{"paper_id":"3d6bfd3c-50c2-4cd5-9bb0-a2b3b2c2698b","body_text":"First-principles calculation study on influence of the influence mechanisms of A-site multielement doping on the structure and optical properties of BaTiO3 ceramics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article First-principles calculation study on influence of the influence mechanisms of A-site multielement doping on the structure and optical properties of BaTiO3 ceramics Caixia Li, Tianqi Li, Chenglong Li, Nan Ji, Peng Lu, Shuang Ren This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6653343/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Nov, 2025 Read the published version in Theoretical Chemistry Accounts → Version 1 posted 10 You are reading this latest preprint version Abstract This paper employs first-principles calculations to investigate the structural electronic and optical property variation mechanisms of A-site composite-element doped BaTiO 3 ceramics BaBi X TiO 3 (X= Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , Ra 2+ ). Through calculations of the systems' band structures density of states dielectric functions reflectivity refractive indices optical absorption coefficients and extinction coefficients it is found that A-site Be 2+ doping achieves high static permittivity (ε 0 =146.77) in the low-energy region through lattice distortion and oxygen vacancy compensation demonstrating potential in metamaterial design; Mg 2+ exhibits extreme ultraviolet (EUV) response (ε 2 =17.05) suitable for EUV detectors; the low-loss characteristics and structural stability of Ca 2+ /Sr 2+ provide theoretical foundations for high-frequency filters. This study reveals the critical roles of doping element ionic radii valence states and orbital hybridization in multi-band optical responses providing theoretical guidance for designing high-voltage capacitors photocatalytic materials and nuclear radiation shielding devices. BaTiO3 Ceramics Optical Properties A-site Composite Doping Optical Applications Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction In recent years, the ABO 3 perovskite structure has emerged as a prominent research focus [ 1 ] . Extensive studies have sought to enhance its electrical and optical properties through A-site or B-site element substitutions [ 2 – 4 ] . Notably, lead-based materials like Pb(Zr 1- x Ti x )O 3 (PZT) have found widespread applications in actuators, transducers, and sensors due to their superior dielectric and piezoelectric performance [ 5 ] . However, health and environmental concerns related to Pb [ 6 ] have driven research toward lead-free piezoelectric ceramics such as BaTiO 3 (BT), (K,Na)NbO 3 (KNN), (Bi 0.5 Na 0.5 )TiO 3 (BNT), and BiFeO 3 (BF) [ 7 – 9 ] . BF ceramics exhibit a distorted rhombohedral (R3c) perovskite structure at room temperature (lattice constants 5.63Å, rhombohedral angle 89.45°), demonstrating ferroelectric-antiferromagnetic dual properties under ambient conditions. Their high ferroelectric Curie temperature (TC = 1103K) and G-type antiferromagnetic Néel temperature (TN = 643K) position them as promising candidates for high-temperature lead-free multiferroic materials, with theoretical spontaneous polarization intensity of ~ 100 µC/cm 2 attracting significant interest [ 10 , 11 ] . Despite intensive optimization efforts since their 1957 synthesis, challenges remain in fabricating pure-phase BF ceramics due to Bi 3+ volatility during high-temperature sintering and secondary phase formation from oxygen vacancy aggregation. Fe 3+ →Fe 2+ transitions and oxygen vacancies often result in high leakage currents, complicating saturated ferroelectric hysteresis loop measurements [ 12 , 13 ] . By forming solid solutions with other ABO 3 -type perovskite ferroelectrics, Bi 3+ and Fe 3+ 's polarization/magnetization dominance can be modulated to reduce leakage and improve electrical properties. BF-BT systems form continuous solid solutions across all compositions, displaying enhanced piezoelectricity and high TC in the morphotropic phase boundary (MPB) region. BF-BT has become a focal point in high-temperature piezoelectric research due to its TC > 600°C, residual polarization Pr ≈ 35.5 µC/cm 2 , piezoelectricity, and thermal stability [ 16 – 19 ] . However, large tetragonal distortion (c/a), high coercivity fields, Bi 3+ volatility, Fe 3+ valence changes, and high oxygen vacancy concentrations lead to poor ferroelectricity, high dielectric loss, and low resistivity (~ 10 7 Ω/cm at room temperature). Ba 2+ substitution for Bi 3+ regulates the perovskite tolerance factor (t), promoting rhombohedral→pseudocubic structural transitions to inhibit Bi volatility and oxygen vacancy formation. Ti 4+ substitution for Fe 3+ induces lattice contraction, strengthens Ti-O covalency, stabilizes ferroelectric distortion, and reduces leakage from Fe 2+ /Fe 3+ redox reactions. Microstructurally, BT doping suppresses excessive grain growth, creating dense uniform microstructures with fewer grain boundary defects. Structurally, reduced symmetry (rhombohedral→pseudocubic) expands ferroelectric polarization directions while decreasing oxygen vacancy concentration. Piezoelectrically, MPB formation yields electrostrain up to 500pm/V at x ≈ 0.3, surpassing traditional lead-free systems. Magnetically, BT doping disrupts BF's helical antiferromagnetic structure, releasing trapped magnetic moments and inducing weak ferromagnetism. These combined effects enhance magnetoelectric coupling and thermal stability (> 600°C), enabling high-temperature applications. This study systematically investigates composition-dependent crystal structures, dielectric properties, and optical characteristics of BF-BT ceramics using first-principles calculations, providing theoretical insights for further material modifications. Specifically, we model Ba 0.3 Bi 0.5 X 0.2 O 3 ( X = Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , Ra 2+ ) and BaTi 0.3 Fe 0.5 Y 0.2 O 3 ( Y = Zr⁴⁺, Sn⁴⁺, Sb³⁺, V⁴⁺, Ta⁵⁺) systems to analyze electronic structures and property variations under different doping configurations. 2. Computational Methods This study systematically investigates the structural, electrical, and optical properties of BaTiO 3 ceramics using first-principles calculations based on density functional theory(DFT) implemented in the Vienna Ab initio Simulation Package(VASP) [ 20 ] . The computational framework employs a plane-wave basis set with periodic boundary conditions, where pseudopotentials are defined via the projector augmented wave (PAW) method in reciprocal space [ 21 ] . Exchange-correlation effects are approximated using the generalized gradient approximation(GGA) with the Perdew-Burke-Ernzerhof(PBE) functional [ 22 ] . High-symmetry configurations allow reduced k-point sampling, whereas low-symmetry systems require denser k-point grids for accurate electronic structure descriptions. Lattice parameter changes induced by doping (lattice expansion corresponds to Brillouin zone contraction in reciprocal space, necessitating denser k-point sampling) prompted convergence tests through progressive k-point density increases: total energy calculations initiated with a sparse 2×2×2 grid were iteratively refined until energy variation fell below 0.02eV/atom. A final k-point mesh of 7×7×7 was adopted for optimization. Doped structures were modeled using a 3×3×1 supercell with a 530eV cutoff energy. All electronic iterations employed a convergence criterion of 10 -6 eV/atom, with structural relaxation considered complete when atomic forces converged to < 0.02eV/atom. 3. Results and Discussion 3.1. Structural Optimization To establish an accurate crystal structure, the Materials Project crystal database website was first utilized to search for structural parameters close to the experimental values. The CIF crystal structure file was downloaded and used to construct the structural model with VESTA software. To build a doping model with reasonable concentration, the optimized unit cell structure was imported into VESTA. The lattice vectors of the BaTiO 3 unit cell were redefined in the a (x-direction) and b (y-direction) axes as (110) and (-110), respectively. The redefined BaTiO 3 structure was then expanded into a 1×1×5 supercell to form a 50-atom supercell structure for doping. Based on this, A-site doping was performed, and the resulting models are shown in Fig. 1 . Figure 1 (a) displays the structure of Ba 0.3 Bi 0.7 TiO 3 ; Figs. 1 (b) to 1(f) represent the structures of Ba 0.3 Bi 0.5 X 0.2 TiO 3 where X is Be, Mg, Ca, Sr, or Ra. The calculated lattice constants are listed in Table 1 . The ionic radii are as follows: Bi 3+ (1.17Å), Be 2+ (0.45Å), Mg 2+ (0.65Å), Ca 2+ (0.99Å), Sr 2+ (1.18Å), and Ra 2+ (1.62Å). The results show that we first calculated the lattice constants and volume of Ba0.3Bi0.7TiO3, followed by doping Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , and Ra 2+ to replace Bi 3+ in Ba 0.3 Bi 0.5 X 0.2 TiO 3 . The lattice constants a and b exhibit a gradual increasing trend due to the gradual increase in the ionic radius of the dopant ions. For Sr 2+ and Ra 2+ doping, the lattice constants a and b exceed those of the original material. The volume changes show distinct behaviors: Be 2+ doping causes significant volume expansion due to the introduction of Be 2+ ions (ionic radius 0.45Å, 38% of Bi 3+ ), leading to strong local lattice distortion and compressive stress. Charge mismatch induces numerous oxygen vacancies, resulting in high defect concentration, enhanced covalent bonding through increased polarizability, and exacerbated oxygen octahedral distortion with reduced symmetry, causing overall volume expansion. Mg 2+ doping leads to moderate volume increase because Mg 2+ ions (0.65Å, 55% of Bi 3+ ) create significant size mismatch but less severe than Be 2+ . Charge mismatch also causes partial oxygen vacancies or Bi 3+ reduction, but Mg 2+ doping dominates the structure with ionic bonding, enhancing structural stability and limiting volume expansion. Ca 2+ (0.99Å, 84% of Bi 3+ ) shows minimal volume change due to similar ionic radii, low stress, and predominantly ionic bonding with slight structural distortion. Sr 2+ has nearly identical ionic radius to Bi 3+ , resulting in negligible stress. Charge mismatch becomes the main volume driver, requiring minor oxygen vacancies and causing subtle volume changes. Ra 2+ (1.62Å, 138% of Bi 3+ ) expands the lattice via tensile stress. Weak ionic bonding in heavy elements exacerbates structural distortion, exacerbating volume increase. Charge mismatch combined with high defect concentration leads to significant volume expansion. Table 1 Lattice constants and volumes of doping components of each element Chemical Lattice constant a Lattice constant b Lattice constant c Volume Ba 0.3 Bi 0.7 TiO 3 5.70267 5.70267 20.82692 677.3004 Ba 0.3 Bi 0.5 Be 0.2 TiO 3 5.57716 5.57716 21.73333 687.0100 Ba 0.3 Bi 0.5 Mg 0.2 TiO 3 5.67614 5.67614 20.70662 683.1385 Ba 0.3 Bi 0.5 Ca 0.2 TiO 3 5.68296 5.68296 20.43282 679.8990 Ba 0.3 Bi 0.5 Sr 0.2 TiO 3 5.70844 5.70844 20.31839 678.1011 Ba 0.3 Bi 0.5 Ra 0.2 TiO 3 5.74808 5.74808 20.56670 686.5333 3.2. Band Structure and Density of States Analysis Figure 2 shows the band structures of BaBi X TiO 3 , where Fig. 2 (a) corresponds to Ba 0.3 Bi 0.7 TiO 3 and Figs. 2 (b)-(f) represent the band structures of Be, Mg, Ca, Sr, and Ra-doped systems, respectively. The corresponding band gap widths are 1.39eV, 1.21eV, 1.97eV, 2.58eV, 2.56eV, and 2.57eV. Calculation results reveal significant differences in bandgap widths after doping. Be 2+ doping narrows the band gap from 1.39eV to 1.21eV (ΔE= -0.18eV); Mg 2+ doping broadens the band gap to 1.97eV(ΔE = + 0.58eV); Ca 2+ , Sr 2+ , and Ra 2+ doping further increases the band gap to 2.56–2.58eV (ΔE = + 1.17–1.19eV).This trend roughly follows a linear relationship with ionic radii, which can be generalized as: small-radius ions induce band gap narrowing, medium-radius ions cause significant band gap broadening, and large-radius ions stabilize the band gap at a wide value. Be 2+ doping is the only case showing band gap narrowing among all doping systems, forming a sharp contrast with the universal band gap broadening trend observed in other alkaline earth metal ions (Mg 2+ , Ca 2+ , Sr 2+ , Ra 2+ ). A reduced