Electronic-reconstruction-enhanced hydrogen evolution catalysis in oxide polymorphs

Transition metal oxides exhibit strong structure-property correlations, which has been extensively investigated and utilized for achieving efficient oxygen electrocatalysts. However, high-performance oxide-based electrocatalysts for hydrogen evolution are quite limited, and the mechanism still remains elusive. Here we demonstrate the strong correlations between the electronic structure and hydrogen electrocatalytic activity within a single oxide system Ti2O3. Taking advantage of the epitaxial stabilization, the polymorphism of Ti2O3 is extended by stabilizing bulk-absent polymorphs in the film-form. Electronic reconstructions are realized in the bulk-absent Ti2O3 polymorphs, which are further correlated to their electrocatalytic activity. We identify that smaller charge-transfer energy leads to a substantial enhancement in the electrocatalytic efficiency with stronger hybridization of Ti 3d and O 2p orbitals. Our study highlights the importance of the electronic structures on the hydrogen evolution activity of oxide electrocatalysts, and also provides a strategy to achieve efficient oxide-based hydrogen electrocatalysts by epitaxial stabilization of bulk-absent polymorphs.

W ith the growing concerns about the environmental pollution, global warming and the rapid depletion of petroleum resources, exploiting alternatively sustainable, clean, and renewable energy sources is becoming the most urgent scientific challenge for us in the modern society 1,2 . Supplying energy without toxic emissions, hydrogen, as a promising energy carrier, is believed to have a crucial role in the future scenario of energy applications 3 . In the past several decades, numerous efforts have been devoted to developing more sustainable hydrogen-production routes from renewable energy sources 3,4 . Among them, electrochemical water splitting using the hydrogen evolution reaction (HER, 2H + + 2e − → H 2 ) is considered as a promising method for hydrogen production [3][4][5] , owing to its unparalleled capacity and carbon-free nature. Thus, the efficiency of hydrogen production through electrolysis mainly depends on the catalytic performance of the HER electrocatalysts. Currently, the state-of-the-art electrocatalyst for HER is Pt/C, but it suffers from the prohibitive cost and scarcity 2 . Hence, it is highly desirable to explore new efficient HER electrocatalysts with low-cost and earth-abundant elements.
Transition metal oxides (TMOs) have attracted great interest in both condensed matter physics and materials science due to their fascinating tunable physical and chemical properties with high stability, low cost, and environmental friendliness [6][7][8] . Titanium dioxide (TiO 2 ) is one of the most studied TMOs, and has been extensively explored as a photocatalyst for water splitting. Its efficiency can be dramatically enhanced by increasing its light absorption via fabricating black hydrogenated TiO 2 nanocrystals 9,10 . The perovskite oxides with a general formula of ABO 3 have been well studied as electrocatalysts for water splitting, and high-performance oxygen evolution reaction (OER) was realized in them [11][12][13][14] . Then, substantial efforts were devoted to understanding its mechanism and investigate the fundamental parameters that govern the catalytic activity [15][16][17][18][19][20] . Consequently, tuning the electronic structures of the electrocatalysts has been considered as an efficient method to enhance the OER activity of TMOs with stronger metal-oxygen (M-O) hybridization or higher covalency of the M-O bonds 12,20,21 . For HER, pure oxides were usually inactive, because of the extremely strong hydrogen adsorption on oxygen atoms. Nevertheless, most recently, several oxides (such as Pr 0.5 (Ba 0.5 Sr 0.5 ) 0.5 Co 0.8 Fe 0.2 O 3-δ 2 , SrNb 0.1 Co 0.7 -Fe 0.2 O 3-δ (nanorods) 22 , and CoO (nanorods) 23 ) were reported to exhibit efficient HER activities. However, the origin of TMObased HER mechanism with oxides' characteristics, e.g., metal-oxygen hybridization, and the fundamental parameters that dominate the HER activity still remains unclear.
