Correlation between Bulk Modulus, Microhardness and Electronic Properties in D-Block Metal Halides

Abstract: D-block metal halides have emerged as an important class of functional materials owing to their diverse crystal structures, tunable electronic configurations, and potential applications in optoelectronics, catalysis, spintronics, and energy-related technologies. In the present study, a systematic first-principles investigation was carried out to explore the correlation between bulk modulus, microhardness, and electronic properties of selected D-block metal chlorides and bromides. Density Functional Theory (DFT) calculations were employed to optimize crystal structures and evaluate elastic, mechanical, and electronic properties. Elastic constants were calculated using the stress–strain method, while bulk modulus values were obtained through the Voigt–Reuss–Hill approximation. Microhardness was estimated using the Chen, Tian, and Mazhnik–Oganov models. Electronic properties were analyzed through band structure, density of states (DOS), partial DOS, and charge density distribution calculations. The results reveal that chloride compounds generally exhibit shorter bond lengths, higher bulk modulus, and greater hardness than their bromide counterparts due to stronger metal–halogen bonding interactions. Electronic structure analysis indicates a transition from metallic to semiconducting behavior across the investigated compounds, with significant contributions from transition-metal d-orbitals near the Fermi level. Statistical correlation analysis demonstrates a strong positive relationship between bulk modulus and microhardness (r = 0.981), while band gap and charge transfer exhibit positive correlations with mechanical strength. Conversely, the density of states at the Fermi level shows a negative correlation with both bulk modulus and hardness. A predictive regression model was developed, revealing that mechanical performance can be effectively estimated from electronic descriptors. The findings establish a comprehensive structure–property relationship framework and provide valuable guidelines for the design and development of mechanically robust and electronically functional D-block metal halides for advanced technological applications.

Keywords: D-block metal halides, bulk modulus, microhardness, band structure, density of states, electronic properties, correlation analysis