Relativistic Effects on Electron-Nucleus Hyperfine Coupling Studied with an Exact 2-Component (X2C) Hamiltonian

Area of Science:

• Quantum Chemistry
• Atomic and Molecular Physics
• Computational Chemistry

Background:

• Accurate calculation of hyperfine coupling constants is crucial for understanding atomic and molecular properties.
• Traditional 4-component relativistic methods can be computationally expensive.
• Developing efficient 2-component methods is essential for relativistic quantum chemistry.

Purpose of the Study:

• To implement and validate an exact 2-component (X2C) transformation for nuclear hyperfine magnetic field operators.
• To assess the accuracy of the X2C method for calculating hyperfine coupling constants in various atomic and molecular systems.
• To provide reference data for 2-component relativistic calculations.

Main Methods:

• Utilized an exact 2-component (X2C) transformation of the one-electron Hamiltonian.
• Applied spin-unrestricted scalar X2C Hartree-Fock and Kohn-Sham theory.
• Performed numerical calculations for one-electron atoms, many-electron atoms, and the HgH radical.

Main Results:

• The X2C transformed hyperfine operators accurately predict hyperfine coupling constants for one-electron atomic n s states (n=1-3).
• Kohn-Sham calculations showed minimal one-electron self-interaction errors for these states.
• The X2C method demonstrated promising performance for many-electron systems.

Conclusions:

• The developed X2C transformation provides an accurate and efficient method for calculating hyperfine coupling constants.
• The approach is readily implementable in computational codes using 1-component or 2-component spinor orbitals.
• This work advances relativistic quantum chemical calculations of magnetic properties.