Dirac-Fock calculations on molecules in an adaptive multiwavelet basis

Area of Science:

• Quantum Chemistry
• Computational Physics
• Relativistic Quantum Mechanics

Background:

• Relativistic effects are crucial for accurate quantum chemical calculations, especially for heavy elements.
• Existing methods often rely on approximations or specific basis sets that can limit applicability.
• A fully numerical approach offers a potential pathway to higher accuracy and broader applicability.

Purpose of the Study:

• To develop and present the first fully numerical approach for relativistic quantum chemical calculations applicable to molecules.
• To implement this approach using an adaptive basis of multiwavelet functions.
• To demonstrate the accuracy and applicability of the method for both atoms and molecules.

Main Methods:

• Solving the full four-component Dirac-Coulomb equation numerically.
• Utilizing an adaptive basis of multiwavelet functions for efficient and accurate representation.
• Comparing results with established computational chemistry packages (GRASP for atoms, DIRAC for molecules).

Main Results:

• The numerical approach achieves user-specified accuracy for relativistic quantum chemical calculations.
• Ground state energy calculations for atoms show excellent agreement with GRASP.
• Ground state calculations for simple molecules, including heavy water analogs, demonstrate the method's applicability.

Conclusions:

• The presented fully numerical approach is a significant advancement for relativistic quantum chemistry.
• This method provides a robust and accurate tool for studying molecules, particularly those with heavy elements.
• The multiwavelet-based Dirac-Coulomb solver offers a promising direction for future computational chemistry research.