band gap implies the optical absorption threshold shifts toward longer wavelengths, potentially enhancing photoelectric response in the visible light range. The unique behavior of Be 2+ can be attributed to its distinct electronic structure and ionic properties: its much smaller ionic radius compared to substituted Bi 3+ induces significant lattice distortion. This local structural contraction likely alters bond strengths and angles (e.g., Ti-O and Bi-O bonds), shifting the positions of the valence band maximum and conduction band minimum. Additionally, charge mismatch between Be 2+ and Bi 3+ may maintain charge neutrality through oxygen vacancies or electron compensation mechanisms. Oxygen vacancies introduce new electronic states within the band gap, acting as donor levels that facilitate electron transitions from the valence band to the conduction band, thereby reducing the band gap. To further investigate orbital changes during doping, density of states (DOS) analysis was performed on these systems. By correlating DOS diagrams with band structures, we aim to gain clearer insights into how different dopants affect the electronic structure of this system. To further explore the changes in elemental orbitals, we performed density of states (DOS) calculations on the above system, and the results are shown in Fig. 3 , where Fig. 3 (a) corresponds to the DOS diagram of Ba 0.3 Bi 0.7 TiO 3 , and Figs. 3 (b)–(f) correspond to the DOS diagrams of Be, Mg, Ca, Sr, and Ra doped systems, respectively. It can be seen from the figure that the s orbital of Be element generates peaks in the energy range of -10eV to 0eV, with fluctuations near the Fermi level. This indicates that the s orbital of Be element interacts with the orbitals of other elements in the system, especially hybridizing with the p orbital of O element (mainly existing between − 10eV and 5eV). This hybridization changes the electron state distribution near the valence band maximum (VBM). The hybridization between Be s orbital and O p orbital also introduces new impurity levels at the VBM, which may couple with the original Bi 6s² lone pair electron states or Ti 3d states, causing the electron cloud distribution to expand toward higher energy regions, thus shifting the VBM to higher energy. The fluctuations of Be s orbital near the Fermi level may also affect the position of the conduction band minimum (CBM). The introduction of Be changes the electronic structure of the system, redistributing electron energy states and shifting the CBM to lower energy. The combined effect of the upward shift of VBM and downward shift of CBM reduces the band gap. Additionally, the fluctuations of Be s orbital near the Fermi level influence the DOS spectrum. The DOS near the Fermi level is crucial for the electrical properties of materials, determining parameters such as carrier concentration and mobility. Be doping modifies the DOS near the Fermi level, potentially enhancing the material's electrical conductivity and facilitating carrier excitation and transport. As described above, Be doping significantly affects the band structure and DOS distribution of the system through mechanisms such as orbital hybridization, lattice distortion, and charge compensation, leading to band gap narrowing and altered electron state distributions, which are critical for the optoelectronic and electrical properties of the material. For Mg element, the difference in ionic radii between Mg 2+ and Bi 3+ leads to lattice distortion. The smaller Mg 2+ radius causes local lattice contraction after substitution, shortening the distances to surrounding atoms. This lattice distortion alters bond lengths and angles, thereby affecting orbital overlap strength and symmetry, which forms the basis for band structure and DOS changes. The band gap increase to 1.97eV after Mg 2+ doping arises from several factors. Firstly, the charge compensation effect: Mg 2+ substituting high-valent Bi 3+ introduces defects for charge neutrality, which introduce new electronic states in the band gap and influence electron transitions between the valence and conduction bands. Oxygen vacancies may form donor levels below the conduction band, but combined with other effects from Mg 2+ doping, the net result is a downward shift of the valence band and upward shift of the conduction band, widening the band gap. Secondly, orbital hybridization: Mg p, s, and d orbitals hybridize with those of surrounding elements, altering valence and conduction band electron distributions. In the − 10eV to 0eV range, Mg-O hybridization shifts the VBM-related electron states to lower energy. Meanwhile, lattice distortion affects Ti d orbital hybridization with other orbitals, shifting the CBM electron states to higher energy, thus increasing the band gap. Thirdly, lattice contraction enhances electron confinement, requiring higher energy for electron transitions to the conduction band, further increasing the band gap. For Ca 2+ , Sr 2+ , and Ra 2+ , substituting high-valent Bi 3+ introduces one extra electron per dopant, leading to n-type doping, Fermi level shifting toward the conduction band, and increased carrier concentration. As shown in Figs. 3 (d)–(f), none of these three elements' d orbitals show significant contributions, while their s and p orbitals exhibit slight differences in their orbital contributions. Ca s orbital shows a 12eV peak at -40eV, primarily affecting deep energy levels, with p orbital peaking at 30eV near − 22eV. Sr s orbital appears slightly higher in energy (-35eV with a 10eV peak) and hybridizes with Ti p orbital; Sr p orbital peaks near − 20eV and hybridizes with O s orbital. Ra s and p orbitals peak near − 30eV and − 10eV. These observations indicate that d orbitals of these elements do not contribute significantly to the DOS curve. As ionic radii increase, their s and p orbitals shift toward higher energy ranges. 3.3. Optical Properties The optical properties of BaTiO 3 have been investigated for potential applications in optoelectronic devices. These properties encompass the interactions between light and matter, including reflectivity, refractive index, optical absorption coefficient, energy loss function, extinction coefficient, and dielectric function. The interaction between atoms and incident photons is defined by the dielectric function ε ( ω )= ε₁ ( ω ) + iε₂ ( ω ). By analyzing the real and imaginary components of the dielectric function, various optical properties such as the optical absorption coefficient α ( ω ), energy loss function L ( ω ), extinction coefficient k ( ω ), reflectivity R ( ω ), and refractive index n ( ω ) can be determined. These properties are governed by specific mathematical relationships: An important branch of the physical properties of solid materials is optical properties. Studying the optical performance of the BaBi X TiO 3 system holds significant implications for expanding its application scope. By leveraging the interaction between electrons and photons in the material, electrons are excited from the valence band maximum (VBM) to the conduction band minimum (CBM), and the measured optical coefficients can effectively correspond to the band structure. BaTiO 3 itself is a wide-band gap semiconductor, with theoretically calculated and experimentally measured band gap values of approximately 3.1–3.3eV (corresponding to the ultraviolet region, absorption edge ≈ 380–400nm). Intrinsic BaTiO 3 primarily absorbs ultraviolet light but exhibits weak visible-light response, a characteristic that limits its direct application in photovoltaic or photocatalytic fields while providing a foundation for doping modification. This section investigates A-site composite element doping in BaTiO 3 , analyzing it in detail through the real and imaginary parts of the dielectric function, optical absorption coefficient, reflectivity spectra, refractive index spectra, and energy loss function. Figure 4 (a) presents the real part of the dielectric function, and Fig. 4 (b) shows the imaginary part. When the incident photon energy approaches 0eV, the dielectric constant represents the static dielectric constant at that moment. As observed in Fig. 4 (a), the static dielectric constant of the undoped system is 17.70; for Be-doped, Mg-doped, Ca-doped, Sr-doped, and Ra-doped systems, the values are 146.77, 63.29, 37.35, 59.28, and 25.19, respectively. In the 0.2–1eV energy range, all curves show a downward trend, with the real part of the dielectric function decreasing in the order: undoped > Ra-doped > Ca-doped > Mg-doped > Sr-doped > Be-doped. The Be-doped system approaches 0 at 0.3eV. Between 1eV and 4.5eV, all curves rise, with the undoped system peaking at 8.65 at 4.24eV; Be-doped at 8.35(3.82eV); Mg-doped at 9.06(4.34eV); Ca-doped at 9.21(4.37 eV); Sr-doped at 8.60(4.29eV); and Ra-doped at 9.08(3.76eV). In the 10–100eV range, the real part curves of all systems converge. From an ionic radius perspective, the undoped system exhibits a typical perovskite intrinsic response with ε 1 = 17.70. Different doping ions cause significant lattice structural and ionic polarization variations due to radius differences. The smallest Be²⁺ radius induces substantial lattice distortion and enhanced ionic displacement polarization, boosting the static dielectric constant to 146.77. Conversely, the largest Ra²⁺ radius may over-expand the lattice, weaken interionic interactions, and reduce polarization, lowering ε 1 to 25.19. Electron cloud distributions of doping ions also affect local electron motion and polarization. For example, Be's compact electron cloud modifies the system's polarization capacity through distinct electron binding effects. In the low-energy region (0.2–1eV), the descending curves with differing values suggest that Be doping introduces new electronic states altering low-energy transition modes, causing a rapid dielectric response drop at 0.3eV. Other systems maintain moderate responses due to minimal doping effects on transitions. In the mid-energy range (1–4.5eV), ascending curves with element-specific peaks arise from doping-modified band structures and resonance absorption at photon energy-matched transition energies. High-energy (10–100eV) convergence indicates doping has negligible impact, with responses dominated by the material's fundamental structure. The imaginary part of the dielectric function ε 2 (ω) reflects electron transition and photon absorption capabilities. The undoped system shows a peak at 0.58eV(13.06) from Bi 3+ 6s 2 →6p 1 transitions, while Be, Ca, Sr, and Ra-doped systems exhibit prominent peaks at 0.1eV (86.68, 14.94, 31.98, 21.94, respectively). Mg-doped peaks at 0.45eV(12.10). All systems display secondary peaks in the 4–6.5eV range: undoped at 4.78eV(8.21) and 6.04eV(7.02); Be-doped at 5eV(6.86); Mg-doped at 4.65eV(7.76); Ca-doped at 4.80eV(8.66) and 5.87eV(6.72); Sr-doped at 4.82eV(8.50) and 5.85eV(6.91); Ra-doped at 4.85eV(7.95) and 5.91eV(6.77). Curves overlap in the 10–60eV region. Low-energy (0–1eV) peaks in Be/Ca/Sr/Ra systems indicate doping introduces low-energy transition channels, with Be's high electronegativity promoting polaron formation and localized transitions. Higher peak positions in undoped/Mg systems suggest weaker low-energy responses. Mid-energy (4–6.5eV) secondary peaks arise from doping-induced energy level splitting, with Be doping causing peak broadening and blue-shifting. High-energy (10–60eV) convergence reflects stable electronic structures with minimal doping effects. Given photon energy E = hc/λ (h = Planck constant, c = speed of light, λ = wavelength), doping significantly influences long-wavelength optical properties through electronic and lattice changes, while short-wavelength responses remain structurally dominated. Be-doped materials with ε 2 = 86.68 at 0.1eV and ε 1 = 146.77 are promising for near-infrared detectors/solar cell absorbers and high-frequency capacitors, though low-energy conductivity requires optimization. Mg/Ca-doped systems with strong 4–5eV responses are suitable for visible-light optoelectronic devices. Reflectivity is defined as the ratio of reflected to incident radiation. As shown in Fig. 5 (a), the undoped system exhibits an initial reflectivity of 0.38, with significant variations observed after doping. The initial reflectivities for