In the present work, the orthorhombic structure of the RbSrBr₃ perovskite that is crystallized with cm cm space group (No. 63) has been optimized using GGA-PBE, GGA-PBEsol, GGA-PW91, and LDA-CAPZ functionals to find out the details of the structure and to judge the functional variation on the properties of the studied compound. The optimized geometrical structure of orthorhombic RbSrBr₃ perovskite obtained using various functionals has been depicted in Figure 1 . The lattice constants (Å), cell volume (ų), ground state energy (eV), and bulk modulus have been presented in Table 1 . The minimum values of lattice constants, volume, and ground state energy have been observed by utilizing the LDA-CAPZ functional. The GGA-PBE, GGA-PBEsol, GGA-PW91, and LDA-CAPZ functionals have been revealed in the orthorhombic phase of RbSrBr₃ perovskite. Compared to other methods, PBEsol-GGA lattice constants were comparable to experimental values.

The elastic constants C_ij describes the crystal’s mechanical and dynamical nature and shows how pressure deforms matter and subsequently returns it to its original shape [31] . Elastic constants impact qualities such as anisotropy, ductility, and hardness and are governed by stress-strain relationships. In an orthorhombic structure, the nine independent elastic constants C_ij (C₁₁, C₁₂, C₁₃, C₂₂, C₂₃, C₃₃, C₄₄, C₅₅, C₆₆) can satisfy the Born stability conditions, which are provided in Table 2 and elastic stability criteria are C₁₁ > 0, C₄₄ > 0, C₅₅ > 0, C₆₆ > 0, C₁₁C₂₂ > C²₁₂, C₁₁C₂₂C₃₃ + 2C₁₂C₁₃C₂₃ - C₁₁C²₂₃ - C₂₂C² ₁₃ - C₃₃C²₁₂ > 0 [32] .

The elastic constants presented in Table 2 indicate that orthorhombic RbSrBr₃ has met all stability criteria, indicating mechanical stability for all the functionals. The elastic constants found for RbSrBr₃ are consistent with the theoretical results given in the literature [33] . The stiffness matrix [34] is positive definite using various functionals, as shown in the eigenvalues listed in Table 3 . Furthermore, the parameters, including Bulk modulus (B), shear modulus (G), Young’s modulus (Y), Pugh’s ratio (B/G), Poisson ratio (υ), and anisotropy (A) were measured. The nature of the bonding can be described by Cauchy pressure (C_p), according to Pettifor [35] . If C_P is positive, it means that the structure is flexible, and if it is negative, the combination will be brittle [36] . According to the condition above, the structure RbSrBr₃ is flexible using various functionals.

The shear modulus (G) shows how resistant the material is to changes in shape (bond angle) when pressure is applied from the outside. The bulk modulus (B) indicates the material’s resistance to volumetric variations (bond length) [37] . ‘E’ represents Young’s modulus, a method for determining the strength of a material. The value equals the stress-to-strain ratio [38] . Several methods, such as the Voigt, Reuss, and Hill techniques, can be used to derive estimates. Voigt suggested that the strain distribution in composite materials is homogenous [39] . The Reuss approximation is a commonly employed micromechanical model for studying composite materials. This model assumes that the composite phases experience equal stress, specifically normal stress [40] . The Hill convention is a numerical method that averages Reuss and Voigt values [41] . The parameters that determine the strength of the structure have been explained in Table 4 .

$B_H=\frac{B_V+B_R}{2}$ (1)

$G_H=\frac{G_V+G_R}{2}$ (2)

These symbols B_H, B_V, B_R, G_H, G_V, and G_R correspond to the Hill bulk modulus, Voigt bulk modulus, Reuss bulk modulus, Hill shear modulus, Voigt shear modulus, and Reuss shear modulus.

Again, the following equation gives Young’s modulus (E) and Poisson’s ratio (υ) [42]

$E=\frac{9B_H{G}_H}{3B_H+G_H}$ (3)

$\upsilon =\frac{3B_H-E}{6B_H}$ (4)

The Poisson ratio is utilized in finite element simulations to design axially stressed components [43] . With the Hill G and B values, we can determine Young’s modulus and Poisson’s ratio. For all functionals, the RbSrBr₃ perovskite has been predicted to be ductile, where υ ≥ 1/3 is comparable to the reference [44] . Pugh’s ratio, Poisson’s ratio, and Cauchy’s pressure correlate with the material’s stability and fragility. Pugh’s ratio [45] suggested that the B/G ratio can indicate brittle or ductile material properties. The material is considered flexible when the ratio B to G is greater than 1.75; otherwise, it is classified as brittle. The orthorhombic of RbSrBr₃ structure has been showing flexible behavior for all the functionals.

