Relativistic electronic structure theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Relativistic Quantum Mechanics

Background:

• Accurate treatment of heavy-atomic molecular systems requires relativistic electronic structure theories.
• Existing methods face challenges in computational efficiency and accuracy for heavy elements.

Purpose of the Study:

• To present theoretical and technical foundations for efficient relativistic electronic structure theories.
• To review four-component and two-component quasi-relativistic computational approaches.
• To introduce novel computational schemes and Hamiltonians for heavy-atom systems.

Main Methods:

• Development of a highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) methods using generally contracted spherical harmonic Gaussian-type spinors (GTSs).
• Implementation and testing of the REL4D program package for four-component relativistic calculations (Dirac-Hartree-Fock and DKS methods).
• Introduction and application of two-component quasi-relativistic Hamiltonians: RESC and higher-order Douglas-Kroll (DK) Hamiltonians.

Main Results:

• The REL4D program package demonstrates the efficiency of the four-component relativistic ab initio MO scheme.
• Illustrative calculations confirm the efficiency of the proposed computational scheme.
• Numerical results show that the third-order DK (DK3) Hamiltonian achieves good accuracy in two-component quasi-relativistic calculations.

Conclusions:

• Efficient relativistic electronic structure theories are crucial for studying heavy-atomic molecular systems.
• The presented four-component and two-component methods offer accurate and efficient approaches.
• The developed computational schemes and Hamiltonians advance the field of relativistic quantum chemistry.