Exchange-Correlation Functionals in 2D Materials: Applications, Challenges, and Limitations

Abstract

The rapid development of two-dimensional (2D) materials has reshaped modern nanoscience, offering properties that differ fundamentally from their bulk counterparts. As experimental discovery accelerates, the need for reliable computational techniques has become increasingly important. Within the framework of density functional theory, this review explores the critical role of exchange-correlation functionals in predicting key material properties such as structural, optoelectronic, magnetic, and thermal. We examine the challenges posed by quantum confinement, anisotropic screening, and van der Waals interactions, which conventional functionals often fail to describe. Advanced approaches, including meta-GGA, hybrid functionals, and many-body perturbation theory (e.g., GW and Bethe-Salpeter equation), are assessed for their improved accuracy in capturing electronic structure and excitonic effects. We further discuss the non-universality of functionals across different 2D material families and the emerging role of machine learning to enhance computational efficiency. Finally, the review outlines current limitations and emerging strategies, providing a roadmap for advancing exchange-correlation functionals and beyond, to enable the practical design and application of 2D materials.

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