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System-Specific Reparameterization of Density Functionals with Machine Learning: Application to Spin-Splitting

Aaron G Garrison1, Heather J Kulik1,2

  • 1Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.

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|February 17, 2026
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Summary

Accurate spin-splitting energy (SSE) calculations for transition metal complexes (TMCs) are improved by adding system-specific Hartree-Fock exchange (HFX) to density functionals. A machine learning model predicts optimal HFX, reducing errors for better catalyst and material design.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Accurate spin-splitting energy (SSE) estimation is crucial for transition metal complex (TMC) catalysts and materials.
  • Current methods struggle with achieving high accuracy for SSE, limiting reliable modeling.
  • Density functional theory (DFT) often requires system-specific tuning for optimal performance.

Purpose of the Study:

  • To develop a reliable method for accurate SSE calculations in TMCs.
  • To investigate the effectiveness of adding Hartree-Fock exchange (HFX) to semilocal functionals.
  • To establish a machine learning (ML) approach for predicting optimal HFX in a system-dependent manner.

Main Methods:

  • System-specific addition of Hartree-Fock exchange (HFX) to semilocal density functionals (e.g., PBE, SCAN).
  • Evaluation against high-level wave function theory (DLPNO-CCSD(T)) benchmarks for over 450 TMCs.
  • Development of a Behler-Parrinello neural network trained on electron density to predict optimal HFX amounts.

Main Results:

  • Adding system-specific HFX significantly reduces errors compared to reference DLPNO-CCSD(T) values.
  • Global reparameterizations, ionization potential tuning, and ML models based on atomic properties were insufficient.
  • The ML approach achieved <5% HFX errors (<3-4 kcal/mol) on unseen data, competitive with state-of-the-art functionals.

Conclusions:

  • A ML-derived, self-tuning functional based on electron density offers a practical and interpretable path to accurate SSE.
  • This method enables more reliable and efficient screening of chemical space for TMC applications.
  • The approach enhances the accuracy of density functionals for critical materials science and catalysis problems.