Unified description of ground and excited states of finite systems: The self-consistentGWapproach

Abstract

GW calculations with a fully self-consistent Green's function G and screened interaction W -based on the iterative solution of the Dyson equation-provide a consistent framework for the description of groundand excited-state properties of interacting many-body systems. We show that for closed-shell systems selfconsistent GW reaches the same final Green's function regardless of the initial reference state. Self-consistency systematically improves ionization energies and total energies of closed-shell systems compared to G 0 W 0 based on Hartree-Fock and (semi)local density-functional theory. These improvements also translate to the electron density, as exemplified by an improved description of dipole moments, and permit us to assess the quality of ground-state properties such as bond lengths and vibrational frequencies. Many-body perturbation theory (MBPT) 1 in the GW approximation of the electronic self-energy 2,3 is presently the state-of-the-art method for describing the spectral properties of solids. 4,5 Recently, it has steadily gained popularity for molecules and nanosystems. 6 In addition, MBPT provides a prescription to extract total energies and structural properties from the GW approximation and therefore is a consistent theoretical framework for single-particle spectra and total energies.Due to its numerical cost and algorithmic difficulties, the GW method has only recently been applied self-consistently (i.e., nonperturbatively) to atoms, 7 molecules, 8 and molecular transport. 6 Predominantly, GW calculations are still performed perturbatively (one-shot G 0 W 0 ) on a set of singleparticle orbitals and eigenvalues obtained from a preceding density-functional theory 9 (DFT) or Hartree-Fock (HF) calculation. This procedure introduces a considerable starting-point dependence, 10-12 which can be eliminated by iterating the Dyson equation to self-consistency. [6][7][8]13 The resulting selfconsistent GW (sc-GW ) framework is a conserving approximation in the sense of Baym and Kadanoff 14 (i.e., it satisfies momentum, energy, and particle number conservation laws). sc-GW gives total energies 15 free from the ambiguities of the G 0 W 0 scheme, in which the results depend on the chosen total energy functional. 7 However, as in any self-consistent theory, the question remains if the self-consistent solution of the Dyson equation is unique. This issue is fundamentally different from the initial-state dependence of G 0 W 0 . For HF (Ref. 16) and local-density approximation (LDA)/generalized gradient approximation + U (GGA + U ) (Ref. 17) calculations, it is well known that the self-consistency cycle can reach many local minima instead of the global minimum. Moreover, a previous sc-GW study for the Be atom showed that normconserving pseudopotential calculations do not produce the same final GW Green's function (and the corresponding ionization potential) as all-electron calculations. 18 In this Rapid Communication, we demonstrate certain key aspects of the sc-GW approximation for closed-shell molecules that make...

molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters

“…In the past, the application of the GW approximation to finite systems was rather infrequent [10,11,12,13]. But there has been much recent increase in interest [14,15,16,17,18,19,20,21,22,23] in the application of the GW approximation to problems involving atoms, molecules, and clusters, in part driven by the quest to develop efficient techniques to address mixed systems such as molecular junctions [24,25,26,27,28].…”

“…The GW approximation has been mentioned so far with the aim of obtaining self-and quasiparticle energies, but it can also be used to calculate total energies [5,75,12,21].…”

“…Nowadays, some groups [51,14,21] are exploring the possibility of fully self-consistent GW calculations. As molgw does not have this capability, we will not mention this any further.…”

Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach

“…18,[21][22][23][24] However, not only is GW computationally much more demanding than DFT, the fact that it is typically employed non-self-consistently also leads to a significant starting-point dependence. [25][26][27][28][29][30][31] For the case of the pentacene molecule, for example, it has been found that nonself-consistent G 0 W 0 calculations based on a (semi-)local DFT starting point underestimate the fundamental gap E g in the gas phase by as much as 0.7 eV, while E g calculated at the same level of theory for the pentacene crystal are found in good agreement with the experimentally determined solid-state E g , likely due to a fortuitous cancelation of errors. 18 The G 0 W 0 accuracy can be significantly improved by the introduction of self-consistency at the level of eigenvalues 26,32 or using "better" DFT starting points such as the global hybrid PBE0, 27,28,33 short-range hybrid Heyd-Scuseria-Ernzerhof (HSE) functionals, 18 as well as standard 33 and nonempirically tuned long-range corrected hybrid functionals.…”

“…[25][26][27][28][29][30][31] For the case of the pentacene molecule, for example, it has been found that nonself-consistent G 0 W 0 calculations based on a (semi-)local DFT starting point underestimate the fundamental gap E g in the gas phase by as much as 0.7 eV, while E g calculated at the same level of theory for the pentacene crystal are found in good agreement with the experimentally determined solid-state E g , likely due to a fortuitous cancelation of errors. 18 The G 0 W 0 accuracy can be significantly improved by the introduction of self-consistency at the level of eigenvalues 26,32 or using "better" DFT starting points such as the global hybrid PBE0, 27,28,33 short-range hybrid Heyd-Scuseria-Ernzerhof (HSE) functionals, 18 as well as standard 33 and nonempirically tuned long-range corrected hybrid functionals. 30,34 However, the application of hybrid functionals for periodic systems is still computationally demanding, in particular when using the large basis sets required to converge a G 0 W 0 calculation.…”