Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation
Abstract
Density functional perturbation theory (DFPT) is an established framework for the computation of derivatives in plane-wave density functional theory (DFT). We present an implementation of DFPT for exchange-correlation (XC) functionals Exc(ρ,τ) that incorporate an explicit dependence on both the density ρ and the kinetic energy density τ. This covers the popular class of semilocal meta-generalized gradient approximations (meta-GGAs) as well as broader nonlocal parametrizations. We sidestep the derivation of cumbersome XC second energy derivative expressions by recasting these derivatives as a Jacobian-vector product of the XC potentials, which we evaluate with algorithmic differentiation (AD) techniques. Integration with our previously developed AD-DFPT framework [N. F. Schmitz et al., npj Comput. Mater. 12, 6 (2026)] provides access to derivatives of arbitrary ground state quantities with respect to arbitrary perturbations. We employ AD-DFPT to compute a range of response properties for ZnO and BaTiO3, and find that the recent r2SCAN01 meta-GGA functional generally outperforms LDA and PBE. Finally, we showcase the optimization of a neural-network meta-GGA to self-consistently reproduce hybrid-DFT reference densities of bulk silicon, using AD-DFPT gradients. Overall, these results establish AD-DFPT as a versatile route for computing DFT derivatives at the meta-GGA level, be they common response properties or the unusual derivatives required for the gradient-based training of novel XC functionals.
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BibTeX
@misc{ploumhans2026density,
title = {{Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation}},
author = {Bruno Ploumhans and Niklas Frederik Schmitz and Michael F. Herbst},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35572},
eprint = {2609.35572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35572},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation
AU - Bruno Ploumhans
AU - Niklas Frederik Schmitz
AU - Michael F. Herbst
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.35572
UR - https://arxiv.org/abs/2609.35572
AB - Density functional perturbation theory (DFPT) is an established framework for the computation of derivatives in plane-wave density functional theory (DFT). We present an implementation of DFPT for exchange-correlation (XC) functionals E_xc(ρ,τ) that incorporate an explicit dependence on both the density ρ and the kinetic energy density τ. This covers the popular class of semilocal meta-generalized gradient approximations (meta-GGAs) as well as broader nonlocal parametrizations. We sidestep the derivation of cumbersome XC second energy derivative expressions by recasting these derivatives as a Jacobian-vector product of the XC potentials, which we evaluate with algorithmic differentiation (AD) techniques. Integration with our previously developed AD-DFPT framework [N. F. Schmitz et al., npj Comput. Mater. 12, 6 (2026)] provides access to derivatives of arbitrary ground state quantities with respect to arbitrary perturbations. We employ AD-DFPT to compute a range of response properties for ZnO and BaTiO3, and find that the recent r2SCAN01 meta-GGA functional generally outperforms LDA and PBE. Finally, we showcase the optimization of a neural-network meta-GGA to self-consistently reproduce hybrid-DFT reference densities of bulk silicon, using AD-DFPT gradients. Overall, these results establish AD-DFPT as a versatile route for computing DFT derivatives at the meta-GGA level, be they common response properties or the unusual derivatives required for the gradient-based training of novel XC functionals.
ER -