Comprehensive DFT analysis of BeHfO3 perovskite: Exploring the structure, mechanical, thermodynamic, and optic properties European Journal of Chemistry 16 (3) (2025) 292-301 European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2025 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. https://dx.doi.org/10.5155/eurjchem.16.3.292-301.2675 European Journal of Chemistry View Journal Online View Article Online Comprehensive DFT analysis of BeHfO3 perovskite: Exploring the structure, mechanical, thermodynamic, and optic properties Md Al Masud 1, Md. Rajib Munshi 2,*, Tanvir Chowdhury 3, Mita Chakraborty 2 and Rakibul Islam 4 1 Department of Industrial and Production Engineering, Faculty of Science and Engineering, European University of Bangladesh, Dhaka-1216, Bangladesh 2 Department of Physics, Faculty of Science and Engineering, European University of Bangladesh, Dhaka-1216, Bangladesh 3 Department of Applied Physics and Electronics, Faculty of Science and Engineering, Jahangirnagar University, Savar, Dhaka -1342, Bangladesh 4 Department of Controller of Examinations, European University of Bangladesh, Dhaka-1216, Bangladesh * Corresponding author at: Department of Physics, Faculty of Science and Engineering, European University of Bangladesh, Dhaka-1216, Bangladesh. e-mail: razibmunshi@eub.edu.bd (M.R. Munshi). 10.5155/eurjchem.16.3.292-301.2675 Received: 24 February 2025 Received in revised form: 1 June 2025 Accepted: 29 June 2025 Published online: 30 September 2025 Printed: 30 September 2025 We performed a thorough study of the electronic, mechanical, thermodynamic, and optical properties of the BeHfO3 perovskite crystal using first-principles calculations featuring density functional theory (DFT). Electronic band structure analysis manifested the material to be semiconducting in nature with calculated band gap values of 0.873 eV (PBE), 0.887 eV (RPBE), 0.781 eV (PBEsol), 0.890 eV (LDA), 1.71 eV (HSE06) and 2.925 eV (B3LYP), reflecting considerable uncertainty in terms of exchange-correlation functionals and emphasizing the utility of hybrid functionals in estimating the band gap. Density of states (DOS) and partial density of states (PDOS) analyses were vital in revealing the role of the participating atoms (Be, Hf, and O) in electronic contribution, orbital hybridization, and the major states close to the Fermi level, highlighting the dominant states near the Fermi level and the role played by them in bonding. The Mulliken population analysis also described the electrostatic interaction and charge reorganization, confirming the mixed ionic-covalent nature of the bonds and revealing the complexity in the nature of bonds in the BeHfO3 lattice. Mechanical stability was thoroughly analyzed using the Born mechanical stability criteria (BMS) which validated the mechanical stability of the compound. The calculation of the elastic constants helped to establish Poisson’s ratio and Pugh’s modulus ratio (B/G) to confirm the mechanical strength and ductility of the compound along with the pronounced anisotropy in the elastic properties, which could be valuable in applications requiring directional devices. The calculation of the optical properties in terms of the frequency- dependent dielectric functions and the absorption coefficients using different DFT approaches proved the material to be a powerful absorber in both the ultraviolet (UV) and visible parts of the spectrum, which establishes the material as a valuable contender in the field of optoelectronic and photocatalytic technology. Elastic Optical Structural Electronic Absorption Photocatalyst Cite this: Eur. J. Chem. 2025, 16(3), 292-301 Journal website: www.eurjchem.com 1. Introduction The investigation and identification of semiconductor materials with innovative and unexplored characteristics have been propelled by the growing necessity to commercialize breakthrough technology. Numerous materials that had been neglected until recently after discovery are now receiving renewed attention due to their potential practical uses [1,2]. Oxide-based compounds have a broad range of characteristics and are promising for several technical applications, including refractory ceramics, superconductors, ferroelectrics, and solar energy materials. Their applications include solid oxide fuel cells, sensors, random access memory, high-density capacitors, catalysts, magnets, and high k dielectrics [3-5]. BeHfO3 has been proven