Accurate Binding and Band Gaps at low computational cost with a non-empirical Meta-GGA

In materials discovery, balancing accuracy and computational efficiency is essential. Semi-local density functional theory is often the only affordable option. However, existing semi-local functionals tend to predict either band gaps accurately (e.g., TASK) or energetic bonds (e.g., (r²)SCAN or M06-L)—but not both. Yet, accurately capturing the electronic structure is often key to reliably predicting energetic trends, and many applications demand both.

Recently, Lebeda, Aschebrock, and Kümmel introduced the non-empirical meta-GGA LAK [1], a semi-local density functional that combines hybrid-level (HSE06) accuracy for semiconductor band gaps with state-of-the-art (SCAN-level) accuracy for energetic bonds—all at semi-local computational cost. Additionally, LAK is remarkably accurate for noncovalent interactions even without a dispersion correction, and performs exceptionally well on the comprehensive thermochemistry benchmark GMTKN55 [2]. Owing to its non-empirical design, LAK’s accuracy is expected to generalize reliably to novel materials.

The functional’s performance stems from a more balanced treatment of the gradient expansion—balancing contributions from the density gradient ∇n and the kinetic energy density τ [1]. Furthermore, LAK demonstrates numerical stability on the S22 set of weak interactions—effectively addressing a frequent limitation of early meta-GGAs. Notably, this accuracy comes at a fraction of a hybrid functional’s computational cost: meta-GGAs like LAK are typically only ~3× more expensive than GGAs, but 20–30× faster than hybrid functionals in materials simulations [3].

LAK matches or surpasses earlier meta-GGAs for all properties tested so far—except for lattice constants, which it tends to overestimate, particularly in systems containing heavy atoms. In such cases, (r²)SCAN remains a reliable choice for geometry optimizations. Caution is also advised when applying LAK to strongly correlated systems or those affected by significant self-interaction errors, although a recent study suggests LAK LAK surprisingly achieves excellent results even in such challenging scenarios [4].

While still new and undergoing broader benchmarking, LAK already shows strong potential as a low-cost alternative for high-throughput band gap screening, as well as for defect studies, surfaces and interfaces, and biological systems in which covalent and non-covalent interactions play together. Particularly in semiconductor applications, LAK’s improved description of the electronic structure often leads to greater accuracy across multiple observables.

The meta-GGA LAK is available in AMS since version 2025.1, and can be used by specifying MetaGGA lak in the xc input block.