Large-scale Dirac-Fock-Breit method using density fitting and 2-spinor basis functions.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Relativistic Quantum Mechanics

Background:

• Accurate computation of electronic wave functions is crucial for understanding molecular properties.
• Relativistic effects become significant for heavy elements, necessitating four-component methods like Dirac-Fock.
• Previous relativistic calculations were computationally demanding, limiting their application to smaller systems.

Purpose of the Study:

• To present an efficient theory and algorithm for four-component relativistic Dirac-Fock calculations.
• To implement density fitting for improved computational efficiency.
• To investigate the accuracy of fitting basis sets for different relativistic interactions.

Main Methods:

• Developed an algorithm for computing Dirac-Fock wave functions using Coulomb, Gaunt, and Breit interactions.
• Employed density fitting and 2-spinor basis functions for the small components.
• Utilized factorization of 3-index half-transformed integrals for efficient Fock matrix evaluation.

Main Results:

• The computational cost for the Fock operator evaluation is only 70-90 times that of non-relativistic Hartree-Fock for Coulomb interaction.
• Prefactors for Gaunt and Breit interactions are 170 and 350-450, respectively.
• Successfully applied the method to a 130-atom complex, with one iteration taking ~1100s on 1024 CPU cores.
• Identified that standard fitting basis sets are inadequate for Gaunt and Breit interactions, proposing new accurate fitting basis sets.

Conclusions:

• The developed density-fitted Dirac-Fock method is efficient and applicable to large molecular systems with heavy elements.
• The factorization strategy is key to the computational efficiency of the Fock operator.
• New fitting basis sets are required for accurate Dirac-Fock-Gaunt and Dirac-Fock-Breit calculations.