to be effective as a ceramic substrate of high k dielectric capacitor, thermal insulator and scintillator in rapid response detectors, attributed to its solid phase stability, elevated melting point, high thermal expansion coefficient, low thermal conductivity and substantial density [6-9]. The static dielectric constant, a crucial metric for device manufacturing, is often elevated in these materials, thus improving their functional performance. Transition-metal oxides are distinguished by their photocatalytic activity, photoluminescence, and increased chemical reactivity, increasing their utility [10]. Perovskite materials, characterized by the general formula ABX3, have attracted considerable interest for their many applications in semiconductors, energy storage, and optoelectronics [11]. Halide perovskites are particularly attractive because of their adjustable bandgaps and elevated absorption coefficients, making them suitable for use in solar cells, light-emitting diodes (LEDs), and scintillators. However, concerns about lead toxicity and environmental instability have restricted their commercial use. This has inspired theoretical investigations into lead-free halide perovskites, including LiBeCl3 and LiMgCl3 [12,13]. ABSTRACT RESEARCH ARTICLE KEYWORDS https://dx.doi.org/10.5155/eurjchem.16.3.292-301.2675 https://www.eurjchem.com/ https://dx.doi.org/10.5155/eurjchem.16.3.292-301.2675 mailto:razibmunshi@eub.edu.bd http://www.eurjchem.com/ https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.16.3.292-301.2675&domain=pdf&date_stamp=2025-09-30 Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 293 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Table 1. Optimized lattice parameter, cell volume, and final energy of BeHfO3 crystal. Compound Lattice parameter a=b=c (Å) Initial cell volume (Å3) Optimized cell volume (Å3) Final energy (eV) Methods BeHfO3 3.346402 54.010152 37.474382 -1410.976738180 PBE 3.356706 54.010152 37.821604 -1411.855961562 RPBE 3.334390 54.010152 37.072281 -1407.297375017 PBE sol 3.317263 54.010152 36.503941 -1410.935450263 LDA 3.780 54.010152 54.112 -1405.541434666 B3LYP Density Functional Theory (DFT) analyses demonstrate that these materials possess broad indirect bandgaps, dynamic stability, and advantageous optical characteristics, suggesting their potential for optoelectronic applications such as energy storage and scintillation devices. Oxide perovskites have garnered scientific attention due to their structural stability and broad bandgaps, making them suitable for use in lenses, lithography, and energy storage. Silicon-based oxide perovs- kites, including SiMO3 (M: Sn, Ge), demonstrate mechanical stability and semiconductor properties, with band gaps appropriate for ultraviolet (UV) applications [14,15]. Recent computational investigations employing DFT have focused on silicon-based XSiO3 (X: Sc, Y) compounds, emphasizing their advantageous structural, elastic, electrical, and optical properties for optoelectronic applications [16]. Computational studies of CaQCl3 (Q: Li, K) chloroperovskites have disclosed favorable structural, elastic, electrical, and optical features for these applications [17]. Tl-based fluoro-perovskites (e.g., TlVF3 and TlNbF3) have semiconducting properties, mechanical stability, and ferromagnetism, rendering them viable candidates for optoelectronic and photovoltaic applications [18]. The structural adaptability and compositional variety of perovskite materials provide an extensive array of mechanical, electrical, magnetic, optical, and transport capabilities, permitting their application in domains such as optoelectronics, photonics, and spintronics. Chloroperovskites, containing chlorine as the halogen, exhibit broad band gaps, ideal for ultraviolet light applications and energy storage. They also possess ferroelectric and semiconductive properties beneficial for scintillating materials in medical imaging and high-energy physics [19,20]. Although comprehensive theoretical investigations have been performed on different aspects of several semiconductors, including BaHfO3 [21,22], CaHfO3, and SrHfO3 [23,24], the compound BeHfO3 has not been thoroughly examined. Due to the prevalent application of Hf-based high-k dielectrics such as HfO2 in contemporary electronics, BeHfO3 emerges as a viable alternative with distinctive characteristics. The photocatalytic uses of hafnia derivatives have recently