Why Variational Density Functional Theory Is More Accurate Than Time-Dependent Density Functional Theory for Certain...

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Time-dependent density functional theory (TDDFT) excels for many excited states but struggles with charge-transfer, core excitations, and inverted singlet-triplet gap molecules.
• Variational excited-state density functional theory (eDFT) shows comparable accuracy to TDDFT for standard systems and superior performance for challenging ones.

Purpose of the Study:

• To investigate the origins of successes and failures in eDFT and TDDFT for specific excitation types.
• To compare the energy equations of eDFT and two-state Tamm-Dancoff approximation (TDA) TDDFT.
• To analyze the impact of functionals and density sensitivity on excitation energies.

Main Methods:

• Developed a general decomposition method for singlet and triplet excitation energies.
• Compared energy equations of eDFT and TDA-TDDFT.
• Analyzed functional effects and density sensitivity in excitation energy calculations.

Main Results:

• eDFT exhibits higher contributions from Hartree and exchange-correlation kernels compared to TDDFT.
• Greater kernel contributions alone do not ensure improved accuracy in eDFT.
• Orbital relaxation combined with increased kernel contributions drives eDFT's superior performance for difficult excited states.

Conclusions:

• eDFT provides a more robust framework for calculating challenging excited states than TDDFT.
• Understanding the interplay of kernel contributions and orbital relaxation is key to improving excited-state calculations.
• The developed decomposition method aids in analyzing the performance of quantum chemical methods.