GW method and Bethe-Salpeter equation for calculating electronic excitations

Polarizable Continuum Models and Green's Function GW Formalism: On the Dynamics of the Solvent Electrons

The many-body GW formalism, for the calculation of ionization potentials or electronic affinities, relies on the frequency-dependent dielectric function built from the electronic degrees of freedom. Considering the case of water as a solvent treated within the polarizable continuum model, we explore the impact of restricting the full frequency-dependence of the solvent electronic dielectric response to a frequency-independent (ϵ∞) optical dielectric constant. For solutes presenting small to large highest-occupied to lowest-unoccupied molecular orbital energy gaps, we show that such a restriction induces errors no larger than a few percent on the energy level shifts from the gas to the solvated phase. We further introduce a remarkably accurate single-pole model for mimicking the effect of the full frequency dependence of the water dielectric function in the visible-UV range. This allows a fully dynamical embedded GW calculation with the only knowledge of the cavity reaction field calculated for the ϵ∞ optical dielectric constant.

B-O-O-B Impurity Induces Ultralong Room-Temperature Phosphorescence of Boric Acid

Organic materials that can emit ultralong room-temperature phosphorescence (RTP) have attracted a great deal of interest. Whether the pure boric acid (BA) solid can emit RTP and the origin of the RTP in BA caused a debate recently. Herein, our first-principles calculations and experimental measurements suggest that RTP of BA originates from the B-O-O-B group in a (H2BO3)2 species, which can be formed by polymerization of two dehydrogenated BA molecules under light irradiation. The calculated absorption, fluorescence, and phosphorescence spectra of B-O-O-B match well with the experiments. Experimental X-ray photoelectron and X-ray absorption spectra evidence the existence of B-O-O-B in BA. The O-O bond in B-O-O-B can break upon optical excitation, creating two B-O radicals. Radiative transition from localized dangling orbitals of the B-O radicals to the delocalized orbitals of the crystal bulk leads to the observed RTP. Our calculated phosphorescence lifetime is ∼1 s, which agrees well with the experiment.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory

X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.

Static versus dynamically polarizable environments within the many-body GW formalism

Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.

Broken Symmetry Optical Transitions in (6,5) Single-Walled Carbon Nanotubes Containing sp3 Defects Revealed by First-Principles Theory

We present a first-principles many-body perturbation theory study of nitrophenyl-doped (6,5) single-walled nanotubes (SWCNTs) to understand how sp3 doping impacts the excitonic properties. sp3-doped SWCNTs are promising as a class of optoelectronic materials with bright tunable photoluminescence, long spin coherence, and single-photon emission (SPE), motivating the study of spin excitations. We predict that the dopant results in a single unpaired spin localized around the defect site, which induces multiple low-energy excitonic peaks. By comparing optical absorption and photoluminescence from experiment and theory, we identify the transitions responsible for the red-shifted, defect-induced E11* peak, which has demonstrated SPE for some dopants; the presence of this state is due to both the symmetry-breaking associated with the defect and the presence of the defect-induced in-gap state. Furthermore, we find an asymmetry between the contribution of the two spin channels, suggesting that this system has potential for spin-selective optical transitions.

Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References

The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.

The charge-transfer states and excitation energy transfers of halogen-free organic molecules from first-principles many-body Green's function theory

The organic solar cells based on halogen-free components, have been the new favorites to develop green and renewable energy. PBDB-T and its derivatives are considered the superior electron donors to construct the solar cells. Although there are plenty of researches about them, the charge-transfer mechanisms and excitation energy transfers of relative organic solar cells are still unclear, the developments of photovoltaic devices are restricted consequently. In this work, we calculate the electronic structures and excited-state properties of PBDB-T, PBT1-C, PBT1-O and PBT1-S donors in the gas phase from the many-body Green's function theory. With BTP-IC and BTP-IS as the acceptors, we consider the Förster, Dexter, and overlap electronic couplings to compute the excitation energy transfers of the dimers. The ionization energies and excited-state energies of the four donors calculated by GW + BSE are in good agreement with experiments, and they are sensitive to the functionals in the computation. We find two charge transfer schemes. The thienyl of PBDB-T molecule makes its charge-transfer state at the lowest energy, and the total electronic coupling of PBDB-T based dimer is the strongest. The Dexter, and overlap types electronic couplings are significant to study the excitation energy transfer of organic heterojunctions. We provide a theoretical guide in the design and synthesis of higher-performance halogen-free donors.

