All-order explicitly correlated relativistic computations for atoms and molecules

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Physics

Background:

• Accurate calculation of atomic and molecular energies is crucial for understanding chemical and physical phenomena.
• Existing methods face challenges in achieving high precision, especially for heavier elements.
• Relativistic effects become significant in accurate energy calculations.

Purpose of the Study:

• To develop and test a variational solution procedure for the many-particle no-pair Dirac-Coulomb and Dirac-Coulomb-Breit Hamiltonians.
• To achieve parts-per-billion (ppb) convergence for atomic and molecular energies.
• To evaluate the procedure's performance for nuclear charge numbers from Z = 1 to 28.

Main Methods:

• Implementation of a variational solution procedure.
• Utilizing the fixed nuclei approximation.
• Testing the method across a range of nuclear charges (Z=1 to 28).

Main Results:

• The procedure successfully computes atomic and molecular energies with parts-per-billion accuracy.
• Significant deviations were observed compared to leading-order Foldy-Woythusen perturbation theory, even for low Z values.
• These deviations were found to be smaller than estimated self-energy and vacuum polarization corrections.

Conclusions:

• The developed variational procedure offers a highly accurate approach for relativistic energy calculations.
• The findings highlight the limitations of perturbation theory for precise energy determinations.
• The method provides a robust framework for future investigations in relativistic quantum chemistry.