Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

Area of Science:

• Quantum Chemistry
• Atomic and Molecular Physics
• Computational Chemistry

Background:

• Accurate solutions to the Dirac-Coulomb equation are crucial for understanding relativistic effects in atoms and molecules.
• Existing methods often face challenges in achieving the high precision required for spectroscopic applications.

Purpose of the Study:

• To develop and implement a computational method for solving the Dirac-Coulomb equation with high precision.
• To establish a robust framework for future high-resolution atomic and molecular spectroscopy.
• To explore various strategies for positive-energy projection in relativistic quantum calculations.

Main Methods:

• Utilizing explicitly correlated Gaussian functions to solve the Dirac-Coulomb equation.
• Implementing algorithms for parts-per-billion energy convergence.
• Incorporating fundamental spinor structure, permutation, and point-group symmetries.
• Presenting and evaluating different positive-energy projection techniques.

Main Results:

• Achieved parts-per-billion precision in the no-pair Dirac-Coulomb energy calculations.
• Demonstrated the method's applicability to atomic and molecular systems with small nuclear charges.
• Provided a detailed analysis of symmetry implementations and projection procedure options.

Conclusions:

• The developed method offers a reliable and highly accurate approach for relativistic electronic structure calculations.
• The achieved precision serves as a benchmark for further theoretical developments and experimental comparisons.
• This work lays the groundwork for incorporating more complex relativistic effects, such as the Breit interaction, in future studies.