Otello Maria Roscioni
email: om.roscioni@materialx.co.uk

Matteo Ricci

Claudio Zannoni

Gabriele D'avino
email: gabriele.davino@neel.cnrs.fr

Are Coarse-Grained Structures as Good as Atomistic Ones for Calculating the Electronic Properties of Organic Semiconductors?

The quality of amorphous molecular morphologies obtained with a recently-introduced coarse-grained model, representing molecules in terms of connected anisotropic beads (Phys.Chem.Chem.Phys., 2019, 21, 26195), is benchmarked against reference atomistic data. Typical small-molecule organic semiconductors in their pristine and doped form are chosen as a challenging and technologically relevant case study for our comparison, which includes both structural features and the resulting electronic properties, such as charge carrier energy levels, energetic disorder and intermolecular charge transfer couplings. Our analysis shows that our accurate coarse-grained model leads to molecular glasses that are very similar to native atomistic samples, with the discrepancy being further reduced upon backmapping. The electronic properties computed for backmapped morphologies are almost indistinguishable from the atomistic reference, especially for multi-branched poly(hetero)cyclic hydrocarbons usually employed as organic semiconductors. This study provides a proof of principle for highly-accurate large-scale simulations of complex molecular systems at a reduced computational cost.

Introduction

Atomistic molecular dynamics (MD) corresponds to a bottom-up modelling and simulation approach aimed at calculating properties of materials, where molecules are described using all the constituting atoms, connected according to the structural formula and represented as classical spherical particles subject to a certain set of interactions (Force Field) [START_REF] Riniker | Fixed-charge atomistic force fields for molecular dynamics simulations in the condensed phase: An overview[END_REF][START_REF] Jorgensen | Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids[END_REF][START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF][START_REF] Allen | Computer Simulation of Liquids[END_REF] tuned at least in part with Quantum Mechanics (QM) calculations. Atomistic MD simulations have proved to yield reliable morphologies and their changes according to thermodynamic state for a variety of organic functional materials or systems of biological interest. Indeed, these simulations can provide realistic physical properties for a variety of soft materials, e.g. order parameters and phase transition temperatures for low molar mass liquid crystals or lipid membranes with structural results that compare well with experimental ones (X-ray, NMR, Raman, etc.) [START_REF] Tiberio | Towards in silico liquid crystals. Realistic transition temperatures and physical properties for n-cyanobiphenyls via molecular dynamics simulations[END_REF][START_REF] Zannoni | Liquid Crystals and their Computer Simulations[END_REF] In addition, the detailed atomistic information of a condensed-phase molecular system can readily be used as an input for subsequent QM calculations. This strategy has been largely applied in the field of organic semiconductors we are interested in this work, where charge transfer rates based on Marcus theory, fed with electronic structure calculation inputs (e.g. transfer integrals, energy levels, etc.), provided fair estimates of charge transport properties. [START_REF] Coropceanu | Charge transport in organic semiconductors[END_REF][START_REF] Ruhle | Microscopic simulations of charge transport in disordered organic semiconductors[END_REF][START_REF] Brédas | The WSPC Reference on Organic Electronics: Organic Semiconductors[END_REF][START_REF] Friederich | Toward design of novel materials for organic electronics[END_REF][START_REF] Baggioli | Atomistic simulation of phase transitions and charge mobility for the organic semiconductor Ph-BTBT-C10[END_REF][START_REF] Li | Developing molecular-level models for organic field-effect transistors[END_REF] In many ways atomistic MD with properly tuned force fields together with appropriate QM calculations thus provide a "gold standard" for predicting the electronic and transport properties needed for designing or optimizing at molecular level the materials for organic electronics. [START_REF] Ruhle | Microscopic simulations of charge transport in disordered organic semiconductors[END_REF][START_REF] Kotadiya | Rigorous characterization and predictive modeling of hole transport in amorphous organic semiconductors[END_REF] Unfortunately, molecules of interest for organic electronics, even the so called "low molar mass" ones, are rather complex in terms of the number of atoms (of the order of one hundred atoms or more as we see for example in Fig. 1), and of the sample size required (say nanometers). Thus, even if efficient atomistic MD packages exist, like LAMMPS, [START_REF] Plimpton | Fast Parallel Algorithms for Short-Range Molecular Dynamics[END_REF][START_REF]LAMMPS Molecular Dynamics Simulator[END_REF] GROMACS, [START_REF] Abraham | the GROMACS development team, GROMACS user manual version[END_REF] NAMD 16 the cost in terms of computational resources and actual turnaround time makes the all-atoms approach hardly feasible for the predictive workflow expected by industry. [START_REF] Mityashin | New predictive modeling approach to boost the development of organic electronics[END_REF] In view of this, coarse-grained (CG) molecular models, in which the full atomistic detail is replaced by a representation of molecules in terms of a relatively small number of effective particles (beads), represent a great opportunity to extend the reach of classical molecular dynamics simulations to large and complex molecular systems and to length and time scales that are prohibitive at the atomistic level, e.g. to model static and dynamic properties of biological systems like lipids, 18 proteins, [START_REF] Monticelli | The MARTINI coarse-grained force field: Extension to proteins[END_REF][START_REF] Shen | An anisotropic coarse-grained model for proteins based on Gay-Berne and electric multipole potentials[END_REF] DNA, [START_REF] Brandner | Exploring DNA dynamics within oligonucleosomes with coarse-grained simulations: SIRAH force field extension for protein-DNA complexes[END_REF] functional materials [START_REF] Alessandri | Bulk heterojunction morphologies with atomistic resolution from coarse-grain solvent evaporation simulations[END_REF][START_REF] Huang | Coarse-grained computer simulations of polymer/Ffllerene bulk heterojunctions for organic photovoltaic applications[END_REF][START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] or polymers. [START_REF] Sun | Systematic coarse-graining of atomistic models for simulation of polymeric systems[END_REF][START_REF] Gartner | Modeling and simulations of polymers: A roadmap[END_REF][START_REF] Cohen | Anisotropic coarse-grained model for conjugated polymers: investigations into solution morphologies[END_REF][28] While CG models are often adequate to provide a basic understanding of the relation between molecular structure and phase organization, they inevitably lead to losing the information about atomic positions, which would be also needed for the calculation of any electronic property of interest at the QM level. To remedy this, it is important to develop reversible CG models, where atomic positions can be back-mapped from the position and orientations of the CG beads. [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF][START_REF] Peter | Classical simulations from the atomistic to the mesoscale and back: coarse graining an azobenzene liquid crystal[END_REF][START_REF] Peter | Multiscale simulation of soft matter systems -from the atomistic to the coarse-grained level and back[END_REF] In the context of speeding up the statistical sampling of quantum properties though coarse graining, it is worth mentioning a series of novel machine learning approaches to obtain electronic properties directly from a reduced subset of structural degrees of freedom, [START_REF] Jackson | Electronic structure at coarse-grained resolutions from supervised machine learning[END_REF][START_REF] Jackson | Efficient Multiscale Optoelectronic Prediction for Conjugated Polymers[END_REF] in some case obtained from CG simulations, [START_REF] Simine | Predicting optical spectra for optoelectronic polymers using coarse-grained models and recurrent neural networks[END_REF] bypassing the atomistic back-mapping. While these techniques are definitely promising in the perspective of drastically reducing the computational cost associated with electronic structure calculations, they still hinge on the availability of atomistic structures to build training and test sets, as well as accurate CG force fields.

