Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Basis set size is crucial for accurate quantum mechanical calculations.
• Understanding electron interactions is fundamental in chemistry and physics.
• The canonical ensemble is a standard framework for thermodynamic properties.

Purpose of the Study:

• To investigate the impact of basis set size on interacting electron systems.
• To analyze the convergence properties of different energy components.
• To explore stable methods for calculating thermodynamic properties.

Main Methods:

• Exact diagonalization (finite temperature full configuration interaction).
• Calculations on two-electron model systems: uniform electron gas (UEG) and helium atom.
• Analysis of internal energy, kinetic energy, exchange energy, and correlation energy.

Main Results:

• Observed a competition in internal energy convergence between correlation and kinetic energies.
• Demonstrated that separating free energy allows for monotonic convergence with basis set size.
• Found free energy convergence properties mirrored internal energy convergence.
• Compared basis set convergence of hydrogen atom and helium atom in a box.

Conclusions:

• Free energy calculations offer a more robust method for basis set convergence.
• Nuances exist in breaking down internal energy into components.
• Helium atom convergence trends in reduced box sizes resemble the UEG.