Towards GW Calculations on Thousands of Atoms

Abstract

The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is $O(N^4)$ in the system size N, which prohibits its application to many systems of interest. We present a full-frequency GW algorithm in a Gaussian type basis, whose computational cost scales with $N^2$ to $N^3$. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the GW100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction.

References in corpus (5)

• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• A Benchmark of GW Methods for Azabenzenes: Is the GW Approximation Good Enough?
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Ab initio quantum transport through armchair graphene nanoribbons: Streamlines in the current density
• Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

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• Koopmans Meets Bethe-Salpeter: Excitonic Optical Spectra without GW
• Frequency dependence in GW made simple using a multi-pole approximation
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies
• Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies