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Investigating interacting electrons, this study reveals how basis set size impacts energy calculations for the uniform electron gas and helium atom. Free energy calculations show monotonic convergence, offering a more stable approach.

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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.