Hello, A new project on the LCRC cluster has been requested. Please forward the information on to the LCRC Allocation sub-committee. Applicant's name: Kenley Pelzer Applicant's institution: ANL Applicant's division: NST Project Name: OPV Project title: Mesoscale modeling of charge transport in organic photovoltaics Associated funding: Project is funded by Argonne's Aneesur Rahman named fellowship. Other Systems: We currently have a NERSC allocation with 60,270 remaining hours and an allocation at Argonne's Center for Nanoscale Materials that has 7,108 remaining hours. Science: In recent years, organic photovoltaics (OPVs) have attracted much attention as a source of renewable energy due to their low cost of production and composition from abundant materials. However, to achieve the high efficiencies necessary for economic viability of OPVs, a better understanding of the relationship between structure and efficiency in OPVs is needed. Kozub et al. state: “the full potential of these devices can only be realized through extensive trial and error on every donor-acceptor combination or with an understanding of the variables which govern the morphology and device performance”. Ideally, theoretical models would predict the most promising structures to be pursued in the laboratory. In this proposal, I suggest a new theoretical approach in which charge transport is treated via Langevin molecular dynamics (LMD) to explore the elusive structure/efficiency relationship in OPVs. In a bulk heterojunction OPV, the active layer is comprised of a mixture of electron-donating molecules (usually polymers) and electron-accepting molecules (usually fullerenes). Upon illumination by sunlight, excitons (bound electron/hole pairs) are generated that diffuse to donor/acceptor heterojunctions. At these heterojunctions, the excitons separate into individual charges. These charges are localized by deformation of the nuclei around them, forming polarons. Via a hopping process, the polarons travel the electrodes, where charge collection occurs. The efficiency of a solar cell is determined by several processes: photon absorption, exciton generation, exciton migration, charge separation, charge dissociation, and charge transport. Charge transport, in which the charges travel from the site of charge dissociation to the electrodes, is by far the slowest of these processes, occurring over microseconds. The earlier steps are of great importance because they determine the number of charges that are generated relative to the number of photons that strike the cell. Therefore, in a microsecond-scale time-domain model of photovoltaic activity, the initial steps in the process can be treated in an approximate manner as long as the number of charges generated per unit time is roughly correct. The step that must be treated precisely in such a simulation is charge transport. The disorder and low dielectric constant of OPVs leads charges to form polarons, charges dressed by phonons and localized by the deformation of the nearby nuclear structure. Polaron transport is generally believed to be dominated by thermally activated hopping, with tunneling effects becoming negligible as temperature increases. Modeling of transport must consider deformation of the nuclei, the electric field created by the electrodes, the possibility of charges becoming trapped, repulsion from polarons with like charges, attraction (and risk of recombination) with polarons of opposite charges, and thermal energy. All of these influences are accounted for in the proposed model, in which polarons are treated as pseudoatoms and simulated using LMD. The distances and timescales of polaron transport make atomistic LMD too expensive for current computational capabilities. I propose a model that involves a novel simplification of the active layer in which LMD is performed only on the polarons. Polarons can be treated as pseudoatoms by defining an effective mass and a spatial position defined by the center of the polaron’s charge density. A typical active layer thickness is ~100 nm, and polaron density in OPVs is generally 10^21-10^23 polarons per cubic meter. Thus, in a 100 nm × 100 nm × 100 nm region, on average only 1−100 polarons are present (in contrast to the millions of atoms that are present). Performing LMD on 100 pseudoatoms, even for long time scales, is computationally manageable. First, I will develop code for the donor/acceptor combination poly-(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene) (PBTTT)/ phenyl-C71-butyric acid methyl ester (PC71BM). This OPV provides an ideal test case because a wealth of experimental data is available for benchmarking, and Prof. M. McGehee (Stanford) has agreed to provide data on PBTTT/PC71BM structure. Next, I will extend the code to other donor/acceptor combinations and explore a range of possible active layer structures. Project description: Research Plan Months 1-6: The necessary information from a quantum description of a polaron can be incorporated into this model by an accurate definition of the potential energy surface (PES) and the effective mass. Polaron transport can be modeled with classical LMD because of the deformation of the nuclei