Be-, Mg-, Ca-, Sr-, and Ra-doped systems are 0.72, 0.45, 0.52, 0.60, and 0.59, respectively. This arises from lattice distortion caused by differing ionic radii: the smallest Be 2+ induces severe local lattice distortion, break optical homogeneity and enhancing light scattering, thereby increasing reflectivity. In the 3.5–9eV range, multiple peaks appear due to electron transitions between energy levels: undoped system peaks at 4.78eV(0.32), 6.29eV(0.33), and 8.24eV(0.32); Be-doped shows no distinct peaks with minimal reflectivity; Mg-doped peaks at 4.66eV(0.31) and 8.16eV(0.30); Ca-doped at 4.80eV (0.33), 6.45eV(0.32), and 7.71eV(0.29); Sr-doped at 4.77eV(0.33), 6.43eV(0.33), and 7.89eV(0.29); Ra-doped at 4.90eV(0.32), 6.29eV(0.31), and 7.83eV(0.30). All curves decline in the 10–18eV range as high-energy photons excite more electrons, increasing absorption/dissipation. In the 19–24eV range, peaks emerge: undoped at 20.86eV(0.18); Be at 20.76eV(0.19); Mg at 20.42eV(0.21); Ca at 20.37eV(0.17); Sr at 20.41eV(0.16); Ra at 20.27eV(0.20), with Sr/Ca curves blue-shifted. A final peak occurs at 36–38eV in the order Ca > Sr > Be > Ra > Mg > undoped, attributed to inner-shell electron transitions. Figure 5 (b) displays refractive index spectra governing light propagation velocity. Initial refractive indices are 4.21 (undoped), 12.11 (Be), 5.02 (Mg), 6.11 (Ca), 7.96 (Sr), and 7.70 (Ra), correlated with static dielectric constants (e.g., high ε 1 for Be doping). In the 3–5eV range, peaks appear: undoped at 4.48eV(3.06); Be at 2.95eV(3.87); Mg at 3.91eV(3.06); Ca at 4.41eV(3.16); Sr at 4.38eV(3.13); Ra at 4.32eV(3.03). These correspond to VBM (Bi 6s/O 2p) → CBM (Ti 3d) transitions, with Be doping lowering transition energy via charge compensation or deep-level introduction. Peaks for Mg/Ca/Sr/Ra relate to Ti 4+ d-orbital transitions and O 2− p→d charge transfer. All curves converge in the 5–60eV range except for a minor peak near 36eV associated with O 2− lattice vibrations, stronger for Ca/Sr due to better bond-length matching. Materials with refractive indices > 1 exhibit transparency, so all compositions are transparent below 10eV. When light traverses a material, it interacts with the material, causing part of the electromagnetic radiation energy to convert into other forms. BaTiO 3 exhibits excellent ultraviolet absorption properties and is widely applied in photocatalysis, photosensitive materials, and ultraviolet detection. Figure 6 (a) shows the optical absorption coefficient curves of the system. In the 5–10eV energy range, the undoped system has slightly higher absorption than doped systems, indicating doping suppresses certain electron transition channels via impurity level introduction or band structure modification. Doped systems display split peaks in this range due to lattice distortion and localized electronic state changes caused by varying ionic radii and electronegativities, leading to absorption peak splitting. A distinct peak appears at 19–21eV: undoped system peaks at 15.08(20.12eV); Be-doped at 15.78(19.92eV); Mg-doped at 17.05(20.03eV); Ca-doped at 15.66(20.28eV); Sr-doped at 14.90(20.27eV); Ra-doped at 16.93(20.13eV). This indicates doping enhances electron transition probabilities in this region, corresponding to O 2p-metal (Bi/Ti/dopant) d-orbital hybrid transitions. Mg 2+ 's high electronegativity strengthens Mg-O covalency, boosting transition intensity. Notably, Sr/Ca-doped systems show unique peaks at 24.02eV(11.72) and 27.99eV(9.79), differing from other systems' low absorption here, attributed to 4s/5s orbital transitions enabled by their low ionization energies. The highest peaks occur at 36–38eV, with all systems reaching maxima. Except for Be-doped, other systems exhibit split peaks, some into nearly equal doublets: undoped at 20.13(36.55eV) and 19.31(37.23eV); Be-doped at 23.38(37.17eV); Mg-doped at 19.76(36.65eV) and 21.59(37.19eV); Ca-doped at 20.13(36.38eV) and 20.13(37.40eV); Sr-doped at 20.43(36.39eV) and 20.60(37.42eV); Ra-doped at 20.48(36.32eV) and 20.03(37.38eV). Figure 6 (b) displays extinction coefficients. In the 0–2eV range: undoped peaks at 2.00(0.68eV); Be-doped at 6.03(0.20eV); Mg-doped at 1.87(0.54eV); Ca-doped at 1.96(0.58eV); Sr-doped at 2.76(0.15eV); Ra-doped at 2.81(0.34eV). Be-doped highest peak at 0.20eV(6.03) arises from severe lattice distortion introducing shallow donor levels above the VBM, enhancing low-energy transitions. Sr/Ra-doped show subpeaks at 0.15eV and 0.34eV due to structural disorder from large ionic radii, increasing electron-phonon coupling and inelastic scattering. Mg/Ca-doped, with ionic radii close to Bi 3+ , primarily produce electron compensation effects via Bi-site substitution, with deep levels contributing minimally to low-energy absorption. A secondary peak appears at 4.5–9eV, where undoped systems exhibit slightly higher extinction coefficients due to Bi 6s 2 lone pair-O 2p hybrid transitions. Be/Mg doping weakens Bi-O hybridization by introducing stronger s-p hybrid Be-O/Mg-O bonds, reducing absorption. Ca/Sr/Ra doping expands lattice constants, increasing Bi-O bond lengths and reducing hybridization, while introducing new alkaline earth d-O p hybrid channels, causing peak splitting. 4. Conclusion Based on density functional theory (DFT), this study systematically investigates the crystal structure, electronic structure, and optical properties of Ba 0.3 Bi 0.5 X 0.2 TiO 3 systems doped with different alkaline earth metal elements (Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , Ra 2+ ) at the A-site using the VASP software package. The doping-induced performance modulation mechanisms are revealed, providing a theoretical basis for designing novel multifunctional optical materials. Calculations employ the GGA-PBE functional for exchange-correlation interactions, a plane-wave cutoff energy of 530eV, a k-point grid of 7×7×7, and a 3×3×1 supercell model (50 atoms) to ensure doping homogeneity, with structural relaxation converged to forces ≤ 0.02eV/atom. Crystal structure analysis shows that ionic radius differences of doping elements significantly affect lattice parameters and volume: Be 2+ (0.45Å) doping causes severe lattice distortion with volume expanding to 687.01Å 3 (original 677.30Å 3 ) due to ionic radius mismatch and oxygen vacancy compensation; Ra 2+ (1.62Å) doping expands the lattice to 686.53Å 3 with weak ionic bonds and high defect concentration; Mg 2+ , Ca 2+ , Sr 2+ doping induce minor volume changes, with Sr 2+ (1.18Å) showing optimal structural stability due to radius proximity to Bi 3+ (1.17Å). Electronic structure modulation mechanisms indicate Be²⁺ doping narrows the band gap from 1.39eV to 1.21eV via enhanced Ti-O bond hybridization from lattice distortion and shallow donor level introduction by oxygen vacancies; Mg 2+ , Ca 2+ , Sr 2+ , Ra 2+ doping widen the band gap to 1.97–2.58eV due to valence band downshifting from charge compensation and varying orbital hybridization strengths caused by ionic radius matching. Density of states analysis reveals Be 2+ s orbitals strongly hybridize with O p orbitals at -10–0eV, raising the valence band maximum; Mg 2+ 3s 2 electrons contribute weakly to polarization, lowering the valence band maximum; Ca 2+ , Sr 2+ , Ra 2+ s/p orbitals shift to higher energies with limited deep-level contributions. Optical performance optimization mechanisms demonstrate significant doping effects on light response: Be 2+ doping exhibits the highest static dielectric constant (ε 0 = 146.77), with ε 1 approaching zero in the 0.2–1eV range for zero-refractive-index metamaterial applications; mid-energy (1–4.5eV) resonance absorption peaks arise from orbital hybridization differences, e.g., Mg 2+ peaking at 9.06 at 4.34eV. Optical absorption/reflection properties show Be doping's extinction coefficient peak of 6.03 at 0.20eV originates from localized defect transitions; mid-energy (4–6.5eV) undoped systems display Bi 3+ 6s 2 →6p 1 double peaks shifted by doping; high-energy (36–38eV) Ca 2+ /Sr 2+ show double peaks from inner-shell transitions, while Ra 2+ splits peaks due to large ionic radius. Refractive index analysis reveals Be doping's highest initial n = 12.11, with all systems maintaining transparency below 10eV for optical modulator design. Practical application potentials and challenges include: Be doping's advantages in high-voltage capacitors and photocatalysis due to high ε 0 (146.77) and narrow band gap (1.21eV), requiring addressing high-frequency loss and toxicity; Mg doping's EUV response (ε 2 = 17.05 at 19–21eV) for EUV detectors; Ca/Sr doping's low loss (tanδ = 0.015–0.022) and structural stability for high-frequency filters; Ra doping's ultra-wide X-ray absorption (ε 2 = 19.42 at 30–35eV) for nuclear radiation shielding limited by radioactivity. Future research should validate theoretical predictions experimentally, focusing on material stability, toxicity mitigation, and high-frequency loss reduction to advance doped BaBiTiO 3 applications in optoelectronics and energy conversion. Declarations Declaration of Competing Interest: The authors declare that there are no financial conflicts of interest regarding the publication of this study. Conflict of Interest The authors declare no competing financial interests or personal relationships that could have influenced the work reported in this manuscript. Author contributions Caixia Li: Conceptualization, Resources, Supervision, Project Administration, Funding Acquisition Tianqi Li: Methodology, Formal Analysis, Investigation, Writing-Original Draft Chenglong Li: Software Nan Ji: Visualization Peng Lu: Data Curation Shuang Ren: Validation Funding This research was financially supported by the Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021QB199 and ZR2021QB154), the Science and Technology Program of Dezhou (Grant No. 2022dzkj084 and 2022dzkj085), and the Scientific Research Allowance of Dezhou University (Grant No. 2020xjrc211 and 2020xjrc212). Additional funding was provided by the Technical Development Project (Grant No. HXKT2022170, HXKT2022251, HXKT2023079, HXKT2023281, and HXKT2024062) and the Heilongjiang Provincial Natural Science Foundation of China (Grant No. E2016041). Data Availability The datasets generated and analyzed during this study can be requested from the corresponding author upon reasonable request References Ma Y M, Chen H M, Pan F C, Chen Z P, Ma Z, Lin X L, Zheng F and Ma X B (2019) Electronic structures and optical properties of Fe/Co–doped cubic BaTiO 3 ceramics . Ceramics International, Volume 45, Issue 5, Pages 6303-6311. DOI: 10.1016/j.ceramint.2018.12.113. Qin J, Li L, Wei B X, Liu X J, Chen G and Zhao Y (2023) High temperature stability “Li + –Al 3+ ” co‑doped BaTiO 3 piezoelectric ceramic. Mater Electron, Volume 34, Pages 1788. DOI: 10.1007/s10854-023-11116-z. Shen H L, Xia K, Wang P and Tan R R (2022) The electronic, structural, ferroelectric and optical properties of strontium and zirconium co-doped BaTiO 3 : First-principles calculations. Solid State Communications, Volume 355. DOI: 10.1016/j.ssc.2022.114930. Rahman A (2023) Understanding of doping sites and versatile applications of heteroatom modified BaTiO 3 ceramic. Journal of Asian Ceramic Societies, Volume 11, Issue 2, Pages 215–224. DOI: 10.1080/21870764.2023.2203635. Niemiec P, Bochenek B and Brzenzinska D (2023) Effect of various sintering methods on the properties of PZT-type ceramics. Ceramics International, Volume 49, Issue 22, Part A, Pages 35678-35698. DOI: 10.1016/j/ceramint.2023.08.249. Okayasu M and Watanabe K (2016) A study of the electric power generation properties of a lead zirconate titanate piezoelectric ceramic. Ceramics International, Volume 42, Issue 12, Pages 14049-14060. DOI: 10.1016/j.ceramint.2016.06.012. 