Quantum-Quantum and Quantum-Quantum-Classical Schemes for Near-Gap Excitations with Projection-Based-Embedded GW-Bethe-Salpeter Equation.

We present quantum-quantum and quantum-quantum-classical schemes based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE) employing projection-based-embedding (PbE). Such approaches allow defining active and inactive subsystems of larger, complex molecular systems, with only the smaller active subsystem being explicitly treated by GW-BSE offering significant computational advantages. However, as PbE can modify the single-particle states in the Kohn-Sham (KS) ground state calculation and screening effects from the inactive region are not automatically included in GW-BSE, results from such PbE-GW-BSE calculations can deviate from a full-system reference. Here, we scrutinize in detail, e.g., the individual and combined effects of different choices of active regions, the influence of omitting the screening from the inactive region, and strategies for basis set truncation on frontier orbital and near-gap electron-hole excitation energies. As prototypical systems, we consider a diketopyrrolopyrrole bicyclic ring including side-chains, a polarity-sensitive dye (prodan) in aqueous environment, and a π-stacked dimer of benzene and tetracyanoethylene in water, respectively, covering a variety of excitation characters in molecular systems with complex chemical environments and photoinduced processes. Our results suggest that to obtain agreement of approximately 0.1 eV between near-gap excitation energies from embedded and full calculations, the active region should be chosen based on the Mulliken population of the full highest-occupied molecular orbital and that careful benchmarking should be done on the KS level before the actual GW-BSE steps when basis set truncation is used. We find that PbE-GW-BSE offers significant reductions in computation times and, more importantly, memory requirements, making calculations for considerably larger systems tractable.

Electronic Couplings and Conversion Dynamics between Localized and Charge Transfer Excitations from Many-Body Green's Functions Theory.

We investigate the determination of electronic coupling between localized excitations (LEs) and charge-transfer (CT) excitations based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE). Using a small molecule dimer system, we first study the influence of different diabatization methods, as well as different model choices within GW-BSE, such as the self-energy models or different levels of self-consistency, and find that these choices affect the LE-CT couplings only minimally. We then consider a large-scale low-donor morphology formed from rubrene and fullerene and evaluate the LE-CT couplings based on coupled GW-BSE-molecular mechanics calculations. For these disordered systems of bulky molecules, we observe differences in the couplings based on the Edmiston-Ruedenberg diabatization compared to the more approximate Generalize Mulliken-Hush and fragment charge difference diabatization formalisms. In a kinetic model for the conversion between LE and CT states, these differences affect the details of state populations in an intermediate time scale but not the final populations.

Effect of Solvent Removal Rate and Annealing on the Interface Properties in a Blend of a Diketopyrrolopyrrole-Based Polymer with Fullerene.

We study the effect of solvent-free annealing and explicit solvent evaporation protocols in classical molecular dynamics simulations on the interface properties of a blend of a diketopyrrolopyrrole (DPP) polymer with conjugated substituents (DPP2Py2T) and PCBM[60]. We specifically analyze the intramolecular segmental mobility of the different polymer building blocks as well as intermolecular radial and angular distribution functions between donor and acceptor. The annealing simulations reveal an increase of the glass-transition temperature of 45 K in the polymer-fullerene blend compared to that of pure DPP2Py2T. Our results show that the effective solvent evaporation rates at room temperature only have a minor influence on the segmental mobility and intermolecular orientation, characterized in all cases by a preferential arrangement of PCBM[60] close to the electron-donating substituents in DPP2Py2T. In contrast, solvent-free annealing from a liquid yields clustering of the fullerene close to the electron-withdrawing DPP, generally considered to be detrimental for application in organic solar cells. We find that the difference can be attributed to differences in the behavior of 2-hexyldecyl side-chains, which collapse toward DPP when solvent is explicitly removed, thereby blocking access of PCBM[60].

Machine Learning of Quasiparticle Energies in Molecules and Clusters.

We present a Δ-machine learning approach for the prediction of GW quasiparticle energies (ΔMLQP) and photoelectron spectra of molecules and clusters, using orbital-sensitive representations (OSRs) based on molecular Cartesian coordinates in kernel ridge regression-based supervised learning. Coulomb matrix, bag-of-bond, and bond-angle-torsion representations are made orbital-sensitive by augmenting them with atom-centered orbital charges and Kohn-Sham orbital energies, both of which are readily available from baseline calculations at the level of density functional theory (DFT). We first illustrate the effects of different constructions of the OSRs on the prediction of frontier orbital energies of 22k molecules of the QM8 data set and show that it is possible to predict the full photoelectron spectrum of molecules within the data set using a single model with a mean absolute error below 0.1 eV. We further demonstrate that the OSR-based ΔMLQP captures the effects of intra- and intermolecular conformations in application to water monomers and dimers. Finally, we show that the approach can be embedded in multiscale simulation workflows, by studying the solvatochromic shifts of quasiparticle and electron-hole excitation energies of solvated acetone in a setup combining molecular dynamics, DFT, the GW approximation, and the Bethe-Salpeter equation. Our findings suggest that the ΔMLQP model allows us to predict quasiparticle energies and photoelectron spectra of molecules and clusters with GW accuracy at DFT cost.

Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory.

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation (BSE) employing numerical gradients. We scrutinize the influence of several typical approximations in the GW-BSE framework; we used one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm-Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC) method, second-order approximate coupled cluster (CC2) method, and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants based on a PBE0 ground state, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield excitation energies but also geometries in good agreement with established higher-order wave function methods.

Development and Testing of an All-Atom Force Field for Diketopyrrolopyrrole Polymers with Conjugated Substituents.

We develop an all-atom force field for a series of diketopyrrolopyrrole polymers with two aromatic pyridine substituents and a variable number of π-conjugated thiophene units in the backbone (DPP2PymT), used as donor materials in organic photovoltaic devices. Available intrafragment parameterizations of the individual fragment building blocks are combined with interfragment bonded and nonbonded parameters explicitly derived from density functional theory calculations. To validate the force field, we perform classical molecular dynamics simulations of single polymer chains with m = 1, 2, 3 in good and bad solvents and of melts. We observe the expected dependence of the chain conformation on the solvent quality, with the chain collapsing in water, and swelling in chloroform. The glass-transition temperature for the polymer melts is found to be in the range of 340-370 K. Analysis of the mobility of the conjugated segments in the polymer backbone reveals two relaxation processes: a fast one with a characteristic time at room temperature on the order of 10 ps associated with nearly harmonic vibrations and a slow one on the order of 100 ns associated with temperature-activated cis-trans transitions.

Ultrafast Formation of the Charge Transfer State of Prodan Reveals Unique Aspects of the Chromophore Environment.

Lipophilic dyes such as laurdan and prodan are widely used in membrane biology due to a strong bathochromic shift in emission that reports the structural parameters of the membrane such as area per molecule. Disentangling of the factors which control the spectral shift is complicated by the stabilization of a charge-transfer-like excitation of the dye in polar environments. Predicting the emission therefore requires modeling both the relaxation of the environment and the corresponding evolution of the excited state. Here, an approach is presented in which (i) the local environment is sampled by a classical molecular dynamics (MD) simulation of the dye and solvent, (ii) the electronically excited state of prodan upon light absorption is predicted by numerical quantum mechanics (QM), (iii) the iterative relaxation of the environment around the excited dye by MD coupled with the evolution of the excited state is performed, and (iv) the emission properties are predicted by QM. The QM steps are computed using the many-body Green's function in the GW approximation and the Bethe-Salpeter equation with the environment modeled as fixed point charges, sampled in the MD simulation steps. The comparison to ultrafast time-resolved transient absorption measurements demonstrates that the iterative molecular mechanics (MM)/QM approach agrees quantitatively with both the polarity-dependent shift in emission and the time scale over which the charge transfer state is stabilized. Together the simulations and experimental measurements suggest that the evolution into the charge transfer state is slower in amphiphilic solvents.

Backbone Chemical Composition and Monomer Sequence Effects on Phenylene Polymer Persistence Lengths.

Despite a vast body of the literature devoted to the use of phenylene polymers in the fabrication of graphene nanoribbons, the study of the physical properties of these precursors still poses open questions whose answers will certainly contribute to the design of more efficient/precise synthesis protocols. Particularly, persistence length measurements combined with size exclusion chromatography techniques assign both semiflexible to semirigid structures depending on the molecular weight of the precursor (NaritaNat. Chem.2014, 6, 126-132). Peculiarly, these results suggest an apparent structural change upon increasing the length of the polymers. To address this puzzle, we use single-chain models to study the stiffness of polyphenylene precursors in a theta-like solvent as a function of chain composition and monomer sequence. Steric effects are isolated by considering random walk chains with segment length distributions and the position of monomers determined by the nature of the arene substitution along the backbone. Moreover, two homopolymer limiting cases are defined, that is, meta and para sequences, by associating two types of monomers to each possible substitution pattern. We consider, within these two limiting cases, chains with different compositions and monomer sequences. We compute persistence lengths, mean square end-to-end distances, and gyration and hydrodynamic radii. We find that distinct values of the persistence length for apparently the same chain chemistry are the result of different mixing ratios and the arrangement along the chain of the two positional isomers of the same monomer. Finally, we discuss the relation between two-dimensional density of the number of crossings and the length of polyphenylene segments as they would occur upon strong chain adsorption onto a substrate.

Insights into the Kinetics of Supramolecular Comonomer Incorporation in Water.

