Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• The time-dependent exact-exchange (TDEXX) method offers an exact treatment of the frequency-dependent exchange kernel in density-functional theory.
• The original TDEXX method requires a computationally intensive frequency iteration for each excitation energy calculation.
• Accurate calculation of electronic excitation energies is crucial for understanding molecular properties and reactivity.

Purpose of the Study:

• To reformulate the TDEXX method for more efficient calculation of electronic excitation energies.
• To enable the use of standard and generalized eigenvalue solvers for TDEXX calculations.
• To explore methods for incorporating electron correlation alongside exact exchange in the TDEXX framework.

Main Methods:

• Reformulation of the TDEXX method into a linear generalized eigenvalue problem.
• Application of Davidson algorithms (standard and generalized) for efficient eigenvalue computation.
• Utilizing series expansion of the TDEXX eigenvalue equation for analysis and solver application.
• Investigating correlation treatment via Kohn-Sham eigenvalue scaling, approximate correlation potentials, and kernel mixing.

Main Results:

• The reformulated TDEXX method allows electronic excitation energies to be computed by solving a generalized eigenvalue problem, eliminating the need for frequency iteration.
• Efficient calculation of lowest excitation energies is achievable using Davidson algorithms or standard eigensolvers via series expansion.
• The relationship between TDEXX and time-dependent Hartree-Fock is elucidated through the series expansion.
• Various strategies for including correlation effects in TDEXX are presented and discussed.

Conclusions:

• The reformulated TDEXX method significantly enhances computational efficiency for determining electronic excitation energies.
• The new approach facilitates the application of established numerical techniques for solving large eigenvalue problems.
• The study provides a foundation for further development of TDEXX methods incorporating electron correlation for accurate molecular simulations.