Defect Chemistry in Rare-Earth High-Entropy Oxides for Solar-Driven CO₂ Conversion

Abstract

Up to date, the development of highly efficient, visible light-active catalysts remains a formidable challenge due to the enhanced rising of atmospheric CO₂ concentration. This study discusses a class of ceria-based high-entropy oxides designed to optimize charge carrier dynamics, surface reactivity, and CO₂ activation efficiency. Due to the advantages of high configurational entropy and multi-element synergy, these materials achieved improved photocatalytic performance, surpassing conventional ceria-based systems. Structural and spectroscopic analyses reveal that Pr³⁺/Pr⁴⁺ redox pairs and abundant oxygen vacancies create an electronically disordered yet thermodynamically stable environment, which enhances charge separation and suppresses electron-hole recombination. Photocatalytic experiments demonstrated that Ce_0.2Zr_0.2La_0.2Pr_0.2Sm_0.2O_2−δ (CZLPS) achieves the highest CO₂ conversion rate, reaching a conversion of 20.3% under visible light irradiation, significantly surpassing pure ceria (1.4%), with a calculated space-time yield (STY) of 10.15 mol_COkg^–1h^–1 under the same conditions. First-principles density functional theory (DFT) simulations were employed to investigate the CO₂ reduction mechanism on CZLPS catalysts. The study elucidates the Gibbs free energy changes (ΔG) for each step of the reaction pathways leading to CO and HCOOH formation, highlighting the Zr site of CZLPS as the most active for the CO₂RR, which is responsible for the outstanding catalytic activity.

1. Introduction

The growing global population and escalating energy demands have increased the necessity for clean and renewable fuels. Fossil fuel combustion, the traditional energy source, has expectedly led to significant CO₂ emissions, followed by climate change and global warming. Even though CO₂ has an important role in maintaining Earth’s temperature balance, the rising levels of CO₂ in the atmosphere pose serious environmental threats. Consequently, converting CO₂ into valuable chemicals and fuels has become an unavoidable strategy to defy global warming and create a more sustainable environment. Numerous CO₂ capture and/or conversion methods have been developed, proving how dedicated the scientific community is to solving these environmental issues through innovative approaches. , Given the stability of the CO₂ molecule, this process requires either highly efficient catalysts or substantial energy input to accelerate the conversion into valuable chemicals.

The significance of photocatalytic CO₂ reduction lies in its potential to transform a prevalent greenhouse gas into valuable energy and chemical products, utilizing sustainable solar energy without relying on external energy sources. By harnessing solar energy, photocatalytic reduction supports the development of green technologies and reduces the carbon footprint. One of the primary challenges is the extremely low utilization of solar energy since most photocatalysts have a bandgap wider than 3.2 eV, which means they can only be excited by ultraviolet light. As UV light constitutes only about 4% of the total solar radiation reaching Earth’s surface, a large portion of solar energy, particularly visible light, remains unutilized. The development of photocatalysts that can efficiently absorb and utilize a broader range of the solar spectrum remains a key research focus. Efforts are directed toward creating materials that can harness visible light more effectively by narrowing their bandgaps, thereby increasing their solar light absorption. ,

Cerium oxide (CeO₂) or commonly known as ceria, a rare earth oxide, has gained attention for its extensive application in catalysis. − One of its most notable features is the stable Ce³⁺/Ce⁴⁺ redox couple, which facilitates the formation of abundant oxygen vacancies. These oxygen vacancies enhance the material’s photocatalytic activity by reducing electron–hole recombination. This characteristic is vital for enhancing the photocatalytic activity, as it prolongs the lifespan of charge carriers, allowing more time for the photocatalytic reactions to occur. By tuning the size, structure, and exposed crystal planes of CeO₂, more efficient CeO₂-based photocatalysts can be obtained. One of the most promising methods to improve its photocatalytic activity is by introducing configurational entropy into the crystal structure until high-entropy oxide (HEO) is formed. , HEOs are defined by their composition of five or more metal cations in equimolar ratios into a single-phase solid solution characterized by high configurational entropy. This unique structure, where multiple cations are uniformly distributed within a lattice, gives rise to remarkable and often unexpected properties that distinguish HEOs from traditional oxides. The high entropy effect stabilizes the phase structure of HEOs, making them highly resistant to thermal and chemical changes. − This stability is critical for various high-performance applications, especially in catalysis. The random distribution of cations in HEOs creates a multitude of active sites, enhancing their catalytic activity compared to traditional oxides. Despite their promising properties, the design and synthesis of HEO-based materials require careful consideration of their composition and structure to achieve the desired functional properties. , In the context of photocatalysis, these features synergistically improve light harvesting, charge separation, and redox activity. Despite significant advances, the application of HEOs in CO₂ photoreduction is still in the developing phase. Only a limited number of studies have explored their photocatalytic potential, particularly under visible light. Recent reports − showed that incorporating rare-earth elements in HEOs exhibit pronounced defect chemistry, notably oxygen vacancies, and mixed-valence states, which are crucial for CO₂ activation and reduction. Furthermore, the compositional flexibility of HEOs allows for fine-tuning of their electronic structure and surface reactivity, making them ideal candidates for reactions activated by solar light, such as solar fuel generation, hydrogen generation, etc.

Rare earth HEOs have been synthesized and evaluated as photocatalysts for UV light driven CO₂ hydrogenation. Remarkably, only the HEOs without praseodymium (Pr) as a constituent element exhibited significant photocatalytic activity toward UV light driven CO₂ hydrogenation, while Pr-containing HEOs demonstrated only moderate photocatalytic activity. This observation suggests that HEOs incorporating Pr, due to their narrower bandgap, are more suitable for photocatalysis under visible light, and this was the main motivation for further investigation into Pr-containing HEOs. In this work, we present ceria-based HEOs with Pr as one of the constituent elements. These HEOs showed a narrower bandgap and a higher concentration of oxygen vacancies due to the mixed oxidation states of Pr (Pr^3+/4+). These properties, along with other defects, including oxygen vacancies, contribute to their potential as stable and highly efficient catalysts for photocatalytic CO₂ reduction under visible light, which allowed us to evaluate the potential of ceria-based HEOs with Pr for effective and sustainable photocatalytic applications under visible light.

Despite recent progress in high-entropy oxides toward enhanced light absorption, defect engineering, and redox capacity for CO₂ photoreduction, existing studies often stop short of identifying which atomic sites perform the crucial adsorption or activation steps. Recent perspectives and experimental reports point out that HEOs can deliver higher conversion rates, but the mechanistic understanding, especially the role of specific cations in CO₂ binding, intermediate stabilization, and oxygen vacancy formation, remains underdeveloped. In the present work, we address this gap by investigating several ceria-based high-entropy oxides, combining surface chemical characterization with theoretical modeling. With this approach, we are able to correlate cation composition and oxygen defect chemistry with CO₂ adsorption energetics and hydrogenation performance, establishing a more specific and predictive design principle for HEOs in CO₂ photoreduction.

2. Experimental Section

2.1. Materials

For the synthesis of ceria-based high-entropy oxides, commercially available metal nitrates were used as purchased. Cerium­(III) nitrate hexahydrate (99.9%), zirconium­(IV) oxynitrate hydrate (99.9%), lanthanum­(III) nitrate hexahydrate (99.9%), praseodymium­(III) nitrate hexahydrate (99.9%), neodymium­(III) nitrate hexahydrate (99.9%), and samarium­(III) nitrate hexahydrate (99.9%) were obtained from Sigma-Aldrich, Germany. Yttrium­(III) nitrate hexahydrate (99.9%) was procured from Alfa Aesar, Germany. Citric acid monohydrate (99.9%) was purchased from T.T.T., Croatia, and concentrated ammonia solution (25%) was supplied by Gram-Mol, Croatia.

The strategic selection of Ce, Zr, La, Pr, Y, Nd, and Sm in the design of the HEO photocatalysts was grounded in both structural compatibility and functional synergy. Central to this framework is the concept of redox flexibility, a property predominantly contributed by cerium and praseodymium. Both Ce and Pr can reversibly switch between +3 and +4 oxidation states, thereby enhancing oxygen vacancy formation and promoting dynamic charge carrier behavior essential for photocatalytic activity under visible light irradiation. Lattice compatibility was also a critical consideration. The chosen rare-earth and transition metal cations possess closely matched ionic radii and exhibit compatibility with the fluorite crystal structure, which facilitates the stabilization of a homogeneous single-phase oxide. This uniformity suppresses phase segregation and supports long-range electronic and ionic transport within the material. Furthermore, the configurational entropy introduced by incorporating five or more distinct cations in near-equimolar ratios enhances the thermodynamic stability at elevated temperatures. The electronic contribution of Nd and Sm further refines the photocatalytic performance with the introduction of 4f electronic states that assist in visible-light absorption and can also influence the band edge positions. Zr, on the other hand, not only influences mechanical and thermal stability but also modulates the local coordination environment and strengthens metal–oxygen bonds, thereby improving the overall surface reactivity.

