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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Kohn-Sham (KS) density functional theory (DFT) is widely used for electronic structure calculations.
  • Accurately describing excited states, especially those involving ionization and charge transfer, remains a significant challenge in KS-DFT.
  • Common exchange-correlation (xc) approximations often fail for excited states due to the lack of a derivative discontinuity (Δ) in the xc energy.

Purpose of the Study:

  • To analytically and numerically demonstrate the relationship between KS and many-electron energies.
  • To explain the origin of step structures in the exact xc potential.
  • To explore methods for improving excited-state calculations in DFT.

Main Methods:

  • Analytical derivation of the relationship between KS and many-electron energies.
  • Numerical simulations of electron addition, molecular dissociation, excitation, and charge transfer.
  • Investigation of ensemble DFT methods, including the local density approximation (LDA).

Main Results:

  • Demonstrated how the KS-many-electron energy relationship leads to step structures in the exact xc potential.
  • Identified four key scenarios where these steps are observed: electron addition, molecular dissociation, finite system excitation, and charge transfer.
  • Showed that steps in the potential can be reproduced using simple approximations like LDA from an ensemble perspective.

Conclusions:

  • Capturing the KS-many-electron energy relationship is crucial for accurate excited-state calculations in DFT.
  • Advanced xc approximations are needed to correctly describe the derivative discontinuity and potential steps.
  • This understanding is vital for calculating not only excited states but also ground-state properties of systems with distinct subsystems.