attracted attention; however, the potential of BeHfO3 in this domain remains inadequately explored. The capacity to adjust the optical bandgap in these materials presents significant possibilities for enhancing photocatalysts. Hybrid Density Functional Theory (Hybrid-DFT) techniques offer the most precise framework for forecasting the electrical and structural characteristics of semiconductors, addressing the shortcomings of traditional DFT methodologies [25]. As far as current understanding goes, there are no theoretical investigations into its physical properties. However, one of the most effective methods to perform theoretical assessments of these features is first-principles computation. Rapid computational execution and somewhat precise predictions of the structural and energetic charac- teristics of various materials are the primary grounds for the utilization of LDA and GGA functionals [26]. In this study, the physical characteristics of BeHfO3 perovskite were investigated employing a variety of exchange correlation functionals within the context of density functional theory (DFT) under the CASTEP module in Materials Studio. Some of the functionals that were chosen include the Generalized Gradient Approximation (GGA) with Perdew- Burke-Ernzerhof (PBE), the Local Density Approximation (LDA) with Ceperley-Alder and Perdew-Zunger (CA-PZ), and the hybrid HSE06, B3LYP functional. The structural, electrical, mechanical, thermodynamic, and optical characteristics of the compound may be thoroughly examined using this multi- functional method, which allows for an evaluation of the changes based on the functions. Each function affects the precision of the findings in a distinct way. GGA-PBE and its variations (RPBE and PBEsol) are widely utilized to predict structural and elastic characteristics; nevertheless, they often underestimate band gaps and marginally overestimate lattice parameters. LDA (CA-PZ) often yields more compact structures, owing to its underestimating of lattice constants. On the contrary, the HSE06 and B3LYP hybrid functional, which includes a fraction of exact exchange, yields more precise electronic structure predictions, especially for band gap values, while it incurs a greater computational expense. The use of several functionals enhances the dependability of results and elucidates the sensitivity of anticipated features to the selection of an exchange-correlation functional, hence facilitating a more robust interpretation of material behavior. 2. Computational method The ab initio calculations in this study were performed using the CASTEP code within the Materials Studio package. A plane-wave basis set with a cutoff energy of 450 eV was used along with norm-conserving pseudopotentials. A 6 × 6 × 6 Monkhorst–Pack k-point grid was employed to ensure accurate Brillouin zone sampling. The geometry optimization convergence criteria were found to be total energy tolerance: 2.0×10-4 eV/atom, maximum ionic force: 5.0×10-2 eV/Å, maximum stress: 1.0×10-1 GPa, maximum atomic displacement: 2.0×10-3 Å. 3. Results and discussion 3.1. Optimization of crystal structure We performed full structural optimization of the BeHfO3 crystal prior to DFT calculations. The initial lattice parameters (a = b = c = 3.780 Å; α = β = γ = 90°) were taken from previous literature [20], and the structure was optimized to its ground state using DFT. The final configuration retained the cubic symmetry (space group Pm3-m [221]), confirming the stability of the structure. This procedure ensures the reliability of the calculated properties. The Hall symbol -P423 represents the crystal system, providing further information about it. The conclusive configu- ration of the BeHfO3 crystals is showed in Table 1 and illustrated in Figure 1. The data presented in Table 1 were obtained through full structural optimization of the BeHfO3 crystal using density functional theory (DFT) with different exchange-correlation functionals (PBE, RPBE, PBEsol, LDA, and B3LYP). The initial lattice parameters (a = b = c = 3.780 Å) were taken from the literature [20], and each structure was relaxed to its ground state by minimizing the total energy and atomic forces. For each functional, we report the optimized lattice parameter (a = b = c), the corresponding cell volume after relaxation, and the final total energy. 