Linear-response time-dependent density-functional theory with pairing fields.

Area of Science:

• Quantum Chemistry
• Theoretical Physics
• Computational Chemistry

Background:

• Recent advancements in particle-particle random phase approximation (pp-RPA) have expanded its application to ground state correlation energies and N ± 2 excitation energies.
• Current pp-RPA calculations primarily use Hartree-Fock or approximated density-functional orbitals.

Purpose of the Study:

• To explore pairing matrix dependent functionals by developing linear-response time-dependent density-functional theory with pairing fields.
• To apply this theory to normal, non-superconducting systems for calculating correlation energies and excitation energies.

Main Methods:

• Developed linear-response time-dependent density-functional theory incorporating adiabatic and frequency-dependent pairing field kernels.
• Established the theory based on the representability assumption of the pairing matrix due to the absence of a proven one-to-one mapping for time-dependent systems.
• Utilized approximated density-functionals within the linear-response framework.

Main Results:

• The developed linear-response theory justifies the use of approximated density-functionals in pp-RPA calculations.
• This theoretical framework is applicable to normal, non-superconducting systems, extending the reach of pp-RPA.
• The study lays the groundwork for future density-functional developments.

Conclusions:

• The presented theory provides a robust foundation for enhancing the description of ground state correlation energies and N ± 2 excitation energies.
• It validates the use of approximated density-functionals in pp-RPA, simplifying calculations.
• This research opens new avenues for developing more accurate functionals in quantum mechanical modeling.