In this work, we demonstrate the close correlation between the electronic structures and HER catalytic activities in a single-oxide system (Ti 2 O 3 ) with strongly correlated electrons. Generally, Ti 2 O 3 has a corundum structure 24,25 in bulk with an ultra-narrow bandgap (E g ≈ 0.1 eV), exhibiting excellent photothermal effect 26 and mid-infrared photodetection 27 . Interestingly, a new orthorhombic Ti 2 O 3 polymorph that is absent in bulk was stabilized on Al 2 O 3 single-crystal substrates via epitaxial stabilization, with intriguing emergent properties 28,29 . Here, extension of the polymorphism of Ti 2 O 3 is further achieved by epitaxially stabilizing a cubic phase, which has not been reported before and is also bulkabsent. Taking advantages of the excellent structural flexibility of Ti 2 O 3 , we are able to explore the correlation between the physical electronic structures and HER activities within a single-material system, which provides a more precise understanding on the correlation without disturbance of varied elements. Systematical investigations are performed on the electronic structures, transport properties, and HER activities of three Ti 2 O 3 polymorphs. Evident electronic reconstructions are observed in the epitaxially stabilized orthorhombic and cubic phases with modulated electron-electron interactions and charge-transfer energy. Importantly, smaller charge-transfer energy leads to the stronger hybridization strength of the Ti 3d -O 2p orbitals, which lower the d-band center of Ti and weakens the H adsorption, further resulting in the enhanced HER activity in those epitaxially stabilized polymorphs. This electronic-reconstruction enhanced HER activity, achieved in the structure-tailored Ti 2 O 3 , introduces a previously unrecognized route to explore more efficient TMObased HER electrocatalysts by enhancing the metal-oxygen hybridization via selective stabilization of polymorph phases.

Results
Fabrication and structural characterizations of Ti 2 O 3 polymorphs. Three Ti 2 O 3 polymorphs were successfully fabricated in the epitaxial film form by using the pulsed laser deposition (PLD) technique (Fig. 1a). During the film growth, the same corundum (trigonal) Ti 2 O 3 target was used for stabilizing all Ti 2 O 3 polymorphs. The phase separation was controlled by carefully varying deposition temperature and substrates' symmetry, which are widely used for the oxides epitaxial stabilization 30,31 . With the advent of thin-film epitaxial stabilization, new polymorphs that do not exist in bulk could be stabilized on single-crystal substrates 28,29,31 , resulting in the extension of the oxides' polymorphism. Polymorphism describes the occurrence of different lattice structures and symmetries in a crystalline material with identical composition, which is a critical and attractive phenomenon in material science and condensed matter physics 32,33 . Polymorphs would exhibit different physical, chemical, and mechanical properties due to their varied structural characteristics 34-37 , e.g., the polymorph-dependent metal-semiconductor transitions in Ti 3 O 5 38,39 .
By recrystallization on the substrates during epitaxial growth (Fig. 1a), three different Ti 2 O 3 polymorphs (Fig. 1b) Supplementary Fig. 3, the root mean square (RMS) roughness for all Ti 2 O 3 samples is quite similar and close to 1 nm, which is very small with respect to their thickness (~300 nm), indicating the flat surfaces that are further confirmed by the scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) images ( Supplementary Fig. 4). Interestingly, unexpected fascinating properties (such as ferromagnetism 28 and superconductivity 29 ) were discovered in the o-Ti 2 O 3 , demonstrating strong structure-property correlations in Ti 2 O 3 , which motivated us to further explore the polymorphism of Ti 2 O 3 . Figure 1c-e shows the in-plane epitaxial relationships for γ-, o-, and α-Ti 2 O 3 film/substrate heterostructures, respectively. The corresponding high-resolution X-ray diffraction (XRD) patterns are shown in Fig. 1f. The epitaxial relations for αand o-Ti 2 O 3 have been determined to be (0001) α-Ti 2 O 3 || (0001) α-Al 2 O 3 and (011) o-Ti 2 O 3 || (0001) α-Al 2 O 3 by high-resolution STEM and selected area electron diffraction (SAED) 29 . Since γ-Ti 2 O 3 is a newly stabilized polymorph, we utilized HR-XRD and HR-STEM ( Fig. 2) to investigate its epitaxial growth on STO. As shown in Fig. 1f, (004) γ-Ti 2 O 3 was directly grown on (002) STO ( Supplementary Fig. 5), indicating a cubic-on-cubic growth. Figure 2a schematically illustrates the epitaxial growth of γ-Ti 2 O 3 on STO, which is further confirmed by in-plane synchrotronbased X-ray φ-scan (Supplementary Fig. 6 and Supplementary Note 2). As isomorphs of γ-Ti 2 O 3 , γ-Al 2 O 3 40,41 , and γ-Fe 2 O 3 42 were also stabilized on STO with the same epitaxial relationship. Moreover, γ-Ti 2 O 3 is also successfully stabilized on LaAlO 3 (LAO) substrates, which is identical with that on STO ( Supplementary Fig. 6).
