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Singularity Correction for Long-Range-Corrected Density Functional Theory with Plane-Wave Basis Sets.

Yukio Kawashima1, Kimihiko Hirao1

  • 1RIKEN Advanced Institute for Computational Science , 7-1-26 minatojima-minami-machi, Chuo-ku, Kobe 650-0047, Japan.

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|February 16, 2017
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Summary
This summary is machine-generated.

We developed two methods to fix singularity issues in long-range corrected density functional theory (LC-DFT) calculations using plane-wave basis sets. These corrections are crucial for accurate electronic structure and excitation energy calculations in various systems.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Long-range corrected density functional theory (LC-DFT) is vital for accurate electronic structure calculations.
  • Plane-wave basis sets are commonly used for periodic systems but can introduce singularities in Hartree-Fock (HF) exchange calculations.
  • Singularities in HF exchange can lead to inaccuracies in LC-DFT results.

Purpose of the Study:

  • To introduce and validate methods for correcting singularities in long-range HF exchange calculations within LC-DFT using plane-wave basis sets.
  • To assess the impact of singularity correction on the accuracy of electronic and excitation energies for both isolated and extended systems.
  • To investigate the role of excitonic effects on the band gaps of extended systems.

Main Methods:

  • Developed two singularity correction methods: auxiliary function and truncated Coulomb potential.
  • Applied the LC-BLYP functional with corrected and uncorrected methods to naphthalene and pyridine.
  • Performed electronic structure calculations on extended systems (Si, SiC) using the corrected LC-DFT approach.
  • Calculated excitation energies and analyzed excitonic effects using a supercell model.

Main Results:

  • Singularity correction was confirmed as essential for accurate total and HOMO energies in LC-DFT calculations with plane-wave basis sets.
  • LC-DFT calculations with corrected methods showed rapid convergence and good agreement with Gaussian basis set results.
  • Accurate orbital and excitation energies were obtained for isolated molecules.
  • Singularity correction proved important for extended systems, with results converging well with respect to k-point sampling.
  • Excitonic binding energy was found to be significant for the studied inorganic semiconductors, impacting band gap calculations.

Conclusions:

  • The introduced methods effectively resolve the singularity problem in HF exchange calculations for LC-DFT.
  • Singularity correction is critical for obtaining reliable electronic and excitation energies in both molecular and extended systems.
  • Careful treatment of singularities is necessary for accurate excitation state calculations.
  • Excitonic effects can substantially influence band gaps in extended systems, warranting further investigation.