Quantum dynamical simulations of intra-chain exciton diffusion in an oligo (para-phenylene vinylene) chain at finite temperature

Coherent Transient Localization Mechanism of Interchain Exciton Transport in Regioregular P3HT: A Quantum-Dynamical Study

Transient localization has been proposed as a transport mechanism in organic materials, for both charge carriers and excitons. Here, we characterize a quantum coherent transient localization mechanism using full quantum simulations of an H-aggregated model system representative of regioregular poly(3-hexylthiophene) (rrP3HT). A Frenkel-Holstein Hamiltonian parametrized from first principles is considered, including local high-frequency modes and anharmonic, site-correlated interchain modes. Quantum-dynamical calculations are carried out using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method for a 13-site system with 195 vibrational modes, under periodic boundary conditions. It is shown that temporary localization of exciton polarons alternates with resonant transfer driven by interchain modes. While the transport process is mainly determined by exciton-polarons at the low-energy band edge, persistent coupling with the excitonic manifold is observed, giving rise to a nonadiabatic excitonic flux. This elementary transport mechanism remains preserved for limited static disorder and gives way to Anderson localization when the static disorder becomes dominant.

Charge carrier dynamics in conducting polymer PEDOT using ab initio molecular dynamics simulations

As conducting polymers become increasingly important in electronic devices, understanding their charge transport is essential for material and device development. Various semi-empirical approaches have been used to describe temporal charge carrier dynamics in these materials, but there have yet to be any theoretical approaches utilizing ab initio molecular dynamics. In this work, we develop a computational technique based on ab initio Car-Parrinello molecular dynamics to trace charge carrier temporal motion in archetypical conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Particularly, we analyze charge dynamics in a single PEDOT chain and in two coupled chains with different degrees of coupling and study the effect of temperature. In our model we first initiate a positively charged polaron (compensated by a negative counterion) at one end of the chain, and subsequently displace the counterion to the other end of the chain and trace polaron dynamics in the system by monitoring bond length alternation in the PEDOT backbone and charge density distribution. We find that at low temperature (T = 1 K) the polaron distortion gradually disappears from its initial location and reappears near the new position of the counterion. At the room temperature (T = 300 K), we find that the distortions induced by polaron, and atomic vibrations are of the same magnitude, which makes tracking the polaron distortion challenging because it is hidden behind the temperature-induced vibrations. The novel approach developed in this work can be used to study polaron mobility along and between the chains, investigate charge transport in highly doped polymers, and explore other flexible polymers, including n-doped ones.

WaveTrain: A Python package for numerical quantum mechanics of chain-like systems based on tensor trains

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.

A Comprehensive Approach to Exciton Delocalization and Energy Transfer

Electrostatic intermolecular interactions lie at the heart of both the Förster model for resonance energy transfer (RET) and the exciton model for energy delocalization. In the Förster theory of RET, the excitation energy incoherently flows from the energy donor to a weakly coupled energy acceptor. The exciton model describes instead the energy delocalization in aggregates of identical (or nearly so) molecules. Here, we introduce a model that brings together molecular aggregates and RET. We will consider a couple of molecules, each described in terms of two diabatic electronic states, coupled to an effective molecular vibration. Electrostatic intermolecular interactions drive energy fluxes between the molecules, that, depending on model parameters, can be described as RET or energy delocalization. At variance with the standard Förster model for RET and of the exciton model for aggregates, our approach applies both in the weak and in the strong coupling regimes and fully accounts for the quantum nature of molecular vibrations in a nonadiabatic approach. Coupling the system to a thermal bath, we follow RET and energy delocalization in real time and simulate time-resolved emission spectra.

Quantum dynamical study of inter-chain exciton transport in a regioregular P3HT model system at finite temperature: HJ vs. H-aggregate models

We report on quantum dynamical simulations of inter-chain exciton transport in a model of regioregular poly(3-hexylthiophene), rr-P3HT, at finite temperature, using the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method for a system of up to 63 electronic states and 180 vibrational modes. A Frenkel Hamiltonian of HJ aggregate type is used, along with a reduced H-aggregate representation; electron-phonon coupling includes local high-frequency modes as well as anharmonic intermolecular modes. The latter are operative in mediating inter-chain transport, by a mechanism of transient localization type. Strikingly, this mechanism is found to be of quantum coherent character and involves non-adiabatic effects. Using periodic boundary conditions, a normal diffusion regime is identified from the exciton mean-squared displacement, apart from early-time transients. Diffusion coefficients are found to be of the order of 3 x 10-3 cm2/s, showing a non-monotonous increase with temperature.

Intrachain Exciton Motion Can Compete with Interchain Hopping in Conjugated Polymer Films with a Strong J-Aggregate Property

Understanding exciton diffusion properties in organic semiconductor films is crucial for organic solar cells because excitons need to diffuse to an electron donor/acceptor interface to dissociate into charges. We previously found that singlet excitons generated in the thin films of a novel naphthobisoxadiazole-based low-bandgap polymer PNOz4T exhibit two-dimensional exciton diffusion characteristics along the backbone and π-stacking directions owing to the HJ-aggregate property of PNOz4T. However, the diffusion constants along these directions could not be determined owing to the difficulty of data analysis. Herein, we present a detailed analysis based on a simulated annealing metaheuristic. We found that intrachain exciton motion can be faster than interchain hopping. On the basis of temperature dependence measurements, we found that exciton diffusion is more favorable at lower temperatures because the coherent component partly contributes to exciton motion.

Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich-Holstein type Hamiltonians.

Signatures of coherent vibronic exciton dynamics and conformational control in two-dimensional electronic spectroscopy of conjugated polymers

Two-dimensional electronic spectroscopy (2DES) signals for homo-oligomer J-aggregates are computed, with a focus on the role of structural change induced by low-frequency torsional modes along with quasi-stationary trapping effects induced...

The fate of molecular excited states: modeling donor-acceptor dyes

We investigate the relaxation of a coherently excited molecule in the Redfield approximation. The molecular model, parametrized to describe donor-acceptor dyes that represent a large family of molecules of interest...

Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

Quantum Dynamics of Exciton Transport and Dissociation in Multichromophoric Systems

Due to the subtle interplay of site-to-site electronic couplings, exciton delocalization, nonadiabatic effects, and vibronic couplings, quantum dynamical studies are needed to elucidate the details of ultrafast photoinduced energy and charge transfer events in organic multichromophoric systems. In this vein, we review an approach that combines first-principles parameterized lattice Hamiltonians with accurate quantum dynamical simulations using advanced multiconfigurational methods. Focusing on the elementary transfer steps in organic functional materials, we address coherent exciton migration and creation of charge transfer excitons in homopolymers, notably representative of the poly(3-hexylthiophene) material, as well as exciton dissociation at polymer:fullerene heterojunctions. We emphasize the role of coherent transfer, trapping effects due to high-frequency phonon modes, and thermal activation due to low-frequency soft modes that drive a diffusive dynamics.