In-depth STEM measurements were performed to investigate the cubic γ-Ti 2 O 3 on STO. Figure 2b shows the cross-section lowresolution STEM image of the spinel/perovskite γ-Ti 2 O 3 /STO heterointerface. The thickness of the γ-Ti 2 O 3 film is about~300 nm. It needs to be pointed out that the thickness for all Ti 2 O 3 films is fixed at around~300 nm in order to get the bulk intrinsic properties of these polymorphs. High-resolution high-angle annular dark-field (HAADF) STEM imaging (Fig. 2c)

Determination of electronic reconstructions in Ti 2 O 3 polymorphs.
With an unpaired 3d 1 election, α-Ti 2 O 3 is regarded as an antiferromagnetic Mott insulator with a unique and broad metal-insulator transition (MIT) [45][46][47] . In strongly correlated TMO systems, the electron-electron interaction, represented by the on-site Coulomb repulsion U, is significant, and opens the Mott-Hubbard gap inside the transition metal 3d band between the lower Hubbard band (LHB) and upper Hubbard band (UHB). Charge-transfer energy Δ, the energy difference between the oxygen 2p band and transition metal 3d band, is another crucial parameter in determining the physical and chemical properties of TMOs 20,48 . As illustrated in Fig. 3a, depending on the relative magnitudes of U and Δ, strongly correlated TMOs could be classified into Mott insulators (U < Δ) and charge-transfer insulators (U > Δ). With tunable U and Δ, modulations of the electronic properties that impact on electrochemical activities could be achieved [49][50][51] . Proposed by Goodenough et al. 52 , the electronic band structure of α-Ti 2 O 3 could be well described using the molecular orbital theory (Fig. 3b). The trigonal crystal field splits Ti 3d t 2g orbitals into a pair of e π g orbitals and an a 1g orbital near the Fermi level. Furthermore, the a 1g band splits into the bonding a 1g and the antibonding a Ã 1g bands, while the e π g band splits into the bonding e π g and the antibonding e πÃ g bands, mainly because of the hybridization of the Ti-Ti orbitals. (The e π g and e πÃ g bands are usually located at the same energy level, since the e π g − e πÃ g splitting is very small.) The MIT of Ti 2 O 3 could be explained by the band-crossing scenario 53,54 . That is, the metallic state emerges when the e π g and a 1g bands overlap with increased temperature, while the insulating state occurs when a gap arises between the e π g and a 1g bands with decreased temperature 54 . At room temperature, the bandgap of insulating α-Ti 2 O 3 is around 0.1 eV, which was verified by both electrical and optical measurements 24,28 . Based on the above proposed electronic structure, the U and Δ in Ti 2 O 3 could be assigned specifically to the a 1g − e π g and O 2p − e π g transitions, respectively. To quantify the U and Δ in different Ti 2 O 3 polymorphs, spectroscopic ellipsometry and light absorption measurements were performed at room temperature. Figure 3c-e shows the optical conductivity (σ) of α-, o-, and γ-Ti 2 O 3 , respectively, demonstrating the a 1g − e π g and a 1g − a Ã 1g interband transitions are located at around 1 and 3 eV 55 . Concomitant with the different lattice symmetries, substantial electronic reconstructions were observed among the three Ti 2 O 3 polymorphs. Specifically, the U ða 1g À e π g Þ in α-, o-, and γ-Ti 2 O 3 polymorphs increase from 0.85 eV to 1.01 eV, then to 1.10 eV, respectively, revealing stronger electron-electron interactions. Moreover, typical Drude absorptions are observed in o-and γ-Ti 2 O 3 at low photon energies (ħω), indicating high free electron concentrations in these two polymorphs. This point will be discussed later, combined with the electronic transport results. The Δ ðO 2p À e π g Þ in the Ti 2 O 3 polymorphs were obtained from the UV-Vis light absorption data, which are correspondingly shown as insets of Fig. 3c-e. The absorption coefficients (α) of Ti 2 O 3 polymorphs are in the range of~0.6 to 2.1 × 10 5 cm −1 at the UV-Vis range, demonstrating a strong light absorption. In order to extract the Polymorphism Similarly, the a 1g À a Ã 1g transitions are still located at around 3 eV, which is consistent with the ellipsometry results. Importantly, the Δ ðO 2p À e π g Þ for α-, o-, and γ-Ti 2 O 3 polymorphs are verified to be 4.78, 4.48, and 4.37 eV, respectively. As a result, the Δ decreases in the Ti 2 O 3 polymorphs with increasing U (Fig. 3f). According to these electronic reconstructions, strong polymorph-dependent properties could be expected in Ti 2 O 3 . It is well known that Δ is directly related to the hybridization of M-O orbitals, which would further impact on the conductivity [48][49][50] and electrochemical activity 20,51 .

