Efficient Four-Component Dirac-Coulomb-Gaunt Hartree--Fock in Pauli Spinor Representation

TL;DR

This paper introduces a novel Pauli quaternion formalism for efficient four-component Dirac-Coulomb-Gaunt Hartree--Fock calculations, enabling explicit spin separation and reducing computational complexity for heavy element systems.

Contribution

It presents a new formalism that simplifies relativistic electronic structure calculations and allows detailed analysis of spin effects and relativistic trends.

Findings

Reduced floating-point operations in calculations

Explicit separation of spin physics in two-electron interactions

Analysis of relativistic effects in gold systems

Abstract

Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method less common, even though we can consider the Dirac Hartree--Fock Hamiltonian the "ground truth" of electronic structure, barring explicit quantum-electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component- and spin-separation for computing the Dirac-Coulomb-Gaunt Hartree--Fock ground state, with a minimal floating-point-operation count algorithm. This approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and the spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table, and analyze the basis set dependence of atomic gold and gold dimer systems.