2.2. Preparation of the Compounds

The synthesis procedure was conducted in a 250 mL laboratory flask by using a DLAB MSH–S magnetic stirrer. To prepare a 10% solution of citric acid, citric acid and ultrapure Milli-Q water were used. Stoichiometric amounts of metal salts were added to the previously prepared citric acid solution. Concentrated ammonia solution and an HANNA pH–211 pH meter were used to adjust the pH value to 5. The solution was kept under constant stirring, at 393 K, until a black resin was formed. An Instrumentaria ST–01/02 oven was utilized for black resin drying at 393 K, while a Nabertherm LT5/11/B410 muffle furnace was used for calcination at 973 K with a 4 K/min heating rate. Chemical formulas of prepared compounds are presented in Table , along with acronyms used further in the text.

1. Prepared Compound Acronyms along with Their Corresponding Chemical Formulas.

Synthesized Compound	Chemical Formulas
Ceria	CeO2
CZLP	Ce0.25Zr0.25La0.25Pr0.25O2−δ
CZLPY	Ce0.2Zr0.2La0.2Pr0.2Y0.2O2−δ
CZLPN	Ce0.2Zr0.2La0.2Pr0.2Nd0.2O2−δ
CZLPS	Ce0.2Zr0.2La0.2Pr0.2Sm0.2O2−δ

2.3. Structural Characterization

2.3.1. X-ray Diffraction

The crystal structure and microstructure of the synthesized materials were analyzed using X-ray powder diffraction (XRD), using a PANalytical Aeris diffractometer (Malvern PANalytical, UK) with a Cu Kα radiation source (at 40 kV and 15 mA). FULLPROF software was used, along with the Rietveld refinement method to analyze PXRD patterns with the purpose of extracting important microstructural and structural information, and the structure was visualized using VESTA software.

2.3.2. X-ray Photoelectron Spectroscopy

XPS analysis was conducted using a Supra+ instrument (Kratos, Manchester, UK) equipped with an Al Kα X-ray excitation source. A charge neutralizer remained active throughout the measurements. The electron detection angle relative to the sample surface was set at 90° (take-off angle). Measurements were performed at a pass energy of 20 eV. Powdered samples were attached to carbon tape mounted on a silicon wafer. Data acquisition and analysis were carried out using ESCApe 1.5 software (Kratos) with the binding energy scale calibrated to the C–C/C–H peak at 284.8 eV within the C 1s spectrum.

2.3.3. Electron Microscopy Study

The surface structure analysis was carried out using a Thermo Fisher Scientific Apreo C scanning electron microscope (Thermo Fisher Scientific, Waltham, MA, USA). Images were captured using a Zeiss ULTRA Plus field emission scanning electron microscope (FE-SEM, Zeiss, Germany) in secondary electron mode with an InLens detector set at a cathode voltage of 20 kV and a working distance of about 5.5 mm. The powdered samples were adhered to aluminum stubs with double-sided carbon conductive tape and coated with a conductive layer of Au/Pd (∼10 nm thick) using a high sputter coater (Quorum Q150T ES, UK). Elemental mapping was performed using an Oxford Instruments microanalysis system equipped with a 50 mm² silicon drift detector (X–Max50, Oxford Instruments plc, Tubney Woods, Abingdon, UK). The resulting element distribution maps were processed by using Inca software (Oxford Instruments, UK). Furthermore, the synthesized catalysts were examined with a Tecnai G² 20 X–Twin high-resolution transmission electron microscope (HR-TEM, FEI Company, Hillsboro, OR, USA), which is equipped with electron diffraction capabilities and operates at 200 kV. All microscopy images were analyzed using ImageJ software.

2.3.4. Raman Spectroscopy

Raman spectra were acquired using a Confocal microscope (Sentera II, Bruker) with a 532 nm wavelength source. The measurements were conducted at a laser power of 2.50 mW and a spectral resolution of 4 cm^–1. A 50× optical objective with an aperture of 50 × 1000 μm was utilized, and each measurement consisted of 3 coadditions, each lasting 10 000 ms.

2.3.5. UV–vis Spectroscopy

The UV–vis spectra and optical bandgap were determined using a solid–state UV/vis/NIR spectrophotometer (UV–3600Plus, Shimadzu, Japan).

2.3.6. Photoluminescence Spectroscopy

The measurements were conducted in emission mode with each sample excited at 325 and 450 nm in medium sensitivity mode. The excitation and emission bandwidths were set to 5 nm with a scan speed of 500 nm/min and a data interval of 0.5 nm. All measurements were performed using a FP–8550 spectrofluorometer (JASCO Inc., USA) with sample solutions prepared at 0.1 mg/mL concentration in Milli-Q water. Post-measurement data processing included several spectral corrections: smoothing was applied using the Savitzky–Golay method with a convolution width of 25; baseline adjustments were made, and the spectra were normalized.

Continuous-wave (cw) electron paramagnetic resonance (EPR) measurements were performed to investigate the defect structure and paramagnetic centers in the high-entropy fluorite oxides. Precisely weighed powdered samples of 6.5 mg (CZLPS) and 6.9 mg (CZLPY) were loaded into 250 mm quartz EPR tubes to prevent ambient degradation. The spectra were acquired on a Bruker E500 X-band spectrometer operating at 9.4057 GHz using a Bruker 4122SHQE cylindrical resonator. The measurements were carried out between room temperature and 6 K with a microwave power of 10.17 mW (13 dB attenuation), magnetic field modulation amplitude of 5 G, and receiver gain of 60 dB. The Oxford Instrument ESR900 cryostat coupled to an ITC503 temperature controller ensured a temperature stability of ±0.05 K. Multiple scans were accumulated to improve the signal-to-noise ratio.

Diffuse reflectance infrared Fourier transform spectroscopy experiments were performed using an Agilent Cary 670 FTIR spectrometer equipped with a Harrick Praying Mantis diffuse reflectance accessory and BaF₂ windows. Prior to the measurements, the catalyst samples were subjected to the same pretreatment procedure as that used in the photocatalytic experiments. After pretreatment, the spectra were recorded under a flowing reaction mixture of CO₂/H₂ (1:2), reproducing the conditions applied in the catalytic tests. During the DRIFTS measurements, the samples were simultaneously irradiated with the same light source used in the photocatalytic setup to monitor the surface species under realistic reaction conditions.

2.4. Photocatalytic CO₂ Hydrogenation Experiment

Photocatalytic CO₂ reduction experiments were carried out using a flow microreactor, which comprised an inner quartz cylinder (25 cm in height, 6.4 cm in diameter) and an outer quartz cylinder (25 cm in height, 10.2 cm in diameter). For visible light irradiation, an 11 W LED (OSRAM DULUX D, λ_max ≥ 420 nm) was employed. 250 mg of the synthesized compounds was ultrasonically dispersed in a few milliliters of absolute ethanol and subsequently immobilized on the outer surface of the inner quartz cylinder. The tested catalyst was then pretreated at 523.15 K using a heating rod with the sequential introduction of various gases into the space between the cylinders: argon (Ar) for 20 min to purge the system, oxygen (O₂) for 30 min to oxidize and remove any trace organics or residual carbon, argon (Ar) for 10 min, and hydrogen (H₂) for 60 min, which ensured surface reduction. Following pretreatment, a light source was placed inside the inner quartz tube so that irradiation occurred directly through the catalyst-coated surface.

A gas mixture of CO₂ and H₂ in a 1:2 ratio was introduced into the reactor via a mass flow controller (Aalborg) at a volumetric feed flow rate of 15 mL/min. This reactant gas mixture was recirculated between the reactor and a gas chromatograph (GC) using a pump. The identification and separation of products and reactants were performed with an HP 5890 Series II GC equipped with a packed Porapak QS column (0.635 cm in diameter, 2 m in length). The resulting products were detected using both a thermal conductivity detector or a flame ionization detector. The photocatalytic test reaction flowchart is shown in Figure .

1.

Photocatalytic CO₂ reduction experiment flowchart.

