Dynamics of a one-dimensional Holstein polaron: The multiconfigurational Ehrenfest method

Full wave function cloning for improving convergence of the multiconfigurational Ehrenfest method: Tests in the zero-temperature spin-boson model regime

In this paper, we report a new algorithm for creating an adaptive basis set in the Multiconfigurational Ehrenfest (MCE) method, which is termed Full Cloning (FC), and test it together with the existing Multiple Cloning (MC) using the spin-boson model at zero-temperature as a benchmark. The zero-temperature spin-boson regime is a common hurdle in the development of methods that seek to model quantum dynamics. Two versions of MCE exist. We demonstrate that MC is vital for the convergence of MCE version 2 (MCEv2). The first version (MCEv1) converges much better than MCEv2, but FC improves its convergence in a few cases where it is hard to converge it with the help of a reasonably small size of the basis set.

Finite temperature dynamics in a polarized sub-Ohmic heat bath: A hierarchical equations of motion-tensor train study

The dynamics of the sub-Ohmic spin-boson model under polarized initial conditions at finite temperatures is investigated by employing both analytical tools and the numerically accurate hierarchical equations of motion-tensor train method. By analyzing the features of nonequilibrium dynamics, we discovered a bifurcation phenomenon, which separates two regimes of the dynamics. It is found that before the bifurcation time, increasing temperature slows down the population dynamics, while the opposite effect occurs after the bifurcation time. The dynamics is highly sensitive to both initial preparation of the bath and thermal effects.

Consistent Construction of the Density Matrix from Surface Hopping Trajectories

Proper construction of the density matrix based on surface hopping trajectories remains a difficult problem. Due to the well-known overcoherence in traditional surface hopping simulations, the electronic wave function cannot be used directly. In this work, we propose a consistent density matrix construction method, which takes the advantage of occupation of active states to rescale the coherence calculated by wave functions and ensures the intrinsic consistency of the density matrix. This new trajectory analysis method can be used for both Tully's fewest switches surface hopping (FSSH) and our recently proposed branching corrected surface hopping (BCSH). As benchmarked in both one- and two-dimensional standard scattering models, the new approach combined with BCSH trajectories achieves highly accurate time-dependent spatial distributions of adiabatic populations and coherence compared to exact quantum results.

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.

Simulating optical linear absorption for mesoscale molecular aggregates: An adaptive hierarchy of pure states approach

In this paper, we present dyadic adaptive HOPS (DadHOPS), a new method for calculating linear absorption spectra for large molecular aggregates. This method combines the adaptive HOPS (adHOPS) framework, which uses locality to improve computational scaling, with the dyadic HOPS method previously developed to calculate linear and nonlinear spectroscopic signals. To construct a local representation of dyadic HOPS, we introduce an initial state decomposition that reconstructs the linear absorption spectra from a sum over locally excited initial conditions. We demonstrate the sum over initial conditions can be efficiently Monte Carlo sampled and that the corresponding calculations achieve size-invariant [i.e., O(1)] scaling for sufficiently large aggregates while trivially incorporating static disorder in the Hamiltonian. We present calculations on the photosystem I core complex to explore the behavior of the initial state decomposition in complex molecular aggregates as well as proof-of-concept DadHOPS calculations on an artificial molecular aggregate inspired by perylene bis-imide to demonstrate the size-invariance of the method.

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.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Accurate Simulation of Spectroscopic Signatures of Cavity-Assisted, Conical-Intersection-Controlled Singlet Fission Processes

A numerically accurate, fully quantum methodology has been developed for the simulation of the dynamics and nonlinear spectroscopic signals of cavity-assisted, conical-intersection-controlled singlet fission systems. The methodology is capable of handling several molecular systems strongly coupled to the photonic mode of the cavity and treats the intrinsic conical intersection and cavity-induced polaritonic conical intersections in a numerically exact manner. Contributions of higher-lying molecular electronic states are accounted for comprehensively. The intriguing process of cavity-modified fission dynamics, including all of its electronic, vibrational, and photonic degrees of freedom, together with its two-dimensional spectroscopic manifestation, is simulated for two rubrene dimers strongly coupled to the cavity mode.

Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach

Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.

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...

Efficient quantum dynamics simulations of complex molecular systems: A unified treatment of dynamic and static disorder

We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.

Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach

We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures.

Vibration-mediated resonant charge separation across the donor-acceptor interface in an organic photovoltaic device

Examination of a recent open-system Ehrenfest dynamics simulation suggests that a vibration-mediate resonance may play a pivotal role in the charge transfer across a donor-acceptor interface in an organic solar cell. Based on this, a concise dissipative two-level electronic system coupled to a molecular vibrational mode is proposed and solved quantum mechanically. It is found that the charge transfer is enhanced substantially when the vibrational energy quanta is equal to the electronic energy loss across the interface. This vibration-mediate resonant charge transfer process is ultrafast, occurring within 100 fs, comparable to experimental findings. The open-system Ehrenfest dynamics simulation of the two-level model is carried out, and similar results are obtained, which confirms further that the earlier open-system Ehrenfest dynamics simulation indeed correctly predicted the occurrence of the resonant charge transfer across the donor-acceptor interface.

Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.

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.