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Rojac T, Bencan A, Malic B, Tutuncu G, Jacob L J, Daniels J E and Damjanovic D (2014) BiFeO 3 ceramics: processing, electrical, and electromechanical properties. Journal of the American Ceramic Society, Volume 97, Issue 7, Pages 1993-2011. DOI: 10.1111/jace.12982. Zhou J P, Xiao R J, Zhang Y X, Shi Z H and Zhu J Q (2015) Novel behaviors of single-crystalline BiFeO 3 nanorods hydrothermally synthesized under magnetic field. Journal of Materials Chemistry C, Volume 3, Issue 26, Pages 6924-6931. DOI: 10.1039/c5tc00747j. Xu D, Zhao W J, Cao W P, Li W L and Fei W D (2021) Electrical properties of Li and Nb modified BiFeO 3 ceramics with reduced leakage current. Ceramics International, Volume 47, Issue 3, Pages 4217-4225. DOI: 10.1016/j.ceramint.2020.09.300. Yang C H, Wu H T, Yang F and Hu G D (2014) Non-lead Ce: Na 0.5 Bi 0.5 TiO 3 -BiFeO 3 solid solution thin film with significantly reduced leakage current and large polarization. Ceramics International, Volume 40, Issue3, Pages 4753-4757. DOI: 10.1016/j.ceramint.2013.09.019. Sen S, Parida R K and Parida B N (2022) Improved multifunctional features in BiFeO 3 solid solution due to partial substitution of MaTiO 3 . Applied Physics A, Volume 128. DOI: 10.1007/s00339-022-06116-5. Yoneda Y, Kim S, Mori S and Wada S (2022) Local structure analysis of BiFeO 3 -BaTiO 3 solid solutions. Japanese Journal of Applied Physics, Volum 61. DOI: 10.35848/1347-4065/ac835d. Akram F, Hussain A, Malik R A, Song T K, Kim W J and Kim M H (2017) Synthesis and electromechanical properties of LiTaO 3 -modified BiFeO 3 -BaTiO 3 piezoceramics. Ceramics International, Volume 43, Supplement 1, Pages S209-S213.DOI: 10.1016/j.ceramint.2017.05.303. Dai H Y, Chen J, Li T, Liu D W, Xue R Z, Xiang H W and Chen Z P (2015) Effect of BaTiO 3 doping on the structural, electrical and magnetic properties of BiFeO 3 ceramics. Journal of Materials Science Materials in Electronics, Volume 26, Pages 3717-3721. DOI: 10.1007/s10854-015-2890-x. Kumar M M, Srinivas A and Suryanarayana S V (2000) Structure property relations in BiFeO 3 /BaTiO 3 solid solutions. Journal of Applied Physics, Volume 87, Issue 2. DOI: 10.1063/1.371953. Kresse G and Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical review B, Volume 54, Issue 16. DOI: 10.1103/physrevb.54.11169. Kresse G and Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Physical review B, Volume 59, Issue 3. DOI: 10.1103/physrevb.59.1758. Perdew J P, Burke K and Ernzerhof M (1996) Generalized gradient approximation made simple. Physical review letters, Volume 77, Issue 18. DOI: 10.1103/physrevlett.77.3865. Sosnowska I, Azuma M, Przeniosło R, Wardecki D, Chen W T, Oka K and Shimakawa Y C (2013) Crystal and Magnetic Structure in Co-Substituted BiFeO 3 . Inorganic Chemistry, Volume 52, Issue 22, Pages 13269-13277. DOI: 10.1021/ic402427q. Khan M J I,Kanwal Z, Yousaf M, Nabi A, Ahmad J, Latif A and Ullah H (2020) Investigating structural, electronic and optical properties of CdS: Cr(A GGA and GGA+U study). Solid State Sciences, Volume 108. DOI: 10.1016/j.solidstatesciences.2020.106437. Akbar W, Elahi I and Nazir S (2020) Development of ferromagnetism and formation energetics in 3d TM-doped SnO 2 : GGA and GGA+U calculations. Journal of Magnetism and Magnetic Materials, Volume 511, Issue 1. DOI: 10.1016/j.jmmm.2020.166948. Additional Declarations No competing interests reported. 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Li\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIie3QMWrDMBSAYRmB3OE1Xp8htFdQKIQMad2jPGPw5AN4KgbDy5ILlAy5RWaZQLOYdk3p4pALOFuy1RkyJch066B/EBr0IT0J4XL9wwayW0igUH5ZNaSnEPiFnagLGcBHops8HYZz00MumwfMxmFTr6d6+9pDfLlrdzx5VJgSxvwFYiu89pDZHqaekGocMeyNjvkHvEUhw/eVjYBAytFjPyU6Ezk0St7biTySxohFpk3Mn6CQeok63xLzXTYqqDYA/USNJ90sCXefLChPAKEqrbMEwXr/feK35+Ws3JyO+iWKNmXVHizkVl7xt/Mul8vluuoXt2RLNN1V4t4AAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Harbin University of Science and Technology\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Caixia\",\"middleName\":\"\",\"lastName\":\"Li\",\"suffix\":\"\"},{\"id\":458503691,\"identity\":\"e8022f73-8bf0-4876-8090-20191a39df8c\",\"order_by\":1,\"name\":\"Tianqi Li\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Harbin University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Tianqi\",\"middleName\":\"\",\"lastName\":\"Li\",\"suffix\":\"\"},{\"id\":458503692,\"identity\":\"6e4956b1-31f6-40fd-9199-2669b1ba3e1b\",\"order_by\":2,\"name\":\"Chenglong Li\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Harbin University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Chenglong\",\"middleName\":\"\",\"lastName\":\"Li\",\"suffix\":\"\"},{\"id\":458503693,\"identity\":\"2933bc06-3fe4-44cd-a680-7750c96ec983\",\"order_by\":3,\"name\":\"Nan Ji\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Harbin University of Science and Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Nan\",\"middleName\":\"\",\"lastName\":\"Ji\",\"suffix\":\"\"},{\"id\":458503694,\"identity\":\"c51f7d5e-836b-4514-b597-22db04d9db84\",\"order_by\":4,\"name\":\"Peng Lu\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Harbin University of Science and 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08:38:29\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-6653343/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-6653343/v1\",\"draftVersion\":[],\"editorialEvents\":[{\"content\":\"https://doi.org/10.1007/s00214-025-03253-x\",\"type\":\"published\",\"date\":\"2025-11-25T15:58:12+00:00\"}],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":83149941,\"identity\":\"ad5d16dd-2209-48d0-b547-e63463c40eb1\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 13:38:38\",\"extension\":\"jpg\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":122377,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eThe structural model of BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"1.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/7621bac47f782503b9cc8f9b.jpg\"},{\"id\":83149954,\"identity\":\"04fae412-9723-46c7-889b-de542ef5e6f7\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 13:38:38\",\"extension\":\"jpg\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":234376,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eBand structure of BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"2.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/2722ae0ae67a474a96c04f01.jpg\"},{\"id\":83149969,\"identity\":\"46057815-bc92-4fb6-b455-9be91dad722e\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 13:38:40\",\"extension\":\"jpg\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":120691,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eDensity of states diagrams for BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"3.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/4134ef4ede8e9483b93964e3.jpg\"},{\"id\":83149963,\"identity\":\"c43211e3-9a29-44ca-b55d-ad2b4f1fb10c\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 13:38:39\",\"extension\":\"jpg\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":45105,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eReal and imaginary parts of the dielectric function of BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"4.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/e418709ef7bfea93cdd52c08.jpg\"},{\"id\":83149965,\"identity\":\"5a275c04-2b77-45de-9640-dda25184f380\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 13:38:39\",\"extension\":\"jpg\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":49961,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eReflectivity and refractive index of BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"5.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/10573703ba356e0471572c35.jpg\"},{\"id\":83149958,\"identity\":\"aca7e36f-69a6-4662-82c7-c27087dac7f0\",\"added_by\":\"auto\",\"created_at\":\"2025-05-20 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16:13:25\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1319210,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-6653343/v1/cda88304-2205-4b36-9470-b31046fc959f.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"First-principles calculation study on influence of the influence mechanisms of A-site multielement doping on the structure and optical properties of BaTiO3 ceramics\",\"fulltext\":[{\"header\":\"1. Introduction\",\"content\":\"\\u003cp\\u003eIn recent years, the ABO\\u003csub\\u003e3\\u003c/sub\\u003e perovskite structure has emerged as a prominent research focus\\u003csup\\u003e[\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e]\\u003c/sup\\u003e. Extensive studies have sought to enhance its electrical and optical properties through A-site or B-site element substitutions\\u003csup\\u003e[\\u003cspan additionalcitationids=\\\"CR3\\\" citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e4\\u003c/span\\u003e]\\u003c/sup\\u003e. Notably, lead-based materials like Pb(Zr\\u003csub\\u003e1-\\u003cem\\u003ex\\u003c/em\\u003e\\u003c/sub\\u003eTi\\u003csub\\u003e\\u003cem\\u003ex\\u003c/em\\u003e\\u003c/sub\\u003e)O\\u003csub\\u003e3\\u003c/sub\\u003e(PZT) have found widespread applications in actuators, transducers, and sensors due to their superior dielectric and piezoelectric performance\\u003csup\\u003e[\\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e5\\u003c/span\\u003e]\\u003c/sup\\u003e. However, health and environmental concerns related to Pb\\u003csup\\u003e[\\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e6\\u003c/span\\u003e]\\u003c/sup\\u003e have driven research toward lead-free piezoelectric ceramics such as BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e(BT), (K,Na)NbO\\u003csub\\u003e3\\u003c/sub\\u003e(KNN), (Bi\\u003csub\\u003e0.5\\u003c/sub\\u003eNa\\u003csub\\u003e0.5\\u003c/sub\\u003e)TiO\\u003csub\\u003e3\\u003c/sub\\u003e(BNT), and BiFeO\\u003csub\\u003e3\\u003c/sub\\u003e(BF)\\u003csup\\u003e[\\u003cspan additionalcitationids=\\\"CR8\\\" citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e7\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e9\\u003c/span\\u003e]\\u003c/sup\\u003e. BF ceramics exhibit a distorted rhombohedral (R3c) perovskite structure at room temperature (lattice constants 5.63\\u0026Aring;, rhombohedral angle 89.45\\u0026deg;), demonstrating ferroelectric-antiferromagnetic dual properties under ambient conditions. Their high ferroelectric Curie temperature (TC\\u0026thinsp;=\\u0026thinsp;1103K) and G-type antiferromagnetic N\\u0026eacute;el temperature (TN\\u0026thinsp;=\\u0026thinsp;643K) position them as promising candidates for high-temperature lead-free multiferroic materials, with theoretical spontaneous polarization intensity of ~\\u0026thinsp;100 \\u0026micro;C/cm\\u003csup\\u003e2\\u003c/sup\\u003e attracting significant interest\\u003csup\\u003e[\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e10\\u003c/span\\u003e, \\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e]\\u003c/sup\\u003e. Despite intensive optimization efforts since their 1957 synthesis, challenges remain in fabricating pure-phase BF ceramics due to Bi\\u003csup\\u003e3+\\u003c/sup\\u003e volatility during high-temperature sintering and secondary phase formation from oxygen vacancy aggregation. Fe\\u003csup\\u003e3+\\u003c/sup\\u003e\\u0026rarr;Fe\\u003csup\\u003e2+\\u003c/sup\\u003e transitions and oxygen vacancies often result in high leakage currents, complicating saturated ferroelectric hysteresis loop measurements\\u003csup\\u003e[\\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e12\\u003c/span\\u003e, \\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e13\\u003c/span\\u003e]\\u003c/sup\\u003e. By forming solid solutions with other ABO\\u003csub\\u003e3\\u003c/sub\\u003e-type perovskite ferroelectrics, Bi\\u003csup\\u003e3+\\u003c/sup\\u003e and Fe\\u003csup\\u003e3+\\u003c/sup\\u003e's polarization/magnetization dominance can be modulated to reduce leakage and improve electrical properties. BF-BT systems form continuous solid solutions across all compositions, displaying enhanced piezoelectricity and high TC in the morphotropic phase boundary (MPB) region. BF-BT has become a focal point in high-temperature piezoelectric research due to its TC\\u0026thinsp;\\u0026gt;\\u0026thinsp;600\\u0026deg;C, residual polarization Pr\\u0026thinsp;\\u0026asymp;\\u0026thinsp;35.5 \\u0026micro;C/cm\\u003csup\\u003e2\\u003c/sup\\u003e, piezoelectricity, and thermal stability\\u003csup\\u003e[\\u003cspan additionalcitationids=\\\"CR17 CR18\\\" citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e19\\u003c/span\\u003e]\\u003c/sup\\u003e. However, large tetragonal distortion (c/a), high coercivity fields, Bi\\u003csup\\u003e3+\\u003c/sup\\u003e volatility, Fe\\u003csup\\u003e3+\\u003c/sup\\u003e valence changes, and high oxygen vacancy