294 Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Table 2. Band gap values of the BeHfO3 crystal. Band gap energy (eV) PBE RPBE PBE sol LDA HSE06 B3LYP 0.873 0.887 0.781 0.890 1.71 2.925 Figure 1. Structure (ball and stick) of cubic BeHfO3 crystal. Figure 2. Band structure of BeHfO3 using (a) PBE, (b) RPBE, (c) PBEsol and (d) LDA techniques. The initial cell volume (54.010 Å3) was calculated based on the non-optimized lattice parameter, and the changes after optimization reflect the degree of structural relaxation. These calculations confirm the most stable structure and ensure the reliability of further property predictions. 3.2. Electronic band structure Significant for assessing electrical characteristics, the layout of bands reveals significant details on the energetic concentrations and band widths of an object. Band structures of cubic BeHfO3 at various high-symmetry points within the Brillouin zone, particularly at the (G-R-M-G-R) spot. Computing methods such as PBE, RPBE, PBEsol, LDA are presented in Figure 2, B3LYP (Figure S1, ESI) and HSE06 (Figure S2, ESI) were used to determine the minuscule band gap widths that characterize the spectrum of BeHfO3, indicating that it behaves like a semiconductor. The difference between a direct and indirect band gap is the degree to which the energies of the conduction and valence bands coincide at the identical k-point [27-29]. The findings of our computational analysis demonstrate that BeHfO3 has an indirect band gap, as illustrated in Table 2. The valence band will display a significant number of occupied electronic states, while the conduction band will show a lower number of accessible unoccupied states in the density of states [30]. The plot of electronic states for a metal will exhibit a uniform distribution across a broad spectrum of energies. From Figure 3, and (Figure S3, ESI) it has seen that, valence and conduction band level the highest DOS peak level reached near about 4.00 and 3.8 electrons/eV. On the other hand, in Figure 4 and (Figure S4, ESI) for PDOS, valence band of Be and Hf atom partially dominated by 2s², 5p² and 5d² orbital, respectively, while conduction band, the 2s2 orbital of the Be atom, along with the 5p2 and 5d2 orbitals of the Hf atom, and the 2p2 orbital of the O atom, exhibit the most Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 295 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Table 3. Mulliken atomic population analysis of BeHfO3 perovskites. Methods Mulliken Hirshfeld Element Charge Bonds Populations Bond length (A) Charge PBE Be Hf O 0.37 Be - O 0.75 1.67320 0.07 1.92 Hf - O 0.60 2.36626 0.68 -0.76 O - O -0.46 2.36626 -0.25 Be - Hf -0.84 2.89807 - RPBE Be Hf O 0.38 Be – O 0.74 1.67835 0.07 -0.77 Hf - O 0.61 2.37355 -0.25 1.91 O - O -0.46 2.37355 0.69 Be - Hf -0.77 2.90699 - PBE sol Be Hf O 0.32 Be - O 0.77 1.66720 0.06 1.90 Hf - O 0.60 2.35777 0.65 -0.74 O - O -0.48 2.35777 -0.24 Be - Hf -0.93 2.88767 - LDA Be Hf O 0.30 Be - O 0.78 1.65863 0.07 1.99 Hf - O 0.57 2.34566 0.67 -0.76 O-O -0.49 2.34566 -0.25 Be - Hf -1.03 2.87283 - Figure 3. Total DOS and PDOS of BeHfO3 using the (a) PBE (b) RPBE, (c) PBE sol, and (d) LDA techniques. significant contributions. Lastly, about 3.8 electrons/eV are significantly contributed by the p orbital in the valence band. With almost four electrons/eV, the d orbital makes a substantial contribution to the conduction spectrum [31]. A study of the Mulliken atomic population is also included to supplement the investigation of the bridging features of the BeHfO3 crystal. The veracity of our knowledge of charge transporters and the interactions between atoms in different compounds is verified by studies [32]. The atomic charges of oxygen (O) are negative, whereas those of beryllium (Be) and hafnium (Hf) are positive. Table 3, details the attributes of the BeHfO3 crystal as evaluated using the PBE, RPBE, PBEsol, and LDA techniques. Additionally, the oxygen atom received a charge from the beryllium and hafnium atoms, resulting in an electric charge swap. 3.3. Mechanical properties The elastic constant quantifies a material's susceptibility to deformation, indicating its reaction to tension, compression, and distortion. Elastic constants were calculated utilizing Hooke's law and stress-strain data. For cubic crystals, mechanical stability requires adherence to the Born stability criteria [33]: 𝐶𝐶11 > 0, 𝐶𝐶44 > 0, 𝐶𝐶11−𝐶𝐶 12 > 0, and 𝐶𝐶11+2𝐶𝐶12 > 0. Table 5, presents the mechanical characteristics of BeHfO3 as determined by