Hybridization strength of Ti-O orbitals in Ti 2 O 3 polymorphs.
In order to estimate the hybridization of Ti-O orbitals in Ti 2 O 3 , synchrotron-based X-ray absorption spectroscopy (XAS) was performed to examine the electronic structures of Ti 2 O 3 polymorphs. The experimental XAS configuration is shown as inset in Fig. 4a. Ti L 3 and L 2 -edge transitions (Fig. 4a) in all Ti 2 O 3 polymorphs are located at~458.6 eV and~463.7 eV, respectively, consistent with the bulk Ti 2 O 3 56 . The similar Ti L-edge XAS spectra obtained from the different Ti 2 O 3 polymorphs reveal that they are sharing the same Ti 3+ chemical environment as expected. However, distinct variations are observed at the O K-edge XAS spectra. The O K-edge XAS spectrum has been widely utilized to study the hybridization of the M-O orbitals in oxides 21,57,58 . Notably, the O K-edge pre-edge region near the threshold of the O K-edge XAS demonstrates the hybridization between O 2p and transition metal 3d states 21,57 . As shown in Here, we define a hybridization factor (H.F.) as the integrated intensities of the XAS O K-edge pre-edge region (from 528 to 537.2 eV) with the subtraction of the linear backgrounds (shaded area in Fig. 4c). As a consequence, Ti-O hybridization is the strongest in γ-Ti 2 O 3 with the smallest Δ, while that is the weakest in α-Ti 2 O 3 with the largest Δ (Fig. 4d). The same conclusion about the Ti-O hybridization can be obtained by the X-ray photoelectron spectroscopy (XPS) (Supplementary Fig. 8, Supplementary Table 1 and Supplementary Note 4). Stronger Fe 3d -O 2p hybridization was observed in the γ-Fe 2 O 3 than that in the α-Fe 2 O 3 59 , indicating that the stronger M-O hybridization can be induced by the crystal structure and electronic structure of the γphase. As we know, smaller Δ with stronger hybridization leads to the delocalization of electrons, and thus increases the conductivity of oxides [48][49][50] .
Electronic transport properties of Ti 2 O 3 polymorphs. As expected, various electronic transport behaviors (Fig. 5) are  Fig. 5a), indicating the diversity and complexity of Ti 2 O 3 . In addition to the electron-electron interaction, the electron-phonon interaction is also an important factor in determining the electronic behaviors of the Ti 2 O 3 polymorphs 29,54 , which makes Ti 2 O 3 more complicated and interesting. The change of the resistivity from 400 to 2 K in γ-Ti 2 O 3 is more than one order of magnitude, which is larger than that of α-Ti 2 O 3 and o-Ti 2 O 3 . Moreover, the transport behavior of γ-Ti 2 O 3 is consistent even when its thickness decreases to 20 nm ( Supplementary Fig. 9).
