基于算法微分的meta广义梯度近似的密度泛函微扰理论
Density functional perturbation theory of meta-generalized gradient approximations using algorithmic differentiation
- École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于算法微分的AD-DFPT框架，实现了meta-GGA泛函的密度泛函微扰理论计算，可高效求解响应性质并支持神经网络泛函的梯度训练，优于LDA和PBE。
AI中文摘要：
密度泛函微扰理论（DFPT）是平面波密度泛函理论中计算导数的成熟框架。我们提出了对交换关联（XC）泛函 $E_\mathrm{xc}(\rho,\tau)$ 的DFPT实现，该泛函同时显式依赖于密度 $\rho$ 和动能密度 $\tau$。这涵盖了流行的半局域meta广义梯度近似（meta-GGAs）类别以及更广泛的非局域参数化。我们通过将二阶能量导数重新表示为XC势的雅可比-向量积，并使用算法微分（AD）技术进行评估，从而绕过了繁琐的XC二阶能量导数表达式的推导。与我们先前开发的AD-DFPT框架[N. F. Schmitz et al., npj Comput. Mater. 12, 6 (2026)]的集成，提供了任意基态量相对于任意微扰的导数访问。我们利用AD-DFPT计算了ZnO和BaTiO3的一系列响应性质，并发现最近的r2SCAN01 meta-GGA泛函通常优于LDA和PBE。最后，我们展示了使用AD-DFPT梯度，将神经网络meta-GGA优化为自洽地再现体硅的杂化DFT参考密度。总体而言，这些结果确立了AD-DFPT作为在meta-GGA水平上计算DFT导数的通用途径，无论是常见的响应性质还是用于新型XC泛函基于梯度训练所需的异常导数。
英文摘要：
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 $E_\mathrm{xc}(ρ,τ)$ 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.