PBE, RPBE, and PBEsol, therefore affirming its stability under these circumstances. Mechanical parameters such as elastic constants, bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio characterize the material’s response to applied stress or strain. These parameters are intrinsically linked to the nature of atomic bonding within the material. The atoms in materials with strong covalent bonding are so closely linked that they resist deformation, making the material very stiff and having a large elastic modulus. The directed structures of the ionic bonding and electrostatic interactions cause them to be somewhat stiff, but they are frequently fragile. Because of the delocalized electron cloud that allows for atomic mobility, metallic bonds are linked to excellent ductility and moderate to high elastic moduli. Low elastic moduli and greater deformability are characteristics of 296 Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Table 4. Comparison with related materials predicted by the DFT study. Compound Cutt off energy & K -points Crystal system with space group Lattice parameter (Å) Band gap (eV) Software package Reference BaHfO3 E Cut = 450 eV K = 6 6 6 Cubic (pm3m) 4.2481 2.99 (LDA) Material Studio- Castep [21] BaHfO3 E Cut = 380 eV K = 6 6 6 - a = b = c = 4.24 2.99 (LDA) Material Studio- Castep [22] CaHfO3 - Cubic (pm3m) 4.16 3.77 (SCAN) 5.81 (TB-mBJ) WIEN2k [23] SrHfO3 - Cubic (pm3m) 4.11 4.01 (SCAN) 6.34 (TB-mBJ) WIEN2k [23] SrHfO3 K = 4 4 3 Orthorombic (pbnm) a = 5.86, b = 5.89, c = 8.28 3.4 (LDA) Material Studio- Castep [24] BeHfO3 E Cut = 450 eV K = 6 6 6 Cubic (pm3m) a = b = c = 3.780 α = β = γ = 90° 0.873 (PBE) 0.887 (RPBE) 0.781 (PBE sol) 0.890 (LDA) 2.925 (B3LYP) (HSE06) Material Studio- Castep This work Figure 4. Different partial states of Be, Hf and O atom using the (a) PBE (b) RPBE (c) PBE sol (d) LDA techniques. materials in which van der Waals or other weak interactions predominate. As a result, evaluation of mechanical parameters is a powerful tool for identifying the most common types of bonding in a material, whether they are covalent, ionic, metallic, or weakly bound. A negative Cauchy pressure indicates a nonmetallic and brittle material, whereas a positive value denotes metallic and ductile properties. Positive Cauchy pressure of BeHfO3 indicates its metallic characteristics and ductility. Brittleness is determined by whether the B/G is equal to or greater than 1.75. In contrast, ductile qualities are exhibited by a material with a B/G below 1.75. Using the PBE, RPBE, and PBE sol methods, the Pugh's ratio (B/G) in these calculations was found to be 0.69, 0.75, and 0.72, respectively. On the basis of these results, it appears that the substance is ductile. The fact that our present calculations are supported by the Cauchy pressure and Pugh's ratio indicates that they behave similarly. The ductile characteristics of BeHfO3 perovskite, evidenced by its mechanical properties (such as positive Cauchy pressure, Pugh’s ratio greater than 1.75), indicate its potential use in flexible electronic and mechanical domains. Ductility is an essential characteristic for materials designed for flexible or extensible devices, which allows them to withstand mechanical deformation without breaking. The mechanical flexibility of BeHfO3, together with its advantageous electrical and optical characteristics, positions it as a viable option for applications in next generation flexible optoelectronic and wearable devices. The elevated bulk modulus of BeHfO3 signifies increased elasticity, incompressibility, and rigidity compared to comparable materials. Its high shear modulus verifies the material's resistance to shear distortion and its robustness under shear stress [34]. Substances with Poisson's ratios approaching 0.5 demonstrate poor bonding, whereas lower values signify stiffer and more robust atomic connections. BeHfO3 that exhibits Poisson ratios of 0.17, 0.19, and 0.21, indicates robust atomic bonding and elevated stiffness [35]. The universal anisotropy factor quantifies the changes in stiffness among crystallographic orientations. A number of 1 signifies isotropic elastic characteristics, but values less than 1 imply anisotropy. Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 297 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Table 5. Elastic constants, Cauchy pressure, modulus of bulk, Young, Shear, (B/G), Poisson's ratio and anisotropy factor. Method C11 C12 C44 C12-C44 B Y G B/G v A PBE 12.86 77.44 58.12 19.32 34.01 282.11 48.93 0.69 0.17 0.30 RPBE 15.21 75.18 57.34 17.84 35.05 249.93 46.48 0.75 0.19 0.38 PPBEsol 14.11 71.29 57.93 13.36 36.15 276.65 49.84 0.72 0.21 0.23 Figure 5. Enthalpy, entropy, free energy of BeHfO3 in (a) PBE, (b) RPBE, (c) PBEsol and (d) LDA methods. Figure 6. (a) Optical reflectivity and (b) Loss function of the BeHfO3 crystal. The anisotropy index of BeHfO3, measuring 0.30, 0.38, and 0.23, indicates directional discrepancies in its elastic charac- teristics, encompassing stiffness [36]. External pressure or strain markedly affects the mechanical characteristics of perovskite materials, such as BeHfO3. Pressure or epitaxial strain can influence elastic constants, bulk modulus, and shear modulus, frequently increasing mechanical stability by diminishing structural distortions and increasing bond strength. In the case of BeHfO3, external modulation, such as compressive or tensile stress, can stabilize the perovskite phase by modifying the lengths and angles of the Hf-O and Be-O link, which influences the lattice dynamics and resistance to deformation. Consequently, strain engineering presents a feasible approach to enhance the structural integrity and mechanical efficacy of BeHfO3, possibly enhancing its use in functional devices. 3.4. Thermo-physical features Entropy is a crucial and significant factor in the fields of physics, chemistry, and many other scientific disciplines that span different fields. Based on thermodynamic principles, a highly organized system will have a marginal entropy value [37]. The statistics illustrated in Figures 5a-d demonstrate that the entropy at 1000 K corresponds to a value of 0.5 eV. This suggests that BeHfO3 may have a reduced level of instability or molecular disturbances. Excluding mechanical effort, the interplay of thermal energy and the environment, elucidated by enthalpy [38], ranging from 0.01 to 0.45 eV at temperatures between 200 and 1000 K, is illustrated in Figures 5a-d. The variability in free energy determines the transformation pathway and the maximum effort achievable in thermal processes, such as chemical reactions [39]. Our empirical findings indicate that the free energy of the BeHfO3 crystal starts at 0.02 eV at 190 K and increases steadily to 0.40 eV at 1000 K, as shown in Figures 5a-d. Heat capacity measures the amount of warmth required to change the temperature of a material, reflecting its ability to absorb or release energy. Figure S5a-d (ESI) demonstrates that BeHfO3 attains its maximum heat capacity at 1000 K, showcasing varying energy levels evaluated using different methodologies. 3.5. Optical properties A magnitude of 0.1 eV Gaussian smearing has been used across all computational approaches to explore the optical characteristics of the BeHfO3 [40]. A material's reflectivity- its capacity to return energy or light to its source- is fundamental for comprehending its opacity, translucency, or transparency [41]. A notable increase in reflectance from 0.23 eV to 30 eV for BeHfO3 is demonstrated by the results 0.85, 0.88, 0.82, 0.85, and 0.75 eV showed significant amounts of reflection in different methods shown in Figure 6a. An important optical feature, the energy loss function affects optoelectronic efficiency through- out both the low and high photon energy ranges [42]. According to Figure 6b, the LDA technique results in the largest energy loss for BeHfO3, whereas PBEsol yields the least. Choosing 298 Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 Figure 7. (a) Refraction index and (b) absorption curve of the BeHfO3 crystal. Figure 8. Wavelength-dependent absorption curve of BeHfO3 crystal in (a) PBE, (b) RPBE, (c) PBEsol, and (d) LDA methods. computational methods to reliably forecast the optical characteristics of BeHfO3 requires this understanding. The capacity of a substance to carry light is measured by its optical conductivity [43]. The actual component of BeHfO3 is visible in Figure S6a (ESI) and is dominant up to 11.0 eV, after which it steadily drops by 30 eV. The energy absorption through electron-material contacts is shown by the fictitious part being greater than the real component after 11.0 eV. An essential step in comprehending and creating optically customized materials is the estimation of electric dipoles, which are dielectric functions [44]. From 0 to 5.0 eV, the real component of BeHfO3 