Furthermore, the carrier information of the Ti 2 O 3 polymorphs was investigated by Hall-effect measurement. Interestingly, o-Ti 2 O 3 and γ-Ti 2 O 3 are confirmed to be n-type semiconducting, whereas α-Ti 2 O 3 is a p-type semiconductor. As shown in Fig. 5b, high electron concentrations at the scale of~10 22 cm −3 are observed in o-Ti 2 O 3 and γ-Ti 2 O 3 , which could contribute to the strong Drude absorptions in Fig. 3d, e. Surprisingly, an unexpected increase is observed in the carrier concentration of o-Ti 2 O 3 at T < 250 K, while that of γ-Ti 2 O 3 decreases continuously below 400 K. Increase of the carrier concentration in o-Ti 2 O 3 may be correlated to its superconductivity at lower temperatures, which needs further investigations. Lower carrier concentration (~10 21 cm −3 ) is observed in α-Ti 2 O 3 , which is about one order of magnitude lower than in o-Ti 2 O 3 and γ-Ti 2 O 3 . However, the carrier mobility (>10 cm 2 V −1 s −1 ) in α-Ti 2 O 3 is about one order of magnitude higher than those in o-Ti 2 O 3 and γ-Ti 2 O 3 (Fig. 5c). It should be noted that higher electron concentration leads to more carrier scattering, which results in the lower electron mobility in o-Ti 2 O 3 and γ-Ti 2 O 3 . Besides, the more significant change of the resistivity (400-2 K) in γ-Ti 2 O 3 results from the constructive effect between the decreased carrier concentration and mobility, while destructive effects between the carrier concentration and mobility are observed in the α-Ti 2 O 3 and o-Ti 2 O 3 that results in the smaller change of the resistivity (400-2 K). More details are shown in Supplementary Note 5. Notably, the carrier concentrations of Ti 2 O 3 polymorphs at 300 K increases with smaller Δ (Fig. 3f) that result in more delocalized electrons, consistent with the previous scenario [48][49][50] .
Correlation between HER activity and electronic reconstructions. In order to elucidate the relationship between the electronic reconstructions and HER catalytic activity, Ti 2 O 3 polymorphs were used directly as the working electrodes for HER measurements in 0.5 M H 2 SO 4 . The configuration of the HER electrochemical cell is schematically illustrated as the inset of Fig. 6a. Obviously, the electronic reconstructions in Ti 2 O 3 influenced the HER activities significantly, representing strong polymorph dependence. The influence of the surface microstructure or defect on the observed polymorph-dependent HER performance in Ti 2 O 3 is discussed and ruled out in Supplementary Note 6. As shown in Fig. 6a, b, the newly stabilized γ-Ti 2 O 3 has the best activity with the smallest Tafel slope (199 mV dec −1 ), while the bulk-phase α-Ti 2 O 3 is the least active HER catalyst with the largest Tafel slope (241 mV dec −1 ). Noticeably, the γ-Ti 2 O 3 displays the smallest overpotential of 271 mV (Fig. 6c) to produce a current density of 10 mA cm −2 , which is a~45% reduction compared with that of the α-Ti 2 O 3 (495 mV). The Tafel plots observed here are a little bit larger than those of the nanostructured oxide samples 22,23 , which would be caused by the limited surface area of our film samples. Thus, further improvements could be expected by nanostructure-array fabrications on the films with increased surface areas.
Impressively, the enhanced HER activities are observed in those epitaxially stabilized phases (o-and γ-Ti 2 O 3 ) that do not exist in bulk form, which may be applicable to other oxide materials. Hence, efficient TMO-based HER catalysts could be achieved by the selective stabilization of bulk-absent polymorphic phases. Most importantly, the HER activity of the Ti 2 O 3 polymorphs are strongly correlated to their electronic structures. As shown in Fig. 6d, the overpotentials of HER decreases with smaller Δ accompanied with stronger Ti-O hybridization, unambiguously demonstrating the HER activity is highly enhanced by the electronic reconstructions. Noteworthily, the Faradaic resistances of Ti 2 O 3 polymorphs, obtained from the electrochemical impendence spectra ( Supplementary Fig. 10), do not follow the trend of their HER performances, indicating the enhanced activity is not simply derived from their electrical conductivity, but indeed from the electronic reconstructions. The overall HER catalytic activity of γ-Ti 2 O 3 may not be comparable with those of the state-of-the-art noble metals (e.g., Pt/C), but considering the tiny weight of the γ-Ti 2 O 3 film (~100 μg for 300 nm on 1 × 1 cm substrates), the activity of γ-Ti 2 O 3 is still remarkable as an oxide material. (More discussion is presented in Supplementary Note 7). Moreover, the correlation between the electronic reconstructions and HER activities in the Ti 2 O 3 polymorphs are robust.