surrounding polarons: because nuclei are heavy, tunneling effects are small in processes involving nuclear rearrangement, with tunneling most negligible at higher temperatures. Density functional theory (DFT) can describe the diabatic potential energy surfaces associated with charge transfer, a method recently applied to charge transport in organic semiconductors. Because diabatic PESs can cross and are coupled to one another, charge transfer can be approximately treated as polaron transfer between diabats, provided that the necessary thermal energy is available to surmount the potential energy barrier. We will use code developed by our collaborator Prof. T. Van Voorhis (MIT) to obtain adiabatic potential energy surfaces, which are derived from the diabatic surfaces and incorporate the necessary information on couplings between the diabatic surfaces. These adiabatic potential energy surfaces will serve as the PESs for the LMD code. DFT calculations also describe vibrational modes of the material, which can be used to derive effective mass: preliminary calculations performed on a sample donor/acceptor pair indicate that this approach will capture the tendency of less rigid molecules to deform around a charge and create a heavier polaron. The DFT calculations will be performed using the NWChem software package, which scales well to many thousands of cores. These calculations will be computationally expensive due to the large size of the molecules involved. Our initial calculations using the B3LYP functional and the 6-31G* basis set give a modest cost of about 200 CPU hours for a single point energy calculation of a fullerene dimer. However, for each possible orientation between two molecules, constrained DFT geometry optimizations will be necessary that will likely cost tens of thousands of hours (initial calculations showed a cost of about 20,000 CPU hours for a DFT geometry optimization of a fullerene dimer). To calculate an appropriate reaction coordinate for charge transfer for a particular structure, three geometry optimizations are needed (initial state, final state, and transition state). Given the disordered nature of OPVs and the fact that charge transfer is highly sensitive to small changes in the re lative position of the molecules, a range of possible orientations must be tested for dimers of each molecule. For each orientation, many points along the reaction coordinate must be tested to create a smooth PES. If we calculate 20 points along the PES for each charge transfer event, and 20 possible orientations are tested for both C70 dimers and PBTTT dimers, I will require 2×3x20×20,000=2,400,000 CPU hours for geometry optimizations, and 2x20x20x200=160,000 CPU hours for single point calculations, to build an accurate potential energy surface for PBTTT/PC71BM. Allowing some room for convergence issues or other unexpected computational expenses, we estimate that the costs of DFT for a given donor/acceptor pair will be approximately 4,000,000 CPU hours. Months 7-9: The next task will be to develop the molecular dynamics code. As discussed above, the early stages of the photovoltaic conversion process (photon absorption, exciton generation, exciton migration, charge separation, and charge dissociation) need not be treated explicitly as long as these steps are treated in a way that leads to the correct polaron density in the OPV. However, some explicit treatment of charge generation is needed to account for the fact that structural changes influence the number of charges generated under a given illumination. Fortunately, exciton diffusion length (the average distance that an exciton diffuses before recombining or separating) is often available in the literature and is known for PBTTT/PC71BM. I propose a simple approach in which any photon that is absorbed by the cell within the diffusion length of a heterojunction is assumed to instantaneously produce two separated charges at the nearest heterojunction. The incidence of photon s and their frequency distribution will be set to be consistent with solar illumination, and the percentage of photons of a particular wavelength that are absorbed is easily found in the literature for existing donor/acceptor combinations in OPVs. When the code is extended to donor/acceptor pairs not yet tested in the laboratory, photon absorption will be inferred from similar compounds. The LMD code will propagate the following equation in time: MX’’ = -(dU/dX) - γMX’ + R(t) where M refers to the polaron effective mass, U refers to the PES, X refers to polaron position, γ refers to friction from the environment, and R is a temperature-dependent random-force vector that determines when random kicks of energy from vibrational motions in the environment occur. This Langevin molecular dynamics is ideal for our model because the thermal effects of the environment are inherently built into the model with the random-force vector R without explicit treatment of the donor and acceptor atoms. The PES U will combine the PES derived from DFT with the energetic influence of the electrodes and the other polarons, which will both influence potential energy via Coulombic interactions. The reduction of the LMD simulation to a treatment of approximately 100 pseudoatoms makes it possible to treat distances and timescales outside the reach of standard molecular dynamics methods. However, due to the long timescales of charge transport (microseconds), the computational cost remains significant and parallelization of the code will be necessary. The time step for molecular dynamics calculations is generally around 1 fs, meaning that 10 billion time steps would be necessary to simulate 10 microseconds of dynamics. Access to high-performance computing resources will be crucial as we explore how to effectively parallelize the LMD code to simulate microseconds of transport in a reasonable amount of time. We suggest that 250,000 CPU hours would be a reasonable starting allocation for the development of the LMD code. Months 10-12: A wealth of experimental data on PBTTT/PC71BM is available that can be used to test the accuracy of this model. Data on charge mobility has been gathered that can be used to test the accuracy of our charge transport rates. There is also significant data comparing efficiency for different PBTTT/PC71BM structures: for example, one study compared various experimental measures of efficiency for a 1:1 versus 1:10 ratio of PBTTT to PC71BM, while another study compared 1:1 and 1:4 ratios. Such data is ideal for benchmarking the relationship between structure and efficiency. Thus, months 10-12 will be devoted to such comparisons with experimental data and the necessary adjustments. Months 13-24: During the first year, work will focus on well-understood OPVs that can help us to verify the validity of this model. During the second year, the model will be put to use in calculating structure/efficiency relationships for structures that have not been thoroughly explored experimentally, in the hopes of shedding light on what directions may be useful to pursue in the design of new OPV materials. The specific directions pursued in the second year will depend somewhat on the progress in the field over the next eighteen months, and what questions are most pressing when this time arrives. I will conduct some exploration of new structures for the PBTTT/PC71BM combination (because the CDFT data will already have been gathered for this donor/acceptor combination, new morphologies can be tested without significant additional computational cost). Structural changes that could be explored include changes in the size and shape of the pure donor or acceptor domains, the distance between pure domains, and the orientation of such domains. However, I will also extend the model to consider at least one additional donor/acceptor combination for which new structural arrangements are of interest. For each new donor/acceptor combination, I estimate that it will take three months to perform the necessary CDFT calculations, calculate the effective mass of polarons in the new material, and link the molecular dynamics code to this new information. Thus, it is realistic to plan exploration of some new PBTTT/PC71BM structures during this year, and one to two other donor/acceptor combinations. Each new donor/acceptor calculation will require access to about 4,000,000 CPU hours for the necessary DFT calculations (more or less depending on the size of the donor and acceptor molecules). Conclusions I propose a novel treatment of charge mobility in OPVs that applies quantum mechanical insights from DFT to a mesoscale treatment of the photovoltaic active layer. A Blues allocation can provide the cutting edge leadership computing resources that are capable of supporting a project of this magnitude. The calculation of the PESs using NWChem software will allow scaling up to thousands of cores: with access to Blues, this efficient scaling can be exploited to complete these very expensive electronic structure calculations in the proposed time frame. The proposed model treats length and timescales that are beyond the reach of many computational methods: By explicitly calculating the molecular dynamics of polaron pseudoatoms without involving dynamics of the atoms of the active layer, the microsecond timescales and nanometer-scale distances relevant to polaron transport are accessible. This model will compute charge transfer rates and provide insights into power conversion efficiency, shedding light on the structure/efficiency relationship in OPVs. These insights will have implications that reach beyond OPVs: technologies ranging from field-effect transistors to light-emitting diodes involve polaron transport in organic semiconducting materials. The proposed model can apply high-performance computing to study the crucial question of polaron transport efficiency in a variety of organic electronic devices. Industry partnership: Project URL: Requested allocation: 4250000 Q1: 1000000 Q2: 2000000 Q3: 1000000 Q4: 250000 Justification: The vast part of the computational expense of our project is in the DFT calculations performed with the NWChem software. NWChem is known to scale well to thousands of cores (see https://asc.llnl.gov/computing_resources/bluegenel/papers/apra.pdf). Storage requirements: 1 TB should be sufficient. 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