Density-Matrix Coupled Time-Dependent Exchange-Correlation Functional Approximations.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Time-dependent density functional theory (TDDFT) is a powerful tool for studying electronic dynamics.
• Adiabatic approximations in TDDFT often fail to capture essential dynamic features of the exchange-correlation potential.
• Accurate approximations are needed to improve the predictive power of TDDFT.

Purpose of the Study:

• To develop a new class of nonadiabatic approximations for the time-dependent exchange-correlation potential in TDDFT.
• To address the limitations of current adiabatic approximations in reproducing dynamical features.
• To investigate the performance of these novel approximations.

Main Methods:

• Derivation of nonadiabatic approximations from an exact expression for the time-dependent exchange-correlation potential.
• Approximation of the one-body reduced density-matrix as a functional of the Kohn-Sham density-matrix.
• Systematic testing of two proposed approximations on four benchmark examples.

Main Results:

• The new approximations successfully reproduce dynamical step and peak features present in the exact potential.
• These features are notably absent in standard adiabatic approximations.
• Performance evaluation on four examples demonstrates the potential of the developed approximations.

Conclusions:

• The proposed nonadiabatic approximations offer a significant improvement over existing adiabatic methods in TDDFT.
• These approximations provide a more accurate description of electronic dynamics by capturing essential features of the exchange-correlation potential.
• The findings pave the way for more reliable quantum simulations in various chemical and physical systems.