Crucial Role of Defect States in the Ultralong Phosphorescence of Organic Molecular Crystals

Ultralong organic phosphorescence (UOP) in pure organic molecular crystals has attracted a lot of interest recently. There is much debate on the emission mechanism of this UOP. Two recent experimental works published in Nat. Photonics 2019, 13, 406-411 and Nat. Mater. 2021, 20, 175-180 attribute UOP in the 2,4,6-trimethoxy-1,3,5-triazine (TMOT) crystals and the carbazole crystals to H-aggregation of the TMOT molecules or the formation of charge-transfer excitons between the carbazole and impurity molecules. Our first-principles many-body Green's function theory calculations show that the lowest triplet states of these two crystals are in fact the localized defect states originating from the twisted TMOT molecules and the impurities, respectively. Energies of the H-aggregation-induced exciton and the charge-transfer exciton are too high to account for UOP. UOP should be mainly due to the little orbital overlap between the localized defect state and the delocalized band edges of the crystal. Strong intermolecular interactions suppress nonradiative decay of the triplet exciton localized on the defect.

Light-Induced Degradation of Metal-Free Organic Perovskites

Perovskites have attracted great interest in optoelectronics and photonics. As a new class of perovskites, metal-free perovskites have drawn growing attention due to the absence of toxic metal elements in them and their wide chemical diversity. Taking MDABCO-NH₄I₃ (MDBACO = N-methyl-N'-diazabicyclo[2.2.2]octonium) and MDABCO-NH₄Br₃ as examples, our first-principles calculations discover two fundamental features of metal-free perovskites that should be crucial for their applications. First, their photoluminescence emission originates from halogen vacancies, instead of the self-trapped exciton generally suggested. Second, in the vicinity of a halogen vacancy, optical excitation from the valence bands to the empty defect bands may cause release of H₂ and NH₃ molecules, which will not only lead to degradation of the perovskite but also quench its photoluminescence. To prevent the degradation and protect the optoelectronic and photonic performances of metal-free perovskites, short-wavelength illumination needs to be shielded.

The Excited State and Charge Transfer of Two Nonfullerene Acceptors from First-Principles Many-Body Green’s Function Theory

Nonfullerene acceptors (NFAs) have shown an outstanding performance upon producing highly efficient and sustainable organic solar cells (OSC). Recently, a growing group of researchers denoted to modify the structures of acceptor−donor−acceptor-type NFAs to raise the power conversion efficiencies (PCEs) when they are blended with a variety of polymer donors in OSC. In 2020, the ketone on the ending groups of BTP-IC were substituted for sulfonyl; the new NFA named BTP-IS was synthetized. The PCE of BTP-IS based OSC is 5.25% higher than that of the BTP-IC device. Based on this, the many-body Green’s function theory, combined with other quantum chemical methods, is conducted to study their ground electronic structures, excited states, and absorption spectra. The ground-state geometries, ionization energies, and the excited state energies are deeply sensitive to exchange-correlation functionals used in calculations. The lowest excited state energies calculated by full-BSE method using DFT-PBE as the starting point is 0.07~0.14 eV smaller than that by TDDFT-PBE method, which is more consistent with experimental data. This provided a methodology for future research on similar NFA systems. The first charge-transfer states and transfer mechanism of two molecules are proposed in this paper. Furthermore, we found that the reason for more efficient charge transport in BTP-IS-based OSC is the larger ionization energies and much weaker electron-hole interaction in BTP-IS. This finding is conducive to the better application of BTP-IS in OSC field.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Scalable Molecular GW Calculations: Valence and Core Spectra

We present a scalable implementation of the GW approximation using Gaussian atomic orbitals to study the valence and core ionization spectroscopies of molecules. The implementation of the standard spectral decomposition approach to the screened-Coulomb interaction, as well as a contour-deformation method, is described. We have implemented both of these approaches using the robust variational fitting approximation to the four-center electron repulsion integrals. We have utilized the MINRES solver with the contour-deformation approach to reduce the computational scaling by 1 order of magnitude. A complex heuristic in the quasiparticle equation solver further allows a speed-up of the computation of core and semicore ionization energies. Benchmark tests using the GW100 and CORE65 data sets and the carbon 1s binding energy of the well-studied ethyl trifluoroacetate, or ESCA molecule, were performed to validate the accuracy of our implementation. We also demonstrate and discuss the parallel performance and computational scaling of our implementation using a range of water clusters of increasing size.

The GW/BSE Method in Magnetic Fields

The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States

This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.

