Coarse-Graining Organic Semiconductors: The Path to Multiscale Design

Accessing the electronic structure of liquid crystalline semiconductors with bottom-up electronic coarse-graining

Understanding the relationship between multiscale morphology and electronic structure is a grand challenge for semiconducting soft materials. Computational studies aimed at characterizing these relationships require the complex integration of quantum-chemical (QC) calculations, all-atom and coarse-grained (CG) molecular dynamics simulations, and back-mapping approaches. However, these methods pose substantial computational challenges that limit their application to the requisite length scales of soft material morphologies. Here, we demonstrate the bottom-up electronic coarse-graining (ECG) of morphology-dependent electronic structure in the liquid-crystal-forming semiconductor, 2-(4-methoxyphenyl)-7-octyl-benzothienobenzothiophene (BTBT). ECG is applied to construct density functional theory (DFT)-accurate valence band Hamiltonians of the isotropic and smectic liquid crystal (LC) phases using only the CG representation of BTBT. By bypassing the atomistic resolution and its prohibitive computational costs, ECG enables the first calculations of the morphology dependence of the electronic structure of charge carriers across LC phases at the ∼20 nm length scale, with robust statistical sampling. Kinetic Monte Carlo (kMC) simulations reveal a strong morphology dependence on zero-field charge mobility among different LC phases as well as the presence of two-molecule charge carriers that act as traps and hinder charge transport. We leverage these results to further evaluate the feasibility of developing mesoscopic, field-based ECG models in future works. The fully CG approach to electronic property predictions in LC semiconductors opens a new computational direction for designing electronic processes in soft materials at their characteristic length scales.

Assessing molecular doping efficiency in organic semiconductors with reactive Monte Carlo

The addition of molecular dopants into organic semiconductors (OSCs) is a ubiquitous augmentation strategy to enhance the electrical conductivity of OSCs. Although the importance of optimizing OSC-dopant interactions is well-recognized, chemically generalizable structure-function relationships are difficult to extract due to the sensitivity and dependence of doping efficiency on chemistry, processing conditions, and morphology. Computational modeling for an integrated OSC-dopant design is an attractive approach to systematically isolate fundamental relationships, but requires the challenging simultaneous treatment of molecular reactivity and morphology evolution. We present the first computational study to couple molecular reactivity with morphology evolution in a molecularly doped OSC. Reactive Monte Carlo is employed to examine the evolution of OSC-dopant morphologies and doping efficiency with respect to dielectric, the thermodynamic driving for the doping reaction, and dopant aggregation. We observe that for well-mixed systems with experimentally relevant dielectric constants, doping efficiency is near unity with a very weak dependence on the ionization potential and electron affinity of OSC and dopant, respectively. At experimental dielectric constants, reaction-induced aggregation is observed, corresponding to the well-known insolubility of solution-doped materials. Simulations are qualitatively consistent with a number of experimental studies showing a decrease of doping efficiency with increasing dopant concentration. Finally, we observe that the aggregation of dopants lowers doping efficiency and thus presents a rational design strategy for maximizing doping efficiency in molecularly doped OSCs. This work represents an important first step toward the systematic integration of molecular reactivity and morphology evolution into the characterization of multi-scale structure-function relationships in molecularly doped OSCs.

Effect of Hydrodynamic Interactions and Flow on Charge Transport in Redox-Active Polymer Solutions

Redox-active polymers (RAPs) are a subclass of polyelectrolytes that can store charge and undergo redox self-exchange reactions. RAPs are of great interest in the field of redox flow batteries (RFBs) due to their ability to quickly charge and discharge, their chemical modularity, and their molecular size. However, designing RAPs for efficient charge transport at the molecular level requires a fundamental understanding of the charge transport mechanisms that occur in RFBs. Previous work from our group has explored these mechanisms, and in this paper, we seek to improve upon the previous model by incorporating both hydrodynamic interactions (HIs) and out-of-equilibrium dynamics, which are both highly pertinent to flow battery systems. We use a hybrid Brownian dynamics and Monte Carlo simulation to model redox-active polymer chains in both dilute and semidilute solutions. This model is used to show that HI is an important feature when charge hopping is not the major mechanism for charge displacement and leads to more rapid segmental and translational motion of polymer chains that expedites charge transport at low polymer concentrations. We demonstrate that strong extensional flows may result in either enhanced or decreased transport depending on the fraction of charges present on the RAP chain. We show that flow not only can promote charge transport by extending polymer conformations but can also suppress nonadjacent charge hopping processes that are important for transport at high charge fractions. Shear flows can similarly enhance charge transport through chain extension, but tumbling dynamics lead to oscillatory displacements that become dominant features with high charge fractions and strong flows.

