Abstract
Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.
Highlights
The GW approximation (GWA) to Hedin’s equations (Hedin, 1965) is a popular approach to calculate charged excitations in molecular systems
3.1.1 Comparison of Exchange-Correlation Potentials in QP self-consistent GW (qsGW) We already noticed in section 2 that the correlated part of the exchange-correlation potential of qsGW can be defined in different ways
For the 10 converged calculations differences in the final QP energies are small; for both, ionization potentials (IP) and electron affinities (EA), both variants differ by only 20 meV on average, i. e the error introduced by averaging over the offdiagonal elements of the self-energy are small
Summary
The GW approximation (GWA) to Hedin’s equations (Hedin, 1965) is a popular approach to calculate charged excitations in molecular systems. The GWA has been implemented into an increasing number of molecular electronic structure codes (Ke, 2011; Caruso et al, 2012; Caruso et al, 2013; Ren et al, 2012; Van Setten et al, 2013; Kaplan et al, 2015, 2016; Bruneval et al, 2016; Wilhelm et al, 2016; Tirimbò et al, 2020b) These implementations use localized basis functions and the resolutionof the identity or density fitting approximation (Baerends et al, 1973; Whitten, 1973; Dunlap et al, 1979) within the global Coulomb metric (RI-V) (Vahtras et al, 1993), leading to a scaling of N4 with system size. Systems of around 100 atoms are within reach on standard hardware (Knight et al, 2016), while highly parallel implementations enable applications to systems with more than 300 atoms on modern supercomputers (Wilhelm et al, 2016; Wilhelm et al, 2018; Wilhelm et al, 2021)
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