TDΔSCF: Time-Dependent Density Functional Theory with a Non-Aufbau Reference for Near-Degenerate States

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Single-reference density functional theory (DFT) struggles with near-degenerate electronic structures.
• Accurate modeling of excited states and challenging electronic configurations is crucial in computational chemistry.

Purpose of the Study:

• To develop and evaluate a novel linear-response scheme, time-dependent ΔSCF (TDΔSCF), for systems with near-degenerate electronic structures.
• To compare the performance of TDΔSCF against spin-flip TDDFT (SF-TDDFT) for various challenging chemical problems.

Main Methods:

• Proposed TDΔSCF, a linear-response scheme using a non-Aufbau ΔSCF determinant as a reference for TDDFT.
• Applied TDΔSCF to prototypical problems: ethylene torsion, diradical singlet-triplet gaps, benzyne isomer geometry, and bond dissociation curves (HF, F2).

Main Results:

• TDΔSCF demonstrates weaker functional dependence and a more balanced description of singlet states than SF-TDDFT.
• Achieved smooth torsional potentials, improved singlet-triplet gaps, consistent benzyne structures, and better bond dissociation descriptions.
• Identified overestimation of singlet energies and potential accuracy loss when the reference is ill-suited; noted numerical instabilities in non-Aufbau calculations.

Conclusions:

• TDΔSCF shows promise as a low-cost method for singlet states with near-degenerate electronic structures.
• The method offers advantages over SF-TDDFT but has limitations, including potential overestimation of energies and numerical instabilities.
• Further development is needed to address identified limitations for broader applicability.