Accurate double excitations from ensemble density functional calculations.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Standard time-dependent density functional theory (TDDFT) with the adiabatic approximation often fails to capture double excitations.
• Accurate calculation of double excitations is crucial for understanding complex electronic phenomena and chemical reactions.

Purpose of the Study:

• To investigate a new ensemble approach within density functional theory (DFT) for calculating double excitations.
• To assess the accuracy of ensemble DFT corrections compared to standard TDDFT methods.
• To analyze the theoretical underpinnings and limitations of TDDFT for excited states.

Main Methods:

• Utilized a novel ensemble DFT method incorporating direct corrections to Kohn-Sham transitions.
• Performed exact calculations and analytic derivations on the Hubbard dimer model system.
• Analyzed formal arguments concerning TDDFT and its limitations.

Main Results:

• The new ensemble DFT approach successfully yields double excitations, which are typically missed by standard TDDFT.
• While accuracies for double excitations are lower than for single excitations, the method shows significant improvement.
• Demonstrated that ensemble DFT with exchange-level corrections can accurately predict double excitations in the weakly correlated limit.

Conclusions:

• Ensemble DFT offers a viable pathway to include elusive double excitations in theoretical calculations.
• Further development, potentially including a correction kernel, may be needed to enhance accuracy for double excitations.
• Identified and explained errors in existing formal arguments within TDDFT concerning double excitations.