Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The particle-particle random phase approximation (pp-RPA) method has shown promise for describing challenging electronic excitations.
• Its computational cost (O(N^6)) limited its application to smaller systems.
• Conventional time-dependent density functional theory (TDDFT) faces limitations with certain excitation types.

Purpose of the Study:

• To reduce the computational scaling of the pp-RPA method for large molecules.
• To implement a Davidson iterative algorithm to enable calculations on larger systems.
• To benchmark the performance of the optimized pp-RPA method against established methods like CIS and TDDFT.

Main Methods:

• Derivation and implementation of a Davidson iterative algorithm for pp-RPA.
• Reduction of formal computational scaling from O(N^6) to O(N^4).
• Benchmark calculations on significantly larger molecules using a substantial basis set.

Main Results:

• Accurate calculation of the lowest few electronic excitations for converged systems.
• pp-RPA shows no systematic bias, with a mean signed error near zero.
• Mean absolute error comparable to TDDFT, indicating pp-RPA's viability for large molecules.
• Excited states with significant non-HOMO contributions are well-described if HOMO contributions are also substantial.

Conclusions:

• The O(N^4) pp-RPA method is a reliable and general approach for calculating electronic excitations in large molecules.
• It offers a competitive alternative to TDDFT, particularly for challenging excitation types.
• Further demonstrates the potential of pp-RPA as a robust computational tool in quantum chemistry.