Basis-Set-Error-Free Random-Phase Approximation Correlation Energies for Atoms Based on the Sternheimer Equation

Area of Science:

• Quantum chemistry
• Computational physics
• Electronic structure theory

Background:

• Finite basis set errors limit the accuracy of electronic structure calculations.
• Random-Phase Approximation (RPA) is a powerful method for correlation energy, but sensitive to basis sets.

Purpose of the Study:

• Analyze and mitigate finite basis set errors in all-electron RPA correlation energy calculations for atoms.
• Develop techniques to achieve basis-set-error-free RPA results.

Main Methods:

• Resolution-of-Identity (RI) RPA framework.
• Solving the Sternheimer equation on a dense radial grid to eliminate single-particle basis set incompleteness.
• Optimizing auxiliary basis sets (ABS) using variational properties.

Main Results:

• Incompleteness of single-particle atomic orbitals is the dominant source of basis set error in RI-RPA.
• Basis-set-error-free RPA correlation energies for atoms H to Kr were obtained.
• Error from finite ABS can be minimized by increasing ABS size or iterative eigenmode determination.

Conclusions:

• Numerical techniques effectively eliminate major basis set errors in atomic RPA calculations.
• The developed methods provide a pathway to accurate RPA correlation energies for atoms.
• Implications for molecular and solid-state RPA calculations are discussed.