Computational design of quantum and functional materials for next generation electronic and energy technologies

The growing demand for high performance electronics and sustainable energy storage and conversion architectures has accelerated the search for novel quantum and functional materials. Traditional experimental workflows are increasingly limited by vast structural and compositional configuration spaces, establishing computational design as a pivotal paradigm in modern materials science. This review provides a comprehensive analysis of state of the art computational methodologies used to predict, optimize, and discover advanced materials prior to physical synthesis. We trace the development of core atomistic techniques, beginning with standard Density Functional Theory frameworks, moving to advanced multi body corrections such as Time Dependent Density Functional Theory, the GW approximation, and the Bethe Salpeter Equation, and exploring classical or ab initio molecular dynamics and thermodynamic Monte Carlo simulations. Crucially, we highlight the paradigm shifting integration of machine learning frameworks, data driven inverse design, and emerging quantum computing architectures such as the Variational Quantum Eigensolver. The efficacy of these single method and hybrid paradigms is critically evaluated across key technological domains, including semiconductor electronics, optoelectronics, spintronics, flexible wearable devices, photovoltaics, battery storage, and electrocatalysis. Lastly, we addressed prevailing structural boundaries, such as multiscale integration gaps and data interpretability limitations, and outline future horizons for autonomous self-driving materials discovery platforms.