Multicomponent supramolecular polymers are a versatile platform to prepare functional architectures, but a few studies have been devoted to investigate their noncovalent synthesis. Here, we study supramolecular copolymerizations by examining the mechanism and time scales associated with the incorporation of new monomers in benzene-1,3,5-tricarboxamide (BTA)-based supramolecular polymers. The BTA molecules in this study all contain three tetra(ethylene glycol) chains at the periphery for water solubility but differ in their alkyl chains that feature either 10, 12 or 13 methylene units. C10BTA does not form ordered supramolecular assemblies, whereas C12BTA and C13BTA both form high aspect ratio supramolecular polymers. First, we illustrate that C10BTA can mix into the supramolecular polymers based on either C12BTA or C13BTA by comparing the temperature response of the equilibrated mixtures to the temperature response of the individual components in water. Subsequently, we mix C10BTA with the polymers and follow the copolymerization over time with UV spectroscopy and hydrogen/deuterium exchange mass spectrometry experiments. Interestingly, the time scales obtained in both experiments reveal significant differences in the rates of copolymerization. Coarse-grained simulations are used to study the incorporation pathway and kinetics of the C10BTA monomers into the different polymers. The results demonstrate that the kinetic stability of the host supramolecular polymer controls the rate at which new monomers can enter the existing supramolecular polymers.

Evolutionary Approach to Constructing a Deep Feedforward Neural Network for Prediction of Electronic Coupling Elements in Molecular Materials.

We present a general framework for the construction of a deep feedforward neural network (FFNN) to predict distance and orientation dependent electronic coupling elements in disordered molecular materials. An evolutionary algorithm automatizes the selection of an optimal architecture of the artificial neural network within a predefined search space. Systematic guidance, beyond minimizing the model error with stochastic gradient descent based backpropagation, is provided by simultaneous maximization of a model fitness that takes into account additional physical properties, such as the field-dependent carrier mobility. As a prototypical system, we consider hole transport in amorphous tris(8-hydroxyquinolinato)aluminum. Reference data for training and validation is obtained from multiscale ab initio simulations, in which coupling elements are evaluated using density-functional theory, for a system containing 4096 molecules. The Coulomb matrix representation is chosen to encode the explicit molecular pair coordinates into a rotation and translation invariant feature set for the FFNN. The final optimized deep feedforward neural network is tested for transport models without and with energetic disorder. It predicts electronic coupling elements and mobilities in excellent agreement with the reference data. Such a FFNN is readily applicable to much larger systems at negligible computational cost, providing a powerful surrogate model to overcome the size limitations of the ab initio approach.

Improved general-purpose five-point model for water: TIP5P/2018.

A new five point potential for liquid water, TIP5P/2018, is presented along with the techniques used to derive its charges from ab initio per-molecule electrostatic potentials in the liquid phase using the split charge equilibration of Nistor et al. [J. Chem. Phys. 125, 094108 (2006)]. By taking the density and diffusion dependence on temperature as target properties, significant improvements to the behavior of isothermal compressibility were achieved along with improvements to other thermodynamic and rotational properties. While exhibiting a dipole moment close to ab initio values, TIP5P/2018 suffers from a too small quadrupole moment due to the charge assignment procedure and results in an overestimation of the dielectric constant.

Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP.

Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. The results show that VOTCA-XTP's GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.

Intermolecular Singlet and Triplet Exciton Transfer Integrals from Many-Body Green's Functions Theory.

A general approach to determine orientation and distance-dependent effective intermolecular exciton transfer integrals from many-body Green's functions theory is presented. On the basis of the GW approximation and the Bethe-Salpeter equation (BSE), a projection technique is employed to obtain the excitonic coupling by forming the expectation value of a supramolecular BSE Hamiltonian with electron-hole wave functions for excitations localized on two separated chromophores. Within this approach, accounting for the effects of coupling mediated by intermolecular charge transfer (CT) excitations is possible via perturbation theory or a reduction technique. Application to model configurations of pyrene dimers shows an accurate description of short-range exchange and long-range Coulomb interactions for the coupling of singlet and triplet excitons. Computational parameters, such as the choice of the exchange-correlation functional in the density-functional theory (DFT) calculations that underly the GW-BSE steps and the convergence with the number of included CT excitations, are scrutinized. Finally, an optimal strategy is derived for simulations of full large-scale morphologies by benchmarking various approximations using pairs of dicyanovinyl end-capped oligothiophenes (DCV5T), which are used as donor material in state-of-the-art organic solar cells.

Getting excited: challenges in quantum-classical studies of excitons in polymeric systems.

A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe the conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's function theory within the GW approximation and the Bethe-Salpeter (GW-BSE) equation were utilized to describe the excited states of the systems. The reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for the calculation of excitation energies based on MM/MD conformations.

Impact of mesoscale order on open-circuit voltage in organic solar cells.

