs from slightly lower energy of 4.0 eV, however, reducing the concentration to within the range at which monomers are expected to dominate (1.75–0.11 mM) gives values of 4.3 (4.9) eV consistent with the other monomers (Fig. 3a and b, S14 and S15). [Ti(OEt)₄]_n, which is expected to be mainly trimeric in solution,^44,59 absorbs from 3.6 eV (Fig. 3a and b, S16 and S17, [Ti] = 35 mM), with a significantly lower onset energy than the other alkoxides at the same [Ti] concentration (Table S2, N.B. identical spectra are also recorded in THF or EtOH solution).

Monomeric [Ti(OAd)₄] and tetrameric [{Ti(OMe)₄}₄] were also studied in the solid-state by DRS (Fig. 3c, S18–S20). The absorption onset of tetrameric [{Ti(OMe)₄}₄], at 3.4 (3.8) eV, is red shifted relative to [Ti(OAd)₄] which absorbs from 3.6 (4.1) eV consistent with the degree of oligomerisation in the structure. It is again worth noting the difference between solid-state and solution methods for [Ti(OAd)₄]. This compound is highly air sensitive and, even in a vacuum grease sealed quartz cell, the spectrum of [Ti(OAd)₄] develops a shoulder over time (after three days the onset becomes shifted to 3.5 (3.7), Fig. S20), indicating some hydrolysis of the structure and formation of extended multinuclear species.

Immediate red-shifts in the absorption onset of [Ti(OⁱPr)₄] are observed in solution upon adding trace water or exposing to air, as species such as [Ti₃O(OⁱPr)₁₀] are generated (Fig. S21).⁴⁵ Ti-oxo-alkoxides ([Ti₃O(OⁱPr)₉(OMe)], (Ti₃);⁴⁵ [Ti₇O₄(OEt)₂₀], (Ti₇);⁶² [Ti₁₁O₁₃(OⁱPr)₁₈], (Ti₁₁);⁴⁸ [Ti₁₂O₁₆(OⁱPr)₁₆], (Ti₁₂);⁴⁸ [Ti₁₆O₁₆(OEt)₃₂], (Ti₁₆);⁵⁰ Ti₁₇,⁴⁹ [Ti₁₈O₂₈H(O^tBu)₁₇], (Ti₁₈),⁵¹ see Table S3 for sizes) were prepared as crystalline solids by hydrolysis and condensation reactions, and purity was confirmed by solution ¹H NMR spectroscopy (Fig. S22–S26). Note that as Ti₃ is susceptible to forming equilibria in solution, the structure was confirmed by single crystal X-ray diffraction, and the most reliable absorption spectrum was measured in the solid state. The solution spectra for all other compounds (Fig. 4, S27–S50), dissolved in pentane, display Beer–Lambert behaviour across a wide concentration range.⁴⁵

Fig. 4 Solution (a) [Ti] = 35 mM; (b) [Ti] = 0.11 mM (for [Ti] = 1.75 mM see Fig. S50) and (c) solid-state DRS absorption spectra of titanium-oxo-alkoxides.

Ti₃ shows an onset of 3.5 (3.6) eV in the solid-state, similar to that of similarly sized [{Ti(OMe)₄}₄] (Fig. 4c, S27 and S28), and an approximate value of 3.7 (4.5) eV in solution (noting possible equilibria) which is similar to trimeric [Ti(OEt)₄]_n (Fig. S29). The absorption onsets of the larger Ti-oxo-alkoxide clusters have similar onsets to each other (Table S2), with minor shifts that do not correlate with nuclearity (Ti₇, Ti₁₁, Ti₁₂, Ti₁₆, Ti₁₇: solution (indirect) data range, 3.5–3.6 eV; solid state (direct) data range, 3.4–3.6 eV). Across this size range (maximum core dimension 0.9–1.3 nm, Table S3) small increases in nuclearity have a minor effect, and other factors such as coordination geometry and structural distortion may be influential in determining their exact absorption onsets, masking any size effects (N.B. due to differing shapes Ti₁₆ has a larger maximum dimension than Ti₁₈). All clusters do remain blue-shifted relative to bulk TiO₂ hinting that to reach bulk values, further order-of-magnitude increases in nuclearity are required.¹³ When compared to the effective mass approximation prediction (Fig. 1a, S51), the data collected in this study shows a slower change in energy gap with decreasing size. Of course, the structures at this size no longer resemble bulk anatase or rutile and, therefore, the theoretical model (designed for larger nanomaterials with consistent structure and properties) becomes less valid.

It is noteworthy that after partial hydrolysis, these larger Ti-oxo-alkoxide clusters are more stable to onward hydrolysis than the previously discussed Ti-alkoxides. The powder X-ray diffraction pattern of microcrystalline Ti₁₆ was collected after various times under air, and these results show that crystallinity is retained for over 24 hours but is lost after 1 week (Fig. S52).