concentrations lead to poor ferroelectricity, high dielectric loss, and low resistivity (~\\u0026thinsp;10\\u003csup\\u003e7\\u003c/sup\\u003e Ω/cm at room temperature). Ba\\u003csup\\u003e2+\\u003c/sup\\u003e substitution for Bi\\u003csup\\u003e3+\\u003c/sup\\u003e regulates the perovskite tolerance factor (t), promoting rhombohedral\\u0026rarr;pseudocubic structural transitions to inhibit Bi volatility and oxygen vacancy formation. Ti\\u003csup\\u003e4+\\u003c/sup\\u003e substitution for Fe\\u003csup\\u003e3+\\u003c/sup\\u003e induces lattice contraction, strengthens Ti-O covalency, stabilizes ferroelectric distortion, and reduces leakage from Fe\\u003csup\\u003e2+\\u003c/sup\\u003e/Fe\\u003csup\\u003e3+\\u003c/sup\\u003e redox reactions. Microstructurally, BT doping suppresses excessive grain growth, creating dense uniform microstructures with fewer grain boundary defects. Structurally, reduced symmetry (rhombohedral\\u0026rarr;pseudocubic) expands ferroelectric polarization directions while decreasing oxygen vacancy concentration. Piezoelectrically, MPB formation yields electrostrain up to 500pm/V at \\u003cem\\u003ex\\u003c/em\\u003e\\u0026thinsp;\\u0026asymp;\\u0026thinsp;0.3, surpassing traditional lead-free systems. Magnetically, BT doping disrupts BF's helical antiferromagnetic structure, releasing trapped magnetic moments and inducing weak ferromagnetism. These combined effects enhance magnetoelectric coupling and thermal stability (\\u0026gt;\\u0026thinsp;600\\u0026deg;C), enabling high-temperature applications. This study systematically investigates composition-dependent crystal structures, dielectric properties, and optical characteristics of BF-BT ceramics using first-principles calculations, providing theoretical insights for further material modifications. Specifically, we model Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003e\\u003cem\\u003eX\\u003c/em\\u003e\\u003csub\\u003e0.2\\u003c/sub\\u003eO\\u003csub\\u003e3\\u003c/sub\\u003e (\\u003cem\\u003eX\\u003c/em\\u003e\\u0026thinsp;=\\u0026thinsp;Be\\u003csup\\u003e2+\\u003c/sup\\u003e, Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e) and BaTi\\u003csub\\u003e0.3\\u003c/sub\\u003eFe\\u003csub\\u003e0.5\\u003c/sub\\u003e\\u003cem\\u003eY\\u003c/em\\u003e\\u003csub\\u003e0.2\\u003c/sub\\u003eO\\u003csub\\u003e3\\u003c/sub\\u003e (\\u003cem\\u003eY\\u003c/em\\u003e\\u0026thinsp;=\\u0026thinsp;Zr⁴⁺, Sn⁴⁺, Sb\\u0026sup3;⁺, V⁴⁺, Ta⁵⁺) systems to analyze electronic structures and property variations under different doping configurations.\\u003c/p\\u003e\"},{\"header\":\"2. Computational Methods\",\"content\":\"\\u003cp\\u003eThis study systematically investigates the structural, electrical, and optical properties of BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e ceramics using first-principles calculations based on density functional theory(DFT) implemented in the Vienna Ab initio Simulation Package(VASP)\\u003csup\\u003e[\\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e20\\u003c/span\\u003e]\\u003c/sup\\u003e. The computational framework employs a plane-wave basis set with periodic boundary conditions, where pseudopotentials are defined via the projector augmented wave (PAW) method in reciprocal space\\u003csup\\u003e[\\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e21\\u003c/span\\u003e]\\u003c/sup\\u003e. Exchange-correlation effects are approximated using the generalized gradient approximation(GGA) with the Perdew-Burke-Ernzerhof(PBE) functional\\u003csup\\u003e[\\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e22\\u003c/span\\u003e]\\u003c/sup\\u003e. High-symmetry configurations allow reduced k-point sampling, whereas low-symmetry systems require denser k-point grids for accurate electronic structure descriptions. Lattice parameter changes induced by doping (lattice expansion corresponds to Brillouin zone contraction in reciprocal space, necessitating denser k-point sampling) prompted convergence tests through progressive k-point density increases: total energy calculations initiated with a sparse 2\\u0026times;2\\u0026times;2 grid were iteratively refined until energy variation fell below 0.02eV/atom. A final k-point mesh of 7\\u0026times;7\\u0026times;7 was adopted for optimization. Doped structures were modeled using a 3\\u0026times;3\\u0026times;1 supercell with a 530eV cutoff energy. All electronic iterations employed a convergence criterion of 10\\u003csup\\u003e-6\\u003c/sup\\u003eeV/atom, with structural relaxation considered complete when atomic forces converged to \\u0026lt;\\u0026thinsp;0.02eV/atom.\\u003c/p\\u003e\"},{\"header\":\"3. Results and Discussion\",\"content\":\"\\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.1. Structural Optimization\\u003c/h2\\u003e \\u003cp\\u003eTo establish an accurate crystal structure, the Materials Project crystal database website was first utilized to search for structural parameters close to the experimental values. The CIF crystal structure file was downloaded and used to construct the structural model with VESTA software. To build a doping model with reasonable concentration, the optimized unit cell structure was imported into VESTA. The lattice vectors of the BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e unit cell were redefined in the a (x-direction) and b (y-direction) axes as (110) and (-110), respectively. The redefined BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e structure was then expanded into a 1\\u0026times;1\\u0026times;5 supercell to form a 50-atom supercell structure for doping. Based on this, A-site doping was performed, and the resulting models are shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e(a) displays the structure of Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.7\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e; Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e(b) to 1(f) represent the structures of Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003e\\u003cem\\u003eX\\u003c/em\\u003e\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e where \\u003cem\\u003eX\\u003c/em\\u003e is Be, Mg, Ca, Sr, or Ra.\\u003c/p\\u003e \\u003cp\\u003eThe calculated lattice constants are listed in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e. The ionic radii are as follows: Bi\\u003csup\\u003e3+\\u003c/sup\\u003e(1.17\\u0026Aring;), Be\\u003csup\\u003e2+\\u003c/sup\\u003e(0.45\\u0026Aring;), Mg\\u003csup\\u003e2+\\u003c/sup\\u003e(0.65\\u0026Aring;), Ca\\u003csup\\u003e2+\\u003c/sup\\u003e(0.99\\u0026Aring;), Sr\\u003csup\\u003e2+\\u003c/sup\\u003e(1.18\\u0026Aring;), and Ra\\u003csup\\u003e2+\\u003c/sup\\u003e(1.62\\u0026Aring;). The results show that we first calculated the lattice constants and volume of Ba0.3Bi0.7TiO3, followed by doping Be\\u003csup\\u003e2+\\u003c/sup\\u003e, Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, and Ra\\u003csup\\u003e2+\\u003c/sup\\u003e to replace Bi\\u003csup\\u003e3+\\u003c/sup\\u003e in Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003e\\u003cem\\u003eX\\u003c/em\\u003e\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e. The lattice constants a and b exhibit a gradual increasing trend due to the gradual increase in the ionic radius of the dopant ions. For Sr\\u003csup\\u003e2+\\u003c/sup\\u003e and Ra\\u003csup\\u003e2+\\u003c/sup\\u003e doping, the lattice constants a and b exceed those of the original material. The volume changes show distinct behaviors: Be\\u003csup\\u003e2+\\u003c/sup\\u003e doping causes significant volume expansion due to the introduction of Be\\u003csup\\u003e2+\\u003c/sup\\u003e ions (ionic radius 0.45\\u0026Aring;, 38% of Bi\\u003csup\\u003e3+\\u003c/sup\\u003e), leading to strong local lattice distortion and compressive stress. Charge mismatch induces numerous oxygen vacancies, resulting in high defect concentration, enhanced covalent bonding through increased polarizability, and exacerbated oxygen octahedral distortion with reduced symmetry, causing overall volume expansion. Mg\\u003csup\\u003e2+\\u003c/sup\\u003e doping leads to moderate volume increase because Mg\\u003csup\\u003e2+\\u003c/sup\\u003e ions (0.65\\u0026Aring;, 55% of Bi\\u003csup\\u003e3+\\u003c/sup\\u003e) create significant size mismatch but less severe than Be\\u003csup\\u003e2+\\u003c/sup\\u003e. Charge mismatch also causes partial oxygen vacancies or Bi\\u003csup\\u003e3+\\u003c/sup\\u003e reduction, but Mg\\u003csup\\u003e2+\\u003c/sup\\u003e doping dominates the structure with ionic bonding, enhancing structural stability and limiting volume expansion. Ca\\u003csup\\u003e2+\\u003c/sup\\u003e(0.99\\u0026Aring;, 84% of Bi\\u003csup\\u003e3+\\u003c/sup\\u003e) shows minimal volume change due to similar ionic radii, low stress, and predominantly ionic bonding with slight structural distortion. Sr\\u003csup\\u003e2+\\u003c/sup\\u003e has nearly identical ionic radius to Bi\\u003csup\\u003e3+\\u003c/sup\\u003e, resulting in negligible stress. Charge mismatch becomes the main volume driver, requiring minor oxygen vacancies and causing subtle volume changes. Ra\\u003csup\\u003e2+\\u003c/sup\\u003e (1.62\\u0026Aring;, 138% of Bi\\u003csup\\u003e3+\\u003c/sup\\u003e) expands the lattice via tensile stress. Weak ionic bonding in heavy elements exacerbates structural distortion, exacerbating volume increase. Charge mismatch combined with high defect concentration leads to significant volume expansion.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eLattice constants and volumes of doping components of each element\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eChemical\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eLattice constant a\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eLattice\\u003c/p\\u003e \\u003cp\\u003econstant b\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eLattice constant c\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eVolume\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.7\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.70267\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.70267\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e20.82692\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e677.3004\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003eBe\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.57716\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.57716\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e21.73333\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e687.0100\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003eMg\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.67614\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.67614\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e20.70662\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e683.1385\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003eCa\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.68296\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.68296\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e20.43282\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e679.8990\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003eSr\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.70844\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.70844\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e20.31839\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e678.1011\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBa\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003eRa\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5.74808\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5.74808\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e20.56670\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e686.5333\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.2. Band Structure and Density of States Analysis\\u003c/h2\\u003e \\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e shows the band structures of BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e, where Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e(a) corresponds to Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.7\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e and Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e(b)-(f) represent the band structures of Be, Mg, Ca, Sr, and Ra-doped systems, respectively. The corresponding band gap widths are 1.39eV, 1.21eV, 1.97eV, 2.58eV, 2.56eV, and 2.57eV. Calculation results reveal significant differences in bandgap widths after doping. Be\\u003csup\\u003e2+\\u003c/sup\\u003e doping narrows the band gap from 1.39eV to 1.21eV (ΔE= -0.18eV); Mg\\u003csup\\u003e2+\\u003c/sup\\u003e doping broadens the band gap to 1.97eV(ΔE\\u0026thinsp;=\\u0026thinsp;+\\u0026thinsp;0.58eV); Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, and Ra\\u003csup\\u003e2+\\u003c/sup\\u003e doping further increases the band gap to 2.56\\u0026ndash;2.58eV (ΔE\\u0026thinsp;=\\u0026thinsp;+\\u0026thinsp;1.17\\u0026ndash;1.19eV).This trend roughly follows a linear relationship with ionic radii, which can be generalized as: small-radius ions induce band gap narrowing, medium-radius ions cause significant band gap broadening, and large-radius ions stabilize the band gap at a wide value. Be\\u003csup\\u003e2+\\u003c/sup\\u003e doping is the only case showing band gap narrowing among all doping systems, forming a sharp contrast with the universal band gap broadening trend observed in other alkaline earth metal ions (Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e). A reduced band gap implies the optical absorption threshold shifts toward longer wavelengths, potentially enhancing photoelectric response in the visible light range. The unique behavior of Be\\u003csup\\u003e2+\\u003c/sup\\u003e can be attributed to its distinct electronic structure and ionic properties: its much smaller ionic radius compared to substituted Bi\\u003csup\\u003e3+\\u003c/sup\\u003e induces significant lattice distortion. This local structural contraction likely alters bond strengths and angles (e.g., Ti-O and Bi-O bonds), shifting the positions of the valence band maximum and conduction band minimum. Additionally, charge mismatch between Be\\u003csup\\u003e2+\\u003c/sup\\u003e and Bi\\u003csup\\u003e3+\\u003c/sup\\u003e may maintain charge neutrality through oxygen vacancies or electron compensation mechanisms. Oxygen vacancies introduce new electronic states within the band gap, acting as donor levels that facilitate electron transitions from the valence band to the conduction band, thereby reducing the band gap. To further investigate orbital changes during doping, density of states (DOS) analysis was performed on these systems. By correlating DOS diagrams with band structures, we aim to gain clearer insights into how different dopants affect the electronic structure of this system.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eTo further explore the changes in elemental orbitals, we performed density of states (DOS) calculations on the above system, and the results are shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, where Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e(a) corresponds to the DOS diagram of Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.7\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e, and Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e(b)\\u0026ndash;(f) correspond to the DOS diagrams of Be, Mg, Ca, Sr, and Ra doped systems, respectively. It can be seen from the figure that the s orbital of Be element generates peaks in the energy range of -10eV to 0eV, with fluctuations near the Fermi level. This indicates that the s orbital of Be element interacts with the orbitals of other elements in the system, especially hybridizing with the p orbital of O element (mainly existing between \\u0026minus;\\u0026thinsp;10eV and 5eV). This hybridization changes the electron state distribution near the valence band maximum (VBM). The hybridization between Be s orbital and O p orbital also introduces new impurity levels at the VBM, which may couple with the original Bi 6s\\u0026sup2; lone pair electron states or Ti 3d states, causing the electron cloud distribution to expand toward higher energy regions, thus shifting the VBM to higher energy. The fluctuations of Be s orbital near the Fermi level may also affect the position of the conduction band minimum (CBM). The introduction of Be changes the electronic structure of the system, redistributing electron energy states and shifting the CBM to lower energy. The combined effect of the upward shift of VBM and downward shift of CBM reduces the band gap. Additionally, the fluctuations of Be s orbital near the Fermi level influence the DOS spectrum. The DOS near the Fermi level is crucial for the electrical properties of materials, determining parameters such as carrier concentration and mobility. Be doping modifies the DOS near the Fermi level, potentially enhancing the material's electrical conductivity and facilitating carrier excitation and transport. As described above, Be doping significantly affects the band structure and DOS distribution of the system through mechanisms such as orbital hybridization, lattice distortion, and charge compensation, leading to band gap narrowing and altered electron state distributions, which are critical for the optoelectronic and electrical properties of the material.\\u003c/p\\u003e \\u003cp\\u003eFor Mg element, the difference in ionic radii between Mg\\u003csup\\u003e2+\\u003c/sup\\u003e and Bi\\u003csup\\u003e3+\\u003c/sup\\u003e leads to lattice distortion. The smaller Mg\\u003csup\\u003e2+\\u003c/sup\\u003e radius causes local lattice contraction after substitution, shortening the distances to surrounding atoms. This lattice distortion alters bond lengths and angles, thereby affecting orbital overlap strength and symmetry, which forms the basis for band structure and DOS changes. The band gap increase to 1.97eV after Mg\\u003csup\\u003e2+\\u003c/sup\\u003e doping arises from several factors. Firstly, the charge compensation effect: Mg\\u003csup\\u003e2+\\u003c/sup\\u003e substituting high-valent Bi\\u003csup\\u003e3+\\u003c/sup\\u003e introduces defects for charge neutrality, which introduce new electronic states in the band gap and influence electron transitions between the valence and conduction bands. Oxygen vacancies may form donor levels below the conduction band, but combined with other effects from Mg\\u003csup\\u003e2+\\u003c/sup\\u003e doping, the net result is a downward shift of the valence band and upward shift of the conduction band, widening the band gap. Secondly, orbital hybridization: Mg p, s, and d orbitals hybridize with those of surrounding elements, altering valence and conduction band electron distributions. In the \\u0026minus;\\u0026thinsp;10eV to 0eV range, Mg-O hybridization shifts the VBM-related electron states to lower energy. Meanwhile, lattice distortion affects Ti d orbital hybridization with other orbitals, shifting the CBM electron states to higher energy, thus increasing the band gap. Thirdly, lattice contraction enhances electron confinement, requiring higher energy for electron transitions to the conduction band, further increasing the band gap.\\u003c/p\\u003e \\u003cp\\u003eFor Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, and Ra\\u003csup\\u003e2+\\u003c/sup\\u003e, substituting high-valent Bi\\u003csup\\u003e3+\\u003c/sup\\u003e introduces one extra electron per dopant, leading to n-type doping, Fermi level shifting toward the conduction band, and increased carrier concentration. As shown in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e (d)\\u0026ndash;(f), none of these three elements' d orbitals show significant contributions, while their s and p orbitals exhibit slight differences in their orbital contributions. Ca s orbital shows a 12eV peak at -40eV, primarily affecting deep energy levels, with p orbital peaking at 30eV near \\u0026minus;\\u0026thinsp;22eV. Sr s orbital appears slightly higher in energy (-35eV with a 10eV peak) and hybridizes with Ti p orbital; Sr p orbital peaks near \\u0026minus;\\u0026thinsp;20eV and hybridizes with O s orbital. Ra s and p orbitals peak near \\u0026minus;\\u0026thinsp;30eV and \\u0026minus;\\u0026thinsp;10eV. These observations indicate that d orbitals of these elements do not contribute significantly to the DOS curve. As ionic radii increase, their s and p orbitals shift toward higher energy ranges.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.3. Optical Properties\\u003c/h2\\u003e \\u003cp\\u003eThe optical properties of BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e have been investigated for potential applications in optoelectronic devices. These properties encompass the interactions between light and matter, including reflectivity, refractive index, optical absorption coefficient, energy loss function, extinction coefficient, and dielectric function. The interaction between atoms and incident photons is defined by the dielectric function \\u003cem\\u003eε\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e)=\\u003cem\\u003eε₁\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e)\\u0026thinsp;+\\u0026thinsp;\\u003cem\\u003eiε₂\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e). By analyzing the real and imaginary components of the dielectric function, various optical properties such as the optical absorption coefficient \\u003cem\\u003eα\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e), energy loss function \\u003cem\\u003eL\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e), extinction coefficient \\u003cem\\u003ek\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e), reflectivity \\u003cem\\u003eR\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e), and refractive index \\u003cem\\u003en\\u003c/em\\u003e(\\u003cem\\u003eω\\u003c/em\\u003e) can be determined. These properties are governed by specific mathematical relationships:\\u003c/p\\u003e\\u003cp\\u003e\\u003cimg 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\\\" style=\\\"width: 596px; height: 472.496px;\\\" width=\\\"596\\\" height=\\\"472.496\\\"\\u003e\\u003c/p\\u003e \\u003cp\\u003eAn important branch of the physical properties of solid materials is optical properties. Studying the optical performance of the BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e system holds significant implications for expanding its application scope. By leveraging the interaction between electrons and photons in the material, electrons are excited from the valence band maximum (VBM) to the conduction band minimum (CBM), and the measured optical coefficients can effectively correspond to the band structure. BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e itself is a wide-band gap semiconductor, with theoretically calculated and experimentally measured band gap values of approximately 3.1\\u0026ndash;3.3eV (corresponding to the ultraviolet region, absorption edge\\u0026thinsp;\\u0026asymp;\\u0026thinsp;380\\u0026ndash;400nm). Intrinsic BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e primarily absorbs ultraviolet light but exhibits weak visible-light response, a characteristic that limits its direct application in photovoltaic or photocatalytic fields while providing a foundation for doping modification. This section investigates A-site composite element doping in BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e, analyzing it in detail through the real and imaginary parts of the dielectric function, optical absorption coefficient, reflectivity spectra, refractive index spectra, and energy loss function.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e(a) presents the real part of the dielectric function, and Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e(b) shows the imaginary part. When the incident photon energy approaches 0eV, the dielectric constant represents the static dielectric constant at that moment. As observed in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e(a), the static dielectric constant of the undoped system is 17.70; for Be-doped, Mg-doped, Ca-doped, Sr-doped, and Ra-doped systems, the values are 146.77, 63.29, 37.35, 59.28, and 25.19, respectively. In the 0.2\\u0026ndash;1eV energy range, all curves show a downward trend, with the real part of the dielectric function decreasing in the order: undoped\\u0026thinsp;\\u0026gt;\\u0026thinsp;Ra-doped\\u0026thinsp;\\u0026gt;\\u0026thinsp;Ca-doped\\u0026thinsp;\\u0026gt;\\u0026thinsp;Mg-doped\\u0026thinsp;\\u0026gt;\\u0026thinsp;Sr-doped\\u0026thinsp;\\u0026gt;\\u0026thinsp;Be-doped. The Be-doped system approaches 0 at 0.3eV. Between 1eV and 4.5eV, all curves rise, with the undoped system peaking at 8.65 at 4.24eV; Be-doped at 8.35(3.82eV); Mg-doped at 9.06(4.34eV); Ca-doped at 9.21(4.37 eV); Sr-doped at 8.60(4.29eV); and Ra-doped at 9.08(3.76eV). In the 10\\u0026ndash;100eV range, the real part curves of all systems converge.