Extrapolating Unconverged GW Energies up to the Complete Basis Set Limit with Linear Regression

Abstract

The GW approximation to the electronic self-energy is now a well-recognized approach to obtain the electron quasiparticle energies of molecules and, in particular, their ionization potential and electron affinity. Though much faster than the corresponding wavefunction methods, the GW energies are still affected by slow convergence with respect to the basis completeness. This limitation hinders a wider application of the GW approach. Here, we show that we can reach the complete basis set limit for the cumbersome GW calculations solely based on fast preliminary calculations with an unconverged basis set. We introduce a linear model that correlates the molecular orbital characteristics and the basis convergence error for a large database of approximately 600 states in 104 organic molecules that contain H, C, O, N, F, P, S, and Cl. The model employs molecular-orbital-based non-linear descriptors that encode efficiently the chemical space offering outstanding transferability. Using a low number of descriptors (17) the performance of this extrapolation procedure is superior to that of the earlier more physically motivated approaches. The predictive power of the method is finally demonstrated for a selection of large acceptor molecules.

The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules

“…The miracle of GW is the fact that its in a featherweight class: GW , when combined with the resolution-of-the-identify, has an attractive N 4 scaling. GW now routinely runs on molecular systems with several hundreds of atoms ( Vlček et al, 2017b ; Wilhelm et al, 2018 ; Bruneval et al, 2020 ; Duchemin and Blase, 2021 ).…”

Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules

“…The maximum error never exceeds 50 meV and is of the same order of magnitude than the experimental resolution of photoionization experiments (Knight et al, 2016) of the typical basis set errors of GW calculations after extrapolation. (Knight et al, 2016;Maggio et al, 2017;Govoni and Galli, 2018;Bruneval et al, 2020;Förster and Visscher, 2021). The distribution of iterations required for convergence is displayed in Figure 3.…”

Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W

“…For such largedimensional descriptors, the linear or kernel formalism are much better adapted as the range of the design matrix and the number of parameters are order of K or M , respectively. The suggested QNML approach is well adapted for compact descriptors with D < 100 components, such as angular Fourier series (AFS), bispectrum SO(4) [15], hybrid descriptors [40], or quantum mechanics informed descriptors [25].…”

“…Some innovative descriptors, e.g., proposed by Mallat et al [23,24], are based on the scaling wavelets transformation. Quantum mechanics informed descriptors can be built on physical observables, such as Mulliken charges [25] or partial histograms of electronic density of states [26]. The similarity distance descriptors are based on the distances between pairs of atomic environments, e.g., smooth overlap of atomic positions (SOAP) [15] or graph version [27,28] defined through a functional representation of atomic positions.…”