2.5. First-Principles Density Functional Theory (DFT) Simulations

All DFT calculations were performed using Quantum–ATK, and the visualization of the results was conducted using VNL (Version 2019.12). To represent the experimentally prepared HEO compounds, a cubic unit cell of ceria with a space group Fm3̅m and lattice parameter a = 5.467 Å was initially employed, following literature data. Due to the necessity of doping, a 1 × 5 × 1 supercell of CeO₂ was utilized to build models containing dopants. The local density approximation (LDA) and Perdew–Zunger (PZ) have been used as exchange and correlational functionals, respectively, at Fritz–Haber–Institute (FHI) pseudopotentials with a basis set of the double Zeta polarized method. The electronic properties, such as the density of states (DOS), effective potential, electron difference density (EDD), electrostatic difference potential (EDP), and electron localization functional (ELF) are simulated using the same method. The linear combination of atomic orbital (LCAO) method was employed for Ce, Zr, La, Pr, Sm, O, C, and H atoms. A 3 × 3 × 1 Monkhorst–Pack k-grid with an energy cutoff of 75 hartree is used for the slabs.

The CO₂RR mechanistic study was performed using spin-polarized density functional theory (DFT), which is used in the current study. The Perdew–Burke–Ernzerhof (PBE) functional, which is a specific form of generalized gradient approximation (GGA) used to approximate the exchange–correlation energy in DFT, was installed in the Vienna ab initio simulation package (VASP). , A 2 × 2 × 1 k-point mesh and 520 eV energy cutoff were used for structure optimization. The energy and force were converged to 1 × 10^–5 eV and 0.002 eV/Å, respectively. Vacuum thickness in the z-axis was set to 15 Å to eliminate any possibility of interaction between successive periodic images.

3. Results and Discussion

3.1. Structural Characteristics of the Synthesized Compounds

The materials were thoroughly characterized using structural and spectroscopic techniques with a brief overview provided below to support discussion of their role in photocatalytic CO₂ hydrogenation under visible light. The reported physicochemical properties of the materials are presented in the text below and in Table , and they represent three HEOs, CZLPY (Ce_0.2Zr_0.2La_0.2Pr_0.2Y_0.2O_2−δ), CZLPN (Ce_0.2Zr_0.2La_0.2Pr_0.2Nd_0.2O_2−δ), and CZLPS (Ce_0.2Zr_0.2La_0.2Pr_0.2Sm_0.2O_2−δ), one compound with common elements in an equimolar ratio [CZLP (Ce_0.25Zr_0.25La_0.25Pr_0.25O₂)], and one baseline compound (CeO₂) synthesized using a modified sol-gel method. ,

2. Overview of Structural Characteristics for Synthesized Compounds .

Compound	Lattice Parameter a (Å)	Average Microstrain (×10–4)	S BET [m2g–1]	Bandgap [eV]	Surface at. Concentration (%) Ce3+	Surface at. Concentration (%) Pr3+	Surface at. Concentration (%) Oads
Ceria	5.4170 (2)	20.56 (8)	21.5	3.74	n/a	n/a	n/a
CZLPY	5.4350 (2)	67.11 (3)	24.9	2.73	9.9	0.6	33.1
CZLPN	5.4601 (2)	79.53 (2)	27.3	2.65	7.9	0.4	41.6
CZLPS	5.4639 (2)	59.02 (1)	24.2	2.93	9.8	0.6	30.1

Under UV light, the photocatalytic potential of ceria-based high-entropy oxides has been linked to their structural complexity. The starting method for the investigation was powder X-ray diffraction to better understand the crystalline structure and microstructure of these compounds. The respective X-ray diffractograms are presented in Figure S1, while the visualized structure and Rietveld plot of compound CZLPS are shown in Figure a,b, respectively. We found that these compounds crystallized in the cubic Fm3̅m space group.

2.

(a) Visualized fluorite type structure of synthesized HEOs. (b) Rietveld plot of compound CZLPS. (c) Ce 3d spectra of compound CZLPS and (d) Pr 3d spectra of compound CZLPS.

The fluorite-type structure featured an FCC unit cell of cations and tetrahedrally coordinated oxygen anions with five different rare-earth metal cations randomly occupying the 4a site, creating a disordered structure. Interestingly, CZLPY and CZLPS exhibited an average crystal size of 4 nm, while CZLPN was slightly larger at 5 nm. Comparing these high-entropy oxides with pure CeO₂, our study revealed noticeable differences. The successful incorporation of cations into the CeO₂ lattice was evidenced by increased lattice parameters and unit cell volume, while decreasing an average crystallite size. Lattice parameter variations among HEOs were linked to the ionic radii of cations with larger cations causing lattice expansion. Among the studied compounds, CZLPS stood out, exhibiting the largest cell volume and cell parameter a at 163.1 ų and 5.4639 Å, respectively.

Typically, rare-earth oxides commonly crystallize in either fluorite-type (AO₂) or bixbyite-type (A₂O₃) structures, depending on the oxidation state and ionic radius of the constituent cations. CeO₂ represents the classical fluorite structure, where tetravalent cations occupy 8-fold-coordinated sites within a cubic lattice capable of accommodating oxygen vacancy concentrations. In contrast, trivalent rare-earth oxides adopt the cubic bixbyite structure, which can be considered a defect-ordered derivate of the fluorite lattice. In this type of multicomponent system, the presence of tetravalent cations such as Ce⁴⁺ strongly favors stabilization of the fluorite type lattice. In addition, configuration entropy in high-entropy oxides can suppress phase segregation and stabilize single-phase fluorite solid solutions, which has been widely reported for rare-earth high-entropy oxides.

Physisorption measurements, conducted using nitrogen adsorption–desorption isotherms, indicated that all HEOs exhibited type-IV isotherms characteristic of mesoporous materials. The pore diameters ranged from 10.7 nm for CZLPY to 13.2 nm for CZLPN, suggesting similar pore structures among the catalysts. The specific pore volumes varied from 0.06 to 0.09 cm³/g, and the specific surface areas ranged from 21 to 27 m²/g. Among CeO₂, CZLPY, CZLPN, and CZLPS, HEOs had higher values of S _BET compared to pure CeO₂. As synthesized HEOs exhibited color variations with praseodymium-containing compounds appearing in different shades of brown (CZLPY, CZLPN, and CZLPS). Pr-containing HEOs exhibited a shift of absorption edges toward longer wavelengths into the visible region, indicating a narrowing of the optical bandgaps. Normalized UV–vis spectra of each compound compared with that of pure CeO₂ are presented in Figure S2. X-ray photoelectron spectroscopy measurements showed that all three HEOs had similar surface atomic concentrations of Ce³⁺ and Pr³⁺; the only significant difference was in the surface atomic concentration of adsorbed oxygen species (O_ads), where surface O_ads values decreased in the order CZLPN (41.6%) > CZLPY (33.1%) > CZLPS (30.1%). Regarding the photocatalytic CO₂ hydrogenation reaction, under UV light (11 W, λ = 370 nm), compounds CZLPY, CZLPN, and CZLPS showed only moderate enhancement compared with the photocatalytic activity of pure CeO₂, with the improvement of only 1.12, 1.2, and 1.39 times, respectively.

The relative Ce³⁺ and Pr³⁺ ratios were quantitatively determined using the equations presented in the insets of Figure c,d, respectively, where the relative peak areas of the corresponding spectral components were used to calculate the oxidation state distributions. The surface-adsorbed oxygen species (O_ads) were evaluated by calculating the area of the O_ads component within the overall O 1s spectra, as shown in Figure S3b. DFT simulations conducted in our previous study identified zirconium as a catalytically active center in HEO systems, stabilizing CO₂ intermediates and facilitating charge redistribution across the lattice. Additionally, a detailed surface composition analysis using XPS was performed to quantify the relative atomic concentration of Zr across three representative compositions: CZLPN, CZLPS, and CZLPY. The quantified Zr surface content, expressed in atomic weight percentage, was determined to be 3.7% in CZLPN, 4.2% in CZLPS, and 3.6% in CZLPY. These values reveal that CZLPS exhibits the highest surface Zr concentration, while CZLPY contains the lowest among the tested compounds. This gradient in Zr surface abundance directly correlates with the trend in photocatalytic CO₂ reduction performance, where CZLPS consistently outperforms the other compositions in both the CO yield and selectivity. The slightly higher Zr surface exposure in CZLPS may enhance the availability of active sites for CO₂ adsorption and activation, supporting the mechanistic interpretation derived from our DFT models. XPS survey spectra are presented in Figure S3a.

3.2. Electron Microscopy Studies

The morphology and composition of the HEOs were investigated by using SEM (scanning electron microscopy) equipped with EDX (energy dispersive X-ray spectroscopy). The SEM analysis revealed that the HEOs exhibit a distinctive flake-like morphology with noticeable porosity. The higher magnification SEM images provided a clearer view, showing that these flakes are thin nanosheet-like structures. The EDS analysis was employed to evaluate the elemental composition and homogeneity of the HEOs. The results demonstrated a uniform distribution of elements within the high-entropy compounds, ensuring consistent chemical properties throughout the material, while the EDS sum spectrum of the CZLPS compound is presented in Figure S4.

Figure shows SEM images at various magnifications along with corresponding elemental maps for a selected high-entropy compound, i.e., CZLPN, while Figure S5 shows SEM images of other reported compounds. To further confirm the local crystallinity at the nanoscale, HR-TEM was employed (Figure and Figure S5). The HR-TEM images revealed that the nanoparticle sizes of the CZLNS compound were consistent with the data obtained from the Rietveld analysis, which indicated an average crystallite size of 4–5 nm. To further validate the local crystallinity of the synthesized HEO materials at the nanoscale level, HRTEM was employed in combination with selected area electron diffraction (SAED). The inset in Figure i presents the corresponding SAED pattern for the CZLPS sample. This pattern exhibits distinct, continuous Debye–Scherrer rings as an unmistakable signature of polycrystalline nanomaterials composed of randomly oriented nanocrystallites.

3.

SEM images at different magnifications for the CZLPS compound (a, b); SEM image of the location for EDS mapping (c); elemental maps for Ce (d), Zr (e), La (f), Pr (g), and Sm (h); HR-TEM image of the CZLPS compound with the inset showing an indexed SAED pattern (i).

The SAED rings are well-defined and can be indexed to the cubic fluorite-type structure with the Fm3̅m space group, corroborating the phase purity and structural symmetry obtained from XRD analysis. The spatial overlap of diffraction rings in the SAED pattern further supports the assertion of randomly oriented crystalline domains and rules out the presence of a significant amorphous content or phase segregation.

3.3. Spectroscopic Analyses

Raman spectroscopy provides insights into the structural changes and defect formations in ceria-based materials, especially when rare earth elements are introduced into the CeO₂ lattice to form HEOs. In a perfect fluorite structure like CeO₂, the Raman spectrum typically features a prominent band at around 464 cm^–1, corresponding to the F _2g symmetric vibration mode of the Ce–O bond in its 8-fold coordination. This band serves as a standard reference for comparing various ceria-based systems. When elements are incorporated into the CeO₂ lattice, significant alterations occur in the Raman spectrum. A notable shift of approximately 15 cm^–1 is observed in the F _2g band, moving it from 464 cm^–1 to around 449 cm^–1 in the modified systems. This shift is primarily attributed to expansion of the crystal lattice caused by the incorporation of larger ions, which increases the Ce–O bond lengths and disrupts local symmetry. As the lattice expands, the vibrational frequencies decrease, resulting in the observed shift. , Additionally, the F _2g band broadens in the presence of rare earth elements, indicating chemical substitutions that disrupt the lattice uniformity, leading to variations in M–O bond lengths and the formation of defects like oxygen vacancies. Beyond the F _2g band, new peaks appear in the Raman spectra of HEOs around 600 cm^–1, associated with oxygen vacancies, , as visible in Figure S6a. These defect-related peaks provide a qualitative evaluation of the oxygen defect concentration in the material. The ratio of the integral intensity of the defect-related band (II_D) to the F _2g band (II_F2g) serves as an indicator of the relative concentration of oxygen defects in different systems. A higher ratio suggests a greater concentration of these defects, often correlating with improved catalytic activity. Regarding the three HEO compounds, the one with the highest II_D/II_F2g ratio was CZLPN (5.11), while CZLPY and CZLPS had ratios of 4.01 and 3.64, respectively. These findings corroborate the XPS results presented in Table .

A comparative evaluation of the PL (photoluminescence) spectra from both excitation wavelengths reveals several trends in emission behavior, largely influenced by oxygen vacancies, defect states, and intra-4f electronic transitions of rare-earth dopants. Under 325 nm excitation (Figure S6b), two primary emission peaks emerge at 365 and 536 nm. The peak at 365 nm is associated with near-band-edge luminescence, a characteristic of wide-band gap oxides such as CeO₂. This emission is attributed to excitonic recombination or direct interband electronic transitions, a well-documented phenomenon in cerium-based oxides. , The emission at 536 nm arises from defect-driven luminescence, primarily caused by the presence of oxygen vacancies that create localized energy states within the bandgap, facilitating radiative recombination. In contrast, the PL spectra recorded under 450 nm (Figure S6c) excitation exhibit emission peaks at 530.5 and 616 nm. The 530.5 nm peak is strongly linked to oxygen vacancy-related emissions, which introduce defect states that enable sub-bandgap transitions. Meanwhile, the 616 nm peak corresponds to f–f electronic transitions of rare-earth dopants, particularly Pr³⁺ and Sm³⁺, which exhibit photoluminescence in this spectral region due to partially allowed intra-4f transitions. The reference CeO₂ compound exhibits relatively weak PL intensity under both excitation conditions, suggesting a lower density of defect states and a reduced probability of defect-assisted recombination. In contrast, compounds CZLPY, CZLPN, and CZLPS exhibit significantly stronger PL responses under both excitations. This enhancement can be attributed to the introduction of multiple rare-earth dopants, which modify the local crystal field, induce lattice distortions, and promote the formation of oxygen vacancies, all of which facilitate defect-mediated radiative recombination. Further analysis of the role of oxygen vacancies in shaping the PL behavior under both excitation wavelengths confirms their influence on luminescence efficiency and spectral broadening. The longer-wavelength emissions observed in both spectra are characteristics of oxygen vacancy-induced luminescence, which is typical in ceria-based systems. These vacancies introduce intermediate states that alter carrier recombination lifetimes and enable radiative relaxation through deep-level traps. , The variations in PL intensity among CZLPY, CZLPN, and CZLPS under both excitations indicate a dopant selection role when modifying electronic structure due to specific recombination mechanisms. The most intense luminescence is observed in CZLPY, likely due to its specific combination with two transition metals, which enhance charge transfer interactions and increase defect-mediated recombination efficiency.

Variable oxidation states of Pr (3+/4+) facilitate dynamic redox cycling that promotes oxygen vacancy formation through charge compensation mechanisms. These vacancies act as shallow donor states, enhancing visible light absorption and improving charge carrier dynamics. For instance, Guo et al. demonstrated that Pr doping in ceria-based oxides not only enhances oxygen vacancy concentration but also modifies the local electronic structure, enabling the activation of otherwise inert bonds such as C–H and CO, which are central for CO₂ photoreduction catalysis. As revealed by high-resolution XPS, an elevated proportion of Pr³⁺ relative to Pr⁴⁺ in samples such as CZLPS and CZLPY directly correlate with enhanced oxygen vacancy densities. Raman spectroscopy further supported this by showing amplified defect bands in Pr-doped samples, while photoluminescence (PL) spectra under 325 nm excitation revealed defect-related emission attributable to Pr-associated lattice distortion. These findings are consistent with studies in other Pr-doped systems, where increased oxygen vacancies and narrow band gaps due to Pr incorporation have been linked to enhanced photocatalytic degradation and charge separation efficiency. ,

To further elucidate the nature and distribution of oxygen-related defects, continuous-wave (cw) X-band electron paramagnetic resonance (EPR) measurements were performed at 40 K on the CZLPS and CZLPY compounds. As visible from Figure a, both spectra display prominent overlapping resonance structures dominated by two intense signals, marked with * and °, appearing at g = 2.14(1) and 2.08(1), with g factors slightly varying between the two studied samples (Figure S7). The signal at 2.08 shows a slight hyperfine splitting, which remains partially unresolved under X-band experiments, suggesting coupling between Ce and Pr related paramagnetic centers within the lattice. Additionally, a small signal at g = 2.0030 (marked with +) is consistently observed and assigned to surface-associated defect species such as hydroxyl or superoxide radicals associated with the nanoparticle surface defects. While isolated oxygen vacancy signals in pure CeO₂ typically appear close to the free electron value of 2.0023, the vicinity of Ce atoms and associated local distortion significantly increase g-factor values, as frequently observed by literature. , Accordingly, the two dominant signals at 2.14 and 2.08 are assigned to oxygen vacancies located next to Ce atoms in the bulk, while the minor signal at 2.0030 nm is likely to be associated with the nanoparticle surface defects.

4.

(a) X-band cw-EPR spectra recorded at 40 K of CZLPY and CZLPS, showing the dominant resonances at g = 2.14 and 2.08, attributed to oxygen-vacancy centers near Ce atoms, and a weak signal at g = 2.0030, associated with surface defects. (b) Time resolve diffuse reflectance IR spectroscopy of the compound CZLPS.

As shown from Figure S7, Lorentzian deconvolution reveals distinct differences between the two tested compounds. The CZLPS spectrum exhibits broader and slightly asymmetric peaks with an additional weak component at g = 1.91 and 2.20, consistent with deep defect states or aggregated vacancy clusters. The significant broadening and subtle g-value shifts are most likely enhanced by strong spin–orbit coupling from the heavier rare-earth cations and by local field inhomogeneities resulting from the presence of aliovalent cations. ,− In contrast, the CZLPY compound displays sharper and more symmetric signals centered at g = 2.14 and 2.07, accompanied by weaker background components at g = 2.09 and 2.16. The replacement of Sm³⁺ (4f⁵) with diamagnetic Y³⁺ (4d⁰) reduces magnetic interactions and lattice strain, improving spectral resolution. Similar oxygen vacancy features have been observed in Y₂O₃ materials, where O^– and O₂ ^– centers dominate and trapped electron states appear at g = 2.006–2.007. The higher g-values observed in both compounds indicate the presence of Ce³⁺–O_V complexes and ligand field distortions commonly found in Pr doped ceria. ,, These findings perfectly corroborate with XPS, Raman, and PL studies, confirming the existence of stable abundant oxygen vacancies with distinct local distribution. To definitively identify the atomic structure of the paramagnetic centers and their electronic configurations, further DFT calculations would be required, although such an investigation lies beyond the current scope of this work.

Time resolved DRIFTs spectra from Figure b reveal the gradual evolution of surface species during CO₂ adsorption under reaction conditions. The intense band observed at ∼2350 cm^–1 corresponds to the asymmetric stretching vibration of gaseous CO₂ and remains largely constant during the experiment due to continuous gas flow. Changes observed in the OH stretching region (3700–3500 cm^–1) indicate the involvement of surface hydroxyl groups in CO₂ adsorption and activation, which typically interacts with adsorbed CO₂ to form hydrogen bonded intermediates and bicarbonate species. These surface hydroxyl groups are closely associated with the acid–base properties of oxide catalysts, where metal cations act as Lewis acid sites and lattice oxygen or hydroxyl groups serve as basic sites. Such acid–base pairs facilitate the adsorption and polarization of CO₂ molecules, promoting the formation of carbonate, bicarbonate, and formate intermediates on the surface of the catalyst. In addition, surface hydroxyl species can participate in hydrogen transfer processes during CO₂ hydrogenation. A broader band within 1700–1200 cm^–1 is associated with O–C–O stretching vibrations of surface carbonates, bicarbonates, carboxylates, and formate species formed during CO₂ adsorption and activation on the surface. Surface formate intermediates, as key species in CO₂ hydrogenation pathways, are identified by asymmetric and symmetric O–C–O stretching vibrations located in the 1600–1300 cm^–1 region, while the associated C–H stretching vibrations of formate species appears in the 2900–2800 cm^–1 region, which indicates that CO₂ adsorption proceeds through carbonate-derived intermediates that subsequently transform into formate species prior to product formation. Additional weak features observed in the 1100–1000 cm^–1 region can be assigned to C–O stretching modes associated with alkoxide or methoxy-type intermediates, which may form during the hydrogenation of surface carbon species.

3.4. Photocatalytic CO₂ Hydrogenation Experiment

In this study, synthesized ceria-based HEOs were evaluated for their performance in the visible light-driven photoreduction of CO₂. The results, detailed in Table and illustrated in Figure , indicate the various factors contributing to the enhanced rate of CO production observed in these HEOs. Notably, the presence of lattice defects, such as oxygen vacancies, serves as active sites for the photoreduction process. Additionally, the incorporation of five different cations in the HEO structure enhances activity through a synergistic (cocktail) effect, , while a favorable electronic structure, resulting from the defective nature of HEOs, supports the conversion reactions of CO₂.

3. Overview of the Results of Photocatalytic CO₂ Hydrogenation for Different Synthesized Compounds.

		Selectivity (%)			STYi (molikgcat –1h–1)
Compound	Conversion (%)	CO	CH4	CH3OH	CO	CH4	CH3OH
CeO2	1.4	100			0.74
CZLP	14.5	95.5	4.5		7.35	0.34
CZLPY	13.4	95.2	4.8		6.81	0.34
CZLPN	17.5	97.7	2.0	0.3	9.07	0.18	0.03
CZLPS	20.3	94.3	5.3	0.4	10.15	0.57	0.05

5.

(a) Photocatalytic conversion of CO₂ under visible light. (b) Comparison of conversions at final time interval. (c) Selectivity of the catalysts toward reaction products. (d) Methanol yield. (e) Methane yield. (f) CO yield.

The results presented in Table confirm that the incorporation of a fifth cation significantly improves the photocatalytic performance of the HEOs. The tested five-element compounds showed higher CO production rates compared with the four-element counterparts. The conversion of CO₂ to products was monitored over a 10-interval period with each interval lasting 21 min, followed by an additional 4 min for the gas chromatograph to reach a ready state for further experiments. For the best performing compound (CZLPS), additional experiments were performed to confirm the reproducibility of the catalytic performance. The standard deviation was calculated and reported in Figure S8. Product selectivity remained consistent across all of the measurements. As expected, pure CeO₂ demonstrated the lowest conversion rate, achieving only 1.4%. In contrast, HEO compounds CZLPY, CZLPN, and CZLPS exhibited significantly higher conversion rates of 13.4%, 17.5%, and 20.3%, respectively. Interestingly, the four-element compound (CZLP) achieved a conversion rate of 14.5%, which is slightly higher than that of CZLPY.

In general, the HEOs demonstrated remarkable photocatalytic activity with CZLPS showing activity nearly 15 times higher than that of pure CeO₂. While pure CeO₂ is typically an effective photocatalyst for UV light-driven reactions due to its wider bandgap, its efficiency in visible light-driven reactions is significantly enhanced when transformed into a high-entropy form through the incorporation of additional elements and alteration of its physical properties, including bandgap narrowing. These enhancements, which make HEOs highly efficient for visible light-driven photocatalytic reactions, are presented in Figure b. The selectivity of HEOs was also investigated across each time interval with the final interval’s selectivity results depicted in Figure c.

As expected, similar to UV-light driven photocatalytic CO₂ hydrogenation, pure CeO₂ exhibited 100% selectivity toward CO throughout all time intervals of the reaction. The compounds CZLP and CZLPY showed almost identical selectivity toward CO at 95.5% and 95.2%, respectively, with minor selectivity toward CH₄ (4.5% for CZLP and 4.8% for CZLPY). There was no selectivity toward methanol at any stage of the reaction, indicating that Y in the HEOs does not significantly alter the selectivity toward different products in the visible region. In contrast, the CZLPS and CZLPN compounds not only exhibited better conversion rates but also demonstrated a slightly better selectivity toward methane and methanol. For CZLPN, the selectivity toward CO, CH₄, and CH₃OH was 97.7%, 2.0%, and 0.3%, respectively. On the other hand, CZLPS showed a selectivity of 94.3% toward CO, 5.3% toward CH₄, and 0.4% toward CH₃OH. These results suggest that CZLPS exhibits slightly better catalytic behavior with a notable ability to produce other products alongside CO, making it more versatile.

In general, CZLPY showed decreased photocatalytic activity compared to CZLPN, CZLPS, and CZLP. The addition of Sm and Nd into the ceria lattice results in HEOs with significantly enhanced photocatalytic activity and altered product selectivity. Both Sm and Nd are rare-earth elements with ionic radii similar to that of Ce, which allows them to integrate into the ceria lattice without severely disrupting the crystal structure. The slight selectivity toward CH₄ and CH₃OH observed in CZLPS and CZLPN suggests that these elements create new active sites or modify the surface energy of the catalyst in a way that favors the generation of these products. To evaluate the overall catalytic activity of the various compounds, the space-time yield (STY) was calculated (Figure d–f and Table ). Among the tested HEOs, the CZLPS compound demonstrated a superior catalytic activity. For comparison, pure CeO₂ exhibited a STY toward CO of 0.74 mol_CO kg_cat ^–1 h^–1. In contrast, CZLPS achieved a remarkable CO STY of 10.15 mol_CO kg_cat ^–1 h^–1, alongside a STY of 0.57 mol_CH4 kg_cat ^–1 h^–1 and 0.05 mol_CH3OH kg_cat ^–1 h^–1.