Structural order in organic solar cells is paramount: it reduces energetic disorder, boosts charge and exciton mobilities, and assists exciton splitting. Owing to spatial localization of electronic states, microscopic descriptions of photovoltaic processes tend to overlook the influence of structural features at the mesoscale. Long-range electrostatic interactions nevertheless probe this ordering, making local properties depend on the mesoscopic order. Using a technique developed to address spatially aperiodic excitations in thin films and in bulk, we show how inclusion of mesoscale order resolves the controversy between experimental and theoretical results for the energy-level profile and alignment in a variety of photovoltaic systems, with direct experimental validation. Optimal use of long-range ordering also rationalizes the acceptor-donor-acceptor paradigm for molecular design of donor dyes. We predict open-circuit voltages of planar heterojunction solar cells in excellent agreement with experimental data, based only on crystal structures and interfacial orientation.

Parametrization of Extended Gaussian Disorder Models from Microscopic Charge Transport Simulations.

Simulations of organic semiconducting devices using drift-diffusion equations are vital for the understanding of their functionality as well as for the optimization of their performance. Input parameters for these equations are usually determined from experiments and do not provide a direct link to the chemical structures and material morphology. Here we demonstrate how such a parametrization can be performed by using atomic-scale (microscopic) simulations. To do this, a stochastic network model, parametrized on atomistic simulations, is used to tabulate charge mobility in a wide density range. After accounting for finite-size effects at small charge densities, the data is fitted to the uncorrelated and correlated extended Gaussian disorder models. Surprisingly, the uncorrelated model reproduces the results of microscopic simulations better than the correlated one, compensating for spatial correlations present in a microscopic system by a large lattice constant. The proposed method retains the link to the material morphology and the underlying chemistry and can be used to formulate structure-property relationships or optimize devices prior to compound synthesis.

Electronic Excitations in Push-Pull Oligomers and Their Complexes with Fullerene from Many-Body Green's Functions Theory with Polarizable Embedding.

We present a comparative study of excited states in push-pull oligomers of PCPDTBT and PSBTBT and prototypical complexes with a C60 acceptor using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. We analyze excitations in oligomers up to a length of 5 nm and find that for both materials the absorption energy practically saturates for structures larger than two repeat units due to the localized nature of the excitation. In the bimolecular complexes with C60, the transition from Frenkel to charge transfer excitons is generally exothermic and strongly influenced by the acceptor's position and orientation. The high CT binding energy of the order of 2 eV results from the lack of an explicit molecular environment. External polarization effects are then modeled in a GW-BSE based QM/MM approach by embedding the donor-acceptor complex into a polarizable lattice. The lowest charge transfer exciton is energetically stabilized by about 0.5 eV, while its binding energy is reduced to about 0.3 eV. We also identify a globally unbound charge transfer state with a more delocalized hole at higher energy while still within the absorption spectrum, which opens another potential pathway for charge separation. For both PCPDTBT and PSBTBT, the energetics are largely similar with respect to absorption and the driving force to form intermediate charge transfer excitations for free charge generation. These results support that the higher power conversion efficiency observed for solar cells using PSBTBT as donor material is a result of molecular packing rather than of the electronic structure of the polymer.

Can lattice models predict the density of states of amorphous organic semiconductors?

We extend existing lattice models of small-molecule amorphous semiconductors by accounting for changes in molecular polarizability upon charging or excitation. A compact expression of this contribution to the density of states is provided. Although the lattice model and the description based on a microscopic morphology both qualitatively predict an additional broadening, shift, and an exponential tail (traps) of the density of states, a quantitative agreement between the two cannot be achieved.

Design rules for charge-transport efficient host materials for phosphorescent organic light-emitting diodes.

The use of blue phosphorescent emitters in organic light-emitting diodes (OLEDs) imposes demanding requirements on a host material. Among these are large triplet energies, the alignment of levels with respect to the emitter, the ability to form and sustain amorphous order, material processability, and an adequate charge carrier mobility. A possible design strategy is to choose a π-conjugated core with a high triplet level and to fulfill the other requirements by using suitable substituents. Bulky substituents, however, induce large spatial separations between conjugated cores, can substantially reduce intermolecular electronic couplings, and decrease the charge mobility of the host. In this work we analyze charge transport in amorphous 2,8-bis(triphenylsilyl)dibenzofuran, an electron-transporting material synthesized to serve as a host in deep-blue OLEDs. We show that mesomeric effects delocalize the frontier orbitals over the substituents recovering strong electronic couplings and lowering reorganization energies, especially for electrons, while keeping energetic disorder small. Admittance spectroscopy measurements reveal that the material has indeed a high electron mobility and a small Poole-Frenkel slope, supporting our conclusions. By linking electronic structure, molecular packing, and mobility, we provide a pathway to the rational design of hosts with high charge mobilities.