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

TL;DR

This review analyzes how exchange-correlation functionals shape predictions for 2D materials, emphasizing that quantum confinement, anisotropic screening, and van der Waals forces demand beyond-LDA/GGA treatments. It surveys the performance of LDA/GGA, meta-GGA (notably SCAN/r2SCAN), and hybrid functionals (e.g., HSE06), along with many-body GW+BSE for accurate electronic and excitonic properties, highlighting that no universal functional exists across all 2D families. The paper also discusses the rising role of machine learning to accelerate predictions and proposes a pragmatic, property-specific strategy: use SCAN/r2SCAN for structural benchmarks, HSE06 for electronic gaps with caveats, and GW+BSE for optical excitations, while leveraging ML to scale predictions. Collectively, these insights guide practical design and computational screening of 2D materials, with a clear path toward integrating more accurate, physics-informed functionals and data-driven approaches. The work underscores the importance of basing methodological choices on the material class and target property, and it highlights promising directions in environment-aware XC functionals and beyond-DFT methods to reliably capture excitonic and many-body effects in 2D systems.

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.

Figures (17)

• Figure 1: Families of 2D materials are represented by the outer layer, which shows the material family name, while the inner layer highlights their practical applications across various fields.
• Figure 2: The schematic diagram of KS-DFT. Reprinted from javed2024band, copyright (2024), with permission from Elsevier.
• Figure 3: Jacob’s Ladder in DFT: A hierarchy of XC approximations where each higher rung offers improved accuracy. On the left, the famous functionals along with their years of publication are listed, showcasing the evolution of XC functionals from LDA to hybrid and double-hybrid methods.
• Figure 4: Comparison of optimized lattice constants for TMDC monolayers using different functionals, showing that the SCAN functional provides lattice constants closest to experimental values. Reprinted from javed2025structural, copyright (2025), with permission from Elsevier.
• Figure 5: Lattice parameter $a$ of (a) conventional MOF-5 and (b) its Sr-substituted counterpart, featuring H-passivated (left) and hydroxyl-functionalized (right). The experimental reference for conventional MOF-5 li1999design is marked by a horizontal bar. Reprinted from edzards2025benchmarking_MOF. https://creativecommons.org/licenses/by/4.0/.