Relativistic Effects in the Electronic Structure of Atoms

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Chemistry

Background:

• Relativistic effects are crucial for understanding atomic structure and properties, especially for heavier elements.
• Previous studies have suggested differing influences of relativistic effects on various electron shells.
• The interplay between kinematic and indirect relativistic effects requires detailed investigation across the periodic table.

Purpose of the Study:

• To systematically investigate periodic trends in relativistic effects from hydrogen to lawrencium.
• To compare relativistic spinor energies with nonrelativistic orbital energies for different electron shells (ns, np, nd, nf).
• To elucidate the relative contributions of kinematic, indirect, and direct relativistic effects on atomic electronic structure.

Main Methods:

• Employed Dirac-Hartree-Fock calculations to model relativistic effects.
• Utilized nonrelativistic Hartree-Fock calculations for comparison.
• Analyzed energy trends and orbital/spinor characteristics across elements ₁H to ₁₀₃Lr.

Main Results:

• For ns spinors, relativistic effects generally lower energies (kinematic > indirect), except for specific configurations like Cr, Nb, Mo.
• For np₊ spinors, relativistic effects increase energies (indirect > kinematic), consistent with prior work.
• Direct relativistic effects significantly lower np_- spinor energies in heavy atoms, making them tighter than np₊ spinors.

Conclusions:

• Relativistic effects exhibit distinct periodic trends depending on the electron shell and the nature of the effect (kinematic, indirect, direct).
• The ns₊ and np₊ spinor energy shifts reveal the dominance of kinematic and indirect relativistic effects, respectively.
• Direct relativistic effects play a critical role in the behavior of np_- spinors, particularly in heavy elements.