SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian with Size-Intensive Picture Change

Area of Science:

• Quantum Chemistry
• Relativistic Calculations
• Computational Chemistry

Background:

• Relativistic effects are crucial for accurate electronic structure calculations, especially for heavy elements.
• Existing 1-electron exact 2-component (1eX2C) methods are computationally efficient but lack accuracy for two-electron picture-change effects.
• More complex methods like 4-component Dirac-Hartree-Fock are accurate but computationally expensive.

Purpose of the Study:

• To develop a computationally efficient and accurate relativistic Hamiltonian for electronic structure calculations.
• To model two-electron picture-change effects using a simplified approach.
• To enable accurate calculations for extended systems like large molecules and periodic crystals.

Main Methods:

• Implementation of a Superposition of Atomic Potentials (SAP) approach within the exact 2-component (X2C) framework (SAP-X2C).
• Utilizing Lehtola's SAP method to model two-electron effects.
• Comparison with 4-component Dirac-Hartree-Fock (DHFS) calculations and 1-electron X2C (1eX2C) methods.

Main Results:

• The SAP-X2C Hamiltonian accurately models two-electron picture-change effects.
• SAP-X2C retains the computational efficiency of 1eX2C methods.
• Calculations of total energies, spinor energies, spin-orbit splittings, bond distances, and vibrational frequencies show good agreement with 4-component relativistic methods.
• The method demonstrates a well-defined thermodynamic limit, suitable for extended systems.

Conclusions:

• The SAP-X2C approach provides a balance of accuracy and computational efficiency for relativistic electronic structure calculations.
• It serves as a viable and simpler alternative to more complex relativistic methods like atomic mean-field (AMF) X2C.
• SAP-X2C is applicable to a wide range of systems, including large molecules and periodic solids.