Ranganathan and Ostoja-Starzewski established the universal anisotropic factor [46] to measure crystal anisotropy. The anisotropic factor is essential for understanding defect dynamics, structure stability, and compound elastic anisotropy [47] .

$A=\frac{G_V-G_R}{G_V+G_R}$ (5)

The equation shows that the universal anisotropic A is greater than 1, which means that the crystalline structure of RbSrBr3 has elastic anisotropy [48] .

Young’s modulus, shear modulus, compressibility (the opposite of bulk modulus), and Poisson’s ratio should be spherical for isotropic solids. If they don’t stay in the shape of a sphere, it means that anisotropy is present. Figure 2 revealed the directional dependency of Young’s modulus, shear modulus, compressibility, and Poisson’s ratio for the ELATE-generated RbSrBr₃ system [49] .

The Debye temperature (θ_D), which correlates to the crystal’s most extensive normal mode of vibration, is one of the most fundamental properties of solids. This parameter establishes a relationship between a solid’s elastic and thermodynamic properties, containing phonons, thermal expansion, conductivity, specific heat, and lattice enthalpy. The average sound velocity, V_m and ρ, the mass density of the solid has to be used to calculate the Debye temperature (θ_D) The Debye temperature (θ_D) is given by [50] .

${\theta }_D=\frac{h}{K_B}{V}_m[\frac{3n}{4\text{π}}{\frac{\rho N_A}{M}]}^{\frac{1}{3}}$ (6)

In Equation (6), h represents Planck’s constant, k_B represents Boltzmann’s constant, N_A represents Avogadro’s number, ρ represents mass density, M represents molecular weight, and n represents the number of atoms in the cell. The LDA-CAPZ functional has been calculated to be the highest, and the GGA-PW91 functional has shown the lowest Debye Temperature, (θ_D) for RbSrBr₃, which is listed in Table 5 . The cut-off debye temperature determines the lattice stability [51] . At temperatures below the Debye temperature, the atomic motion within the crystal lattice is negligible, enabling the free movement of electrons through the lattice planes with minimal dispersion due to the low electron-phonon coupling [52] . This solid becomes a weak heat conductor when the scattering level increases above the Debye temperature.

From the obtained bulk modulus (B) and shear modulus (G), the calculations of the average sound velocity (V_m), transverse sound velocity (V_T), and longitudinal sound wave velocity (V_L) are derived using Navier’s equation [53] which is given below:

$V_m=[\frac{1}{3}(\frac{1}{V_L^3}+{\frac{2}{V_T^3})]}^{-\frac{1}{3}}$ (7)

$V_T=\sqrt{\frac{G}{\rho }}$ (8)

$V_L=\sqrt{\frac{3B+4G}{3\rho }}$ (9)

Table 5 shows that the speed of the longitudinal wave is twice that of the transverse wave, which is comparable to the literature [36] .

Fine et al. put together an empirical formula to obtain the melting temperature T_m of this structure via elastic constants [54]

$T_m=354+1.5\left(2C_{11}+C_{33}\right)$ (10)

The melting temperature of crystalline materials indicates cohesive energy, atomic bond strength, and lattice anharmonicity. This material’s melting temperature was found to be low, which means it is soft. The observed T_m values for all the functionals are lower than those of PbMO₃ (M = Sb, Bi) [55] .

The electronic band structure of RbSrBr₃ perovskite has been calculated using various functionals (GGA-PBE, GGA-PBEsol, GGA-PW91, LDA-CAPZ) through the symmetry points of the Brillouin zone (G→Z→T→Y→S→X→U→R) where the valence band maximum (VBM) was fixed at 0 eV. The band structure of RbSrBr₃ perovskite for all the functionals has been presented in Figure 3 . The values of bandgap for four different functions lie between 4.293 eV to 4.494 eV. The lowest band gap has been found using GGA-PBE functional, whereas the highest band gap has been obtained using GGA-PBEsol functional. The obtained values of band gap of the present studied perovskite signify that they are insulating-like. The size, form, symmetry, and geometry of the Brillouin zone have been modified by the band structure [56] . Direct band gap nature has been found in RbSrBr₃ structure for all functions because the valence band maximum (VBM) and conduction band minimum (CBM) have been found at the “G” of the K-point.

