Excitation energies from range-separated time-dependent density and density matrix functional theory

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• Adiabatic time-dependent density functional theory (TD-DFT) struggles with accurate prediction of excitation energies, notably failing to account for doubly excited configurations.
• Time-dependent density matrix functional theory (TD-DMFT) shows promise but requires exact functionals for high accuracy in single and double excitations.
• Existing methods face challenges in describing systems with significant static correlation, such as molecules at dissociation limits.

Purpose of the Study:

• To develop a novel time-dependent functional theory (TD-FT) that incorporates both electron density and one-electron reduced density matrix functionals.
• To address the limitations of TD-DFT by including doubly excited configurations through a range-separated electron-electron interaction operator.
• To provide a practical and accurate method for calculating excited state energies, including challenging cases like dissociation limits.

Main Methods:

• Formulation of a time-dependent functional theory based on range-separation of the electronic interaction operator.
• Application of the adiabatic approximation to short- and long-range components of the coupling matrix in linear response equations.
• Solving for excitation energies as an eigenproblem of a symmetric matrix, with identification of double excitations via transition density matrix elements.

Main Results:

• The proposed method successfully accounts for double excitations in the H(2) molecule and Be atom.
• Excitation energy predictions show improved accuracy compared to TD-DFT-LDA and TD-DMFT-BB, especially when the range-separation parameter is optimized.
• While some double excitations exhibit poor accuracy, the overall quality of other excitations is significantly enhanced.

Conclusions:

• The developed range-separated TD-FT offers a promising avenue for more accurate excited state energy calculations, particularly by including doubly excited states.
• The method demonstrates potential for improved description of molecular systems, including those with strong static correlation effects.
• Further research is needed to optimize the range-separation parameter and improve the accuracy of all predicted excitations.