We investigate the structural and optoelectronic properties of oligothiophene (nT) molecules encapsulated in boron-nitride (BN) nanotubes using density functional theory, many-body GW and Bethe-Salpeter equation approaches. We show that the binding energy is maximized for tube diameters of approximately 10 Å, decreasing gradually for larger diameters. The nT molecules can slide along the tube with a corrugation potential smaller than room temperature thermal energy, promoting their head-to-tail aggregation. Regarding the electronic properties, we find that hybridization with the tube electronic states has a much smaller effect than that of screening, which can close the nT photoemission gap by as much as an eV. A simple model for the polarization of the BN tube demonstrates how these polarization effects decrease with increasing nT molecule length and BN tube diameter. Compared to the gas phase optical properties, structural relaxation, hybridization, and screening can redshift the absorption onset by up to 250 meV for isolated intercalated nTs. Additionally, the study of a head-to-tail sexithiophene dimer reveals an exciton-exciton interaction that splits the absorption onset into a lowest bright exciton, separated by approximately 75 meV from a dark peak. This suggests possible collective effects upon the formation of nT chains inside BN tubes. Our results confirm and clarify experimental data, mitigating the conclusion that insulating BN tubes just act as a protecting environment for encapsulated molecules.

We explore the merits of building the Bethe-Salpeter absorption spectrum in a specific energy range using analytic continuation techniques. Specifically, we calculate iteratively a few α̅̅̅(z_k) polarizability tensors for a coarse set of (z_k) frequencies in the complex-plane. These data allow constructing a continued-fraction representation for (z) that is used to calculate the absorption spectrum close to the real energy axis in the desired energy range. The number and location of these sampling complex frequencies are discussed. The importance of building a continued-fraction representation of the full polarizability tensor with matrix-valued coefficients is emphasized. We show how to extract the poles of the continued fraction as a tool for analyzing the resulting spectra. We study as examples the valence excitations of a paradigmatic dipeptide, the C_60 fullerene and its PCBM derivative, together with the description of the surface plasmon resonance of the Ag_20 silver cluster. Further, the high-energy C_60 X-ray absorption spectrum is explored.

We introduce an alternative route to quasiparticle self-consistent GW calculations (qsGW) on the basis of a joint approximate diagonalization of the one-body GW Green’s functions G(εnQP) taken at the input quasiparticle energies. Such an approach allows working with the full dynamical self-energy, without approximating the latter by a symmetrized static form as in the standard qsGW scheme. Calculations on the GW100 molecular test set lead, nevertheless, to a good agreement, at the 60 meV mean-absolute-error accuracy on the ionization potential, with respect to the conventional qsGW approach. We show further that constructing the density matrix from the full Green’s function as in the fully self-consistent scGW scheme, and not from the occupied quasiparticle one-body orbitals, allows obtaining a scheme intermediate between the qsGW and scGW approaches, closer to coupled-cluster reference values.

We study the optical absorption spectra of small Agn (n = 2, 4, 6, 8) clusters using the Bethe-Salpeter equation (BSE) formalism with a Hamiltonian built from GW quasiparticle energies. Calculations are based on an effective core potential including the 4sp shells in the valence. Non-self-consistent G0W0 calculations relying on input Kohn-Sham eigenstates generated with semilocal functionals lead to very poor BSE absorption spectra, confirming a previous observation. However, eigenvalue or quasiparticle self-consistent GW calculations dramatically improve the agreement with experiments and TD-DFT spectra obtained with range-separated hybrid functionals. The importance of the position of the 4d occupied band is emphasized.

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

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.

Through the development of new non-fullerene electron acceptor (NFA) materials, such as Y6 and its molecular derivatives, the power conversion efficiencies of organic photovoltaics (OPVs) have now exceeded 19%. However, despite this rapid progress, our fundamental understanding of the unique optical and electronic properties of these Y-series NFAs is lacking, and this currently limits progress in material design. In this work, we provide a detailed computational-experimental characterisation of the archetypal NFA, Y6. To explain the significant broadening and red shift of the absorption spectrum observed when moving from the solution phase to the solid state, we first rule out more typical causes, such as J-aggregation. Instead, by considering the role of charge transfer (CT) excitations and their mixing with Frenkel exciton (FE) states, we can computationally reproduce the experimental absorption spectra of Y6 with excellent accuracy. Using transient absorption spectroscopy, we provide evidence for this dense manifold of FE-CT hybrid electronic excitations in Y6 through the prominent sub-picosecond relaxation events following supra band gap excitation. Furthermore, through sub band gap excitation, we also find states with polaronic character in Y6 that are in a dynamic equilibrium with the FE-CT hybrid states. Magnetic resonance spectroscopies reveal that these polaronic states are polaron pairs, most likely located on neighbouring Y6 molecules, not free charge carriers, as has been previously suggested. Thus, this new understanding of how the solid-state packing motif directly controls the optical and electronic properties of Y-series NFAs opens the door to intelligently design NFA materials to further increase OPV performance.

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.

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O(N5) and O(N6) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

We present an original multi-state projective diabatization scheme based on the Green's function formalism that allows the systematic mapping of many-body ab initio calculations onto effective excitonic models. This method inherits the ability of the Bethe-Salpeter equation to describe Frenkel molecular excitons and intermolecular charge-transfer states equally well, as well as the possibility for an effective description of environmental effects in a QM/MM framework. The latter is found to be a crucial element in order to obtain accurate model parameters for condensed phases and to ensure their transferability to excitonic models for extended systems. The method is presented through a series of examples illustrating its quality, robustness, and internal consistency.

We introduce a new numerical method to compute resonances induced by localized defects in crystals. This method solves an integral equation in the defect region to compute analytic continuations of resolvents. Such an approach enables one to express the resonance in terms of a “resonance source”, a function that is strictly localized within the defect region. The kernel of the integral equation, to be applied on such a source term, is the Green function of the perfect crystal, which we show can be computed efficiently by a complex deformation of the Brillouin zone, named Brillouin Complex Deformation (BCD), thereby extending to reciprocal space the concept of complex coordinate transformations.

In this work, we assess the accuracy of the Bethe-Salpeter equation (BSE) many-body Green's function formalism, adopting the eigenvalue-self-consistent evGW exchange-correlation kernel, for the calculation of the excited-state (μES) and excess dipole moments (Δμ), the latter ones being the changes of dipole amplitude between the ground and excited states (ES), in organic dyes. We compare the results obtained with wave-function methods [ADC(2), CC2, and CCSD], time-dependent density functional theory (TD-DFT), and BSE/evGW levels of theory. First, we compute the evolution of the dipole moments of the two lowest singlet excited states of 4-(dimethylamino)benzonitrile (DMABN) upon twisting of the amino group. Next, we use a set of 25 dyes having ES characters ranging from locally excited to charge transfer to determine both μES and Δμ. For DMABN our results show that BSE/evGW provides Δμ values closer to the CCSD reference and more consistent trends than TD-DFT. Moreover, a statistical analysis of both Δμ and μES for the set of 25 dyes shows that the BSE/evGW accuracy is comparable or sometimes slightly better than that of TD-M06-2X and TD-CAM-B3LYP, BSE/evGW outperforming TD-DFT in challenging cases (zwitterionic and cyanine transitions). Finally, the starting point dependency of BSE/evGW seems to be larger for Δμ, ES dipoles, and oscillator strengths than for transition energies.

The puzzling case of the mixing between the charge transfer (CT) and local excited (LE) characters upon twisting of the geometry of N-phenylpyrrole (N-PP) is investigated considering the six low-lying singlet excited states (ES). The theoretical calculations of the potential energy surfaces (PES) have been performed for these states using a Coupled Cluster method accounting for the impact of the contributions from the triples, many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, as well as Time-Dependent Density Functional Theory (TD-DFT) using various exchange-correlation functionals. Our findings confirm that the BSE formalism is more reliable than TD-DFT for close-lying ES with mixed CT/LE nature. More specifically, BSE/GW yields a more accurate evolution of the excited state PES than TD-DFT when compared to the reference coupled cluster values. BSE/GW PES curves also show negligible exchange-correlation functional starting point dependency in sharp contrast with their TD-DFT counterparts.

We present a method to compute the photoionization spectra of atoms and molecules in linear-response, time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set of delocalized functions, obtained as the solution of the inhomogeneous Helmholtz equation, with gaussian basis set functions as the right-hand side. The resulting scheme is able to reproduce the photoionization spectra without any need for artificial regularization or localization. We demonstrate that this Green's function-based approach is able to produce accurate spectra for semilocal exchange-correlation functionals, even using relatively small standard gaussian basis sets.

