Cubic-Scaling All-Electron GW Calculations with a Separable Density-Fitting Space-Time Approach.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate electronic structure calculations are crucial for understanding material properties.
• Existing methods face challenges with computational cost and scalability for large systems.
• The GW approximation is a powerful tool for predicting electronic properties.

Purpose of the Study:

• To present a novel implementation of the GW space-time approach for efficient all-electron calculations.
• To achieve cubic scaling for electronic structure calculations using standard Gaussian basis sets.
• To benchmark the method's accuracy and scalability on various molecular systems.

Main Methods:

• Implementation of the GW space-time approach.
• Construction of independent-electron susceptibility in time representation using real-space locations.
• Optimization within a separable resolution-of-the-identity framework.
• Analytic continuation of the screened Coulomb potential.

Main Results:

• Cubic-scaling all-electron calculations achieved with standard Gaussian basis sets.
• Reproduces Coulomb-fitting calculations with meV accuracy.
• Demonstrated crossover with standard Coulomb-fitting for systems < few hundred electrons.
• Benchmarked on large molecular sets and defected hexagonal boron-nitride flakes up to 6000 electrons.

Conclusions:

• The presented GW space-time approach offers a computationally efficient and accurate method for electronic structure calculations.
• The method scales favorably, enabling the study of larger and more complex systems.
• This work provides a valuable tool for advancing research in computational chemistry and materials science.