In this work, we use the MOLC model, [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] a CG force field that is particularly suited for poly(hetero)cyclic aromatic compounds, as it is based on replacing relatively rigid conjugated moieties with overlapping biaxial Gay-Berne ellipsoids [START_REF] Zannoni | Liquid Crystals and their Computer Simulations[END_REF][START_REF] Berardi | A generalized Gay-Berne intermolecular potential for biaxial particles[END_REF][START_REF] Berardi | A Gay-Berne potential for dissimilar biaxial particles[END_REF] connected with directional bonds and decorated with off-center charges. [START_REF] Berardi | Mimicking electrostatic interactions with a set of effective charges: a genetic algorithm[END_REF] As a result, CG molecules retain some of the internal degrees of freedom, such as rotations around selected bonds, and include anisotropic electrostatic interactions. Using anisotropic, instead of the spherical beads as, for instance, in the MARTINI package often used for modelling biomolecules, [START_REF] Marrink | The MARTINI force field: Coarse grained model for biomolecular simulations[END_REF] or in the VOTCA package for organic semiconductors [START_REF] Ruhle | Microscopic simulations of charge transport in disordered organic semiconductors[END_REF][START_REF] Ruhle | Versatile objectoriented toolkit for coarse-graining applications[END_REF] adds some technical complications, but has advantages for back-mapping and in representing molecular shapes. Indeed a main feature of MOLC is the ability to reproduce the molecular excluded volume and thus molecular packing, which in turn yields accurate mass density and other condensed-phase properties for both amorphous solids [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] and liquids. [START_REF] Bellussi | Anisotropic electrostatic interactions in coarse-grained water models to enhance the accuracy and speed-up factor of mesoscopic simulations[END_REF] Somewhat similar approaches have also been developed recently by Jackson, de Pablo and coworkers, [START_REF] Cohen | Anisotropic coarse-grained model for conjugated polymers: investigations into solution morphologies[END_REF][START_REF] Jackson | Coarse-Graining organic semiconductors: the path to multiscale design[END_REF] and by Khot and Savoie. [START_REF] Khot | Top-Down Coarse-Grained Framework for Characterizing Mixed Conducting Polymers[END_REF] A legitimate question for any CG approach concerns the price one has to pay for downgrading the level of resolution, i.e. the possible sacrifice of the fine accuracy of the resulting structure. [START_REF] Stieffenhofer | Benchmarking coarsegrained models of organic semiconductors via deep backmapping[END_REF] This is particularly important whenever one is interested in the electronic properties of a given system and especially in using the simulated structure as inputs for electronic structure calculations. Electronic properties are notably highly sensitive to the molecular geometry and the supramolecular packing in condensed phases, [START_REF] Coropceanu | Charge transport in organic semiconductors[END_REF][START_REF] D'avino | Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics[END_REF] making accurate morphologies a necessary prerequisite for carrying out reliable electronic structure calculations.

In the present paper, we hence propose a comparative study of CG morphologies against reference atomistic ones, by taking the electronic structure as a severe benchmarking criterion.

Our study is conducted on non-polymeric organic semiconductors, representing a technologically relevant example of disordered and possibly heterogeneous molecular systems.

We specifically focus on two well known and experimentally studied hole-transport materials, 2,2',7,7'-tetrakis(N,N-diphenylamino)-9,9-spirobifluorene (spiro-TAD) [START_REF] Zhang | Investigation of the high electron affinity molecular dopant F6-TCNNQ for hole-transport materials[END_REF][START_REF] Schwarze | Molecular parameters responsible for thermally activated transport in doped organic semiconductors[END_REF] and tris(4carbazoyl-9-ylphenyl)amine (TCTA), [START_REF] Schwarze | Molecular parameters responsible for thermally activated transport in doped organic semiconductors[END_REF][START_REF] Yoshida | Electron affinities of organic materials used for organic lightemitting diodes: A low-energy inverse photoemission study[END_REF] in their pristine form and mixed with the p-type dopant 2,2'-(perfluoronaphthalene-2,6-diylidene)dimalononitrile (F6TCNNQ, see Figure 1). [START_REF] Koech | Synthesis and Application of 1,3,4,5,7,8-Hexafluorotetracyanonaphthoquinodimethane (F6-TNAP): A Conductivity Dopant for Organic Light-Emitting Devices[END_REF] We emphasize that both spiro-TAD and TCTA are fairly-large flexible molecules presenting several soft degrees of freedom that in our model are associated with inter-bead torsional and bending angles. These features make the application of the MOLC model particularly relevant and challenging at the same time.

In order to investigate the electronic properties important for charge transport in organic semiconductors, a comprehensive multiscale procedure is deployed. This starts with the creation and equilibration of pristine and doped samples of organic semiconductors with the MOLC CG force field, followed by back-mapping to atomistic coordinates and short annealing at room temperature with an all-atom (AA) force field to redistribute the thermal energy on the new degrees of freedom. The resulting morphologies are then used to perform electronic-structure calculations to compute charge transport energy levels and intermolecular charge transfer integrals.

The results obtained with this protocol are compared with reference calculations, in which organic semiconductor samples were obtained from independent MD calculations with atomic detail. Our analysis demonstrates an excellent agreement between CG and AA results, both in terms of the structural features and the resulting electronic properties, providing a solid argument in support of accurate and cost-effective simulations with the MOLC model.

Methods

MD simulations

The organic semiconductors studied in this work are parameterized in a bottom-up fashion using the Advanced Topology Builder (ATB) repository, version 3.0, [START_REF] Malde | An automated force field topology builder (ATB) and repository: Version 1.0[END_REF][START_REF] Canzar | Charge group partitioning in biomolecular simulation[END_REF][START_REF] Koziara | Testing and validation of the Automated Topology Builder (ATB) version 2.0: prediction of hydration free enthalpies[END_REF] to assign AA force field parameters based on GROMOS 54A7, [START_REF] Poger | A new force field for simulating phosphatidylcholine bilayers[END_REF][START_REF] Schmid | Definition and testing of the GROMOS force-field versions 54A7 and 54B7[END_REF] and atomic charges computed with the semiempirical molecular-orbital program MOPAC. [START_REF] Chirgwin | The electronic structure of conjugated systems[END_REF][START_REF] Stewart | MOPAC: A semiempirical molecular orbital program[END_REF] The MOLC CG force field is then parametrized using GROMOS-ATB as a reference for the inter-and intra-molecular interactions, following the protocol described in reference. [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] The spiro-TAD and TCTA semiconductors have been modelled with 10 and 6 CG beads (biaxial Gay-Berne ellipsoids), respectively, while for the F6TCNNQ dopant we opted for a single bead representation. A pictorial view of the relationship between molecular fragments and CG beads is shown in Figure 1. Point charges suitably placed inside the ellipsoids were used to account for long-range electrostatic interactions: typically, the set of charges employed is smaller than the number of atoms the bead represents, reducing the computational cost associated with the full electrostatic treatment. The optimal number of CG charges is chosen as to simultaneously reproduce the molecular electrostatic potential, dipole and quadrupole moments of the associated molecular fragment through a genetic algorithm optimisation procedure. [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF][START_REF] Berardi | Mimicking electrostatic interactions with a set of effective charges: a genetic algorithm[END_REF] The model for spiro-TAD includes 30 charges (3 per fluorene bead, 3 per phenyl bead), while TCTA has been described with 24 charges (4 per carbazole bead, 4 per phenyl bead). For F6TCNNQ, we tested two models with respectively 6 and 9 charges, finding that the latter, more detailed, model is necessary to properly describe the molecular electrostatic potential at contact distance and the molecular packing in the amorphous phase (see Supporting Information, SI, Figures S1-S2, Table S1). AA and CG simulations were carried out with the program LAMMPS, 14,55 version 30 October 2019, in house modified to include the MOLC user package. [START_REF]USER-MOLC package is available on GitHub[END_REF] Each CG sample was prepared by placing 1000 randomly-oriented molecules in the sim-ulation box, distributed on the nodes of a cubic grid, with 3D periodic boundary conditions applied. The sample was slowly compressed at 1 K to suppress thermal motions, yielding an amorphous solid. The compression step was carried out with a timestep of 10 fs, with the temperature controlled via a Langevin thermostat with a damping parameter of 10 ps. Each sample was then relaxed with isobaric-isothermal conditions (N P T ensemble) at temperature T = 300 K, pressure P = 1 atm, using a timestep of 20 fs, until thermal equilibrium was reached. A production trajectory of 5 ns was finally collected using a Nosé-Hoover barostat with a stress-damping parameter of 200 ps. The CG samples were back-mapped to their atomistic representation with the open-source program Backmap. [START_REF]Backmap: an open-source program to reverse map coarse-grained trajectories to atomic coordinates[END_REF] The back-mapped samples were then relaxed with the AA GROMOS-ATB force field at T = 300 K and P = 1 atm for 5 ns using a timestep of 2 fs, a Nosé-Hoover barostat with a damping parameter of 2 ps and a Langevin thermostat with a damping parameter of 0.2 ps. The last configuration was finally minimised at 0 K to remove thermal fluctuations and used to carry out electronic-structure calculations.

In order to have a purely-atomistic reference against which benchmarking the backmapped morphologies, we carried out AA simulations using the same protocol described for CG samples, i.e., compressing low-density samples to the desired density and then equilibrating in the N P T ensemble. Along these lines, we obtained native atomistic amorphous morphologies with a completely independent history from the back-mapped CG samples.

Besides bulk morphologies, we have also created thin-film samples that have been used

for the calculations of the energy levels to be compared with photoemission experiments.

CG samples of pristine spiro-TAD, TCTA, and F6TCNNQ in a thin-film configuration were created by removing the periodic boundary along the z-direction and adding empty space, turning the bulk systems into a free-standing slab. Each system was equilibrated in the canonical ensemble (N V T ) at 300 K for 500 ns in order to achieve a complete surface relaxation. The equilibration was carried out with a timestep of 20 fs and a correction term was added to compute the long-range electrostatic interactions for systems with slab geometry. [START_REF] Yeh | Ewald summation for systems with slab geometry[END_REF] After back-mapping to the atomic coordinates, the samples were further equilibrated for 10 ns with a timestep of 2 fs before carrying out the final energy minimisation.

Electronic properties

Following the common assumption of charge carriers localized on individual molecules and a perturbative treatment of inter-molecular interactions, [START_REF] D'avino | Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics[END_REF] the nth energy level of molecule i can be written as

E i n = ε i n + ∆ i n (1)
where ε i n is the molecular gas-phase energy and ∆ i n is the environmental contribution. In the following, we will focus on the levels relevant to hole (n = HOMO) and electron (n = LUMO) transport. Please note that these levels are intended as electron addition (ionization potential, IP=-E HOMO ) and removal (electron affinity, EA=-E LUMO ) energies, and should not be confused with their analogue in mean-field theories (e.g. DFT). The relevant densities of states (DOS) are built as distributions of site energies obtained upon sampling over the molecules of our amorphous morphologies. The width of these distributions, measured by the standard deviation σ, quantifies the energetic disorder in our samples.

Gas-phase energy levels depend on the molecular geometries extracted from MD snapshots. This intra-molecular contribution is computed as

ε i n = ε (GW ) n (r 0 ) + ∆ε (SE) n (r i ) = ε (GW ) n (r r r 0 ) + ε (SE) n (r i ) -ε (SE) n (r 0 ) (2)
where r0 indicates the molecular equilibrium geometry, ri is the geometry of molecule i in the amorphous sample, and the superscripts indicate the level of theory employed in the calculations. This approach hence combines the many-body GW formalism, [START_REF] Hedin | New Method for calculating the one-particle Green's function with application to the electron-gas problem[END_REF][START_REF] Onida | Electronic excitations: density-functional versus many-body Green's-function approaches[END_REF] with the semiempirical (SE) ZINDO method. [START_REF] Ridley | An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines[END_REF] The GW calculations have been performed once at the equilibrium geometry (obtained at PBE0/cc-pVDZ level) for each compound, adopting a partial self-consistency on the eigenvalues (evGW ) and extrapolating the results in the complete basis set limit. [START_REF] Li | Host dependence of the electron affinity of molecular dopants[END_REF] This permits to obtain absolute values for the energy levels with a typical accuracy of 0.1 eV, [START_REF] Blase | First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications[END_REF][START_REF] Faber | Excited states properties of organic molecules: from density functional theory to the GW and Bethe-Salpeter Green's function formalisms[END_REF] as also demonstrated by a recent comparison with reference CCSD(T) data on medium-size molecules. [START_REF] Knight | Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods[END_REF][START_REF] Duchemin | Robust Analytic-Continuation Approach to Many-Body GW Calculations[END_REF] The gas-phase evGW energy levels for the three molecules under examination are reported in the SI, Table S2. ZINDO calculations are instead employed as a cost-effective mean to assess the variation of energy levels with molecular geometry in large samples, assuming that the intrinsic inaccuracy of ZINDO cancels out in the difference ε

(SE) n (r i ) -ε (SE) n (r 0 ) (see Eq. 2)
. Energy levels calculated according to Eq. 1 and Eq. 2 correspond to vertical IE and EA, without accounting for structural relaxation. The spread of gas-phase molecular levels, i.e the standard deviation σ conf , quantifies the energetic disorder of conformational origin. Density functional theory (DFT) and semiempirical electronic-structure calculations have been performed with the ORCA software (version 4.2.1), [START_REF] Neese | The ORCA program system[END_REF][START_REF] Weigend | Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy[END_REF] GW calculation results have been obtained with the Fiesta package. [START_REF] Blase | First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications[END_REF][START_REF] Faber | Excited states properties of organic molecules: from density functional theory to the GW and Bethe-Salpeter Green's function formalisms[END_REF] The intermolecular contribution is sourced from electrostatic interactions in the polarizable molecular environment, and it is here evaluated with classical microlectrostatic (ME) calculations, as implemented in the MESCal code. [START_REF] D'avino | Electronic polarization in organic crystals: a comparative study of induced dipoles and intramolecular charge redistribution schemes[END_REF] The intermolecular interactions consist of an electrostatic and an induction contribution 43

∆ i n = ∆ E,i n + ∆ I,i n (3)
The electrostatic term ∆ E,i n corresponds to the energy necessary to charge a molecule in the field of permanent and induced multipoles of all other molecules in the neutral sample. Due to the inhomogeneity of the electrostatic landscape in disordered samples, this term represents the leading source of environmental energetic disorder, σ env . 70 ∆ E,i n has been evaluated

with self-consistent ME calculations of atomistic resolutions, employing atomic charges from electrostatic potential fitting (ESP scheme) [START_REF] Besler | Atomic charges derived from semiempirical methods[END_REF] and molecular polarizability tensor computed at the PBE0/cc-PVTZ theory level. ME calculations on the neutral systems have been performed accounting for periodic boundary conditions in 3D, except those on slab samples reported in Section 3 that employed 2D periodicity to simulate photoemission spectra at the sample surface. The induction term ∆ I,i n quantifies the reaction of the polarizable environment to an added charge. This term represents an important contribution to the absolute value of charge transport levels, but it is weakly sensitive to the sample morphology, hence it provides an almost negligible contribution to the energetic disorder. It has been evaluated

at the molecular equilibrium geometries once and for all for each chemical species. In this case we performed ME calculations in an effective isotropic polarizable medium (cubic lattice of polarizable points) with dielectric constant arbitrarily set at r = 3, a typical value for organic molecules.

Intermolecular charge transfer couplings have been computed at the ZINDO level with the standard dimer projection method. [START_REF] Valeev | Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors[END_REF] 3 Results and discussion

Structural properties

The multiscale protocol begins with the generation of amorphous samples of pristine spiro-TAD, TCTA, and F6TCNNQ, plus samples of spiro-TAD and TCTA doped with F6TCNNQ in 2% and 10% molar concentrations, similar to the ones used in experiments. [START_REF] Zhang | Investigation of the high electron affinity molecular dopant F6-TCNNQ for hole-transport materials[END_REF] For the sake of illustration, Figure 2 shows two samples of F6TCNNQ-doped spiro-TAD and TCTA, displaying the morphology obtained from CG MD simulations and the atomistic one obtained after back-mapping and thermalization. We characterize the CG samples in terms of their density and radial distribution functions (RDFs), and we compare these observables with the corresponding AA samples.

The computed mass density values for the different samples are reported in was reported for the CG model for α-NPD. [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] A much smaller, ∼ 1%, relative difference has been obtained between the GC and AA sample densities for pure F6TCNNQ. The significant, although not systematic, density deviations between the two models suggest that a reduction in the number of degrees of freedom comes at the expense of a quantitative description of the stress in CG samples. Possible improvement strategies could include density and cohesive energy as additional targets in the model parameterization. The density of the BM samples is typically within ∼ 2% to that of the reference AA simulation, hinting at the fact that the molecular packing of their parent CG sample is an excellent initial guess and that short annealing at room temperature is enough to retrieve the correct density.

To further characterize the relationship between the CG and AA samples, we analyse the RDFs computed between the CG bead centroids, as well as the AA and CG RDFs, obtained with the center of mass of the molecular fragments as defined in Figure 1. The RDFs of pristine spiro-TAD (Figure 3) and TCTA (Figure 4), and F6TCNNQ (SI, Figure S2) show the telltale signature of an amorphous morphology, characterised by broad peaks followed by a flat profile, indicating a homogeneous distribution of molecules at long distance. The intramolecular peaks are marked with a star, while the other peaks show the average distance between molecules in the first coordination shell. Overall, a good agreement is found between In doped samples, the RDF between the F6TCNNQ dopant and the host molecular fragments (gray-shaded panels) are in general noisy due to the low concentration of dopant molecules. For doped spiro-TAD samples (see Figure 3), the RDF between phenyl-F6TCNNQ and fluorene-F6TCNNQ show a shallow profile in all samples suggesting a lack of preferential orientation of dopant molecules and absence of a coordination shell. For doped TCTA samples, a sharp peak at 3.7 Å is observed for the carbazole-F6TCNNQ pair (bottom-central panel in Figure 4), a distance typical of π-π stacking. This neat feature is present in all samples, even though the peak appears sharper in the CG one. The RDF for the phenyl-F6TCNNQ fragments (bottom-right panel in Figure 4) is relatively shallow and close to 1, similar to what seen for the spiro-TAD samples. However, in all samples a small peak is present at 9-10 Å distance that is consistent with the distance of a dopant molecule coordinated with the carbazole fragment. The amorphous matrix of both spiro-TAD and TCTA is not appreciably influenced by the dopant presence, as the RDF fluorene-phenyl and carbazole-carbazole are almost identical to those of the pristine samples. The same results were found for the samples doped with 2% of F6TCNNQ, shown in SI Figures S3-S4.

The analysis of the position and intensity of the main peaks of the RDFs reveals substantial similarities between the morphology of the CG and AA samples obtained independently from one another. This result provides a strong indication that, despite significant differences in density, the CG and AA force fields yield consistent morphologies, albeit not yet attaining the accuracy level of CG model obtained, for instance, by iterative Boltzmann inversion [START_REF] Reith | Deriving effective mesoscale potentials from atomistic simulations[END_REF] or force matching [START_REF] Izvekov | A Multiscale Coarse-Graining Method for Biomolecular Systems[END_REF] techniques. The overall quality of MOLC CG morphologies is further attested by the fact that, upon atomistic back-mapping and a short re-equilibration run, the discrepancy in the RDF against the atomistic reference becomes practically negligible.

In the next section we make one step forward in our benchmark of CG morphologies, by comparing the electronic properties computed for the BM and AA samples.

Electronic structure properties

We start the analysis of the electronic properties from the energy levels of localized charge carriers in pristine and doped materials. The distribution of these quantities, mapping the density of states (DOS) for hole and electron carriers, are shown in Figure 5. The breakdown of the energy levels into intra-and inter-molecular contributions (see Eq. 2), as well as the associated energetic disorder, is reported in Table 2 for the HOMO (LUMO) levels of host (dopant) molecules -see SI Table S3 for complementary data. Our results for TCTA and spiro-TAD are in good agreement with those reported by Kotadiya et al., obtained with a similar approach. [START_REF] Kotadiya | Rigorous characterization and predictive modeling of hole transport in amorphous organic semiconductors[END_REF] We first observe a very good agreement between the set of DOS obtained with AA and BM Figure 5: Densities of states for holes at host, spiro-TAD and TCTA, molecules (orange lines) and electrons at the F6TCNNQ dopant (light blue lines) for pristine and doped bulk systems. Results from QM and ME calculations (see Eq. 2) performed on the native atomistic (thin lines) and back-mapped (thick lines) morphologies. We note the very good agreement between the DOSs computed with AA and BM samples. The DOSs of F6TCNNQ LUMOs in doped samples are noisy because of the poor statistics, especially in the 2% concentration sample.

morphologies, both in terms of mean values and distribution spread. The main significant discrepancy between the two data sets regards the standard deviation of the LUMO levels of the pristine F6TCNNQ, which is 20% higher in the BM sample, with respect to the AA one.

The data in Table 2 allow to safely ascribe this difference to the environmental contribution that is indeed sensitive to the details of molecular packing inherited from the CG simulation history. The DOSs in Figure 5 display a marked dependence of the energy levels on the chemical composition of the system. The most striking variation regards the 0.7-0.8 eV decrease of the F6TCNNQ LUMO level between its pristine phase and when it acts as a dopant impurity in the hole transporting materials spiro-TAD and TCTA. Such a pronounced hostdependence of the acceptor level of dopant impurities has been disclosed previously on the basis of accurate embedded GW calculations. [START_REF] Li | Host dependence of the electron affinity of molecular dopants[END_REF] We also note a smaller variation of the host HOMOs upon doping, with the mean values of their distributions shifting to higher binding energies by about 0.4 and 0.2 eV in spiro-TAD and TCTA, respectively. This effect can be attributed to the short-range interactions between hole carriers and the quadrupole moment of the dopant molecules, as discussed in a recent study. [START_REF] Privitera | Molecular quadrupole moments promote ground-state charge generation in doped organic semiconductors[END_REF] We complement the characterization of molecular site energy levels by discussing the corresponding spatial correlation function

C(r) = 1 σ 2 (E(r i ) -E(r i ) ) (E(r i + r) -E(r i ) ) (4)
where E(r i ) is the energy level of molecule i, σ 2 is the variance of site energy fluctuations, and angle brackets indicate the average over the molecules in the sample. C(r) decays from 1 (full correlation) at r = 0 to 0 (no correlation) a large distance for our pure samples shown in The comparison between AA and BM morphologies reveals qualitative similarities between the two approaches, albeit the MOLC model seems to produce longer-range correlations that are inherited in the BM samples. Quantitatively, significant differences exist between TCTA and F6TCNNQ, with the latter showing a larger relative difference between AA and While charge carries energy levels mostly reflect the impact of electrostatic interactions developing at long range, intermolecular charge transfer couplings J, being related to the quantum overlap between molecular wavefunctions, are instead ideal probes for nearestneighbor molecular contacts. The distributions of intermolecular couplings, shown in Fig-

ure 7, reveal an excellent agreement between AA and BM morphologies for the three pristine samples. The distributions rapidly drops upon increasing J, with a very small fraction of dimers exceeding 10 meV. These are typical feature of amorphous molecular solids. [START_REF] Ruhle | Microscopic simulations of charge transport in disordered organic semiconductors[END_REF][START_REF] D'avino | Do charges delocalize over multiple molecules in fullerene derivatives?[END_REF] The region below 0.1 meV is loosely relevant as it is highly sensitive to the criteria employed in the selection of molecular pairs to be computed, hence not shown.

The information contained in charge transfer integrals is then exploited to quantify the effective electronic connectivity of the different samples. Following Ref., [START_REF] D'avino | Do charges delocalize over multiple molecules in fullerene derivatives?[END_REF] we define the electronic connectivity as the average number of neighbors to which every molecule is coupled by a transfer integral exceeding a given threshold. This is shown for pure TCTA, spiro-TAD and F6TCNNQ samples in Figure 8, as a function of the threshold coupling J thr . The comparison between the connectivity curves of the different materials reveals that TCTA presents a higher connectivity than spiro-TAD, an observation that can be related to the denser molecular packing of the former, less rigid, molecule (see Table 1). F6TCNNQ presents a higher connectivity than the two hosts for J thr > 2 meV, while the situation is reversed for smaller J thr . This can be ascribed to the smaller size of the dopant molecules and to the consequently more localized frontier orbitals, which can give rise to a small number of strong intermolecular coupling. On the other hand, branched molecules as TCTA and spiro-TAD can instead establish a larger number of weaker contacts with other molecules. As for it concerns the comparison between AA and BM morphologies for a given material, we remark also in this case an excellent agreement, with very similar electronic connectivities obtained with the two molecular models, with the only appreciable deviation obtained for F6TCNNQ at low couplings (J thr < 2 meV) .

The results reported in this section overall prove that the electronic properties calculated Figure 8: Intermolecular electronic connectivity for the three pristine samples, defined as the average number of neighbors having a charge transfer coupling larger in magnitude than a given threshold. Solid lines and circles correspond to AA and BM morphologies, respectively. duced upon coarse graining has a larger impact on the electronic properties of F6TCNNQ, described by a single bead. Here, the most significant flaw of BM morphologies is a 20% overestimation of the energetic disorder as compared to AA simulations (see Table 2). The discrepancy between the electronic properties of BM and AA amorphous phases in instead negligible for complex multi-bead molecules such as TCTA and spiro-TAD, i.e. the systems where the MOLC model is mostly advantageous.

Photoemission energy levels

We finally attempt a comparison between our multiscale simulations for charge transport energy levels with available experimental data from photoemission spectroscopies. [START_REF] Zhang | Investigation of the high electron affinity molecular dopant F6-TCNNQ for hole-transport materials[END_REF][START_REF] Yoshida | Electron affinities of organic materials used for organic lightemitting diodes: A low-energy inverse photoemission study[END_REF][START_REF] D'andrade | Relationship between the ionization and oxidation potentials of molecular organic semiconductors[END_REF][START_REF] Yun | Direct comparative study on the energy level alignments in unoccupied/occupied states of organic semiconductor/electrode interface by constructing in-situ photoemission spectroscopy and Ar gas cluster ion beam sputtering integrated analysis system[END_REF][START_REF] Mahns | Electronic properties of spiro compounds for organic electronics[END_REF][START_REF] Belisle | Minimal effect of the hole-transport material ionization potential on the open-circuit voltage of perovskite solar cells[END_REF] To such an aim, we performed a dedicated set of simulations for the organic-vacuum interface, since both direct ultraviolet photoelectron spectroscopy (UPS) and inverse photoemission spectroscopy (IPES) are surface-sensitive techniques, probing only the first 1-2 nanometers of the sample. Such an approach turned out to be essential to obtain a quantitative description of energy levels in molecular crystals and ordered films. [START_REF] D'avino | Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics[END_REF][START_REF] Topham | Ionization in organic thin films: Electrostatic potential, electronic polarization, and dopants in pentacene films[END_REF][START_REF] Li | Accurate description of charged excitations in molecular solids from embedded many-body perturbation theory[END_REF][START_REF] Poelking | Impact of mesoscale order on open-circuit voltage in organic solar cells[END_REF][START_REF] D'avino | Electrostatic interactions shape molecular organization and electronic structure of organic semiconductor blends[END_REF] These slab simulations have been performed with the MOLC model, with subsequent back mapping to atomistics to run electronic the structure calculations. The simulated photemission spectra have been calculated as histograms of molecular site energies weighted by a position-dependent factor exp (-z/λ), where z is the distance of a given molecule from the surface, and λ = 1 nm is the electron mean free path.

Figure 9 shows the calculated photoemission spectra for occupied (holes) and unoccupied (electrons) states, along with experimental values (vertical bars) for ionization potential (IP) and electron affinity (EA), both taken at the respective band onset. We remark a good agreement between simulations and experiments as for it concerns occupied states, with calculations capturing the trends between different materials. It is worth remarking the significant difference between the IP of F6TCNNQ that would be obtained from bulk simulations (6.5 eV, see Figure 5) and the surface value of 7.7 eV. This substantial difference, which is key for reproducing the experiment, is determined by the electrostatic environmental contribution, ∆ E = -0.26 eV at the surface vs. -1.47 eV in the bulk (see Table 2). This large difference in the electrostatic energy landscape results from a large surface reconstruction at the interface to vacuum, which can be appreciated from the visual inspection of the surface as obtained upon cutting the bulk sample, and after thermal annealing, as shown in Figure S5.

The difference in ∆ E between bulk and surface are instead quite modest (< 0.2 eV) for TCTA and spiro-TAD, consistent with a much less important surface reconstruction.

Our calculations do not achieve comparable accuracy for unoccupied states, namely overestimating EA by ∼ 1 eV for F6TCNNQ and underestimating EA of TCTA and spiro-TAD by ∼ 1.2 eV, as compared to IPES data by Zhang and Kahn. [START_REF] Zhang | Investigation of the high electron affinity molecular dopant F6-TCNNQ for hole-transport materials[END_REF] A much better agreement is obtained with the EA of TCTA reported by Yoshida and Yoshizaki [START_REF] Yoshida | Electron affinities of organic materials used for organic lightemitting diodes: A low-energy inverse photoemission study[END_REF] and obtained with lowenergy IPES (LEIPS), a technique that is considered being more accurate than conventional IPES. [START_REF] Yoshida | Near-ultraviolet inverse photoemission spectroscopy using ultra-low energy electrons[END_REF] In general, the comparison between experiments and calculation for photoemission measurements at amorphous films surfaces reveals a satisfactory agreement on occupied en-Figure 9: Simulated photoemission spectra of pristine F6TCNNQ, spiro-TAD and TCTA samples. Filled and empty areas refer to occupied and unoccupied states, respectively. Vertical black lines mark to the IP (valence band top, full line) and the EA (conduction band minimum, dashed line) measured in Ref. [START_REF] Zhang | Investigation of the high electron affinity molecular dopant F6-TCNNQ for hole-transport materials[END_REF] The bar labeled with the star marks the EA of TCTA reported in Ref. [START_REF] Yoshida | Electron affinities of organic materials used for organic lightemitting diodes: A low-energy inverse photoemission study[END_REF] Other works have reported consistent data for the IP of TCTA [START_REF] D'andrade | Relationship between the ionization and oxidation potentials of molecular organic semiconductors[END_REF][START_REF] Yun | Direct comparative study on the energy level alignments in unoccupied/occupied states of organic semiconductor/electrode interface by constructing in-situ photoemission spectroscopy and Ar gas cluster ion beam sputtering integrated analysis system[END_REF] and spiro-TAD. [START_REF] Mahns | Electronic properties of spiro compounds for organic electronics[END_REF][START_REF] Belisle | Minimal effect of the hole-transport material ionization potential on the open-circuit voltage of perovskite solar cells[END_REF] ergy levels, calling at the same time for an improved in the description of unoccupied states.

Conclusions

We have presented a comparative analysis of morphologies obtained from atomistic and coarse-grained molecular dynamics, the latter based on the MOLC model. [START_REF] Ricci | A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials[END_REF] This study covered both the structure of pristine and doped organic semiconductors and the electronic properties governing charge transport in these systems, implementing a multiscale simulation workflow that includes molecular dynamics, atomistic back-mapping for coarse-grained morphologies, classical microelectrostatics, DFT and many-body GW electronic structure calculations.

Our study reveals a substantial agreement between the morphologies simulated with the MOLC CG model and reference atomistic ones. Most interestingly, the reintroduction of the atomistic detail in CG samples (back-mapping) leads to structures that are almost indistinguishable, in a statistical sense, from those obtained from native atomistic simulations.

The same conclusion holds for electronic properties that are known to be highly sensitive to molecular geometries, meaning that atomistic samples obtained upon back-mapping can be used with a high level of confidence for more refined analyses, especially for branched poly-heterocyclic compounds the MOLC model is designed for. Besides the methodological benchmark, we have attempted a comparison of calculated charge transport energy levels with literature data from photoemission spectroscopy, obtaining a very good accord on occupied levels. The agreement with experiments remains qualitative for unoccupied states, calling for additional research effort.

In summary, the MOLC coarse-grained molecular model emerges as very accurate approach for the simulation of complex molecular systems. This enables an important saving of computational resources (two orders of magnitude reduction in the time per simulated nanosecond) and, most interestingly, it paves the way towards the simulation of systems and phenomena whose length and time scales are out of the reach of atomistic techniques, such as those relative to the processing of organic semiconductors over large area, among others.

Figure 1 :

 1 Figure 1: Atomic structure of the organic semiconductors spiro-TAD and TCTA, and the dopant F6TCNNQ. The bottom panel compares the CG structure (semi-transparent ellipsoidal beads) and the classic ball-and-stick representation.

Figure 2 :

 2 Figure 2: Rendering of spiro-TAD and TCTA samples doped with F6TCNNQ (10% molar concentration) as obtained from MD simulations with the CG model and after atomistic backmapping and relaxation. The different beads and fragments are visualized according to the colour scheme defined in Figure 1.

Figure 3 :

 3 Figure3: Radial distribution functions g(r) computed between molecular fragments in the pristine and F6TCNNQ-doped (10% molar concentration) spiro-TAD. Molecular fragments are defined in Fig.1. The gray-shaded panels refer to doped samples, and specifically to the coordination of the F6TCNNQ dopant with the host molecule. The different data sets correspond to all-atom (green solid line), coarse-grained (black solid line), and backmapped atomic (black dotted line) models. The stars mark intra-molecular peaks of the host molecule.

Figure 4 :

 4 Figure4: Radial distribution functions g(r) computed between molecular fragments in the pristine and F6TCNNQ-doped (10% molar concentration) TCTA. Molecular fragments are defined in Fig.1. The gray-shaded panels refer to doped samples, and specifically to the coordination of the F6TCNNQ dopant with the host molecule. The different data sets correspond to all-atom (magenta solid line), coarse-grained (black solid line), and backmapped atomic (black dotted line) models. The stars mark intra-molecular peaks of the host molecule.

Figure 6 :

 6 Figure 6: Spatial correlation function of electrostatic site energies in bulk pristine samples.

Figure 6 ,

 6 Figure6, similar to what reported for other amorphous organic semiconductors,[START_REF] Ruhle | Microscopic simulations of charge transport in disordered organic semiconductors[END_REF][START_REF] D'avino | Do charges delocalize over multiple molecules in fullerene derivatives?[END_REF] and approximately following the 1/r behavior expected for randomly oriented dipoles on a lattice.[START_REF] Novikov | Cluster structure in the distribution of the electrostatic potential in a lattice of randomly oriented dipoles[END_REF]

Figure 7 :

 7 Figure 7: Probability distribution function (PDF) of intermolecular charge transfer couplings (absolute values) between frontier molecular orbitals (see axis label) for pristine spiro-TAD, TCTA, and F6TCNNQ samples.

  on atomistic structures, obtained upon back-mapping CG morphologies simulated with the MOLC model (BM), are almost indistinguishable from those obtained from native atomistic samples (AA). The comparison among different materials show that the loss of detail intro-

Table 1

 1

. The densities obtained with the MOLC model are within 7% of reference AA data, similar to what

Table 1 :

 1

	Sample	CG	BM	AA
	F6TCNNQ	1.216(2) 1.221(2) 1.231(2)
	Spiro-TAD	1.131(1) 1.082(1) 1.091(1)
	Spiro-TAD/F6TCNNQ: 2% 1.129(1) 1.120(1) 1.097(1)
	Spiro-TAD/F6TCNNQ: 10% 1.124(1) 1.090(1) 1.094(1)
	TCTA	1.083(1) 1.147(1) 1.162(1)
	TCTA/F6TCNNQ: 2%	1.087(1) 1.148(1) 1.163(1)
	TCTA/F6TCNNQ: 10%	1.083(1) 1.150(1) 1.164(1)

Density (g/cm 3 ) of amorphous samples of organic semiconductors from coarsegrained (CG), back-mapped (BM), and reference atomic (AA) simulations.

Table 2 :

 2 Charge transport energy levels (mean values, eV units) and energetic disorder (in meV) of pristine systems. Results from QM and ME calculations (see Eq. 2) calculations employing samples obtained with native atomistic simulations (AA) and the back-mapped MOLC model (BM). H and L label HOMO and LUMO levels, respectively. Energy levels account for a geometry-independent induction term ∆ I , equal to -1.00 eV for electrons in F6TCNNQ and 0.54 and 0.61 eV for holes in spiro-TAD and TCTA, respectively.

	material	sample level	E	ε	∆ E	σ σ conf σ env
	F6TCNNQ BM	L	-7.03 -4.55 -1.47 249	14 251
	F6TCNNQ AA	L	-7.09 -4.55 -1.54 206	14 207
	Spiro-TAD BM	H	-5.71 -6.48 0.23 77	33	69
	Spiro-TAD AA	H	-5.70 -6.48 0.24 76	36	67
	TCTA	BM	H	-6.08 -6.73 0.04 117	44 105
	TCTA	AA	H	-6.09 -6.73 0.03 104	45	91

Acknowledgement

This work has received early-stage support from the European Union's Horizon 2020 Framework Programme under grant agreement No. 646176 (EXTMOS). Work in Grenoble has been supported by the French "Agence Nationale de la Recherche", project RAPTORS (ANR-21-CE24-0004-01). High-performance computing resources from GENCI-TGCC (Grant no. 2020-A0090910016) are acknowledged.

Supporting Information Available

The following files are available free of charge.

• supp_info.pdf: additional structural and electronic characterisation.

• osc_multiscale.zip: template files for multiscale simulations of Spiro-TAD, TCTA, and F6TCNNQ.


A "Banquet Fraternal" at Hamburg in 1798: The Irish Connection and the Birth of the Modern Conspiracy Theory

a panel on "revolutionary nationalism in a global perspective" together

By Mathieu Ferradou

At the French National Archives, the carton F 6151 contains three folders of about 100 documents each detailing Léonard Bourdon's mission to Hamburg as special agent of the French Republic from 25 December 1797 to 18 April 1798. Out of the 27 le�ers forming Bourdon's official correspondence with the Directory, 22 have the same handwriting, the same found in another le�er, dated 3 germinal Year VI (22 March 1798) from Hamburg, and signed "W. D.," which was addressed to the editors of the semi-official newspaper Le Conservateur in Paris.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn1) This le�er is an account of a "fraternal" banquet, held in Hamburg for the celebration of spring, a holiday devoted to the sovereignty of the people in the republican calendar. About 80 guests, with Bourdon presiding, assembled in a room with tricolor decorations, sang civic hymns and patriotic songs, and held several toasts before ending the night in a philanthropic display -a quintessential example of a republican festival. This banquet and its account held a deeper meaning and had far-reaching consequences. It was held one day later than it should have been-on the second of germinal, not the first. The account, dated the third of germinal, was an open le�er, meant for publication in Le Conservateur, but it failed to appear in that newspaper's issues during germinal or the following month of floréal. The author of the le�er, recognized by his initials and distinct handwriting, was William Ducke�, Irish revolutionary, who was at that time Bourdon's secretary. In this article, I aim to understand why Ducke� and Bourdon failed to get this account of the feast of spring published, and how this failure can be explained by the European-wide scandal this celebration provoked. To do this, it is necessary first to have the larger context in mind.

The collapse of the First Coalition against France and the French invasion of Swi�erland in January 1798 left only England to fight against France. The driving force behind the First Coalition (and its 7 [1] main source of funds), England faced an existential crisis: the Congress of Rasta� had opened in November 1797 with the objective of a�aining a general peace in continental Europe, which would have allowed France to focus its might against England, most notably in launching a new expedition to Ireland. Plans were already underway, after the failure of the first expedition of December 1796. Hamburg, in this context, played a pivotal role as a neutral city, a status reinforced by English and French blockades, since all traffic had to go through the Hamburg hub.

In this situation, the English government instrumentalized the atmosphere of conspiracy going on in Europe, and notably in central Europe, since the publication in the spring of 1797 in London and Hamburg of the three first volumes of the Abbé Augustin Barruel's Mémoires pour servir à l'histoire du jacobinisme, by linking it to the Irish question. The Illuminati scare was also a green scare: the British government used the fear of revolutionary conspiracy to rally Europe and the United States and reform a coalition against revolutionary France, and the Irish Jacobins were at the very heart of this conspiracist fear. This sequence lasted until the publication of the Report of the Commi�ee of Secrecy of the House of Commons of March 1799, which was followed up in July by the passing of the Unlawful Societies Act and the Act to Prevent Unlawful Combinations of Workmen, respectively targeting secret societies (the Illuminati) and working-class organizations.

In his recent book on the Illuminati, Pierre-Yves Beaurepaire has given a very persuasive account of this sequence of events.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn2) However, he did not include Hamburg in his narrative. Doing so requires examining the Irish question, which helps to bring the rise of modern conspiracy theory by offering a history from below to complete the cosmopolitan narrative. Finally, retracing the personal failure of William Ducke� to get his le�er published encapsulates the larger, ideological failure of revolutionary cosmopolitanism's ability to prevail over rising counter-revolutionary and conspiracist nationalism.

"Le citoyen Bourdon y a présidé"

In the aftermath of the Coup of 18 Fructidor (4 September 1797), republican Director Rewbell and the newly appointed Director Merlin de Douai met with Léonard Bourdon in November. Intelligence received from Hamburg, sent by ambassador Charles-Frédéric Reinhard as well as through other channels, demonstrated that the neutral city had been the center of the royalist conspiracy against the French Directory, one supported by English financing. Bourdon was chosen by Minister of Police Sotin to go to Hamburg and investigate.

Léonard Bourdon (1754-1807) was a former Montagnard deputy at the National Convention, one of the leading men in his radical section of the Gravilliers and in the dechristianization, which had earned him the enmity of Robespierre. He participated in Robespierre's downfall, but was still denounced by Thermidorians, notably Fréron in his newspaper, L'Orateur du peuple, as a "Septembriseur" in Orléans and for his role in the dechristianization. He was jailed from April to October 1795. Participating in the Coup of 18 Fructidor against the royalists, Bourdon staged his political come-back. His appointment as envoy to Hamburg in November-December 1797 was a chance to benefit from the Directory's swing to the left.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn3) Bourdon arrived in Hamburg on January 23, 1798, officially as an agent of the Minister of Finances to secure provisions for France. As soon as he arrived, however, he found to his dismay that the French residents at Hamburg did not celebrate the decadi and other republican holidays. Surrounded by émigrés who had been refugees in the city since the early days of the Revolution, the "good citizens" kept a low profile. With the French consul Lagau and the secretary of the embassy Lemaître, Bourdon tried to rally the French citizens into an assembly which would meet regularly to raise their patriotic spirit. This initiative was far from revolutionary. Indeed, French nationals used to meet in an assembly before 1789. However, Bourdon's move created a political storm in much of central Europe,

[2] [3]
implicating the Hamburger Senate, the Courts of Prussia, Denmark, Austria, and the Circle of Lower Saxony. Much of the consternation was because of the involvement of Bourdon's acquaintanceturned-employee William Ducke�.

"Des patriotes hambourgeois et quelques defenders ont assisté à ce�e fête."

William Ducke� was born in Killarney, Co. Kerry, in Ireland in 1768 (or 1770). As a Catholic and because of the "penal laws," he had to go to the Continent to receive an education. Educated at the Irish College in Paris, he spearheaded a revolt of the students there in October 1792, in the wake of the fall of royalty and the founding of the Republic in France, in connection with the sans-culo�es of the Faubourg Saint Antoine. While the "republic in the college" was short-lived, it is at this moment that he met Bourdon.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn4) Shortly after, having come to the notice of the French republican government, he was sent to Ireland with two other students as propagandists. Between early 1793 and 1795, he traveled throughout Ireland and England and established connections between democratic and radical societies. He was instrumental in the merging between the United Irishmen and the Defenders in Dublin in 1794-5. He published a series of open le�ers in the Morning Chronicle and Morning Post under the pen name of "Junius Redivivus," a�acking the British government of Pi� and its war against France, which a�racted a lot of a�ention and forced him to flee England. In 1796, he was among the Irish patriots around General Hoche who sent him to England to prepare for the Irish expedition to connect with the republicans there and prepare for a general insurrection. To further this aim, he wrote proclamations to the Irish people and to the Irish soldiers and sailors in the English army and navy to incite mutinies and to set the docks on fire. He may have been involved in the mutinies of May and June 1797 in the Navy.

Back from England for the second time in July 1797, he stopped in Hamburg, writing a series of le�ers to the Directory in France. An a�entive examination of the correspondence of the ministers and the Directors shows that it was his information that convinced the Directory that Hamburg had been the center of the royalist conspiracy of Fructidor. In fact, Ducke� was able to spy on the counterrevolutionary networks there thanks to his brother Sidney, who lived in Bremen, and who had befriended an agent of Great Britain, the émigré and adventurer Anne Gédéon Lafi�e, selfappointed "marquis de Pelleport." Through Sidney, William was able to identify a network of false passports and a spying agency headed by English Colonel Donn that involved several French émigrés. (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn5) A graph (fig. 1) of Ducke�'s (large green circle at the center) network along with Bourdon's (large black circle in the center) confirms Mark Granova�er's "strength of weak ties" theory. (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn6) Bourdon was able to identify the British/émigrés networks in northern Germany and Denmark, thanks to the access Sidney Ducke� (green circle at the bo�om left) had to Verteuil, Harcourt, Donn -all leading figures in the royalist/émigrés/British network. Both Ducke�s were commi�ed republicans and adept at navigating the cosmopolitan, Bohemian underworld of spies and refugees who were so numerous in revolutionary Europe. (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn7) William Ducke� also connected Bourdon with the exiled Irish, Sco�ish and English republicans in Hamburg, Britain, and Ireland (green circles on the right) who were in the process of unification through the United Britons. Three figures stand out: Colonel Marcus Edward Despard, whom William Ducke� knew personally, and who was the first to bring him to the a�ention of the Directory, Father James Coigly, who was instrumental in the founding of the United Britons, (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn9) and Irish Defender/United Irishman Peter Carey.

[4] [5] [6] [7]
(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn10) Ducke� knew Coigly from his Irish college years, while he had met Carey in Dublin and Despard in London.

Finally, through Bourdon, William Ducke� connected the Irish and English exiles to the republican citizens of Hamburg who were important figures of the German and Jewish Enlightenments, among whom was Dr. Johan August Unzer (1727-1799), friend of Professor Reimarus, Johann Heinrich Campe and of Moses Mendelsohn, and who, with his wife Charlo�e Ziegler, promoted educational and sanitary reforms, and who advocated in favor of the emancipation of the Jews. They were also connected with the pro-French trading families like the Sievekings and the Ma�hiessens. Johann Georg Kerner, ambassador Reinhard's personal secretary, had founded in April 1797 a philanthropic society in Hamburg which served as a meeting point for all these republicans.

In sum, the fraternal banquet convened by Léonard Bourdon and Ducke� had gathered French citizens, agents of the French Republic, Hamburger citizens and patriots, important figures of the German and Jewish Enlightenments, United Irishmen and Britons, Irish Defenders, who toasted together the future "federation of the republics in Europe" under the approving eye of Bourdon (and [8] [START_REF]Archives Diplomatiques (AD)[END_REF] [10] Ducke�).

The Conspiracist Backlash

The "fête du printemps" and its toasts took place within the backdrop of a conspiracy scare which was exploited to its fullest by the English government. By the late eighteenth-century, European society's obsession with conspiracy theories had reached a fever pitch, only amplified by the dissolution of the Jesuits (h�ps://ageofrevolutions.com/2023/01/16/the-dissolution-of-the-jesuitsand-the-birth-of-an-anti-semitic-conspiracy-theory-in-the-age-of-enlightenment/). The Abbé Barruel exploited this vein when he published in April 1797 his Mémoires pour servir à l'histoire du jacobinisme: The same year, 1797, also saw the publication of John Robison's Proofs of a Conspiracy against all the Religions and Governments. In this book, the respectable professor in Edinburgh denounced, as its complete title clearly suggests, the "secret meetings of free masons, Illuminati, and reading societies" in Great Britain and Ireland.

In Hamburg, Bourdon was warned in February 1798 of the upcoming publication of a pamphlet, entitled Adresse aux souverains de l'Europe, accompanied by a second part, Le�re à Buonaparte, wri�en anonymously in English, translated into French and published by Pierre-François Fauche, the editor of the royalist newspaper Le Spectateur du Nord. This pamphlet presented Bourdon's assembly as the nexus of a conspiracy to overthrow all orders and to "revolutionize" the government in Hamburg. Its goal was to disrupt the ongoing negotiations at Rasta� by accusing France of trying to disrupt all established states. Bourdon, and then Reinhard's successor, Claude Roberjot, managed to prevent the publication of the book. Yet, the Senate forbade Bourdon from holding his planned banquet in a public building. This is why it was delayed and took place in the home of Lagau, the secretary of the French legation.

Across the Atlantic, this atmosphere of conspiracy prompted the United States government to pass the infamous Alien and Sedition Acts in June and July 1798, clearly targeting the Irish refugees from the failed "rebellion."

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn11) In September 1798, former general Dumouriez, published Nouveau tableau spéculatif sur l'Europe, in which he denounced "Jacobine" and "Illuminati" societies of Jews and Irish who, under the aegis of Bourdon (without explicitly naming him), conspired to revolutionize all of Northern Europe.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn12) Dumouriez's informant was an émigré, D'Angely, whose reports held in the National Archive at Kew are quite precise, as he also worked for the British ambassador, Craufurd, who had been appointed in March to watch over the Irish. (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn13) At the same moment, Robert Clifford (who had translated Barruel's book into English), published anonymously his Application of Barruel's Memoirs of Jacobinism to the Secret Societies of Ireland and Great Britain in London.

The Illuminati/ Irish/ Jewish conspiracy was encapsulated in the Report of the Commi�ee of Secrecy of the House of Commons, presented in March 1799. The preparatory documents for the reports, furnished by the Privy Council to the Commi�ee, show that intelligence from Hamburg was collated with reports from all over Ireland and Britain about workers' combinations, reading circles, and philanthropic societies.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn14) In the wake of the Irish "rebellion" of 1798, these societies were targeted as centers of sedition. The final report highlighted these connections (except for the Jewish aspect) to denounce an international Illuminati and French/Irish, i.e., "Jacobine" conspiracy.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn15)

Conclusion

Faced with this international campaign of fear of conspiracy, the French Directory chose to back down. Talleyrand, as Minister of Foreign Affairs, demanded Bourdon's recall to his colleague Sotin. In Hamburg, the philanthropic society was closed by the Senate. The Danish government sent Dr. Unzer to trial in Altona where he had fled, and he lost custody of his children. (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn16) Ducke� had been sent by Bourdon back to France and was employed by the Minister of Marine to convey money to England to pay accomplices who would help him trigger a new mutiny in the Navy in order to facilitate a new French expedition to Ireland. However, he was identified by none other than Pelleport on his way to Hamburg and arrested, which provoked another diplomatic crisis. Ducke� survived a poisoning a�empt. The English government finally ordered Craufurd to let him go, having already accomplished its aim by detaining him in Hamburg. He lingered in the city for a while before returning to Paris.

The 1797-99 moment, when patriots across Europe contemplated a European federation of republics, (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn17) had generated tremendous fear across the Atlantic world. In his Memoirs, Barruel quoted from a document he had supposedly translated from German, in which the Hierophant Adam Weishaupt, the leader of the Illuminati, used the word "nationalism" to denounce the tendency of men to retreat from the great family of mankind, from cosmopolitanism, into nations and empires. Then, the Hierophant denounced patriotism as an expression of localism and "national preference" against cosmopolitanism. This very adroit maneuver enabled Barruel to coin a word, "nationalism," to deride and caricature a political project, the democratic republican nation, as an "illuminated" cosmopolitan delusion, one linked with antislavery, atheism, and anarchy.

(//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn18) In other words, Barruel hijacked the concept of the "nation," redirected it toward the idea of "nationalism," and therefore rendered it desirable for the counterrevolutionaries. Against these alleged conspiracists, the counterrevolutionaries -the real conspiracists -promoted a nationalist version of the nation, depriving it of its democratic republican basis, and drew on these conspiracy fears to split liberals from the emerging left. The English-backed campaign in the international public sphere linked this fear with the fear of Irish and Jewish emancipation. The failure of the Rasta� Congress (with the assassination of the French delegates, including Roberjot, in April 1799), the building of the Second Coalition, and the Coup 18 Brumaire all insured that this conception of the "nationalist nation" prevailed and erased the revolutionary one. A defeat we still live in the wake of today.

Mathieu

Ferradou (h�ps://www.parisnanterre.fr/m-mathieu-ferradou) is maître de conférences (associate professor) at the Université Paris Nanterre and Centre d'histoire des sociétés médiévale et moderne (h�ps://memo.parisnanterre.fr/) (MéMo). He is currently working on his book manuscript provisionally titled, Aux Etats-Unis de France et d'Irlande : une hétérotopie transnationale à l'époque de la République atlantique(publication forthcoming).

Title Image:

The city of Hamburg, 1730. Source: Wikimedia Commons.

Further reading:

Figure 1 :

 1 Figure 1 : The networks of William Ducke� and Léonard Bourdon in Hamburg, 1797-1798. In this map generated from the Fichoz database, (//C50B1D46-711B-4198-A0C8-B302DAD48379#_edn8) individual actors are either mapped in black or green (Irish) circles, collective actors are in red, and cultural actors are in blue. Black lines between two actors indicate a neutral action, red a hostile action and green a friendly action. The size of the circles is proportionate to the number of actions. The data here has been extracted from a plurality of sources in the French, English and Irish archives.


Anthony Bernard
email: anthony.bernard@inra.fr

Joris Molina

Elisabeth Dirlewanger

Fabrice Lheureux

The French walnut improvement program: preliminary investigations

Objectives  The world walnut production in 2016 reached more than 3.5 M tonnes mostly provided by China, U.S.A. and Iran (FAOSTAT)  France in 2016 were the 9 th producer with 39 kt and 21,000 ha with 2 Protected Designation of Origin ('Noix du Périgord' and 'Noix de Grenoble') and walnut is the most important crop other than apple  The firsts breeding programs were led by Eric Germain in INRA and released 7 cultivars (e.g. 'Fernor') but programs ended in 2007 with an insufficient choice of cultivars  The new breeding program is led by Ctifl to better meet current and future needs, particularly in the context of global competition, climate change and reduced use of plant protection products  The genetic lever is based on the 'INNOV'noyer' project [1] which consists on the assessment of the French walnut germplasm genetic diversity, the identification of the genetic determinisms of traits of interest (e.g. pathology, phenology, fruit and kernel quality) by Genome-Wide Association Study and the establishment of necessary tools for a Marker-Assisted Selection achievement

  tolerance of French germplasm to Colletotrichum acutatum using detached leaf assay Study of budbreak date and male/female flowering dates using chronological data • Colletotrichum acutatum: Ascomycota, Glomerellaceae -complex of 29 species [2] • Causes a form of anthracnose disease in a wide range of hosts • Colletotrichum sp. present in French orchards since 1998-2000 [3] and characterized as necrotrophic on walnuts since 2008 • Identification in 2013-2015: 99% C. acutatum and 1% C. gloeosporioides • Symptoms: from black spots with orange acervules on walnut to full necrosis, loss of production Collection of walnut leaflets: 4 tests + 1 control French walnut germplasm: 259 accessions 220 of J. regia from worldwide (194 varieties + 26 hybrids) and 39 of related species, such as Rhysocaryon (J. nigra, J. hindsii, J. microcarpa, J. major, J. mollis) and Cardiocaryon (J. cinerea, J. sieboldiana, J. cathayensis, J. mansdhurica) Disinfection step: 1 bath 70% ethanol -50'' + 3 baths sterile distilled water -50'' Preparation of spores solution: 1.10 5 /mL from acervules grown on Potato Dextrose Agar medium Leaflet inoculation with 10µL deposited on needle wound Leaflets in climatic chamber for 7 days in Petri dishes with moistened paper Day: 23°C for 16h -Night: 18°C for 8h -80% hygrometry at 7 DAI : 4 of J. cinerea and 3 of J. sieboldiana • Monoecious tree, mainly dichogamous • Impact of climate change on plants observed in last decades on phenology, in favor of an advance in flowering dates [4] • Late spring frosts + early leafing = damages, loss of production • Phenological data from 1989 to 2017 on J. regia cv 'Franquette' and cv 'Lara', from INRA (Toulenne), Creysse and SENuRA experimental stations, according to IPGRI descriptors by Eric Germain [

Fig 1 :Fig 2 :Fig 3 :Fig 4 :Fig 5 :

 12345 Fig 1: Detached leaf assay protocol

Acknowledgements  We really want to thank the 'Région Nouvelle-Aquitaine' for funding the project, the 'Cifre' convention by 'ANRT' for funding the PhD (n° convention 2016/1558), the team of the 'Arboriculture Experimental Unit' of Toulenne (INRA) and the 'Prunus/Juglans Genetic Resources Center' for growing trees and providing us plant material and phenological data, the teams from the 2 experimental stations of 'Creysse' and 'SENuRA' for providing us phenological data