Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially...

Area of Science:

• Computational Quantum Chemistry
• Electronic Structure Theory
• Relativistic Quantum Chemistry

Background:

• Accurate prediction of molecular electronic properties is crucial for chemistry and materials science.
• Relativistic effects, particularly spin-orbit coupling, are significant for molecules containing heavy elements.
• The GW approximation (GWA) is a powerful tool for calculating electronic properties like ionization potentials.

Purpose of the Study:

• To develop and implement an all-electron, atomic orbital (AO)-based, two-component (2C) GW approximation (GWA) for closed-shell molecules.
• To incorporate vertex corrections, specifically the G3W2 correction, into the 2C-GWA framework.
• To assess the accuracy of the 2C-GWA for calculating first ionization potentials (IPs) of molecules with heavy elements.

Main Methods:

• Implementation of a space-time formulation of GWA using analytical continuation (AC) and pair-atomic density fitting (PADF).
• Calculation of the dynamical contribution to the GW self-energy at a quasi-one-component level for efficiency.
• Inclusion of the statically screened G3W2 vertex correction.

Main Results:

• The 2C-GWA algorithm is only 2-3 times slower than scalar relativistic calculations.
• Calculated IPs for 67 molecules show mean absolute deviations (MAD) of ~70 meV compared to the WEST code for G0W0@PBE and G0W0@PBE0.
• The 2C-G0W0@PBE0 + G3W2 method achieves the best agreement with experimental IPs, with a MAD of 140 meV.

Conclusions:

• The developed 2C-GWA provides an efficient and accurate method for calculating electronic properties of molecules, especially those with heavy elements.
• Explicit treatment of spin-orbit effects at the 2C level is essential for systematic agreement with experimental ionization potentials.
• The G3W2 vertex correction further improves the accuracy of ionization potential predictions.