Electrochemistry

Cyclic voltammetry measurements were performed on monomeric [Ti(O^tBu)₄], oligomeric [{Ti(OEt)₄}_n] (n ∼ 3) and larger Ti₁₆ and Ti₁₇ to estimate reduction potential and, therefore, LUMO energy (which corresponds to CBM in a molecular species). Electrochemistry was performed inside a glovebox, using a boron-doped diamond working electrode,⁶³ dry supporting electrolyte (0.1 M [^tBu₄N][PF₆] in dichloromethane; 5–6 ppm water), and 100 mV s⁻¹ scan rate in order to successfully observe peaks at significantly reducing voltages. All species show irreversible redox processes and, therefore, Ep_cathodic (maximum peak current of the reductive peak) is extracted as an approximation for redox potential.⁶⁴ The data clearly shows a significant shift in reduction potential to more negative energies with decreasing size. Ti₁₆ and Ti₁₇, with 1.2 nm cores, give similar values of −1.72 and −1.71 V vs. Fc/Fc⁺. These can be compared to the flatband position of rutile in MeCN (10 ppm water), reported at −1.54 vs. Fc/Fc⁺, noting that, in this study, the CBM is estimated ∼0.01–0.1 eV more negative than the flatband value.⁶⁵ This positions the LUMO of 1.2 nm Ti-oxo clusters slightly more negative than Rutile (which is, in turn, generally considered more negative than Anatase by ∼0.16 eV).⁶⁵ [{Ti(OEt)₄}_n] gives a value of −1.92 V, requiring a more reducing voltage to accept an electron, whilst the smallest species [Ti(O^tBu)₄] requires a remarkable −2.56 V to become reduced. The changes in reduction potential (steps of 0.2 & 0.64 V for the sequence Ti₁₆, [{Ti(OEt)₄}_n], [Ti(O^tBu)₄]), are similar to the changes in solution absorption onset (steps of 0.03 & 0.61 eV), which suggests that the major changes in electronic structure are due to a changing LUMO position, and that, if at all, the HOMO may be shifted to slightly more negative values, likely due to different oxygen environments in the smallest species (Fig. 5b). To explore frontier orbital energies further, some ethoxide ligands on Ti₁₆ were exchanged with phenoxide. The high lying π orbitals of the phenoxide ligands provide an approximately ‘pinned’ HOMO level, allowing for analysis of the LUMO energy in this system by the energy gap derived from absorption spectroscopy. The findings, discussed in SI note 2, give a similar result to the electrochemistry studies.

Fig. 5 (a) Cyclic voltammograms of Ti(-oxo)-alkoxides. (b) Approximate energy position of the HOMO–LUMO gap/band gap for selected Ti(-oxo)-alkoxides and TiO₂ polymorphs vs. Fc/Fc⁺. The LUMO of Ti-(oxo-)alkoxides is approximated at the recorded E_p_cathodic values. Anatase and Rutile frontier energies taken from Kavan et al., estimating CBM at −0.06 eV more negative than flatband energy.⁶⁵

Computational studies

DFT calculations were conducted using Gaussian 16 version A03 on [Ti(OⁱPr)₄] (monomer), [{Ti(OⁱPr)₄}₂] (dimeric form with two bridging OⁱPr groups and trigonal bipyramidal coordination geometry at Ti), Ti₃, [{Ti(OMe)₄}₄], Ti₇, Ti₁₁, Ti₁₂, Ti₁₆ and Ti₁₇.^66–69 Density functional approximations (PBE, TPSSh, PBE0, CAM-B3LYP) with different percentage of Hartree–Fock exchange were employed to scrutinize the magnitude of the band gap. The geometry optimizations were performed using the Def2SVP basis set and the associated single point calculations are performed based on the optimized structure under Def2TZVP basis set for organic atoms with Stuttgart-Dresden effective core potential SDD for the titanium atoms.^70,71 A benchmark study of different functionals for computing the HOMO–LUMO gap is presented in Table S4. Four commonly used density functional approximations (DFAs) for both organic and inorganic systems, PBE, TPSSh, PBE0, and CAM-B3LYP, were applied.⁷² Because the Ti cluster is composed of multiple transition metal atoms, the static correlation effect is significant. As shown in Table S4, hybrid and range-separated DFAs overestimate the HOMO–LUMO gap, whereas the pure functional PBE shows the best agreement with the experimental data. Consequently, in the following discussion, only results obtained using the PBE method are presented. However, we expect the trends for different cluster sizes to remain the same with other density functional approximations. The calculations (Table S5) indicate that the LUMO position is the most affected by nuclearity (−1.31 eV change from smallest to largest), with the HOMO remaining similar throughout (all within a 0.39 eV range), consistent with the experimental results (Fig. 6).

Fig. 6 Calculated HOMO and LUMO energy positions for Ti(-oxo)-alkoxides. The (maximum) coordination number of the Ti atoms is highlighted, note that in larger clusters mixtures of coordination geometries are possible.