Exciton effect in new generation of carbon nanotubes: graphdiyne nanotubes

Graphdiyne-based nanotubes (GDNTs) are a novel type of carbon nanotubes. While conventional carbon nanotubes (CNTs) are generated by rolling graphene sheets, GDNTs are generated by rolling sheets that are similar to graphene but where the edges are elongated by the introduction of additional acetylene bonds between vertices (C₆ aromatic rings). Such nanotubes are predicted to have many useful practical applications, but a thorough understanding of the relationship between their structure and their physical properties is still missing. We present a theoretical study of the electronic and optical properties of GDNTs. The structural, electronic, and optical properties of GDNTs with different diameters (i.e., 2-10 additional acetylene bonds) have been studied systematically by using density function theory (DFT) and self-consistent charge density functional tight-binding (SCC-DFTB) and by solving the Bethe-Salpeter equation (BSE), with and without considering the electron-hole interactions. The results indicate that the GDNTs are semiconductors with the direct band gap in close range, which is beneficial for photoelectronic devices and applications. Moreover, the absorption spectra of the GDNTs with different edge structures, (armchair, and zigzag) revealed little differences between the optical spectra of armchair and zigzag GDNTs, which could mean that fine separation between those structures (a process that is likely difficult and expensive in practice) will not be necessary. Importantly, the nanotubes were highly stable based on their cohesive energies, and their exciton binding energies were as large as about ~ 1 eV. From a methodological point of view, SCC-DFTB was found to be in agreement with more elaborate DFT calculations for most systems. Graphical abstract.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Many-body perturbation theory calculations using the yambo code

yambo is an open source project aimed at studying excited state properties of condensed matter systems from first principles using many-body methods. As input, yambo requires ground state electronic structure data as computed by density functional theory codes such as Quantum ESPRESSO and Abinit. yambo's capabilities include the calculation of linear response quantities (both independent-particle and including electron-hole interactions), quasi-particle corrections based on the GW formalism, optical absorption, and other spectroscopic quantities. Here we describe recent developments ranging from the inclusion of important but oft-neglected physical effects such as electron-phonon interactions to the implementation of a real-time propagation scheme for simulating linear and non-linear optical properties. Improvements to numerical algorithms and the user interface are outlined. Particular emphasis is given to the new and efficient parallel structure that makes it possible to exploit modern high performance computing architectures. Finally, we demonstrate the possibility to automate workflows by interfacing with the yambopy and AiiDA software tools.

Charge transfer excitation energies from ground state density functional theory calculations

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N - 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G₀W₀ with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

Optical properties of semiconducting zigzag carbon nanotubes with and without defects

The excited states of a series of semiconducting zigzag (n, 0) tubes are studied using the GW method and the Bethe-Salpeter equation within the ab initio many-body perturbation theory. The optical variation rule of the excitation energy with the tube diameter exhibits a family pattern, which arises from the electronic structure of the pristine tube and depends on the value of n mod 3. The introduction of single vacancy and Stone-Wales defects with different orientations affords an effective route for modulating the band structures and optical spectra, resulting in the variation of the selection rules of the excitons and turning dipole-forbidden excitons into dipole-allowed ones. The new localized impurity states in defected tubes will provide additional optically allowed transitions and give rise to pronounced satellite red-shifted peaks. These findings provide inspiration for the tune of optical properties of carbon nanotubes in the future for applications in optoelectronics.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

Variation of optical spectra of water clusters with size from many-body Green's function theory

Water clusters are an important species in the environment and atmosphere and take part in various chemical and biological reactions. How their optical properties vary with size is still an open question. Using the GW method and Bethe-Salpeter equation within the ab initio many-body Green's function theory, we study the electronic excitations in a series of water clusters (H₂O)_n with n = 1-48. We find that their absorption peaks blueshift with increasing cluster size due to the reducing electron-hole binding energy which arises from the enhanced electronic screening and gradually delocalized excitonic spatial distribution. The position of the first absorption peak has a close relation to the average number of hydrogen bonds per molecule. Off-diagonal matrix elements of the self-energy operator have pronounced effects on the unoccupied electronic levels and optical absorption for small clusters with n ≤ 10 when using density functional theory as the starting point for GW calculations. Although the optical absorption is predominated by delocalized excitons, highly localized excitons on a single water molecule are always present on the cluster surface in the vicinity of the absorption edge. These localized excitons may facilitate the photodissociation of water molecules. This can provide inspiration on the excited-state dynamics and photolysis in water clusters.

Green Functions and Self-Consistency: Insights From the Spherium Model

We report an exhaustive study of the performance of different variants of Green function methods for the spherium model in which two electrons are confined to the surface of a sphere and interact via a genuine long-range Coulomb operator. We show that the spherium model provides a unique paradigm to study electronic correlation effects from the weakly correlated regime to the strongly correlated regime, since the mathematics are simple while the physics is rich. We compare perturbative GW, partially self-consistent GW and second-order Green function (GF2) methods for the computation of ionization potentials, electron affinities, energy gaps, correlation energies as well as singlet and triplet neutral excitations by solving the Bethe-Salpeter equation (BSE). We discuss the problem of self-screening in GW and show that it can be partially solved with a second-order screened exchange correction (SOSEX). We find that, in general, self-consistency deteriorates the results with respect to those obtained within perturbative approaches with a Hartree-Fock starting point. Finally, we unveil an important problem of partial self-consistency in GW: in the weakly correlated regime, it can produce artificial discontinuities in the self-energy caused by satellite resonances with large weights.