Power Series Approximation for the Correlation Kernel Leading to Kohn-Sham Methods Combining Accuracy, Computational...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Time-dependent density-functional theory (TDDFT) is crucial for electronic structure calculations.
• Existing methods struggle with static (strong) correlation and computational scaling.
• Adiabatic-connection fluctuation-dissipation (ACFD) theorem methods face singularity issues.

Purpose of the Study:

• To develop a novel power series approximation for the TDDFT correlation kernel.
• To introduce a new family of Kohn-Sham methods based on this approximation.
• To address limitations of existing electronic structure methods, particularly concerning static correlation and computational efficiency.

Main Methods:

• Developed a power series approximation for the correlation kernel in TDDFT.
• Integrated this approximation into the adiabatic-connection fluctuation-dissipation (ACFD) theorem.
• Formulated new Kohn-Sham methods for electronic structure calculations.

Main Results:

• Achieved unprecedented accuracy in calculating reaction energies and barriers.
• Enabled accurate treatment of static correlation comparable to high-level multireference methods.
• Demonstrated superior computational scaling compared to wave-function-based methods.
• Eliminated singularities in response functions, broadening applicability.

Conclusions:

• The new TDDFT-based methods offer a black-box-like solution for static correlation problems.
• These methods provide a computationally efficient and broadly applicable alternative for electronic structure studies.
• The approach overcomes key limitations of previous ACFD methods.