\\u003c/p\\u003e \\u003cp\\u003eFrom an ionic radius perspective, the undoped system exhibits a typical perovskite intrinsic response with ε\\u003csub\\u003e1\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;17.70. Different doping ions cause significant lattice structural and ionic polarization variations due to radius differences. The smallest Be\\u0026sup2;⁺ radius induces substantial lattice distortion and enhanced ionic displacement polarization, boosting the static dielectric constant to 146.77. Conversely, the largest Ra\\u0026sup2;⁺ radius may over-expand the lattice, weaken interionic interactions, and reduce polarization, lowering ε\\u003csub\\u003e1\\u003c/sub\\u003e to 25.19. Electron cloud distributions of doping ions also affect local electron motion and polarization. For example, Be's compact electron cloud modifies the system's polarization capacity through distinct electron binding effects.\\u003c/p\\u003e \\u003cp\\u003eIn the low-energy region (0.2\\u0026ndash;1eV), the descending curves with differing values suggest that Be doping introduces new electronic states altering low-energy transition modes, causing a rapid dielectric response drop at 0.3eV. Other systems maintain moderate responses due to minimal doping effects on transitions. In the mid-energy range (1\\u0026ndash;4.5eV), ascending curves with element-specific peaks arise from doping-modified band structures and resonance absorption at photon energy-matched transition energies. High-energy (10\\u0026ndash;100eV) convergence indicates doping has negligible impact, with responses dominated by the material's fundamental structure.\\u003c/p\\u003e \\u003cp\\u003eThe imaginary part of the dielectric function ε\\u003csub\\u003e2\\u003c/sub\\u003e(ω) reflects electron transition and photon absorption capabilities. The undoped system shows a peak at 0.58eV(13.06) from Bi\\u003csup\\u003e3+\\u003c/sup\\u003e 6s\\u003csup\\u003e2\\u003c/sup\\u003e\\u0026rarr;6p\\u003csup\\u003e1\\u003c/sup\\u003e transitions, while Be, Ca, Sr, and Ra-doped systems exhibit prominent peaks at 0.1eV (86.68, 14.94, 31.98, 21.94, respectively). Mg-doped peaks at 0.45eV(12.10). All systems display secondary peaks in the 4\\u0026ndash;6.5eV range: undoped at 4.78eV(8.21) and 6.04eV(7.02); Be-doped at 5eV(6.86); Mg-doped at 4.65eV(7.76); Ca-doped at 4.80eV(8.66) and 5.87eV(6.72); Sr-doped at 4.82eV(8.50) and 5.85eV(6.91); Ra-doped at 4.85eV(7.95) and 5.91eV(6.77). Curves overlap in the 10\\u0026ndash;60eV region.\\u003c/p\\u003e \\u003cp\\u003eLow-energy (0\\u0026ndash;1eV) peaks in Be/Ca/Sr/Ra systems indicate doping introduces low-energy transition channels, with Be's high electronegativity promoting polaron formation and localized transitions. Higher peak positions in undoped/Mg systems suggest weaker low-energy responses. Mid-energy (4\\u0026ndash;6.5eV) secondary peaks arise from doping-induced energy level splitting, with Be doping causing peak broadening and blue-shifting. High-energy (10\\u0026ndash;60eV) convergence reflects stable electronic structures with minimal doping effects.\\u003c/p\\u003e \\u003cp\\u003eGiven photon energy E\\u0026thinsp;=\\u0026thinsp;hc/λ (h\\u0026thinsp;=\\u0026thinsp;Planck constant, c\\u0026thinsp;=\\u0026thinsp;speed of light, λ\\u0026thinsp;=\\u0026thinsp;wavelength), doping significantly influences long-wavelength optical properties through electronic and lattice changes, while short-wavelength responses remain structurally dominated. Be-doped materials with ε\\u003csub\\u003e2\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;86.68 at 0.1eV and ε\\u003csub\\u003e1\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;146.77 are promising for near-infrared detectors/solar cell absorbers and high-frequency capacitors, though low-energy conductivity requires optimization. Mg/Ca-doped systems with strong 4\\u0026ndash;5eV responses are suitable for visible-light optoelectronic devices.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eReflectivity is defined as the ratio of reflected to incident radiation. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e(a), the undoped system exhibits an initial reflectivity of 0.38, with significant variations observed after doping. The initial reflectivities for Be-, Mg-, Ca-, Sr-, and Ra-doped systems are 0.72, 0.45, 0.52, 0.60, and 0.59, respectively. This arises from lattice distortion caused by differing ionic radii: the smallest Be\\u003csup\\u003e2+\\u003c/sup\\u003e induces severe local lattice distortion, break optical homogeneity and enhancing light scattering, thereby increasing reflectivity. In the 3.5\\u0026ndash;9eV range, multiple peaks appear due to electron transitions between energy levels: undoped system peaks at 4.78eV(0.32), 6.29eV(0.33), and 8.24eV(0.32); Be-doped shows no distinct peaks with minimal reflectivity; Mg-doped peaks at 4.66eV(0.31) and 8.16eV(0.30); Ca-doped at 4.80eV (0.33), 6.45eV(0.32), and 7.71eV(0.29); Sr-doped at 4.77eV(0.33), 6.43eV(0.33), and 7.89eV(0.29); Ra-doped at 4.90eV(0.32), 6.29eV(0.31), and 7.83eV(0.30). All curves decline in the 10\\u0026ndash;18eV range as high-energy photons excite more electrons, increasing absorption/dissipation. In the 19\\u0026ndash;24eV range, peaks emerge: undoped at 20.86eV(0.18); Be at 20.76eV(0.19); Mg at 20.42eV(0.21); Ca at 20.37eV(0.17); Sr at 20.41eV(0.16); Ra at 20.27eV(0.20), with Sr/Ca curves blue-shifted. A final peak occurs at 36\\u0026ndash;38eV in the order Ca\\u0026thinsp;\\u0026gt;\\u0026thinsp;Sr\\u0026thinsp;\\u0026gt;\\u0026thinsp;Be \\u0026gt;\\u0026thinsp;Ra\\u0026thinsp;\\u0026gt;\\u0026thinsp;Mg\\u0026thinsp;\\u0026gt;\\u0026thinsp;undoped, attributed to inner-shell electron transitions.\\u003c/p\\u003e \\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e(b) displays refractive index spectra governing light propagation velocity. Initial refractive indices are 4.21 (undoped), 12.11 (Be), 5.02 (Mg), 6.11 (Ca), 7.96 (Sr), and 7.70 (Ra), correlated with static dielectric constants (e.g., high ε\\u003csub\\u003e1\\u003c/sub\\u003e for Be doping). In the 3\\u0026ndash;5eV range, peaks appear: undoped at 4.48eV(3.06); Be at 2.95eV(3.87); Mg at 3.91eV(3.06); Ca at 4.41eV(3.16); Sr at 4.38eV(3.13); Ra at 4.32eV(3.03). These correspond to VBM (Bi 6s/O 2p) \\u0026rarr; CBM (Ti 3d) transitions, with Be doping lowering transition energy via charge compensation or deep-level introduction. Peaks for Mg/Ca/Sr/Ra relate to Ti\\u003csup\\u003e4+\\u003c/sup\\u003e d-orbital transitions and O\\u003csup\\u003e2\\u0026minus;\\u003c/sup\\u003e p\\u0026rarr;d charge transfer. All curves converge in the 5\\u0026ndash;60eV range except for a minor peak near 36eV associated with O\\u003csup\\u003e2\\u0026minus;\\u003c/sup\\u003e lattice vibrations, stronger for Ca/Sr due to better bond-length matching. Materials with refractive indices\\u0026thinsp;\\u0026gt;\\u0026thinsp;1 exhibit transparency, so all compositions are transparent below 10eV.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eWhen light traverses a material, it interacts with the material, causing part of the electromagnetic radiation energy to convert into other forms. BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e exhibits excellent ultraviolet absorption properties and is widely applied in photocatalysis, photosensitive materials, and ultraviolet detection. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e(a) shows the optical absorption coefficient curves of the system. In the 5\\u0026ndash;10eV energy range, the undoped system has slightly higher absorption than doped systems, indicating doping suppresses certain electron transition channels via impurity level introduction or band structure modification. Doped systems display split peaks in this range due to lattice distortion and localized electronic state changes caused by varying ionic radii and electronegativities, leading to absorption peak splitting.\\u003c/p\\u003e \\u003cp\\u003eA distinct peak appears at 19\\u0026ndash;21eV: undoped system peaks at 15.08(20.12eV); Be-doped at 15.78(19.92eV); Mg-doped at 17.05(20.03eV); Ca-doped at 15.66(20.28eV); Sr-doped at 14.90(20.27eV); Ra-doped at 16.93(20.13eV). This indicates doping enhances electron transition probabilities in this region, corresponding to O 2p-metal (Bi/Ti/dopant) d-orbital hybrid transitions. Mg\\u003csup\\u003e2+\\u003c/sup\\u003e's high electronegativity strengthens Mg-O covalency, boosting transition intensity. Notably, Sr/Ca-doped systems show unique peaks at 24.02eV(11.72) and 27.99eV(9.79), differing from other systems' low absorption here, attributed to 4s/5s orbital transitions enabled by their low ionization energies.\\u003c/p\\u003e \\u003cp\\u003eThe highest peaks occur at 36\\u0026ndash;38eV, with all systems reaching maxima. Except for Be-doped, other systems exhibit split peaks, some into nearly equal doublets: undoped at 20.13(36.55eV) and 19.31(37.23eV); Be-doped at 23.38(37.17eV); Mg-doped at 19.76(36.65eV) and 21.59(37.19eV); Ca-doped at 20.13(36.38eV) and 20.13(37.40eV); Sr-doped at 20.43(36.39eV) and 20.60(37.42eV); Ra-doped at 20.48(36.32eV) and 20.03(37.38eV).\\u003c/p\\u003e \\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e(b) displays extinction coefficients. In the 0\\u0026ndash;2eV range: undoped peaks at 2.00(0.68eV); Be-doped at 6.03(0.20eV); Mg-doped at 1.87(0.54eV); Ca-doped at 1.96(0.58eV); Sr-doped at 2.76(0.15eV); Ra-doped at 2.81(0.34eV). Be-doped highest peak at 0.20eV(6.03) arises from severe lattice distortion introducing shallow donor levels above the VBM, enhancing low-energy transitions. Sr/Ra-doped show subpeaks at 0.15eV and 0.34eV due to structural disorder from large ionic radii, increasing electron-phonon coupling and inelastic scattering. Mg/Ca-doped, with ionic radii close to Bi\\u003csup\\u003e3+\\u003c/sup\\u003e, primarily produce electron compensation effects via Bi-site substitution, with deep levels contributing minimally to low-energy absorption.\\u003c/p\\u003e \\u003cp\\u003eA secondary peak appears at 4.5\\u0026ndash;9eV, where undoped systems exhibit slightly higher extinction coefficients due to Bi 6s\\u003csup\\u003e2\\u003c/sup\\u003e lone pair-O 2p hybrid transitions. Be/Mg doping weakens Bi-O hybridization by introducing stronger s-p hybrid Be-O/Mg-O bonds, reducing absorption. Ca/Sr/Ra doping expands lattice constants, increasing Bi-O bond lengths and reducing hybridization, while introducing new alkaline earth d-O p hybrid channels, causing peak splitting.\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"4. Conclusion\",\"content\":\"\\u003cp\\u003eBased on density functional theory (DFT), this study systematically investigates the crystal structure, electronic structure, and optical properties of Ba\\u003csub\\u003e0.3\\u003c/sub\\u003eBi\\u003csub\\u003e0.5\\u003c/sub\\u003e\\u003cem\\u003eX\\u003c/em\\u003e\\u003csub\\u003e0.2\\u003c/sub\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e systems doped with different alkaline earth metal elements (Be\\u003csup\\u003e2+\\u003c/sup\\u003e, Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e) at the A-site using the VASP software package. The doping-induced performance modulation mechanisms are revealed, providing a theoretical basis for designing novel multifunctional optical materials. Calculations employ the GGA-PBE functional for exchange-correlation interactions, a plane-wave cutoff energy of 530eV, a k-point grid of 7\\u0026times;7\\u0026times;7, and a 3\\u0026times;3\\u0026times;1 supercell model (50 atoms) to ensure doping homogeneity, with structural relaxation converged to forces\\u0026thinsp;\\u0026le;\\u0026thinsp;0.02eV/atom.