FIRST-PRINCIPLES DESIGN OF ADVANCED FUNCTIONAL MATERIALS USING DENSITY FUNCTIONAL THEORY FOR ELECTRONIC STRUCTURE ENGINEERING, MECHANICAL STABILITY ANALYSIS, AND OPTICAL PROPERTY OPTIMIZATION

Abstract

Density functional theory (DFT) provides a powerful first-principles framework for predicting the structural, electronic, mechanical, and optical properties of functional materials prior to experimental synthesis. This study presents an integrated computational investigation of five candidate material systems comprising the cubic double perovskite Ca₂NbTaO₆ and four quaternary Heusler alloys, XMnCrZ (X = Fe, Co; Z = Si, Ge). Calculations were performed using the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA), the Heyd–Scuseria–Ernzerhof screened hybrid functional (HSE06), and GGA+U corrections where appropriate. The computational workflow combined geometry optimization, formation-energy analysis, elastic stability assessment, electronic band-structure calculations, phonon dispersion, and optical-property evaluation to establish composition–property relationships across the investigated systems.

The reported results indicate negative formation energies and satisfaction of the Born–Huang elastic stability criteria for all five compositions. Ca₂NbTaO₆ exhibited a direct band gap of 2.14 eV at the GGA level, increasing to 2.98 eV with HSE06, corresponding to a 0.84 eV correction. Its calculated elastic properties indicate mechanical robustness with a Pugh’s ratio of approximately 1.71, placing the material near the ductile–brittle boundary. The Heusler alloys exhibited half-metallic electronic behavior under GGA+U, with the representative FeMnCrGe composition showing a minority-spin gap of 0.74 eV and ideal complete spin polarization at the Fermi level. Optical analysis yielded dielectric functions, refractive indices, reflectivity spectra, and absorption coefficients, with the reported Ca₂NbTaO₆ absorption coefficient reaching 4.8 × 10⁵ cm⁻¹. Scissor-corrected optical spectra were used to assess the influence of the HSE06 band-gap correction, while phonon dispersion calculations indicated dynamical stability within the investigated structures. The comparative findings provide a framework for evaluating the potential of these materials in photocatalysis, optoelectronics, and spintronics and for identifying composition-dependent design principles for further computational and experimental investigation.