Data-Driven Design of Polymer-Based Biomaterials: High-throughput Simulation, Experimentation, and Machine Learning

Polymers, with the capacity to tunably alter properties and response based on manipulation of their chemical characteristics, are attractive components in biomaterials. Nevertheless, their potential as functional materials is also inhibited by their complexity, which complicates rational or brute-force design and realization. In recent years, machine learning has emerged as a useful tool for facilitating materials design via efficient modeling of structure-property relationships in the chemical domain of interest. In this Spotlight, we discuss the emergence of data-driven design of polymers that can be deployed in biomaterials with particular emphasis on complex copolymer systems. We outline recent developments, as well as our own contributions and takeaways, related to high-throughput data generation for polymer systems, methods for surrogate modeling by machine learning, and paradigms for property optimization and design. Throughout this discussion, we highlight key aspects of successful strategies and other considerations that will be relevant to the future design of polymer-based biomaterials with target properties.

Distilling coarse-grained representations of molecular electronic structure with continuously gated message passing

Bottom-up methods for coarse-grained (CG) molecular modeling are critically needed to establish rigorous links between atomistic reference data and reduced molecular representations. For a target molecule, the ideal reduced CG representation is a function of both the conformational ensemble of the system and the target physical observable(s) to be reproduced at the CG resolution. However, there is an absence of algorithms for selecting CG representations of molecules from which complex properties, including molecular electronic structure, can be accurately modeled. We introduce continuously gated message passing (CGMP), a graph neural network (GNN) method for atomically decomposing molecular electronic structure sampled over conformational ensembles. CGMP integrates 3D-invariant GNNs and a novel gated message passing system to continuously reduce the atomic degrees of freedom accessible for electronic predictions, resulting in a one-shot importance ranking of atoms contributing to a target molecular property. Moreover, CGMP provides the first approach by which to quantify the degeneracy of "good" CG representations conditioned on specific prediction targets, facilitating the development of more transferable CG representations. We further show how CGMP can be used to highlight multiatom correlations, illuminating a path to developing CG electronic Hamiltonians in terms of interpretable collective variables for arbitrarily complex molecules.

Open Macromolecular Genome: Generative Design of Synthetically Accessible Polymers

A grand challenge in polymer science lies in the predictive design of new polymeric materials with targeted functionality. However, de novo design of functional polymers is challenging due to the vast chemical space and an incomplete understanding of structure-property relations. Recent advances in deep generative modeling have facilitated the efficient exploration of molecular design space, but data sparsity in polymer science is a major obstacle hindering progress. In this work, we introduce a vast polymer database known as the Open Macromolecular Genome (OMG), which contains synthesizable polymer chemistries compatible with known polymerization reactions and commercially available reactants selected for synthetic feasibility. The OMG is used in concert with a synthetically aware generative model known as Molecule Chef to identify property-optimized constitutional repeating units, constituent reactants, and reaction pathways of polymers, thereby advancing polymer design into the realm of synthetic relevance. As a proof-of-principle demonstration, we show that polymers with targeted octanol-water solubilities are readily generated together with monomer reactant building blocks and associated polymerization reactions. Suggested reactants are further integrated with Reaxys polymerization data to provide hypothetical reaction conditions (e.g., temperature, catalysts, and solvents). Broadly, the OMG is a polymer design approach capable of enabling data-intensive generative models for synthetic polymer design. Overall, this work represents a significant advance, enabling the property targeted design of synthetic polymers subject to practical synthetic constraints.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Machine learning based charge mobility prediction for organic semiconductors

Transfer integral is a crucial parameter that determines the charge mobility of organic semiconductors, and it is very sensitive to molecular packing motifs. The quantum chemical calculation of transfer integrals for all the molecular pairs in organic materials is usually an unaffordable task; fortunately, it can be accelerated by the data-driven machine learning method now. In this work, we develop machine learning models based on artificial neutral networks to predict transfer integrals accurately and efficiently for four typical organic semiconductor molecules: quadruple thiophene (QT), pentacene, rubrene, and dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]thiophene (DNTT). We test various forms of features and labels and evaluate the accuracy of different models. With the implementation of a data augmentation scheme, we have achieved a very high accuracy with the determination coefficient of 0.97 and mean absolute error of 4.5 meV for QT, and similar accuracy for the other three molecules. We apply these models to studying charge transport in organic crystals with dynamic disorders at 300 K and obtain the charge mobility and anisotropy in perfect agreement with the brutal force quantum chemical calculation. If more molecular packings representing the amorphous phase of organic solids are supplemented to the dataset, the current models can be refined to study charge transport in organic thin films with polymorphs and static disorders.

A review on microfluidic-assisted nanoparticle synthesis, and their applications using multiscale simulation methods

Recent years have witnessed an increased interest in the development of nanoparticles (NPs) owing to their potential use in a wide variety of biomedical applications, including drug delivery, imaging agents, gene therapy, and vaccines, where recently, lipid nanoparticle mRNA-based vaccines were developed to prevent SARS-CoV-2 causing COVID-19. NPs typically fall into two broad categories: organic and inorganic. Organic NPs mainly include lipid-based and polymer-based nanoparticles, such as liposomes, solid lipid nanoparticles, polymersomes, dendrimers, and polymer micelles. Gold and silver NPs, iron oxide NPs, quantum dots, and carbon and silica-based nanomaterials make up the bulk of the inorganic NPs. These NPs are prepared using a variety of top-down and bottom-up approaches. Microfluidics provide an attractive synthesis alternative and is advantageous compared to the conventional bulk methods. The microfluidic mixing-based production methods offer better control in achieving the desired size, morphology, shape, size distribution, and surface properties of the synthesized NPs. The technology also exhibits excellent process repeatability, fast handling, less sample usage, and yields greater encapsulation efficiencies. In this article, we provide a comprehensive review of the microfluidic-based passive and active mixing techniques for NP synthesis, and their latest developments. Additionally, a summary of microfluidic devices used for NP production is presented. Nonetheless, despite significant advancements in the experimental procedures, complete details of a nanoparticle-based system cannot be deduced from the experiments alone, and thus, multiscale computer simulations are utilized to perform systematic investigations. The work also details the most common multiscale simulation methods and their advancements in unveiling critical mechanisms involved in nanoparticle synthesis and the interaction of nanoparticles with other entities, especially in biomedical and therapeutic systems. Finally, an analysis is provided on the challenges in microfluidics related to nanoparticle synthesis and applications, and the future perspectives, such as large-scale NP synthesis, and hybrid formulations and devices.

A Mori-Zwanzig Dissipative Particle Dynamics Approach for Anisotropic Coarse Grained Molecular Dynamics

Coarse grained (CG) molecular dynamics simulations are widely used to accelerate atomistic simulations but generally lack a formalism to preserve the dynamics of the system. For spherical particles, the Mori-Zwanzig approach, while computationally complex, has ameliorated this problem. Here we present an anisotropic dissipative particle dynamics (ADPD) model as an extension of this approach, which accounts for the anisotropy for both conservative and nonconservative interactions. For a simple anisotropic system we parametrize the coarse grained force field representing ellipsoidal CG particles from the full-atomistic simulation. To represent the anisotropy of the system, both the conservative and dissipative terms are approximated using the Gay-Berne (GB) functional forms via a force-matching approach. We compare our model with other CG models and demonstrate that it yields better results in both static and dynamical properties. The inclusion of the anisotropic nonconservative force preserves the microscopic dynamical details, and hence the dynamical properties, such as diffusivity, can be better reproduced by the aspherical model. By generalizing the isotropic DPD model, this framework is effective and promising for the development of the CG model for polymers, macromolecules, and biological systems.

Formation of Crystalline Bulk Heterojunctions in Organic Solar Cells: Insights from Phase-Field Simulations

The performance of organic solar cells strongly depends on the bulk-heterojunction (BHJ) morphology of the photoactive layer. This BHJ forms during the drying of the wet-deposited solution, because of physical processes such as crystallization and/or liquid-liquid phase separation (LLPS). However, the process-structure relationship remains insufficiently understood. In this work, a recently developed, coupled phase-field-fluid mechanics framework is used to simulate the BHJ formation upon drying. For the first time, this allows to investigate the interplay between all the relevant physical processes (evaporation, crystal nucleation and growth, liquid demixing, composition-dependent kinetic properties), within a single coherent theoretical framework. Simulations for the model system P3HT-PCBM are presented. The comparison with previously reported in situ characterization of the drying structure is very convincing: The morphology formation pathways, crystallization kinetics, and final morphology are in line with experimental results. The final BHJ morphology is a subtle mixture of pure crystalline donor and acceptor phases, pure and mixed amorphous domains, which depends on the process parameters and material properties. The expected benefit of such an approach is to identify physical design rules for ink formulation and processing conditions to optimize the cell's performance. It could be applied to recent organic material systems in the future.