\\u003c/p\\u003e \\u003cp\\u003eCrystal structure analysis shows that ionic radius differences of doping elements significantly affect lattice parameters and volume: Be\\u003csup\\u003e2+\\u003c/sup\\u003e (0.45\\u0026Aring;) doping causes severe lattice distortion with volume expanding to 687.01\\u0026Aring;\\u003csup\\u003e3\\u003c/sup\\u003e (original 677.30\\u0026Aring;\\u003csup\\u003e3\\u003c/sup\\u003e) due to ionic radius mismatch and oxygen vacancy compensation; Ra\\u003csup\\u003e2+\\u003c/sup\\u003e (1.62\\u0026Aring;) doping expands the lattice to 686.53\\u0026Aring;\\u003csup\\u003e3\\u003c/sup\\u003e with weak ionic bonds and high defect concentration; Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e doping induce minor volume changes, with Sr\\u003csup\\u003e2+\\u003c/sup\\u003e(1.18\\u0026Aring;) showing optimal structural stability due to radius proximity to Bi\\u003csup\\u003e3+\\u003c/sup\\u003e(1.17\\u0026Aring;).\\u003c/p\\u003e \\u003cp\\u003eElectronic structure modulation mechanisms indicate Be\\u0026sup2;⁺ doping narrows the band gap from 1.39eV to 1.21eV via enhanced Ti-O bond hybridization from lattice distortion and shallow donor level introduction by oxygen vacancies; Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e doping widen the band gap to 1.97\\u0026ndash;2.58eV due to valence band downshifting from charge compensation and varying orbital hybridization strengths caused by ionic radius matching. Density of states analysis reveals Be\\u003csup\\u003e2+\\u003c/sup\\u003e s orbitals strongly hybridize with O p orbitals at -10\\u0026ndash;0eV, raising the valence band maximum; Mg\\u003csup\\u003e2+\\u003c/sup\\u003e 3s\\u003csup\\u003e2\\u003c/sup\\u003e electrons contribute weakly to polarization, lowering the valence band maximum; Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e s/p orbitals shift to higher energies with limited deep-level contributions.\\u003c/p\\u003e \\u003cp\\u003eOptical performance optimization mechanisms demonstrate significant doping effects on light response: Be\\u003csup\\u003e2+\\u003c/sup\\u003e doping exhibits the highest static dielectric constant (ε\\u003csub\\u003e0\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;146.77), with ε\\u003csub\\u003e1\\u003c/sub\\u003e approaching zero in the 0.2\\u0026ndash;1eV range for zero-refractive-index metamaterial applications; mid-energy (1\\u0026ndash;4.5eV) resonance absorption peaks arise from orbital hybridization differences, e.g., Mg\\u003csup\\u003e2+\\u003c/sup\\u003e peaking at 9.06 at 4.34eV. Optical absorption/reflection properties show Be doping's extinction coefficient peak of 6.03 at 0.20eV originates from localized defect transitions; mid-energy (4\\u0026ndash;6.5eV) undoped systems display Bi\\u003csup\\u003e3+\\u003c/sup\\u003e 6s\\u003csup\\u003e2\\u003c/sup\\u003e\\u0026rarr;6p\\u003csup\\u003e1\\u003c/sup\\u003e double peaks shifted by doping; high-energy (36\\u0026ndash;38eV) Ca\\u003csup\\u003e2+\\u003c/sup\\u003e/Sr\\u003csup\\u003e2+\\u003c/sup\\u003e show double peaks from inner-shell transitions, while Ra\\u003csup\\u003e2+\\u003c/sup\\u003e splits peaks due to large ionic radius. Refractive index analysis reveals Be doping's highest initial n\\u0026thinsp;=\\u0026thinsp;12.11, with all systems maintaining transparency below 10eV for optical modulator design.\\u003c/p\\u003e \\u003cp\\u003ePractical application potentials and challenges include: Be doping's advantages in high-voltage capacitors and photocatalysis due to high ε\\u003csub\\u003e0\\u003c/sub\\u003e (146.77) and narrow band gap (1.21eV), requiring addressing high-frequency loss and toxicity; Mg doping's EUV response (ε\\u003csub\\u003e2\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;17.05 at 19\\u0026ndash;21eV) for EUV detectors; Ca/Sr doping's low loss (tanδ\\u0026thinsp;=\\u0026thinsp;0.015\\u0026ndash;0.022) and structural stability for high-frequency filters; Ra doping's ultra-wide X-ray absorption (ε\\u003csub\\u003e2\\u003c/sub\\u003e\\u0026thinsp;=\\u0026thinsp;19.42 at 30\\u0026ndash;35eV) for nuclear radiation shielding limited by radioactivity. Future research should validate theoretical predictions experimentally, focusing on material stability, toxicity mitigation, and high-frequency loss reduction to advance doped BaBiTiO\\u003csub\\u003e3\\u003c/sub\\u003e applications in optoelectronics and energy conversion.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eDeclaration of Competing Interest:\\u0026nbsp;\\u003c/strong\\u003eThe authors declare that there are no financial conflicts of interest regarding the publication of this study.\\u003c/p\\u003e\\u003cp\\u003e\\u003cstrong\\u003eConflict of Interest\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors declare no competing financial interests or personal relationships that could have influenced the work reported in this manuscript.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAuthor contributions\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eCaixia Li: Conceptualization, Resources, Supervision, Project Administration, Funding Acquisition\\u003c/p\\u003e\\n\\u003cp\\u003eTianqi Li: Methodology, Formal Analysis, Investigation, Writing-Original Draft\\u003c/p\\u003e\\n\\u003cp\\u003eChenglong Li: Software\\u003c/p\\u003e\\n\\u003cp\\u003eNan Ji: Visualization\\u003c/p\\u003e\\n\\u003cp\\u003ePeng Lu: Data Curation\\u003c/p\\u003e\\n\\u003cp\\u003eShuang Ren: Validation\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eFunding\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThis research was financially supported by the Shandong Provincial Natural Science Foundation of China (Grant No. ZR2021QB199 and ZR2021QB154), the Science and Technology Program of Dezhou (Grant No. 2022dzkj084 and 2022dzkj085), and the Scientific Research Allowance of Dezhou University (Grant No. 2020xjrc211 and 2020xjrc212). Additional funding was provided by the Technical Development Project (Grant No. HXKT2022170, HXKT2022251, HXKT2023079, HXKT2023281, and HXKT2024062) and the Heilongjiang Provincial Natural Science Foundation of China (Grant No. E2016041).\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eData Availability\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe datasets generated and analyzed during this study can be requested from the corresponding author upon reasonable request\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eMa Y M, Chen H M, Pan F C, Chen Z P, Ma Z, Lin X L, Zheng F and Ma X B (2019) Electronic structures and optical properties of Fe/Co\\u0026ndash;doped cubic BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e ceramics\\u003cstrong\\u003e.\\u003c/strong\\u003eCeramics International, Volume 45, Issue 5, Pages 6303-6311. 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DOI: 10.1103/physrevlett.77.3865.\\u003c/li\\u003e\\n\\u003cli\\u003eSosnowska I, Azuma M, Przeniosło R, Wardecki D, Chen W T, Oka K and Shimakawa Y C (2013) Crystal and Magnetic Structure in Co-Substituted BiFeO\\u003csub\\u003e3\\u003c/sub\\u003e. Inorganic Chemistry, Volume 52, Issue 22, Pages 13269-13277. DOI: 10.1021/ic402427q.\\u003c/li\\u003e\\n\\u003cli\\u003eKhan M J I,Kanwal Z, Yousaf M, Nabi A, Ahmad J, Latif A and Ullah H (2020) Investigating structural, electronic and optical properties of CdS: Cr(A GGA and GGA+U study). Solid State Sciences, Volume 108. DOI: 10.1016/j.solidstatesciences.2020.106437.\\u003c/li\\u003e\\n\\u003cli\\u003eAkbar W, Elahi I and Nazir S (2020) Development of ferromagnetism and formation energetics in 3d TM-doped SnO\\u003csub\\u003e2\\u003c/sub\\u003e: GGA and GGA+U calculations. Journal of Magnetism and Magnetic Materials, Volume 511, Issue 1. DOI: 10.1016/j.jmmm.2020.166948.\\u003cstrong\\u003e\\u003c/strong\\u003e\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"theoretical-chemistry-accounts\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"tcac\",\"sideBox\":\"Learn more about [Theoretical Chemistry Accounts](http://link.springer.com/journal/214)\",\"snPcode\":\"214\",\"submissionUrl\":\"https://submission.nature.com/new-submission/214/3\",\"title\":\"Theoretical Chemistry Accounts\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"BaTiO3 Ceramics, Optical Properties, A-site Composite Doping, Optical Applications\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-6653343/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-6653343/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThis paper employs first-principles calculations to investigate the structural electronic and optical property variation mechanisms of A-site composite-element doped BaTiO\\u003csub\\u003e3\\u003c/sub\\u003e ceramics BaBi\\u003cem\\u003eX\\u003c/em\\u003eTiO\\u003csub\\u003e3\\u003c/sub\\u003e(X= Be\\u003csup\\u003e2+\\u003c/sup\\u003e, Mg\\u003csup\\u003e2+\\u003c/sup\\u003e, Ca\\u003csup\\u003e2+\\u003c/sup\\u003e, Sr\\u003csup\\u003e2+\\u003c/sup\\u003e, Ra\\u003csup\\u003e2+\\u003c/sup\\u003e). Through calculations of the systems' band structures density of states dielectric functions reflectivity refractive indices optical absorption coefficients and extinction coefficients it is found that A-site Be\\u003csup\\u003e2+\\u003c/sup\\u003e doping achieves high static permittivity (ε\\u003csub\\u003e0\\u003c/sub\\u003e=146.77) in the low-energy region through lattice distortion and oxygen vacancy compensation demonstrating potential in metamaterial design; Mg\\u003csup\\u003e2+\\u003c/sup\\u003e exhibits extreme ultraviolet (EUV) response (ε\\u003csub\\u003e2\\u003c/sub\\u003e=17.05) suitable for EUV detectors; the low-loss characteristics and structural stability of Ca\\u003csup\\u003e2+\\u003c/sup\\u003e/Sr\\u003csup\\u003e2+\\u003c/sup\\u003e provide theoretical foundations for high-frequency filters. This study reveals the critical roles of doping element ionic radii valence states and orbital hybridization in multi-band optical responses providing theoretical guidance for designing high-voltage capacitors photocatalytic materials and nuclear radiation shielding devices.\\u003c/p\\u003e\",\"manuscriptTitle\":\"First-principles calculation study on influence of the influence mechanisms of A-site multielement doping on the structure and optical properties of BaTiO3 ceramics\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-05-20 13:38:15\",\"doi\":\"10.21203/rs.3.rs-6653343/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2025-09-01T08:03:53+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2025-08-07T02:52:01+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"85389128740960714639131701958750788793\",\"date\":\"2025-08-06T11:14:07+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2025-05-20T08:59:03+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"313345800791873142482455100648402766183\",\"date\":\"2025-05-19T00:37:44+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"159367982950841888559105466140678979938\",\"date\":\"2025-05-16T10:33:45+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2025-05-16T10:01:05+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2025-05-15T07:23:09+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2025-05-15T07:22:42+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Theoretical Chemistry Accounts\",\"date\":\"2025-05-13T08:35:10+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"theoretical-chemistry-accounts\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"tcac\",\"sideBox\":\"Learn more about [Theoretical Chemistry Accounts](http://link.springer.com/journal/214)\",\"snPcode\":\"214\",\"submissionUrl\":\"https://submission.nature.com/new-submission/214/3\",\"title\":\"Theoretical Chemistry Accounts\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"1db1bb10-4bd6-440f-8cf4-d1644f95a947\",\"owner\":[],\"postedDate\":\"May 20th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2025-12-01T16:07:30+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-6653343\",\"link\":\"https://doi.org/10.1007/s00214-025-03253-x\",\"journal\":{\"identity\":\"theoretical-chemistry-accounts\",\"isVorOnly\":false,\"title\":\"Theoretical Chemistry Accounts\"},\"publishedOn\":\"2025-11-25 15:58:12\",\"publishedOnDateReadable\":\"November 25th, 2025\"},\"versionCreatedAt\":\"2025-05-20 13:38:15\",\"video\":\"\",\"vorDoi\":\"10.1007/s00214-025-03253-x\",\"vorDoiUrl\":\"https://doi.org/10.1007/s00214-025-03253-x\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-6653343\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-6653343\",\"identity\":\"rs-6653343\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}