ΔSCF Excitation Energies up a Ladder of Ground-State Density Functionals

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density functional theory (DFT) is a standard for ground-state electronic structure.
• Extending DFT to excited states is crucial for understanding material properties and reactions.
• The delta self-consistent field (ΔSCF) method offers a pathway to calculate excited-state energies within DFT.

Purpose of the Study:

• To evaluate the performance of various DFT approximations for calculating excitation energies.
• To assess the accuracy of LSDA, PBE (GGA), and SCAN/r²SCAN (meta-GGA) for atomic and molecular systems.
• To investigate the suitability of these methods for different types of electronic excitations.

Main Methods:

• Utilized the delta self-consistent field (ΔSCF) method to compute excited-state energies.
• Applied LSDA, PBE, and SCAN/r²SCAN functionals to systems ranging from hydrogen to multielectron atoms (Z=1-18).
• Analyzed non-Aufbau and spin-flip excitations, considering the limitations of single-determinant approximations.

Main Results:

• Significant improvement in accuracy for excitation energies was observed progressing from LSDA to PBE to SCAN for the hydrogen atom.
• The r²SCAN functional yielded an effective mass distinct from the bare mass for the uniform electron gas.
• Reasonably accurate excitation energies were obtained for non-Aufbau excitations, while spin-flip excitations showed limitations for single-determinant methods, though spin purification offered improvement.

Conclusions:

• Advanced functionals like SCAN provide enhanced accuracy for excited-state calculations via ΔSCF.
• Spin-flip excitations present a challenge for current single-determinant DFT approaches.
• Further development, potentially including spin purification, is needed to accurately capture all types of electronic excitations.