One of the reliable factors for catalytic performance is the lattice parameter of the HEOs. CZLPS, with a lattice parameter of 5.4639 Å, has the largest and most expanded crystal structure among the tested compounds. This expansion possibly facilitated greater mobility of the charge carriers, which is essential for efficient photocatalysis. Additionally, CZLPS exhibits the lowest average microstrain (59.02 × 10^–4), indicating a more relaxed and less distorted crystal lattice. Lower microstrain reduces the possibility of defects to act as charge recombination centers, followed by improvement of the overall photocatalytic activity, a phenomenon similarly reported in defect-engineered multicomponent ceramics where relaxed lattices improved carrier transport. In contrast, CZLPY, with a lattice parameter of 5.4350 Å and a higher microstrain of 67.11 × 10^–4, may have more structural defects, leading to increased recombination of photogenerated electron–hole pairs and consequently a lower catalytic efficiency. Additionally, CZLPS has the widest bandgap at 2.93 eV among tested HEOs, which could be beneficial for absorbing a broader spectrum of visible light. The relative % (surface atomic concentration in %, normalized to 100%) of Ce³⁺, Pr³⁺, and adsorbed oxygen species significantly influence the redox activity and catalytic performance, aligning with reports on redox-active dopants enhancing oxygen vacancy concentrations and catalytic activity in multicomponent oxides. CZLPS has a higher surface atomic concentration of Ce³⁺ (7.4%) and Pr³⁺ (0.6%), similar to CZLPY, but with slightly lower O_ads (30.1%) compared to that of CZLPY (33.1%). The higher Ce³⁺ and Pr³⁺ content in CZLPS indicates more defects, which are active sites for CO₂ reduction. Although CZLPN has the highest oxidation ratio of O_ads, the lower Ce³⁺ content and higher microstrain suggest that these oxygen species are not as effectively utilized in the photocatalytic process, contributing to its slightly lower photocatalytic activity. The CO₂ conversion rates reflect these structural and electronic differences. CZLPS achieves the highest conversion rate of 20.3%, followed by CZLPN with 17.5% and CZLPY with 13.4%. The superior performance of CZLPS can be attributed to its favorable combination of a larger lattice parameter, lower microstrain, and optimized electronic structure, which together facilitate efficient light absorption, charge separation, etc., consistent with recent insights into the role of lattice expansion and entropy-driven defect chemistry in rare-earth high-entropy catalysts for CO₂ reduction. The slightly lower O_ads in CZLPS may favor the desorption of CO, reducing the possibility of CO poisoning of active sites and allowing other products like CH₄ and CH₃OH to form. In contrast, CZLPY’s higher O_ads may lead to stronger CO binding, hindering its desorption and limiting the formation of other products, thus reducing overall catalytic activity. DFT simulations from previous work further support these observations. CZLPY was found to have the highest affinity for CO₂ adsorption, which, while beneficial for initiating the reaction, may also lead to slower CO desorption, thereby reducing the overall turnover rate. On the other hand, CZLPS exhibits the highest CO desorption efficiency, suggesting that once CO₂ is reduced to CO, it quickly leaves the active site, allowing for continuous reaction cycles and higher overall activity.

The superior CO production observed in the CZLPS can also be attributed to the structural and electronic modifications introduced by Sm incorporation. As evidenced by our XPS O 1s analysis (Table and Figure S3b), CZLPS exhibits a significant proportion of surface-adsorbed oxygen species (O_ads = 30.1%). The generation of such vacancies is facilitated by the multivalent nature of Sm (3+/2+), along with the multivalent nature of Ce and Pr, which has been previously shown to induce defect states within oxide matrices through charge compensation mechanisms. These defect-rich regions have an influence on modulating charge dynamics by acting as electron traps, thereby prolonging carrier lifetimes and suppressing recombination. This was additionally confirmed through PL spectra, where Sm-containing compositions demonstrated enhanced emission intensity in the defect-related region (∼500–600 nm), indicative of increased trap-state density and sub-bandgap transitions. The narrowing of the bandgap in CZLPS (2.93 eV), close to the near UV region in comparison with other tested compounds, additionally suggests that Sm contributes to electronic band restructuring, improving visible light absorption and photocatalytic efficiency. These observations are consistent with literature reports showing that Sm doping in ceria-based materials leads to lattice distortion and increased oxygen mobility, which synergistically enhance surface redox behavior and photocatalytic activity. ,

In previously reported literature, compound CZLNS (Ce_0.2Zr_0.2La_0.2Nd_0.2Sm_0.2O₂) achieved CO and CH₃OH production rates of 14.4 mmol g^–1 h^–1 and 1.27 mmol g^–1 h^–1, respectively, with CO selectivity of 89.26% under ambient pressure and UV light conditions. In comparison, the synthesis of TiZrHfNbTaO₁₁, which required postsynthesis laser fragmentation to achieve CO production <10 μmol g^–1 h^–1, is reported with increased surface area. Other visible-light-driven systems like spinel-type (Ga_0.2Cr_0.2Mn_0.2Ni_0.2Zn_0.2)₃O₄ HEOs reported CO rates of 12.4 μmol g^–1 h^–1. Zirconia-based photocatalysts modified with transition metals have also demonstrated efficient CO₂ photoreduction to methane and CO due to improved charge transfer and surface area. Noble-metal-free FeCoNiCuMn HEA nanoparticles immobilized on TiO₂ showed CO production up to 235.2 μmol g^–1 h^–1, while requiring hybrid support systems. Additionally, commercial photocatalyst P25 TiO₂ and TiZrNbHfTaO11 HEOs tested under UV irradiation delivered 4.63–4.64 μmol g^–1 h^–1 CO. It is important to note, however, that direct comparison of photocatalytic activity across the literature is inherently difficult due to inconsistencies in experimental setups, including differences in reactor design, light sources, irradiation intensities, CO₂ partial pressures, and catalyst loadings.

3.5. First-Principles Density Functional Theory Simulations

In order to convert CO₂ into formic acid (HCOOH) and CO, a straightforward process involves two interconnected steps facilitated by protons and electrons:

CO₂RR to HCOOH:

$$\ast +\mathrm{C}{\mathrm{O}}_{2(g)}+2({\mathrm{H}}^{+}+{\mathrm{e}}^{-})\to \mathrm{H}\mathrm{C}\mathrm{O}{\mathrm{O}}^{\ast }+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}$$ 1

$$\mathrm{H}\mathrm{C}\mathrm{O}{\mathrm{O}}^{\ast }+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to \mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}{\mathrm{H}}^{\ast }$$ 2

$$\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}{\mathrm{H}}^{\ast }\to \mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}{\mathrm{H}}_{(\mathrm{l})}+\ast$$ 3

CO₂RR to CO:

$$\ast +\mathrm{C}{\mathrm{O}}_{2(\mathrm{g})}+2({\mathrm{H}}^{+}+{\mathrm{e}}^{-})\to {}^{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}$$ 4

$${}^{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-}\to {}^{*}\mathrm{C}\mathrm{O}+{\mathrm{H}}_2{\mathbf{O}}_{(\mathrm{l})}$$ 5

$${}^{*}\mathrm{C}\mathrm{O}\to \mathbf{C}{\mathbf{O}}_{(\mathrm{g})}+\ast$$ 6

The active sites are denoted by the asterisk symbol (*), and (l) and (g) signify the liquid and gas phase. The adsorbed intermediates are depicted by HCOOH*, HCOO*, and *CO. To convert the energy calculated by DFT into free energy, the adsorbates are adjusted to account for zero-point energy, entropy, and enthalpy. The Gibbs free energy (G) at zero voltage is determined by utilizing the electronic energy obtained from DFT optimization (E _DFT) along with contributions from zero-point vibrational energy (E _ZPE), entropy (TS), and heat capacity at room temperature (∫C _p dT), as described by eq .

$$\mathrm{G}=E_{\mathrm{D}\mathrm{F}\mathrm{T}}+E_{\mathrm{Z}\mathrm{P}\mathrm{E}}-\mathrm{T}\mathrm{S}$$ 7

