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This study evaluates 11 density functional theory (DFT) functionals for predicting molecular ionization potentials and electron affinities. While hybrid functionals better predict ionization potentials, a correction formula is derived for accurate excitation energy predictions.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Density Functional Theory (DFT) is a powerful computational tool for electronic structure calculations.
  • Accurate prediction of molecular properties like ionization potentials (IPs), electron affinities (EAs), and excitation energies is crucial in chemistry and materials science.
  • Kohn-Sham DFT provides highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues, which are often related to experimental IPs and EAs.

Purpose of the Study:

  • To assess the accuracy of 11 DFT functionals in predicting molecular IPs and EAs using HOMO and LUMO eigenvalues.
  • To evaluate the performance of these DFT functionals and time-dependent DFT (TD-DFT) in predicting lowest excitation energies.
  • To develop a correction formula for improving the prediction of excitation energies based on calculated HOMO-LUMO gaps.

Main Methods:

  • Calculated HOMO and LUMO eigenvalues for a test set of molecules using 11 DFT functionals (LSDA, GGA, hybrid GGA, hybrid, hybrid meta GGA).
  • Compared calculated HOMO eigenvalues with experimental negative ionization potentials (-IPs) and LUMO eigenvalues with experimental electron affinities (EAs).
  • Calculated HOMO-LUMO gaps using time-independent and time-dependent DFT (TD-DFT) and compared them with experimental lowest excitation energies.

Main Results:

  • KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP functionals showed average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV for predicting -IPs, respectively.
  • All tested functionals failed to accurately predict electron affinities (EAs) using LUMO eigenvalues.
  • GGA functionals provided relatively accurate HOMO-LUMO gaps (approx. 0.73 eV error), while hybrid functionals showed increasing errors in HOMO-LUMO gaps with higher Hartree-Fock (HF) exchange content, despite improved HOMO eigenvalue predictions.
  • TD-DFT accurately predicted HOMO-LUMO gaps across all functionals.
  • A linear correlation was found between calculated HOMO eigenvalues and experimental -IPs, and between calculated HOMO-LUMO gaps and experimental excitation energies.

Conclusions:

  • No single DFT functional accurately predicts both IPs and EAs.
  • Hybrid functionals show promise for IP prediction but require careful consideration for EA and excitation energy calculations due to HF exchange effects.
  • A simple correction formula derived from linear correlations can improve the accuracy of predicted excitation energies from DFT calculations.