Self-consistent Hessian-level meta-generalized gradient approximation

TL;DR

This paper introduces a new Hessian-level meta-GGA density functional, $ heta$-PBE, which uses the full density Hessian for improved distinction of density limits, showing promising results for molecular properties.

Contribution

It formulates the $ heta$-MGGA class as Hessian-level functionals, introduces a non-empirical $ heta$-PBE, and demonstrates its implementation and potential advantages.

Findings

$ heta$-PBE accurately predicts chemisorption energies.

It distinguishes between atomic and bonding densities effectively.

Challenges remain in predicting bulk lattice constants.

Abstract

The $\vartheta$-MGGA class of density functionals is formally reformulated as Hessian-level meta-generalized gradient approximations (HL-MGGAs). In contrast to standard meta-GGAs that rely on the orbital-dependent kinetic-energy density or the density Laplacian, HL-MGGAs utilize the full density Hessian. We introduce a simplified, non-empirical functional, $\vartheta$-PBE, and present a roadmap for its self-consistent implementation within the projector augmented-wave (PAW) method. By utilizing the complete set of spatial second-order density derivatives, the functional's underlying descriptor successfully distinguishes between distinct one-electron density limits, such as single-center atomic densities and two-center bonds, that standard iso-orbital indicators often conflate. Benchmarks across molecular and solid-state datasets reveal that while $\vartheta$-PBE delivers accurate chemisorption energies and molecular properties, challenges remain in predicting bulk lattice constants. Ultimately, this work demonstrates the physical utility and feasibility of designing orbital-independent, Hessian-based exchange-correlation functionals.