Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Physics

Background:

• Time-dependent density functional theory (TDDFT) has limitations in accurately describing excited state surfaces and charge transfer energies.
• Adiabatic approximations in TDDFT lead to failures in modeling bond dissociation and doubly excited states.
• Two-electron systems serve as crucial models for understanding these TDDFT deficiencies.

Purpose of the Study:

• To address the known failures of adiabatic TDDFT using time-dependent density matrix functional theory (TDDMFT).
• To investigate the performance of TDDMFT in modeling excited state surfaces and charge transfer excitations.
• To develop and test adiabatic approximations within TDDMFT.

Main Methods:

• Formulation of exact response equations for two-electron systems within TDDMFT.
• Utilizing prototype two-electron systems like dissociating H(2) and HeH(+) to test TDDMFT.
• Developing and evaluating adiabatic approximations for TDDMFT.

Main Results:

• The nonadiabatic formulation of linear response TDDMFT (LR-TDDMFT) yields exact excitation energies.
• LR-TDDMFT correctly represents doubly excited states, a failure in TDDFT.
• Adiabatic approximations in TDDMFT accurately describe bonding-to-antibonding excited states and charge transfer excitations, with a new approximation accounting for double excitations.

Conclusions:

• TDDMFT offers a robust framework to overcome TDDFT's limitations in excited state calculations.
• The developed adiabatic approximations in TDDMFT provide accurate results for various excitation types.
• TDDMFT shows significant promise for future theoretical chemistry and quantum physics applications.