The obtained simulation parameters for the involved gas molecules are depicted in Table S1. The computation of the Gibbs free energy for the proton–electron reaction step is performed using the computational hydrogen electrode (CHE) method. This approach involves calculating the free energy of a proton–electron pair (H⁺ + e^–) as a function of the applied potential relative to a reversible hydrogen electrode (U vs RHE), , i.e., μ­(H⁺) + μ­(e^–) = (1/2)­μ­(H₂) – eU. The calculation of adsorption free energies for HCOO*, HCOOH*, *COOH, and *CO at a specific potential U _RHE can be expressed as follows:

$$\mathrm{\Delta }{G}_1({\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}}^{*})=G({\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}}^{*})-G(*)-G({\mathrm{C}\mathrm{O}}_{2(\mathrm{g})})-\frac{\mathbf{1}}{\mathbf{2}}\mathit{G}({\mathbf{H}}_{\mathbf{2}})-{\mathrm{e}U}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$ 8

$$\mathrm{\Delta }{G}_2({\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}}^{*})=G({\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}}^{*})-G({\mathrm{H}\mathrm{C}\mathrm{O}\mathrm{O}}^{*})-\frac{\mathbf{1}}{\mathbf{2}}\mathit{G}({\mathbf{H}}_{\mathbf{2}})-{\mathrm{e}U}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$ 9

$$\mathrm{\Delta }{G}_3({}^{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H})=G({}^{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H})-G(*)-G({\mathrm{C}\mathrm{O}}_{2(\mathrm{g})})-\frac{\mathbf{1}}{\mathbf{2}}\mathit{G}({\mathbf{H}}_{\mathbf{2}})-{\mathrm{e}U}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$ 10

$$\mathrm{\Delta }{G}_4({}^{*}\mathrm{C}\mathrm{O})=G({}^{*}\mathrm{C}\mathrm{O})-G({}^{*}\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H})+G({\mathrm{H}}_2{\mathrm{O}}_{(1)})-\frac{\mathbf{l}}{\mathbf{2}}\mathbf{G}({\mathbf{H}}_{\mathbf{2}})-{\mathrm{e}U}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$ 11

The DFT optimized bulk structure of CZLPS is cleaved at different directions, and it is found that the surface along (001) is highly stable. In order to find the best catalytic active site, five CO₂ and CO molecules at five different positions are adsorbed as shown in Figures and , respectively. Five CO₂ and CO molecules were added to the slab of CZLPS due to the availability of five different types of atoms. The interactions between the CO₂/CO molecule and catalyst surface are simulated using eq .

$$\mathrm{\Delta }{\mathit{E}}_{\mathrm{ad}}={\mathit{E}}_{\mathrm{surface}@\mathrm{analyte}}-({\mathit{E}}_{\mathrm{analyte}}+{\mathit{E}}_{\mathrm{surface}})$$ 12

where E _{surface@analyte} represents the adsorption energy of the intermediate species; E _surface signifies the DFT energy of the slab without any adsorbate; E _analyte stands for the DFT energies of the molecular gas-phase references (CO₂ or CO).

6.

Optimized geometric structures of CO₂ adsorption on CZLPS. (a) The pristine CZLPS surface; (b–f) the relaxed adsorption configurations with CO₂ interacting at the surface of Ce (b), Zr (c), Pr (d), La (e), and Sm (f), respectively.

7.

Optimized geometric structures of CO adsorption on CZLPS. (a) The pristine CZLPS surface; (b–f) the relaxed adsorption configurations with CO interacting at the surface of Ce (b), Zr (c), Pr (d), La (e), and Sm (f), respectively.

Based on the interaction energy of CO₂ with the surface of the catalyst, it is found that the Zr site of CZLPS is the most effective catalytic site for CO₂RR reduction compared to other atoms. The interaction energies of CO₂ and CO molecules with CZLPS are −2.25 eV and −2.23 eV, respectively, as shown in Figure a,b. Before simulating the thermodynamic CO₂RR process, we also simulated the DOS, ELF, effective potential, and electrostatic difference potential (EDP) of all intermediates. The binding strength of these intermediates can be inferred from comparing the density of states (DOS) of the active Zr site to adsorbates (Figure c). As seen in Figure c, after the CORR intermediate interacts with CZLPS, additional peaks near the Fermi level and the conduction band site in the DOS are observed compared with the pristine catalyst. These peaks correspond to the lowest filling of anti-bonding states, resulting in stronger adsorbate binding energies. As a result, the reduction of CO₂ to CO was the most energetically favorable.

8.

(a) Interaction energies for a single CO₂ at five surface sites (Ce, Zr, La, Pr, and Sm) on CZLPS with the strongest binding at Zr. (b) Interaction energies for a single CO at the same sites with the strongest binding at Ce. (c) Total DOS for pristine and adsorbate-covered surfaces (CO₂, CO, COOH, HCOO, and HCOOH) with the Fermi level set to zero. (d) ELF contour maps for pristine and representative adsorbates. (e) Effective potential V _eff along the c-axis for pristine and adsorbate-covered surfaces. (f) Potential change (ΔV) along the b-axis for pristine and adsorbate-covered surfaces.

The 2D ELF plots of the six species (pristine CZLPS and −CO₂, −HCOOH, −COOH, −HCOOH, and −CO interacting with CZLPS) are shown in Figure d. From the ELF map, we can analyze that all these intermediates have good interactions with the catalyst surface. However, the CO₂ molecule has an excellently shared electronic cloud density with the surface of the catalyst. Comparative analysis of Figure d led us to predict that the Zr site is very active and can easily reduce the level of CO₂.

The strong interaction between the CO₂RR and the surface of CZLPS is also evident from the 2D effective potential map near the 12 to 20 Å range (Figure e), where the pristine CZLPS is compared with the CO₂RR intermediates. Additionally, we calculated the electrostatic difference potential (EDP) of pristine CZLPS with and without the CO₂RR intermediates’ interactions, as shown in Figure f. The ELF, effective potential, and EDP of the pure CZLPS catalyst and CO₂RR intermediates attached to CZLPS clearly reveal electron transfer from the catalyst surface (Zr site) to the CO₂RR intermediates. Notably, the CZLPS@CO₂ interaction is more prominent compared to other species, as seen in Figure f of ESDP. Comparative analysis of Figure predicts that electrons are donated from the catalyst (CZLPS) to the CO₂RR intermediates.

Having confirmed that the Zr site of CZLPS is the most active site, we conducted a systematic investigation into the thermodynamic process of CO₂ electroreduction to understand the mechanistic details of the electrocatalytic performance of CZLPS. This involved computing the Gibbs free energy changes (ΔG) for the individual steps along the reaction pathways leading to the formation of carbon monoxide (CO) and formic acid (HCOOH); the results are summarized in Table S2. According to eqs –, the initial protonation of CO₂ leads to the formation of either *COOH or HCOO*, which can be further protonated to *CO or *HCOOH, respectively. Subsequently, *CO and *HCOOH can detach from the catalyst surface as CO and HCOOH products. The complete reaction pathways of CO₂ electroreduction at 0 V vs RHE, along with the optimized structures of products at each step, are depicted in Figure .

9.

CO₂ reduction reaction pathway along with optimized structures at zero potential on CZLPS.

It illustrates the ΔG values for the CO₂RR reaction pathway at U = 0 V vs RHE on CZLPS. The process involves the transfer of an electron and a proton, initiating CO₂ activation on the surface of CZLPS. Depending on the sequence of intermediate formation, this leads to the creation of either a bound carboxylate intermediate (*COOH) via a carbon atom or a bound formate intermediate (HCOO*) through two oxygen atoms. These intermediates, HCOO* and *COOH, play pivotal roles in the generation of liquid formic acid (HCOOH) and gaseous carbon monoxide (CO). −

The ΔG value for HCOO* production on CZLPS in the HCOOH pathway is 0.31 eV. This significant barrier can be attributed to the inherent stability of CO₂, owing to its electrophilic carbon center and linear molecular structure. As a result, an overpotential of 0.31 V is necessary for the CO₂RR to produce CO. Similarly, in the CO pathway, the ΔG for *COOH formation is 0.17 eV, requiring an overpotential of 0.17 V vs RHE at U = 0 V.

In the CO₂RR, the final products CO and HCOOH are governed by intermediate steps (*COOH and HCOO*). A proficient catalyst enhances the stability of *COOH and HCOO* more effectively than that of *CO and *HCOOH, as highlighted in previous literature. , Our calculations indicate that CZLPS exhibits stronger binding with COOH and HCOO compared to that with CO and HCOOH. Consequently, the CO pathway is more favorable due to its lower energy barrier compared to the HCOOH route.

Recent theoretical and experimental work in the literature strongly supports the conclusion that Zr sites in Ce–Zr-based oxides are likely the primary active centers for CO₂ adsorption, activation, and hydrogenation. ZrO₂ has been shown to act not only as a support or promoter but also as an active species in CO₂ hydrogenation. Li and Chen demonstrate that the weakly hydrophilic character of zirconia combined with its ability to form oxygen vacancies and facilitate electron transfer enable lower activation barriers and stronger CO₂ adsorption. Mixed ceria-zirconia oxides are also widely reported to possess superior oxygen storage capacity, enhanced reducibility, and improved vacancy formation energy compared with pure ceria. These features help stabilize CO₂-derived intermediates and sustain redox cycling. For instance, Biswas et al. show that Fe/Ce _x Zr_1–x O₂ supports outperform Fe/ZrO₂ or Fe/CeO₂ in terms of CO₂ conversion and stability. Theoretical studies of ZnO–ZrO₂ solid solutions also illustrate that dual active sites involving Zr, combined with favorable oxygen vacancy behavior, reduce energy barriers for CO₂/H₂ activation steps. From an electronic and structural standpoint, Zr atoms in mixed oxide lattices tend to lower the oxygen vacancy formation energy, bind oxygen less strongly in some lattice positions, and facilitate charge density redistribution upon CO₂ or CO adsorption.

