Scalar relativistic explicitly correlated R12 methods.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Relativistic Quantum Mechanics

Background:

• Explicitly correlated R12 wave functions improve the description of electron correlation.
• Relativistic effects are crucial for accurate calculations of heavy elements.
• Douglas-Kroll-Hess (DKH) Hamiltonians provide a systematic way to include relativistic effects.

Purpose of the Study:

• To investigate the combination of R12 wave functions with relativistic DKH Hamiltonians.
• To explore different methods for incorporating relativistic terms into R12 calculations.
• To assess the accuracy and numerical stability of these combined methods.

Main Methods:

• Incorporation of relativistic terms into the second-order Møller-Plesset R12 method.
• Evaluation of relativistic terms using double resolution-of-the-identity.
• Explicit evaluation of terms up to O(c(-4)) using the Pauli Hamiltonian.
• Application of Kato's cusp condition to avoid numerical collapse.
• Derivation and implementation of new two-electron integrals for the mass-velocity term.

Main Results:

• Successful combination of R12 wave functions with DKH Hamiltonians.
• Demonstrated accuracy and numerical stability for the helium isoelectronic series.
• Identified strategies to mitigate numerical collapse in relativistic R12 calculations.
• Implemented new integrals for enhanced computational efficiency.

Conclusions:

• The developed methods provide a robust framework for relativistic quantum chemistry.
• These approaches are versatile and can be extended to other relativistic Hamiltonians.
• The study advances the computational treatment of relativistic electronic structures.