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Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package.

James C Womack1, Narbe Mardirossian2, Martin Head-Gordon2

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We enhanced the ONETEP program to support kinetic energy density-dependent meta-generalized-gradient approximation (meta-GGA) functionals. This enables accurate and efficient large-scale density functional theory (DFT) calculations on thousands of atoms.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Accurate and efficient exchange-correlation functionals are essential for linear-scaling density functional theory (DFT).
  • Meta-generalized-gradient approximation (meta-GGA) functionals, dependent on kinetic energy density (τ), offer enhanced accuracy but are computationally demanding for large systems.
  • Existing linear-scaling DFT methods often struggle to incorporate these advanced τ-dependent functionals.

Purpose of the Study:

  • To implement τ-dependent meta-GGA functionals within the ONETEP program's linear-scaling framework.
  • To enable large-scale DFT calculations on systems with thousands of atoms using accurate meta-GGA functionals.
  • To validate the accuracy and computational efficiency of the new implementation.

Main Methods:

  • Theoretical development of expressions for the gradient of τ-dependent exchange-correlation energy for direct minimization.
  • Derivation of τ-dependent exchange-correlation potential and kinetic energy density using localized orbitals.
  • Implementation within the ONETEP program and validation on small molecules and large amyloid fibril systems.

Main Results:

  • Successful implementation of τ-dependent meta-GGA functionals in ONETEP's linear-scaling formalism.
  • Numerical validation shows excellent agreement with established methods for small molecules using minimal basis sets.
  • Demonstrated linear-scaling computational cost and applicability to large systems, including amyloid fibrils up to tens of thousands of atoms.

Conclusions:

  • The integration of τ-dependent meta-GGA functionals into ONETEP significantly advances the capability for large-scale, accurate DFT calculations.
  • This development opens new avenues for studying complex molecular systems with high fidelity and computational efficiency.
  • The ONETEP program now offers a powerful tool for researchers requiring accurate electronic structure calculations on massive systems.