is greater than the imaginary component, as shown in Figure S6b (ESI). However, as the energy approaches 30.0 eV, the real component diminishes. In the range of 5.0 to 30.0 eV, the imaginary part is larger than the actual part. The dielectric response of BeHfO3 perovskite is comparatively elevated in relation to several established halide perovskites. An elevated dielectric constant is beneficial, since it improves charge carrier screening, diminishes exciton binding energy, and promotes effective charge separation essential elements for enhancing the performance of optoelectronic devices, including solar cells, photodetectors, and light-emitting diodes. In contrast to some halide perovskites that exhibit environmental instability and lead toxicity, BeHfO3 presents a potentially more stable and nontoxic alternative with an advantageous dielectric profile, rendering it a promising material for practical and enduring optoelectronic applications. The refractive index plays a vital role in optics, indicating the interaction of light with various materials [45]. Figure 7a illustrates a negative correlation between the real and imaginary components in BeHfO3, while the real part was higher from 0.0 to 5.0 eV, followed by a decrease at 30 eV. The reliable characteristics of BeHfO3 in terms of its absorption and refractive properties have significant implications for the advancement of new optical phenomena. Al Masud et al. / European Journal of Chemistry 16 (3) (2025) 292-301 299 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.292-301.2675 3.5.1. Optical absorption Absorption features transpires when objects consume electromagnetic frequencies, delivering energetic to molecules or atoms, resulting in a boost of their power levels [46,47]. Figure 7b illustrates that BeHfO3 displays a consistent absorption pattern across all methodologies, spanning range from 0 to 35 eV. The substance captures light within the visible spectrum (1.78 to 4.14 eV or 300 to 700 nm), exhibiting a maximum absorption of around 3.5 eV. Additionally, significant absorption spikes are seen in the ultraviolet (UV) range, with the most prominent rise at 24.5 eV, indicating BeHfO3’s ability to hold onto photons in both the visible and UV ranges. Furthermore, Figures 8a-d illustrate the absorption coefficient curve of BeHfO3 that varies with wavelength, employing the methodologies PBE, RPBE, PBEsol, LDA and B3LYP (Figure S8, ESI). The curves exhibit many different absorption maxima throughout the visible spectrum, covering wavelengths from 300 to 700 nm. The calculated maximum absorption wavelengths of BeHfO3 are about 356, 360, 358, 344, and 309 nm for the corresponding techniques. These wave- lengths correlate to the exact areas where BeHfO3 exhibits its most significant light absorption. The significant ultraviolet (UV) absorption of BeHfO3 makes it a good option for UV detector use. Sensitive and selective UV detectors need materials that can easily catch and transform UV rays. The stability and electrical qualities of BeHfO3 also make it a good candidate for UV photodetectors, which means it might be used in future optoelectronic devices that work in the UV region. The existence of these peaks signifies that BeHfO3 has certain absorption properties at these exact wavelengths. Furthermore, the material has considerable sensitivity to visible light, as indicated by its pronounced absorption peaks, establishing BeHfO3 as a very attractive option for opto- electronic and photocatalytic applications, where effective manipulation and detection of visible light are essential [48-50]. 4. Conclusions This investigation employs various computational techniques, such as PBE, RPBE, PBEsol, LDA, HSE06 and B3LYP, to evaluate the bandgap energy, uncovering an indirect bandgap feature with computed values of 0.873, 0.887, 0.780, 0.890, 1.71 and 2.295 eV, accordingly. To gain deeper insight into the electronic structure, a comprehensive and partial density of states (DOS) analysis was performed to elucidate the contributions of atomic orbitals to the electronic properties of the compound. Furthermore, bonding characteristics were analyzed through Mulliken population charge estimations, providing a detailed understanding of the charge distribution and interactions within the crystal lattice. The crystalline structure of BeHfO3 demonstrates remarkable mechanical robustness, which is characterized by its