The total density of state (TDOS) and partial density of state (PDOS) of orthorhombic RbSrBr₃ structure calculated using various functionals have been presented in Figure 4(a)-(d) . Figure 4(e) represents the compared total density of states (TDOS) of RbSrBr₃ structure among four different functions. The atomic bonding in the RbSrBr₃ compound has been investigated through PDOS. The valence band maximum for all functionals has been formed from the p orbital of Br, with a small contribution from the d orbital of Sr. On the other hand, the

conduction band minimum has been derived from the d orbital of Sr with a minor contribution from the s orbital of Sr using various functionals [15] . The total density of states (TDOS) plotted in Figure 4 revealed that the halogen atom (Br) at the Fermi level edges contributes significantly to DOS in VB, resulting in flat bands at the band edges [57] .

The optical characteristics of a material have an inherent connection to its ground-state electrical configuration. Different optical properties of the orthorhombic RbSrBr₃ structure with the variation of energy (eV) for different functions have been presented in Figure 5 and Figure 6 .

The absorption coefficient is a measure of the photon absorption ability of materials [58] . The absorption coefficient of orthorhombic RbSrBr₃ perovskite has been presented in Figure 5(a) . The major absorption peaks have been obtained at 9.21 eV, 9.21 eV, 9.30 eV, and 8.88 eV for GGA-PBE, GGA-PBEsol, GGA-PW91, and LDA-CAPZ, respectively. The higher value of absorption peak (>10⁴ cm⁻¹) has been found almost at the same energy for all functions and all major peaks lie in the UV region.

The optical conductivity spectrum represents the quantity of free charge carriers generated through bond breakage during electron-photon interaction [59] . The optical conductivity is shown in Figure 5(b) . The highest peaks have been obtained at 7.52 eV, 7.73 eV, 7.44 eV, and 7.69 eV for GGA-PBE, GGA-PBEsol, GGA-PW91, and LDA-CAPZ, respectively. In this structure, zero optical conductivity (OC) and higher optical conductivity (OC) have been found in the UV, and Visible regions for all the functions.

Reflectivity measures the fraction of energy that is reflected from the crystal structure [60] . It has been varied from zero to unit. The absorption of light and reflectivity are closely related to each other. The variation of reflectivity with the change of energy in the RbSrBr₃ structure for all functions is presented in Figure 5(c) . The lowest value of reflectivity has been found in the visible and IR regions for all the functions.

The dielectric function can be expressed as [61]

$\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right)$ (11)

Here, ε₁(ω) represents a real part of the dielectric function. The higher value of the real part of the dielectric function indicates a stronger ability of the material to polarize in response to the electric field. The imaginary part ε₂(ω) signifies the molecular polarization loss due to fluctuations in the external electric field [62] . The dielectric function of orthorhombic RbSrBr₃ perovskite has been illustrated in Figure 6(a) . The imaginary part and the real part are connected through the Kramers-Kronig relationships [63] . The absorption coefficient has been found in the imaginary part of the dielectric function. The threshold energy for the imaginary dielectric function has been found at 3.90 eV for all the functionals that were correlated with the energy band gap and worked for the UV-region. The principal peak has been located at 6.87 eV, 7.52 eV, 6.87 eV and 6.24 eV for GGA-PBE, PBEsol, PW91 and LDA-CAPZ functionals, respectively. The static dielectric function has been obtained at 5.67 eV for all functionals. The Penn relation (ε₁(0) ≈ 1 + (ħω/E_g)²) represents that the static dielectric function is inversely proportional to the energy band gap. The dielectric function becomes negative with the increment of energy, indicating that the medium reflects electromagnetic waves, exhibiting its metallic properties.

The complex refractive function has been calculated by the relation:

$N=n\left(\omega \right)+ik\left(\omega \right)$ (12)

where n(ω) and k(ω) are the refractive index and the extinction index, respectively, which could be found from a real and imaginary portion of the dielectric function employing the previously mentioned relation [64] . The refractive function versus energy curve has been found in Figure 6(b) . The value of the refractive index of RbSrBr₃ structure was 1.78, 1.79, 1.70, and 1.87 for GGA-PBE, PBEsol, PW91, and LDA-CAPZ functions, respectively. The refractive index peak is found in the UV region for all the functions, and it decreases with the increase of energy. Extinction coefficient k(ω) signifies the light absorption ability of the compound at a certain range. The profiles of k(ω) and ε₂(ω) were closely connected in their respective functionals. The loss function L(ω) has been displaced in Figure 6(c) . The function L(ω) is essential for representing the energy that fast electrons lose as they move through a solid [65] . The peaks observed in the L(ω) spectra have been suggestive of the properties related to the plasma resonance. The resonant energy loss was obtained at 12.04 eV.