Fast, Faithful Simulations of Donor-Acceptor Interface Morphology

The local structure of conjugated polymers governs key optoelectronic properties, such as charge conduction and photogeneration at donor-acceptor interfaces. Because conjugated polymers are large, stiff, and relax slowly, all-atom molecular dynamics simulations are computationally expensive. Here, we describe a coarse-graining method that exploits the stiffness of constituent aromatic moieties by representing each moiety as rigidly bonded clusters of atoms wherein virtual sites replace several atoms. This approach significantly reduces the degrees of freedom while faithfully representing the shape and interactions of the moieties, resulting in 10 times faster simulations than all-atom simulations. Simulation of a donor polymer (P3HT) and a non-fullerene acceptor (O-IDTBR) validates the coarse-graining method by comparing structural properties from experiments, such as the density and persistence length. The fast simulation produces equilibrated systems with realistic morphologies. The simulation results of an equimolar mixture of P3HT, with a molecular weight of 1332 g mol^-1, and an O-IDTBR mixture suggest that the interface width must be larger than 7 nm. Also, we investigate the effect of slow cooling on morphologies, particularly the number of close contacts that facilitates carrier transport. Slow cooling increases close contacts, and the effect is more pronounced in crystal-forming P3HT than in O-IDTBR, where bulky side-groups hinder crystal formation.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Screening semiconducting polymers to discover design principles for tuning charge carrier mobility

We employ a rapid method for computing the electronic structure and orbital localization characteristics for a sample of 36 different polymer backbone structures. This relatively large sample derived from recent literature is used to identify the features of the monomer sequence that lead to greater charge delocalization and, potentially, greater charge mobility. Two characteristics contributing in equal measure to large localization length are the reduced variation of the coupling between adjacent monomers due to conformational fluctuations and the presence of just two monomers in the structural repeating units. For such polymers a greater mismatch between the HOMO orbitals of the fragments and, surprisingly, a smaller coupling between them is shown to favour greater delocalization of the orbitals. The underlying physical reasons for such observations are discussed and explicit and constructive design rules are proposed.

Controlled Growth and Self-Assembly of Multiscale Organic Semiconductor

Currently, organic semiconductors (OSs) are widely used as active components in practical devices related to energy storage and conversion, optoelectronics, catalysis, and biological sensors, etc. To satisfy the actual requirements of different types of devices, chemical structure design and self-assembly process control have been synergistically performed. The morphology and other basic properties of multiscale OS components are governed on a broad scale from nanometers to macroscopic micrometers. Herein, the up-to-date design strategies for fabricating multiscale OSs are comprehensively reviewed. Related representative works are introduced, applications in practical devices are discussed, and future research directions are presented. Design strategies combining the advances in organic synthetic chemistry and supramolecular assembly technology perform an integral role in the development of a new generation of multiscale OSs.

Systematic bottom-up molecular coarse-graining via force and torque matching using anisotropic particles

We derive a systematic and general method for parametrizing coarse-grained molecular models consisting of anisotropic particles from fine-grained (e.g. all-atom) models for condensed-phase molecular dynamics simulations. The method, which we call anisotropic force-matching coarse-graining (AFM-CG), is based on rigorous statistical mechanical principles, enforcing consistency between the coarse-grained and fine-grained phase-space distributions to derive equations for the coarse-grained forces, torques, masses, and moments of inertia in terms of properties of a condensed-phase fine-grained system. We verify the accuracy and efficiency of the method by coarse-graining liquid-state systems of two different anisotropic organic molecules, benzene and perylene, and show that the parametrized coarse-grained models more accurately describe properties of these systems than previous anisotropic coarse-grained models parametrized using other methods that do not account for finite-temperature and many-body effects on the condensed-phase coarse-grained interactions. The AFM-CG method will be useful for developing accurate and efficient dynamical simulation models of condensed-phase systems of molecules consisting of large, rigid, anisotropic fragments, such as liquid crystals, organic semiconductors, and nucleic acids.

Development of hybrid coarse-grained atomistic models for rapid assessment of local structuring of polymeric semiconductors

Decades of work in the field of computational study of semiconducting polymers using atomistic models illustrate the challenges of generating equilibrated models for this class of materials. While adopting a coarse-grained model can be helpful, the process of developing a suitable model is particularly non-trivial and time-consuming for semiconducting polymers due to a large number of different interactions with some having an anisotropic nature. This work introduces a procedure for the rapid generation of a hybrid model for semiconducting polymers where atoms of secondary importance (those in the alkyl side chains) are transformed into coarse-grained beads to reduce the computational cost of generating an equilibrated structure. The parameters are determined from easy-to-equilibrate simulations of very short oligomers and the model is constructed to enable a very simple back-mapping procedure to reconstruct geometries with atomistic resolution. The model is illustrated for three related polymers containing DPP (diketopyrrolopyrrole) to evaluate the transferability of the potential across different families of polymers. The accuracy of the model, determined by comparison with the results of fully equilibrated simulations of the same material before and after back-mapping, is fully satisfactory for two out of the three cases considered. We noticed that accuracy can be determined very early in the workflow so that it is easy to assess when the deployment of this method is advantageous. The hybrid representation can be used to evaluate directly the electronic properties of structures sampled by the simulations.

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 10⁷ speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. We show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.