ductility, elastic anisotropy, and significant mechanical and thermal stability. These properties indicate a high degree of structural resistance under various conditions. Additionally, the optical properties of BeHfO3 underscore its promise for photocatalytic applications, owing to its chop bandgap and remarkable absorption aptitude throughout the visible and ultraviolet exposure range. It additionally highlights BeHfO3 as a notable contender in the realm of semiconducting photocatalysts, suggesting its potential utility in sophisticated optoelectronic systems. An in- depth look offers a basic understanding of versatile charac- teristics, enabling its incorporation into various technological fields. Acknowledgements The authors thank the Department of Physics and ICT, European University of Bangladesh, Dhaka-1216, for providing facilities and support to carry out this research. Supporting information Electronic supplementary information (ESI) available: Figure S1. Band structure of BeHfO3 using the B3LYP method. Figure S2. Band structure of BeHfO3 using the HSE06 method. Figure S3. DOS and PDOS of BeHfO3 using the B3LYP method. Figure S4. Different partial states of BeHfO3 using the B3LYP method. Figure S5. Heat capacity of BeHfO3 in (a) PBE, (b) RPBE (c) PBE sol and (d) LDA methods. Figure S6. (a) Optical conductivity and (b) Dielectric function of BeHfO3 in GGA using the PBE, RPBE, PBE sol, LDA and B3LYP methods. Figure S7. Optical absorption of BeHfO3 using B3LYP method. Disclosure statement Conflict of interests: The authors declare that they have no conflict of interest. Ethical approval: All ethical guidelines have been adhered. Sample availability: Samples of the compounds are available from the author. CRediT authorship contribution statement Conceptualization: Md. Al Masud, Md. Rajib Munshi; Methodology: Md. Al Masud, Md. Rajib Munshi; Software: Md. Rajib Munshi; Validation: Md. Al Masud, Md. Rajib Munshi; Formal Analysis: Md. Al Masud, Md. Rajib Munshi, Tanvir Chowdhury, Mita Chakraborty, Rakibul Islam; Investigation: Md. Al Masud, Md. Rajib Munshi, Tanvir Chowdhury, Mita Chakraborty, Rakibul Islam; Resources: Md. Rajib Munshi; Data Curation: Md. Rajib Munshi; Writing - Original Draft: Md. Al Masud, Md. Rajib Munshi, Tanvir Chowdhury, Mita Chakraborty, Rakibul Islam; Writing - Review and Editing: Md. Al Masud, Md. Rajib Munshi, Tanvir Chowdhury, Mita Chakraborty, Rakibul Islam; Visualization: Md. Rajib Munshi; Funding acquisition: Md. Rajib Munshi; Supervision: Md. Rajib Munshi; Project Administration: Md. Rajib Munshi. ORCID and Email Md Al Masud almasud2509@gmail.com https://orcid.org/0009-0006-2109-6947 Md. Rajib Munshi razibmunshi@eub.edu.bd https://orcid.org/0000-0002-5594-1014 Tanvir Chowdhury tanvirchowdhury2@gmail.com https://orcid.org/0009-0002-9434-2433 Mita Chakraborty mita76h@gmail.com https://orcid.org/0009-0009-9038-7301 Rakibul Islam rakib133@gmail.com https://orcid.org/0009-0005-4294-7280 References [1]. Deng, M.; Shen, S.; Wang, X.; Zhang, Y.; Xu, H.; Zhang, T.; Wang, Q. Controlled synthesis of AgInS2 nanocrystals and their application in organic–inorganic hybrid photodetectors. CrystEngComm. 2013, 15 (33), 6443. [2]. Holladay, J.; Hu, J.; King, D.; Wang, Y. An overview of hydrogen production technologies. Catalysis Today 2009, 139 (4), 244–260. [3]. Sen, S. K.; Munshi, M. R.; Kumar, A.; Mortuza, A. A.; Manir, M. S.; Islam, M. A.; Hossain, M. N.; Hossain, M. K. 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Permissions for commercial use of this work beyond the scope of the License (https://www.eurjchem.com/index.php/eurjchem/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). https://www.eurjchem.com/index.php/eurjchem/terms http://creativecommons.org/licenses/by-nc/4.0 https://www.eurjchem.com/index.php/eurjchem/terms 1. Introduction 2. Computational method 3. Results and discussion 3.1. Optimization of crystal structure 3.2. Electronic band structure 3.3. Mechanical properties 3.4. Thermo-physical features 3.5. Optical properties 3.5.1. Optical absorption 4. Conclusions Acknowledgements Supporting information Disclosure statement CRediT authorship contribution statement ORCID and Email References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField15: PrintField16: PrintField17: PrintField18: PrintField19: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: PrintField25: PrintField26: PrintField27: PrintField28: PrintField29: