Self-consistentGW: All-electron implementation with localized basis functions

Abstract

This paper describes an all-electron implementation of the self-consistent GW (sc-GW ) approach-i.e., based on the solution of the Dyson equation-in an all-electron numeric atom-centered orbital basis set. We cast Hedin's equations into a matrix form that is suitable for numerical calculations by means of (i) the resolution-of-identity technique to handle four-center integrals and (ii) a basis representation for the imaginary-frequency dependence of dynamical operators. In contrast to perturbative G 0 W 0 , sc-GW provides a consistent framework for ground-and excited-state properties and facilitates an unbiased assessment of the GW approximation. For excited states, we benchmark sc-GW for five molecules relevant for organic photovoltaic applications: thiophene, benzothiazole, 1,2,5-thiadiazole, naphthalene, and tetrathiafulvalene. At self-consistency, the quasiparticle energies are found to be in good agreement with experiment and, on average, more accurate than G 0 W 0 based on Hartree-Fock or density-functional theory with the Perdew-Burke-Ernzerhof exchange-correlation functional. Based on the Galitskii-Migdal total energy, structural properties are investigated for a set of diatomic molecules. For binding energies, bond lengths, and vibrational frequencies sc-GW and G 0 W 0 achieve a comparable performance, which is, however, not as good as that of exact-exchange plus correlation in the random-phase approximation and its advancement to renormalized second-order perturbation theory. Finally, the improved description of dipole moments for a small set of diatomic molecules demonstrates the quality of the sc-GW ground-state density. Many-body perturbation theory (MBPT) 1 in the GW approach for the electron self-energy 2-4 provides a natural framework for an ab initio, parameter-free description of photo-ionization processes and charged excitations. 5 In recent years, the GW approach has become a popular method for the computation of band gaps and charged excitation energies for extended 6,7 and finite systems. 8,9 In numerical implementations, following Hybertsen and Louie, 10 it is standard practice to treat the GW self-energy as a single-shot perturbation (G 0 W 0 ) acting on a Kohn-Sham (KS) or Hartree-Fock (HF) reference system. Thus, excitation energies are evaluated from first-order Feynman-Dyson perturbation theory as corrections to a set of single-particle eigenvalues.The popularity of the G 0 W 0 approximation stems from the substantial reduction in the complexity of Hedin's equations at first-order perturbation theory: The KS or HF eigenstates from a self-consistent field calculation can be used as basis functions and provide a convenient representation in which the noninteracting Green's function is diagonal. In this basis, only diagonal matrix elements of the self-energy are needed to evaluate quasiparticle corrections at first order. Thus, G 0 W 0 grants a considerable simplification of the linear algebra operations which is decisive for applying the theory to large molecules and solids.Although num...

Many-body dispersion effects in the binding of adsorbates on metal surfaces

“…Accurate treatment of long-range correlation and their manifestation as dispersion interaction is key to correctly describe the bonding of adsorbate-surface complexes. While many approaches beyond semi-local DFT exist trying to incorporate an improved description of exchange and correlation, either on the basis of the adiabatic connection fluctuation-dissipation theorem (ACFDT) 20,21 or many-body perturbation theory [22][23][24] , it may still be desirable to retain the simplicity and computational efficiency of semi-local functionals, but somehow incorporate a physically correct description of long-range correlation as it is given by wavefunction approaches.…”

Quasi-particle energy spectra in local reduced density matrix functional theory

“…Marom et al 26 Table I compared with experimental results. the performance of a hierarchy of GW approximations for benzene, pyridine, and the diazines and compared the quasiparticle spectrum with PES. Caruso and co-workers [27][28][29] developed an all electron implementation of self-consistent GW (sc-GW ) with localized basis functions and showed that it is more accurate than other approximations lower in GW hierarchy. They applied sc-GW on five molecules relevant for organic photovoltaics 28 obtaining an average error of 0.4 eV (maximum error 1.2 eV).…”

“…The Perdew-Zunger self-interaction correction (SIC) method 17 in DFT offers a correction to this problem and was found to yield orbital energies closer to the experimental IPs 18 improving several other properties as well. [18][19][20] The GW method [21][22][23] was initially introduced to improve the obtained quasiparticle spectrum of solids but in the last decade, GW at various levels of approximations was also applied to finite systems [24][25][26][27][28][29][30] improving significantly the quasiparticle excitation energies with respect to standard DFT-approximations. Those calculations suffer from a strong initial state dependence and the good agreement found could be just fortuitous.…”

“…Those calculations suffer from a strong initial state dependence and the good agreement found could be just fortuitous. In this context, self-consistent GW [27][28][29] was found to systematically improve ionization energies and total energies of closed shell systems. The single electron spectral properties are in very close agreement with experiment avoiding the starting-point dependence.…”

Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule

“…[19][20][21][22][23][24][25] for examples of fully self-consistent GW calculations). These types of approximations tend to yield accurate band gaps and spectral properties.…”