First-principles quantum simulations of exciton diffusion on a minimal oligothiophene chain at finite temperature

Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms

The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.

Nonadiabatic Exciton Dynamics and Energy Gradients in the Framework of FMO-LC-TDDFTB

We introduce a novel methodology for simulating the excited-state dynamics of extensive molecular aggregates in the framework of the long-range corrected time-dependent density-functional tight-binding fragment molecular orbital method (FMO-LC-TDDFTB) combined with the mean-field Ehrenfest method. The electronic structure of the system is described in a quasi-diabatic basis composed of locally excited and charge-transfer states of all fragments. In order to carry out nonadiabatic molecular dynamics simulations, we derive and implement the excited-state gradients of the locally excited and charge-transfer states. Subsequently, the accuracy of the analytical excited-state gradients is evaluated. The applicability to the simulation of exciton transport in organic semiconductors is illustrated on a large cluster of anthracene molecules. Additionally, nonadiabatic molecular dynamics simulations of a model system of benzothieno-benzothiophene molecules highlight the method's utility in studying charge-transfer dynamics in organic materials. Our new methodology will facilitate the investigation of excitonic transfer in extensive biological systems, nanomaterials, and other complex molecular systems consisting of thousands of atoms.

The photoactivated dynamics of dGpdC and dCpdG sequences in DNA: a comprehensive quantum mechanical study

Study of alternating DNA GC sequences by different time-resolved spectroscopies has provided fundamental information on the interaction between UV light and DNA, a process of great biological importance. Multiple decay paths have been identified, but their interplay is still poorly understood. Here, we characterize the photophysics of GC-DNA by integrating different computational approaches, to study molecular models including up to 6 bases described at a full quantum mechanical level. Quantum dynamical simulations, exploiting a nonadiabatic linear vibronic coupling (LVC) model, coupled with molecular dynamics sampling of the initial structures of a (GC)5 DNA duplex, provide new insights into the photophysics in the sub-picosecond time-regime. They indicate a substantial population transfer, within 50 fs, from the spectroscopic states towards G → C charge transfer states involving two stacked bases (CTintra), thus explaining the ultrafast disappearance of fluorescence. This picture is consistent with that provided by quantum mechanical geometry optimizations, using time dependent-density functional theory and a polarizable continuum model, which we use to parametrize the LVC model and to map the main excited state deactivation pathways. For the first time, the infrared and excited state absorption signatures of the various states along these pathways are comprehensively mapped. The computational models suggest that the main deactivation pathways, which, according to experiment, lead to ground state recovery on the 10-50 ps time scale, involve CTintra followed by interstrand proton transfer from the neutral G to C-. Our calculations indicate that CTintra is populated to a larger extent and more rapidly in GC than in CG steps and suggest the likely involvement of monomer-like and interstrand charge transfer decay routes for isolated and less stacked CG steps. These findings underscore the importance of the DNA sequence and thermal fluctuations for the dynamics. They will also aid the interpretation of experimental results on other sequences.

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.

Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics

We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms, including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.

Modeling the Effect of Disorder in the Two-Dimensional Electronic Spectroscopy of Poly-3-hexyltiophene in an Organic Photovoltaic Blend: A Combined Quantum/Classical Approach

We introduce a first-principles model of the 12-mer poly-3-hexyltiophene (P3HT) polymer system in the realistic description of an organic photovoltaic blend environment. We combine Molecular Dynamics (MD) simulations of a thin-film blend of P3HT and phenyl-C61-butyric acid methyl ester (PCBM) to model the interactions with a fluctuating environment with Time-Dependent Density Functional Theory (TDDFT) calculations to parametrize the effect of the torsional flexibility in the polymer and construct an exciton-type Hamiltonian that describes the photoexcitation of the polymer. This allows us to reveal the presence of different flexibility patterns governed by the torsional angles along the polymer chain which, in the interacting fluctuating environment, control the broadening of the spectral observables. We identify the origin of the homogeneous and inhomogeneous line shape of the simulated optical signals. This is paramount to decipher the spectroscopic nature of the ultrafast electron-transfer process occurring in organic photovoltaic (OPV) materials.

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.

Exciton Dissociation in a Model Organic Interface: Excitonic State-Based Surface Hopping versus Multiconfigurational Time-Dependent Hartree

Quantum dynamical simulations are essential for a molecular-level understanding of light-induced processes in optoelectronic materials, but they tend to be computationally demanding. We introduce an efficient mixed quantum-classical nonadiabatic molecular dynamics method termed eXcitonic state-based Surface Hopping (X-SH), which propagates the electronic Schrödinger equation in the space of local excitonic and charge-transfer electronic states, coupled to the thermal motion of the nuclear degrees of freedom. The method is applied to exciton decay in a 1D model of a fullerene-oligothiophene junction, and the results are compared to the ones from a fully quantum dynamical treatment at the level of the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) approach. Both methods predict that charge-separated states are formed on the 10-100 fs time scale via multiple "hot-exciton dissociation" pathways. The results demonstrate that X-SH is a promising tool advancing the simulation of photoexcited processes from the molecular to the true nanomaterials scale.

A New Frontier in Exciton Transport: Transient Delocalization

Efficient exciton transport is crucial to the application of organic semiconductors (OSCs) in light-harvesting devices. While the physics of exciton transport in highly disordered media is well-explored, the description of transport in structurally and energetically ordered OSCs is less established, despite such materials being favorable for devices. In this Perspective we describe and highlight recent research pointing toward a highly efficient exciton transport mechanism which occurs in ordered OSCs, transient delocalization. Here, exciton-phonon couplings play a critical role in allowing localized exciton states to temporarily access higher-energy delocalized states whereupon they move large distances. The mechanism shows great promise for facilitating long-range exciton transport and may allow for improved device efficiencies and new device architectures. However, many fundamental questions on transient delocalization remain to be answered. These questions and suggested next steps are summarized.

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.

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...

(De)localization dynamics of molecular excitons: comparison of mixed quantum–classical and fully quantum treatments

Molecular excitons play a central role in processes of solar energy conversion, both natural and artificial. It is therefore no wonder that numerous experimental and theoretical investigations in the last...

Ultrafast Fluorescence Depolarization in Conjugated Polymers

We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylenevinylene). Our theoretical model describes Frenkel exciton coupling to both fast, quantized C-C bond vibrations and slow, classical torsional modes. We also incorporate system-bath interactions. The dynamics is simulated using the time evolution block decimation method, which avoids the failures of the Ehrenfest approximation to describe decoherence processes and nonadiabatic interstate conversion. System-bath interactions are modeled using quantum trajectories and Lindblad quantum jump operators. We find that following photoexcitation, the quantum mechanical entanglement of the exciton and C-C bond phonons causes exciton-site decoherence. Next, system-bath interactions cause the stochastic collapse of high-energy delocalized excitons into chromophores. Finally, torsional relaxation causes additional exciton-density localization. We relate these dynamical processes to the predicted fluorescence depolarization, extract the time scales corresponding to them, and thus interpret the observed sub-ps fluorescence depolarization.

Revealing generation, migration, and dissociation of electron-hole pairs and current emergence in an organic photovoltaic cell

Using an innovative quantum mechanical method for an open quantum system, we observe in real time and space the generation, migration, and dissociation of electron-hole pairs, transport of electrons and holes, and current emergence in an organic photovoltaic cell. Ehrenfest dynamics is used to study photoexcitation of thiophene:fullerene stacks coupled with a time-dependent density functional tight-binding method. Our results display the generation of an electron-hole pair in the donor and its subsequent migration to the donor-acceptor interface. At the interface, electrons transfer from the lowest unoccupied molecular orbitals (LUMOs) of thiophenes to the second LUMOs of fullerene. Further migration of electrons and holes leads to the emergence of current. These findings support previous experimental evidence of coherent couplings between electronic and vibrational degrees of freedom and are expected to stimulate further work toward exploring the interplay between electron-hole pair (exciton) binding and vibronic coupling for charge separation and transport.

