Fabio Caruso

Unified description of ground and excited states of finite systems: The self-consistent GW approach

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 G0W0 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.

Self-consistent GW: an all-electron implementation with localized basis functions

This paper describes an all-electron implementation of the self-consistent GW (sc-GW) approach—i.e., based onthesolutionoftheDysonequation—inanall-electronnumericatom-centeredorbitalbasisset.WecastHedin’s equations into a matrix form that is suitable for numerical calculations by means of (i) the resolution-of-identity techniquetohandlefour-centerintegralsand(ii)abasisrepresentationfortheimaginary-frequencydependenceof dynamical operators. In contrast to perturbative G0W0 ,s c-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 G0W0 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 G0W0 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.

Bond breaking and bond formation: How electron correlation is captured in many-body perturbation theory and density-functional theory

For the paradigmatic case of H(2) dissociation, we compare state-of-the-art many-body perturbation theory in the GW approximation and density-functional theory in the exact-exchange plus random-phase approximation (RPA) for the correlation energy. For an unbiased comparison and to prevent spurious starting point effects, both approaches are iterated to full self-consistency (i.e., sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with noninteracting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, sc-RPA outperforms sc-GW when it comes to bond breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.

First-principles description of charge transfer in donor-acceptor compounds from self-consistent many-body perturbation theory

This work was supported by the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), the European Commission within the FP7 CRONOS project (ID 280879), Spanish Grant (FIS2010-21282-C02-01), Ikerbasque and Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13).

Origin of the crossover from polarons to Fermi liquids in transition metal oxides

Transition metal oxides host a wealth of exotic phenomena ranging from charge, orbital and magnetic order to nontrivial topological phases and superconductivity. In order to translate these unique materials properties into device functionalities these materials must be doped; however, the nature of carriers and their conduction mechanism at the atomic scale remain unclear. Recent angle-resolved photoelectron spectroscopy investigations provided insight into these questions, revealing that the carriers of prototypical metal oxides undergo a transition from a polaronic liquid to a Fermi liquid regime with increasing doping. Here, by performing ab initio many-body calculations of angle-resolved photoemission spectra of titanium dioxide, we show that this transition originates from non-adiabatic polar electron–phonon coupling, and occurs when the frequency of plasma oscillations exceeds that of longitudinal-optical phonons. This finding suggests that a universal mechanism may underlie polaron formation in transition metal oxides, and provides a pathway for engineering emergent properties in quantum matter.

GW100: Benchmarking G0W0 for Molecular Systems.

We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.

Benchmark of GW methods for azabenzenes

Many-body perturbation theory in the GW approximation is a useful method for describing electronic properties associated with charged excitations. A hierarchy of GW methods exists, starting from non-self-consistent G0W0, through partial self-consistency in the eigenvalues (ev-scGW) and in the Green function (scGW0), to fully self-consistent GW (scGW). Here, we assess the performance of these methods for benzene, pyridine, and the diazines. The quasiparticle spectra are compared to photoemission spectroscopy (PES) experiments with respect to all measured particle removal energies and the ordering of the frontier orbitals. We find that the accuracy of the calculated spectra does not match the expectations based on their level of self-consistency. In particular, for certain starting points G0W0 and scGW0 provide spectra in better agreement with the PES than scGW.

Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation

We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H2 and LiH molecules. Although both approximations contain topologically identical diagrams, the nonlocality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies, which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation, their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulas for the GW Green’s function and total energy of a simplified two-level model providing additional insights into the dissociation limit.

Benchmark of GW Approaches for the GW100 Test Set

For the recent GW100 test set of molecular ionization energies, we present a comprehensive assessment of different GW methodologies: fully self-consistent GW (scGW), quasiparticle self-consistent GW (qsGW), partially self-consistent GW0 (scGW0), perturbative GW (G0W0), and optimized G0W0 based on the minimization of the deviation from the straight-line error (DSLE-min GW). We compare our GW calculations to coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] reference data for GW100. We find scGW and qsGW ionization energies in excellent agreement with CCSD(T), with discrepancies typically smaller than 0.3 eV (scGW) and 0.2 eV (qsGW), respectively. For scGW0 and G0W0 the deviation from CCSD(T) is strongly dependent on the starting point. We further relate the discrepancy between the GW ionization energies and CCSD(T) to the deviation from straight line error (DSLE). In DSLE-minimized GW calculations, the DSLE is significantly reduced, yielding a systematic improvement in the description of the ionization energies.

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

Since the earliest implementations of the various GW approximations and cumulant expansion in the calculations of quasiparticle propagators and spectra, several attempts have been made to combine the advantageous properties and results of these two theoretical approaches. While the GW-plus-cumulant approach has proven successful in interpreting photoemission spectroscopy data in solids, the formal connection between the two methods has not been investigated in detail. By introducing a general bijective integral representation of the cumulants, we can rigorously identify at which point these two approximations can be connected for the paradigmatic model of quasiparticle interaction with the dielectric response of the system that has been extensively exploited in recent interpretations of the satellite structures in photoelectron spectra. We establish a protocol for consistent practical implementation of the thus established GW+cumulant scheme and illustrate it by comprehensive state-of-the-art first-principles calculations of intrinsic angle-resolved photoemission spectra from Si valence bands.