Subsequently, the mechanism behind the electronicreconstruction enhanced HER activity in Ti 2 O 3 is explored. In general, a multi-step electrochemical process would take place, during the HER, on the surface of the electrocatalyst, where gaseous hydrogen (H 2 ) is generated. In acid solution, the HER would proceed via either Volmer-Heyrovsky or Volmer-Tafel pathways 61 (Volmer: H þ þ M þ e À !M À H Ã ; Heyrovsky: where H * designates a hydrogen atom chemically adsorbed on the active sites of the electrocatalyst surface (M)). The hydrogen adsorption free energy (ΔG H* ) is a well-known descriptor for the HER activity, and its optimal value |ΔG H* | should be zero, indicating the H * adsorption is neither too strong nor too weak 61 . Because the H * adsorption is excessively strong on the oxygen atoms, TMOs are usually considered to be inactive HER electrocatalysts. However, the H * adsorption on oxides could be weakened by increasing the covalency of the M-O bonds, which results in an activated or enhanced HER efficiency 23 . The top valence band of Ti 2 O 3 (Fig. 3b), just below the Fermi level, is derived from the Ti 3d orbitals (a 1g band), whose center is the so called d-band center in the d-band theory 62 Supplementary Fig. 12a), respectively. The difference of the d-band center in Ti 2 O 3 polymorphs can be attributed to their distinct hybridization strength between the Ti 3d and O 2p orbitals. Since the O 2p band is further away from the Fermi level than the Ti 3d (a 1g ) band (Fig. 3b), stronger Ti-O hybridization could make the d-band center downshift  (Fig. 6c), where it can be found that the overpotential is the smallest (0.271 V) on the γ-Ti 2 O 3 (001) surface and the largest (0.495 V) on the α-Ti 2 O 3 (0001) surface. It should be noted that the difference between theoretical and experimental values may arise from the theoretical perfect surface models without considering any intrinsic defects, whereas experimental samples may contain some intrinsic defects on the surfaces. Nevertheless, our calculated ΔG H* can act as a descriptor for the experimental HER performance of the Ti 2 O 3 polymorphs as they show the same tendency (Table 1).

Discussion
In summary, we systematically studied the strong correlations between the polymorphism (lattice symmetry), electronic structure, and HER activity in the epitaxial Ti 2 -band center). Thus, epitaxial stabilization of bulk-absent polymorphs is demonstrated to be an effective way to discover more efficient HER electrocatalysts in oxides. Moreover, we envision that greater enhancement of the HER activity could be realized by further decreasing the Δ via doping, or increasing the surface area via nanostructure-array fabrications. Our work provides an unambiguous descriptor for the HER activities of Ti 2 O 3 polymorphs, which could be applied to other strongly correlated TMO systems.

Methods
Fabrication of Ti 2 O 3 epitaxial films. All Ti 2 O 3 films were deposited on singlecrystal substrates using pulsed laser deposition (PLD), with a 248 -nm Laser (KrF, Coherent). The thickness of the films is~300 nm. αand o-Ti 2 O 3 films were deposited on (0001) Al 2 O 3 substrates at 600°C and 900°C, respectively 29 . The phase separation between αand o-Ti 2 O 3 was controlled by deposition temperature. γ-Ti 2 O 3 films were deposited on (001) SrTiO 3 and (001) LAO substrates at 600°C. The pressure of the PLD chamber was lower than 3.0 × 10 −6 Torr. The energy density of the laser on the target was fixed to~2 J cm −2 . The same corundum α-Ti 2 O 3 target (Sigma-Aldrich 99.99%) was used for all films' deposition.
Structural characterizations. X-ray diffraction patterns were recorded using a Bruker D8 DISCONVER high-resolution diffractometer, which is equipped with Cu Kα radiation source and LynxEye detector. During the measurements, the diffractometer was operated at 35 kV and 50 mA. In-plane φ scans were performed using the synchrotron-based XRD in the Singapore Synchrotron Light Source (SSLS) with a step size of 0.02°. STEM-HAADF images and EELS spectra were collected using the JEOL-ARM200F microscope equipped with an ASCOR aberration corrector, operated at 200 kV. The cross-section TEM samples were prepared by the focused ion beam technique. The EELS line scans were collected with an energy resolution of~0.1 eV and a spatial resolution of~0.4 nm.