We present an implementation of excited-state analytic gradients within the Bethe-Salpeter equation formalism using an adapted Lagrangian Z-vector approach with a cost independent of the number of perturbations. We focus on excited-state electronic dipole moments associated with the derivatives of the excited-state energy with respect to an electric field. In this framework, we assess the accuracy of neglecting the screened Coulomb potential derivatives, a common approximation in the Bethe-Salpeter community, as well as the impact of replacing the GW quasiparticle energy gradients by their Kohn-Sham analogs. The pros and cons of these approaches are benchmarked using both a set of small molecules for which very accurate reference data are available and the challenging case of increasingly extended push-pull oligomer chains. The resulting approximate Bethe-Salpeter analytic gradients are shown to compare well with the most accurate time-dependent density-functional theory (TD-DFT) data, curing in particular most of the pathological cases encountered with TD-DFT when a nonoptimal exchange-correlation functional is used.

The change of molecular dipole moment induced by photon absorption is key to interpret the measured optical spectra. Except for compact molecules, time-dependent density functional theory (TD-DFT) remains the only theory allowing to quickly predict excited-state dipoles (μES), albeit with a strong dependency on the selected exchange-correlation functional. This Letter presents the first assessment of the performances of the many-body Green's function Bethe-Salpeter equation (BSE) formalism for the evaluation of the μES. We explore increasingly long push-pull oligomers as they present an excited-state nature evolving with system size. This work shows that BSE's μES do present the same evolution with oligomeric length as their CC2 and CCSD counterparts, with a dependency on the starting exchange-correlation functional that is strongly decreased as compared to TD-DFT. This Letter demonstrates that BSE is a valuable alternative to TD-DFT for properties related to the excited-state density and not only for transition energies and oscillator strengths.

We present a many-body $GW$ formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential $W$, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.

We study defect energy levels in hexagonal boron-nitride with varying number of layers using a fragment many-body $GW$ formalism, taking as examples the paradigmatic carbon-dimer and $C_BV_N$ defects. We show that a single layer can be fragmented in polarizable finite-size areas reproducing faithfully the effect of the dielectric environment, dramatically facilitating the study at the many-body level of point defects in the dilute limit. The evolution of defect energy levels from the monolayer to a $n$-layer system due to increased screening, labeled polarization energies, follow a simple $({\Delta P}/n + P_{\infty})$ behavior. The coefficients $\Delta P$ and $P_{\infty}$ are found to be close-to-universal, with opposite signs for holes and electrons, characterizing mainly the host and the position of the defect (surface or bulk), but hardly the defect type. Our results rationalize the evolution of defect energy levels with layers number, allowing to safely extrapolate results obtained for the monolayer to few-layers, surface or bulk \textit{h}-BN. The present many-body fragment approach further opens the door to studying disordered 2D layers.

We present a benchmark study of excited state potential energy surfaces (PES) using the many-body Green's function GW and Bethe-Salpeter equation (BSE) formalisms, coupled cluster methods, as well as Time-Dependent Density Functional Theory (TD-DFT). More specifically, we investigate the evolution of the two lowest excited states of 4-(dimethylamino)benzonitrile (DMABN) upon the twisting of the amino group, a paradigmatic system for dual fluorescence and excited-state benchmarks. Our results demonstrate that the BSE/GW approach is able to reproduce the correct topology of excited state PES upon geometry changes in both gas and condensed phases. The vertical transition energies predicted by BSE/GW are indeed in good agreement with coupled cluster values, including triples. The BSE approach ability to include both linear response and state-specific solvent corrections further enables it to accurately describe the solvatochromism of both excited states during the twisting of DMABN. This contribution stands as one of the first proof-of-concept that BSE/GW PES should be accurate in cases for which TD-DFT struggles, including the central case of systems embedded in a dielectric environment.

High tensile strained Ge cavities in crossbeam are promising for the development of integrated laser sources on Si. However, the optimization of such cavities remains more challenging than the uniaxial beams. Indeed, the spatial distributions of both the optical field and the material gain have to be simultaneously defined by the nuances of complex cavity geometry. In this work, we simulate spatial distribution of the bandgap in bi-axially strained Ge crossbeams. Starting from stress map calculations, we achieved the bandgaps mapping for all possible suspended strain configuration (i.e ϵ xx , ϵ yy and ϵ xy ), when merged with bandgaps modeling. A trade-off is evidenced between membrane orientation and arm curvature to reach the largest possible volume of amplifying material. Our work highlights the fundamental importance of these two parameters for Ge crossbeam design and presents a relevant modeling tool to define suitable cross designs for laser applications.