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Updated: Jan 13, 2026

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Algorithmic differentiation for plane-wave DFT: materials design, error control and learning model parameters.

Niklas Frederik Schmitz1,2, Bruno Ploumhans1,2, Michael F Herbst1,2

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Summary
This summary is machine-generated.

We introduce a new framework combining algorithmic differentiation (AD) and density-functional perturbation theory (DFPT) for accurate calculations in materials modeling. This approach automates derivative computations, enabling advanced applications like inverse design and parameter learning.

Keywords:
ChemistryMaterials scienceMathematics and computingPhysics

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Area of Science:

  • Computational Materials Science
  • Quantum Chemistry
  • Solid-State Physics

Background:

  • Density-Functional Theory (DFT) is a cornerstone for materials modeling.
  • Calculating derivatives of DFT outputs with respect to input parameters is crucial but often complex.
  • Existing methods require manual derivation of gradient expressions, limiting applicability.

Purpose of the Study:

  • To develop a unified framework for automated derivative calculations in DFT.
  • To combine the strengths of algorithmic differentiation (AD) and density-functional perturbation theory (DFPT).
  • To enable accurate computation of derivatives for any DFT output with respect to any input parameter.

Main Methods:

  • Implementation of a forward-mode AD approach within the DFPT framework.
  • Integration of the AD-DFPT method into the Density-Functional ToolKit (DFTK).
  • Validation through diverse applications including inverse design and uncertainty propagation.

Main Results:

  • The AD-DFPT framework accurately computes derivatives without manual gradient derivation.
  • Demonstrated broad applicability across various materials modeling tasks.
  • Successfully applied to inverse design of semiconductor band gaps and learning exchange-correlation functional parameters.

Conclusions:

  • The AD-DFPT framework significantly advances first-principles materials modeling by automating derivative calculations.
  • Opens new research avenues through gradient-driven workflows.
  • Facilitates complex tasks such as parameter optimization and uncertainty quantification in materials science.