Synchrotron-based XAS measurements. All the XAS data were taken in an ultrahigh-vacuum chamber with a base pressure of~1 × 10 −10 mbar at the Surface, Interface and Nanostructure Science (SINS) beam-line 64 of SSLS. The XAS data were obtained by using linear polarized X-rays impinging at an incidence angle of Ѳ = 90°from the sample surface (Fig. 4a) at the Ti L 2,3 -edge and O K-edge regions. The data were obtained by averaging 20 XAS spectra. All spectra were recorded at room temperature (300 K) using the total electron yield (TEY) mode. The photon energy was calibrated using a standard gold sample in the chamber. In order to record the intrinsic bulk electronic structures of Ti 2 O 3 polymorphs, samples measured by the synchrotron-based XAS were sputter-cleaned before the measurements.
Spectroscopic ellipsometry and light absorption measurements. The ellipsometry parameters Ψ (the ratio between the amplitude of p-and s-polarized reflected light) and Δ (the phase difference between of p-and s-polarized reflected light) were measured using spectroscopic ellipsometer with a photon range of 0.5-4 eV at incident angles 60°, 65°, and 70°at room temperature. The optical conductivity of Ti 2 O 3 films was extracted from the parameters Ψ and Δ utilizing an air/ Ti 2 O 3 /Al 2 O 3 (or air/Ti 2 O 3 /LaAlO 3 ) multilayer model, where the Ti 2 O 3 films were considered as average homogeneous and uniform mediums. The light absorption of the Ti 2 O 3 films was measured by a UV-Vis spectrophotometer (Shimadzu SolidSpec-3700) in the transmission mode. Backgrounds from the Al 2 O 3 and LaAlO 3 substrates were all subtracted.
Electronic transport and electrochemical measurements. The electronic transport properties of the Ti 2 O 3 films were measured in a Quantum Design physical property measurement system (PPMS). The resistivity and Hall effect were collected using the Van der Pauw geometry. The sample size was 5 × 5 mm. Al wires were used to connect the samples and the PPMS puck. The electrochemical measurements were performed in a three-electrode electrochemical cell with a standard VMP3 electrochemical workstation (Bio-logic Inc) at room temperature. During the HER measurements, Hg/HgO and graphite plate were used as the reference and counter electrodes, respectively, while the Ti 2 O 3 polymorphs films on 10 × 10 mm 2 single-crystal substrates were acting as the working electrodes directly. The polarization curves were recorded in 0.5 M H 2 SO 4 with a scan rate of 5 mV s −1 . All potentials were calibrated with respect to the reversible hydrogen electrode (RHE) using the equation 65 : where E vsHg/HgO was the potential measured against the Hg/HgO reference electrode.
First-principles calculations. All the calculations were carried out using DFT + U (U eff = U − J = 1.9 − 2.3 eV) 66 with the generalized Perdew-Burke-Ernzerhof (PBE) 67 and the projector augmented-wave (PAW) pseudopotential plane-wave method 68 as implemented in the VASP code 69 . For the PAW pseudopotentials, we considered 1s 1 for H, 3d 3 4s 1 for Ti, and 2s 2 sp 4 for O. The Monkhorst-Pack (MP) k-point grids of 6 × 6 × 2, 2 × 6 × 8, and 2 × 2 × 1 were used for α-Ti 2 O 3 , o-Ti 2 O 3 , and γ-Ti 2 O 3 unit cell geometry optimization calculations with a plane-wave basis set with an energy cutoff of 500 eV, respectively. Good convergence was obtained with these parameters, and the total energy was converged to 1.0 × 10 −6 eV per atom, as well as the stress exerted on the cell is less than 0.1 kbar and the forces exerted on the atoms are less than 0.01 eV/Å. Optimized unit cells were used to build surface models for H Gibbs free energy calculations ( Supplementary Fig. 11 are the total energies of the surface with one adsorbed hydrogen atom and the clean surface, respectively, E H 2 is the energy of hydrogen gas phase. ΔE ZPE and ΔS H are the differences in zero-point energy (ZPE) and entropy between the adsorbed H Ã and gas phase H 2 . The calculated correction value of ΔE ZPE À TΔS H at the temperature (T) of 300 K is~0.216 eV in this study.

Data availability
All relevant data presented in this paper are available from the authors upon reasonable request. The source data underlying