The DFT adsorption and activation energy data presented in this paper indeed show that, among Ce, Pr, Zr, and other possible surface centers, the Zr-centered site in compound CZLPS yields the most favorable adsorption energy and electron donation, consistent with the literature results. Taken together, the literature and our theoretical modeling provide a mechanistic picture in which Zr sites serve as the key adsorption/activation centers for CO₂, while Ce and Pr contribute by enabling redox processes, stabilizing oxygen vacancies, and modulating electron transfer.

3.6. Photocatalytic Mechanism

The photocatalytic CO₂ hydrogenation mechanism in ceria-based HEOs is dictated by photoinduced charge carrier generation, CO₂ adsorption and activation, and subsequent hydrogenation steps, which determine the product selectivity between CO and CH₄. The reaction efficiency is linked to the electronic structure of the catalyst, as characterized by XPS-derived valence band maxima (VBM), conduction band minima (CBM) calculations, in situ spectroscopic data from a compositionally similar material, in situ DRIFTs under experiment conditions for the compound CZLPS, DFT modeling, and photocatalytic performance results. The process initiates photon absorption and charge carrier excitation, wherein exposure to UV or visible light promotes electrons (e^–) from the valence band (VB) to the conduction band (CB), leaving behind holes (h⁺) in the VB. The XPS-derived VBM values for CZLPY, CZLPS, and CZLPN are 1.79, 0.70, and 0.56 eV, respectively, obtained by linearly extrapolating the low binding energy edge intersecting with the XPS background and depicted in Figure S9. The corresponding CBM positions were calculated as −0.94 eV, −2.23 eV, and −2.09 eV, respectively, according to the optical bandgap. These band edge positions define the thermodynamic feasibility of CO₂ reduction, as only materials with CBM values more negative than the CO₂ reduction potential can efficiently drive CO₂ hydrogenation reactions. , Notably, the standard reduction potential for CO₂ to CO, CO₂ to CH₄, and CO₂ to HCOOH was discussed in depth by Fang and Hu over different temperatures and pressures, and at normal pressure and room temperature, the reduction potentials for reactions CO₂ to CO and CH₃OH and H₂O to O₂ are −0.52, −0.38, and 0.82 eV, respectively, vs NHE.

These findings confirm that all three materials possess the necessary reduction potential for CO₂ conversion, but their selectivity is influenced by charge transport, active site availability, and surface adsorption characteristics. Upon charge carrier generation, the photoexcited electrons migrate to catalytically active sites, particularly oxygen vacancies and Zr-rich domains, where CO₂ molecules are adsorbed and activated. , DFT calculations confirm that Zr sites serve as electron-accumulating centers, effectively lowering the activation energy required for the hydrogenation of CO₂ hydrogenation.

Oxygen vacancies stabilize the adsorbed CO₂ ^δ− species, thereby reducing charge recombination and improving the catalytic performance. Gibbs free energy calculations from DFT modeling indicate that CO₂ hydrogenation follows a stepwise mechanism in which CO₂ initially binds to oxygen vacancies to form a bent CO₂ ^δ− species, a key intermediate for subsequent hydrogenation steps. The reaction proceeds through sequential electron and proton transfers, ultimately leading to either CO formation via the reverse water–gas shift (RWGS) pathway or CH₄ formation via full hydrogenation through formate intermediates. In situ DRIFTS analysis from a compositionally similar system (CZLNS) provides spectroscopic confirmation of the reaction intermediates involved in CO₂ hydrogenation. The detection of adsorbed formate and carboxyl species confirms that CO₂ hydrogenation occurs predominantly via a formate-mediated pathway. Additionally, the presence of CO bands in the 2050–2200 cm^–1 range further supports CO as an intermediate in the RWGS mechanism. The emergence of CH₂O (1720 cm^–1) and CH₄ (near 3000 cm^–1) signals in the DRIFTS spectra strongly suggests that methanation proceeds through the progressive hydrogenation of surface-bound carbon intermediates. Regarding photocatalytic application results, all three HEOs predominantly produce CO, aligning with the RWGS pathway, in which CO₂ undergoes a single-step hydrogenation to CO, which desorbs before further hydrogenation. This behavior is attributed to faster electron transfer kinetics, which favors CO desorption over full hydrogenation.

In contrast, CZLPS exhibits slightly higher CH₄ selectivity, indicating that formate-mediated hydrogenation is more efficient, likely due to a higher density of hydrogenation-active sites and superior charge separation dynamics. The overall mechanism can be divided into three fundamental stages: (i) charge generation and separation, (ii) CO₂ activation and surface intermediate formation, and (iii) product selectivity dictated by competing reaction pathways. In the first stage, light absorption generates electron–hole pairs with charge separation efficiency dictated by oxygen vacancy concentrations and cationic doping-induced disorder. The second stage involves DFT-predicted CO₂ adsorption and activation, where Zr sites and oxygen vacancies serve as the primary catalytic centers. In addition to oxygen vacancies, surface hydroxyl groups and acid–base surface sites have important roles in CO₂ activation on ceria-based oxides. The basic surface atoms and hydroxyl groups facilitate adsorption of CO₂ molecules and promote the formation of bicarbonate and carbonate intermediates. Subsequently, dissociated hydrogen species interact with these surface intermediates, enabling the formation of formate species that act as key intermediates in the reaction pathway. The third stage, as confirmed by photocatalytic activity data, follows either the RWGS reaction or full hydrogenation with the selectivity determined by surface reaction kinetics and active site distribution. The RWGS pathway dominates where rapid charge transport and weaker hydrogenation kinetics favor the CO formation. The proposed mechanism of photocatalytic CO₂ hydrogenation is shown in Figure .

10.

Conduction band and valence band positions of the studied photocatalysts and the redox potentials for CO₂ reduction.

4. Conclusions

This study demonstrates that ceria-based high-entropy oxides are promising photocatalysts for CO₂ hydrogenation under visible light. The combination of high configurational entropy, multielement synergy, and defect engineering enhances catalytic performance, as compared to pure CeO₂. Among the synthesized HEOs, CZLPS demonstrated the highest photocatalytic activity, achieving a CO₂ conversion rate of 20.3%, with high selectivity toward CO. Structural and spectroscopic analyses indicate that Pr^3+/4+ redox pairs and abundant oxygen vacancies are responsible for improving charge separation and suppressing electron–hole recombination. The space-time yield values reinforce this trend, with CZLPS achieving 10.15 mol_COkg^–1h^–1, outperforming CZLPN (9.07 mol_COkg^–1h^–1) and CZLPY (6.81 mol_COkg^–1h^–1). Our computational study demonstrates that the Zr site on CZLPS displays exceptional catalytic activity for CO₂ reduction, as evidenced by lower Gibbs free energy values compared with other atoms on the surface. These findings highlight CZLPS as a promising catalyst for the efficient electrochemical conversion of CO₂ to CO with significant implications for sustainable energy applications.

The photocatalytic mechanism was thoroughly investigated using DFT simulations and experimental spectroscopic analyses, revealing that CO₂ adsorption, charge transfer, and product formation are strongly influenced by the structural and electronic properties of CZLPS. This confirmed that its band edge positions align well with the thermodynamic requirements for CO₂ hydrogenation.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/prechem.5c00456.

• XRD patterns of HEO catalysts; UV–vis absorbance spectra; XPS survey spectra and fitted O 1s spectra; EDS spectrum; SEM and HR-TEM images; Raman, photoluminescence, and EPR spectra; reproducibility test of CO₂ conversion; DFT calculation parameters and thermodynamic data for gas molecules and reaction intermediates; XPS valence band spectra (PDF)

Conceptualization: D.T., H.U., M.Y.; Data curation: T.S., J.P., K.D.; Formal analysis: D.T., M.Y., J.K., S.Š., C.B.P., A.P., M.F.; Funding acquisition: A.S., Z.K., A.K.; Investigation: D.T., M.Y., H.U., S.A., J.K.; Methodology: D.T., M.Y., S., D.A. S.Z., A.S., I.D.; Project administration: S.Z., A.S., A.K., Z.K., I.D.

The project is funded by the European Union – Next Generation EU under the number 581-UNIOS-105. However, the views and opinions expressed are solely those of the author(s) and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

The authors declare no competing financial interest.

Published as part of Precision Chemistry special issue “Precision Chemistry for High Entropy Nanomaterials”.