Multi-layer Gaussian-based multi-configuration time-dependent Hartree (ML-GMCTDH) simulations of ultrafast charge separation in a donor-acceptor complex

We report on first applications of the Multi-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (ML-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] beyond its basic two-layer variant. The ML-GMCTDH scheme provides an embedding of a variationally evolving Gaussian wavepacket basis into a hierarchical tensor representation of the wavefunction. A first-principles parameterized model Hamiltonian for ultrafast non-adiabatic dynamics in an oligothiophene-fullerene charge transfer complex is employed, relying on a two-state linear vibronic coupling model that combines a distribution of tuning type modes with an intermolecular coordinate that also modulates the electronic coupling. Efficient ML-GMCTDH simulations are carried out for up to 300 vibrational modes using an implementation within the QUANTICS program. Excellent agreement with reference ML-MCTDH calculations is obtained.

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.

Simulating Quantum Vibronic Dynamics at Finite Temperatures With Many Body Wave Functions at 0 K

For complex molecules, nuclear degrees of freedom can act as an environment for the electronic “system” variables, allowing the theory and concepts of open quantum systems to be applied. However, when molecular system-environment interactions are non-perturbative and non-Markovian, numerical simulations of the complete system-environment wave function become necessary. These many body dynamics can be very expensive to simulate, and extracting finite-temperature results—which require running and averaging over many such simulations—becomes especially challenging. Here, we present numerical simulations that exploit a recent theoretical result that allows dissipative environmental effects at finite temperature to be extracted efficiently from a single, zero-temperature wave function simulation. Using numerically exact time-dependent variational matrix product states, we verify that this approach can be applied to vibronic tunneling systems and provide insight into the practical problems lurking behind the elegance of the theory, such as the rapidly growing numerical demands that can appear for high temperatures over the length of computations.

Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

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

We report on quantum dynamical simulations of exciton diffusion in an oligo(para-phenylene vinylene) chain segment with 20 repeat units (OPV-20) at finite temperature, complementary to our recent study of the same system at T = 0 K [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. Accurate quantum dynamical simulations are performed using the multi-layer multi-configuration time-dependent Hartree method as applied to a site-based Hamiltonian comprising 20 electronic states of Frenkel type and 460 vibrational modes, including site-local quinoid-distortion modes along with site-correlated bond-length alternation (BLA) modes, ring torsional modes, and an explicit harmonic-oscillator bath. A first-principles parameterized Frenkel-Holstein type Hamiltonian is employed, which accounts for correlations between the ring torsional modes and the anharmonically coupled BLA coordinates located at the same junction. Thermally induced fluctuations of the torsional modes are described by a stochastic mean-field approach, and their impact on the excitonic motion is characterized in terms of the exciton mean-squared displacement. A normal diffusion regime is observed under periodic boundary conditions, apart from transient localization features. Even though the polaronic exciton species are comparatively weakly bound, exciton diffusion is found to be a coherent-rather than hopping type-process, driven by the fluctuations of the soft torsional modes. Similar to the previous observations for oligothiophenes, the evolution for the most part exhibits a near-adiabatic dynamics of local exciton ground states (LEGSs) that adjust to the local conformational dynamics. However, a second mechanism, involving resonant transitions between neighboring LEGSs, gains importance at higher temperatures.

Excitation transport in molecular aggregates with thermal motion

Molecular aggregates can under certain conditions transport electronic excitation energy over large distances due to dipole-dipole interactions. Here, we explore to what extent thermal motion of entire monomers can guide or enhance this excitation transport. The motion induces changes of aggregate geometry and hence modifies exciton states. Under certain conditions, excitation energy can thus be transported by the aggregate adiabatically, following a certain exciton eigenstate. While such transport is always slower than direct migration through dipole-dipole interactions, we show that transport through motion can yield higher transport efficiencies in the presence of on-site energy disorder than the static counterpart. For this we consider two simple models of molecular motion: (i) longitudinal vibrations of the monomers along the aggregation direction within their inter-molecular binding potential and (ii) torsional motion of planar monomers in a plane orthogonal to the aggregation direction. The parameters and potential shapes used are relevant to dye-molecule aggregates. We employ a quantum-classical method, in which molecules move through simplified classical molecular dynamics, while the excitation transport is treated quantum mechanically using Schrödinger's equation. For both models we find parameter regimes in which the motion enhances excitation transport, however these are more realistic for the torsional scenario, due to the limited motional range in a typical Morse type inter-molecular potential. We finally show that the transport enhancement can be linked to adiabatic quantum dynamics. This transport enhancement through adiabatic motion appears a useful resource to combat exciton trapping by disorder.

First-Principles Quantum and Quantum-Classical Simulations of Exciton Diffusion in Semiconducting Polymer Chains at Finite Temperature

We report on first-principles quantum-dynamical and quantum-classical simulations of photoinduced exciton dynamics in oligothiophene chain segments, representative of intrachain exciton migration in the poly(3-hexylthiophene) (P3HT) polymer. Following up on our recent study (Binder R.; Burghardt, I. Faraday Discuss. 2020, 221, 406), multilayer multiconfiguration time-dependent Hartree calculations for a short oligothiophene segment comprising 20 monomer units (OT-20) are carried out to obtain full quantum-dynamical simulations at finite temperature. These are employed to benchmark mean-field Ehrenfest calculations, which are shown to give qualitatively correct results for the present system. Periodic boundary conditions turn out to significantly improve earlier estimates of diffusion coefficients. Using the Ehrenfest approach, a series of calculations are subsequently carried out for larger lattices (OT-40 to OT-80), leading to estimates for temperature-dependent mean-squared displacements, which are found to exhibit a near-linear dependence as a function of time. The resulting diffusion coefficient estimates are an increasing function of temperature, whose detailed functional form depends on the degree of static disorder. With a realistic static disorder parameter (σ_s ≃ 0.06 eV), the diffusion coefficients decrease from D ∼ 1 × 10^-2 cm² s^-1 to D ∼ 1 × 10^-3 cm² s^-1, in qualitative agreement with experimental data for P3HT. The dynamical scenario obtained from our simulations shows that exciton migration in P3HT-type chains is a largely adiabatic process throughout the temperature regime we investigated (i.e., T = 50-300 K). The resulting picture of exciton migration is a coherent, but not bandlike, motion of an exciton-polaron driven by fluctuations induced by low-frequency modes. This process acquires partial hopping character if static disorder becomes prominent and Anderson localization sets in.

Design Rules to Maximize Charge-Carrier Mobility along Conjugated Polymer Chains

The emergence of polymeric materials displaying high charge-carrier mobility values despite poor interchain structural order has spawned a renewal of interest in the identification of structure-property relationships pertaining to the transport of charges along conjugated polymer chains and the subsequent design of optimized architectures. Here, we present the results of intrachain charge transport simulations obtained by applying a robust surface hopping algorithm to a phenomenological Hamiltonian parametrized against first-principles simulations. Conformational effects are shown to provide a clear signature in the temperature-dependent charge-carrier mobility that complies with recent experimental observations. We further contrast against molecular crystals the evolution with electronic bandwidth and electron-phonon interactions of the room-temperature mobility in polymers, showing that intrachain charge-carrier mobility values in excess of 100 cm²/(V s) can be achieved through a proper chemical engineering of the backbones.

First-principles description of intra-chain exciton migration in an oligo(para-phenylene vinylene) chain. I. Generalized Frenkel-Holstein Hamiltonian

A generalized Frenkel-Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel-Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)].