The DFT calculations reveal the most significant differences in the electronic structures occur in the smallest systems, caused by changing coordination geometry at Ti (tetrahedral to trigonal bipyramidal to octahedral on increasing nuclearity from one to three) and/or significant mixing of the additional atomic orbitals upon oligomerisation. Monomeric [Ti(OⁱPr)₄] shows the expected (e + t₂) LUMO energy levels for d orbitals in a tetrahedral geometry (Fig. S53), while the HOMO is constructed from the 2p orbitals of four interacting O atoms. Overlap of the 3d orbitals on the two Ti centres in the dimeric form, [{Ti(OⁱPr)₄}₂], creates bonding and antibonding energy d-levels, generating a lower lying LUMO state (0.5 eV more stable than in the monomer). The O based HOMO (already built from a combination of O atomic orbitals) is destabilised by a smaller value of 0.2 eV during dimerization. On extending to Ti₃, now with an oxo ligand, the LUMO is further stabilised by enhanced 3d interactions (−0.13 eV), but with a significantly smaller jump than from monomer to dimer. The HOMO is also raised by +0.19 eV, with the influence of the oxo ligand observed in the HOMO−1 orbital (Fig. S53). Beyond this size the HOMO remains similarly positioned, with slight deviations across the series, whilst the LUMO steadily drops, with the LUMO of Ti₁₇ stabilised by 0.7 eV compared to Ti₃, presumably due to increasing mixing of d-orbitals with size.

The HOMO and LUMO orbitals of the largest clusters Ti₁₆ and Ti₁₇ are shown in Fig. 7 and S54, in these cases the HOMO is predominantly located on surface oxygens (noting that most oxygens are surface in these small structures). This is consistent with the concept that low coordinate or strained O sites contribute to the highest energy filled electronic states.^24,73,74 The LUMOs are located on Ti 3d orbitals; for Ti₁₆ all Ti are six-coordinate, but the LUMO is mainly located on the most enclosed (core like) sites surrounded by oxo ligands, with much smaller contributions from titaniums with multiple connections to surface alkoxides. In Ti₁₇, six-coordinate Ti sites dominate the LUMO with no contribution from the five and four coordinate sites. Interestingly the central TiO₄ unit in the centre of Ti₁₇ does not strongly contribute to HOMO or LUMO.

Fig. 7 Calculated HOMO orbitals for Ti₁₆ (top) and Ti₁₇ (bottom).

Conclusions

Electronic size effects are explored in the smallest Ti/O based systems ranging from a single Ti atom to Ti-oxo-alkoxide clusters with ∼1.2 nm Ti/O cores. The predominant trend clearly shows that the energy gaps in these systems is related to their size, with energy gap increasing at smallest sizes mostly due to an increase in (Ti-based) LUMO energy. Stabilisation of the LUMO with increasing size is caused by cooperative interactions of the Ti 3d orbitals. The greatest changes are observed at the very smallest sizes (e.g. comparing monomer to dimer). More subtle changes in HOMO position are also observed across the series. Changes in coordination geometry at Ti, and surface structure, may also influence electronic structure across these size scales. Clusters with 7–18 Ti atoms appear to have similar energy gaps, with some showing minor red-shifts relative to Ti₃, but all remain blue shifted relative to bulk TiO₂. To realise further notable changes in electronic structure the particles must become significantly bigger, e.g. approaching 100 Ti atoms.¹⁸

These results demonstrate that size effects in Ti/O systems are similar to other semiconducting oxides like ZnO, but that they occur only at very small (<2 nm) sizes at which point the structures have adapted from that of bulk TiO₂ and, therefore, other structural effects are also important. Understanding of these properties are crucial for the application of Ti/O based semiconducting materials constructed from ultrasmall Ti/O units, such as those found in Ti-based MOFs. The fundamental understanding of size effects at the smallest scales is also important for developing other metal oxide materials, enabling band gap engineering and frontier orbital positioning for photocatalyst materials and charge transport layers in electronic devices.

Author contributions

Concept by SDP, Synthesis and spectroscopy by TJB and SDP, Electrochemistry by ES, Computational studies by BW and FDP. All Authors contributed to preparing the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

All raw data has been deposited in the University of Warwick's database, WRAP, and can be found at https://wrap.warwick.ac.uk/197288/.

Supplementary information (SI): experimental methods, supporting characterisation and spectra, computational data, supporting notes. See DOI: https://doi.org/10.1039/d5qi02443a.

Acknowledgements

We are grateful for support from the Royal Society for a Royal Society University Research Fellowship supporting SDP and TJB (URF/R1/191458) and Research Grant (RG/R2/232264). TJB also acknowledges the University of Warwick CDT in Analytical Science. ES thanks the EPSRC for a studentship through a Doctoral Training Partnership (DTP) Grant. We thank the Macpherson Group at the University of Warwick for assistance with boron-doped diamond electrodes. BW and FDP acknowledge support of the Research Foundation Flanders (FWO) and the Vrije Universiteit Brussel through a Strategic Research Program awarded to the Research Group of General Chemistry (SRP73). We thank support from the EUTOPIA Connected Research Community scheme.

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