Insights into the mechanisms of optical cavity-modified ground-state chemical reactions.

In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.

How an electrical current can stabilize a molecular nanojunction.

The stability of molecular junctions under transport is of the utmost importance for the field of molecular electronics. This question is often addressed within the paradigm of current-induced heating of nuclear degrees of freedom or current-induced forces acting upon the nuclei. At the same time, an essential characteristic of the failure of a molecular electronic device is its changing conductance - typically from a finite value for the intact device to zero for a device that lost its functionality. In this publication, we focus on the current-induced changes in the molecular conductance, which are inherent to molecular junctions at the limit of mechanical stability. We employ a numerically exact framework based on the hierarchical equations of motion approach, which treats both electronic and nuclear degrees of freedom on an equal footing and does not impose additional assumptions. Studying generic model systems for molecular junctions with dissociative potentials for a wide range of parameters spanning the adiabatic and the nonadiabatic regime, we find that molecular junctions that exhibit a decrease in conductance upon dissociation are more stable than junctions that are more conducting in their dissociated state. This represents a new mechanism that stabilizes molecular junctions under current. Moreover, we identify characteristic signatures in the current of breaking junctions related to the interplay between changes in the conductance and the nuclear configuration and show how these are related to properties of the leads rather than characteristics of the molecule itself.

Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes.

Current-induced bond rupture is a fundamental process in nanoelectronic architectures, such as molecular junctions, and scanning tunneling microscopy measurements of molecules at surfaces. The understanding of the underlying mechanisms is important for the design of molecular junctions that are stable at higher bias voltages and is a prerequisite for further developments in the field of current-induced chemistry. In this work, we analyze the mechanisms of current-induced bond rupture employing a recently developed method, which combines the hierarchical equations of motion approach in twin space with the matrix product state formalism and allows accurate, fully quantum mechanical simulations of the complex bond rupture dynamics. Extending previous work [Ke et al. J. Chem. Phys. 154, 234702 (2021)], we consider specifically the effect of multiple electronic states and multiple vibrational modes. The results obtained for a series of models of increasing complexity show the importance of vibronic coupling between different electronic states of the charged molecule, which can enhance the dissociation rate at low bias voltages profoundly.

Tree tensor network state approach for solving hierarchical equations of motion.

The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a continuous environment into a set of effective bath modes that allow for more efficient cutoff at finite temperatures. Based on this understanding, one can map the HEOM method into a Schrödinger-like equation, with a non-Hermitian super-Hamiltonian for an extended wave function being the tensor product of the central system wave function and the Fock state of these effective bath modes. In this work, we explore the possibility of representing the extended wave function as a tree tensor network state (TTNS) and the super-Hamiltonian as a tree tensor network operator of the same structure as the TTNS, as well as the application of a time propagation algorithm using the time-dependent variational principle. Our benchmark calculations based on the spin-boson model with a slow-relaxing bath show that the proposed HEOM+TTNS approach yields consistent results with those of the conventional HEOM method, while the computation is considerably sped up. In addition, the simulation with a genuine TTNS is four times faster than a one-dimensional matrix product state decomposition scheme.

Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach.

The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy experiments. In this work, we outline a fully quantum mechanical, numerically exact approach to describe chemical reaction rates in such nonequilibrium situations. The approach is based on an extension of the flux correlation function formalism to nonequilibrium conditions and uses a mixed real and imaginary time hierarchical equations of motion approach for the calculation of rate constants. As a specific example, we investigate current-induced intramolecular proton transfer reactions in a molecular junction for different applied bias voltages and molecule-lead coupling strengths.

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space.

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation [R. Borrelli, J. Chem. Phys. 150, 234102 (2019)] to nonequilibrium scenarios where the open quantum system is coupled to a hybrid fermionic and bosonic environment. The key ideas used in the extension are a reformulation of the hierarchical equations of motion for the auxiliary density matrices into a time-dependent Schrödinger-like equation for an augmented multi-dimensional wave function as well as a tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems. The performance of the method is demonstrated for a model of a molecular junction exhibiting current-induced mode-selective vibrational excitation.

Unraveling current-induced dissociation mechanisms in single-molecule junctions.

Understanding current-induced bond rupture in single-molecule junctions is both of fundamental interest and a prerequisite for the design of molecular junctions, which are stable at higher-bias voltages. In this work, we use a fully quantum mechanical method based on the hierarchical quantum master equation approach to analyze the dissociation mechanisms in molecular junctions. Considering a wide range of transport regimes, from off-resonant to resonant, non-adiabatic to adiabatic transport, and weak to strong vibronic coupling, our systematic study identifies three dissociation mechanisms. In the weak and intermediate vibronic coupling regime, the dominant dissociation mechanism is stepwise vibrational ladder climbing. For strong vibronic coupling, dissociation is induced via multi-quantum vibrational excitations triggered either by a single electronic transition at high bias voltages or by multiple electronic transitions at low biases. Furthermore, the influence of vibrational relaxation on the dissociation dynamics is analyzed and strategies for improving the stability of molecular junctions are discussed.

Effect of charge-transfer states on the vibrationally resolved absorption spectra and exciton dynamics in ZnPc aggregates: Simulations from a non-Makovian stochastic Schrödinger equation.

The vibrationally resolved absorption spectra of zinc phthalocyanine (ZnPc) aggregates (up to 70 monomers) are explored using the non-Markovian stochastic Schrödinger equation. Various types of local excitations, charge-transfer (CT) excitations, and exciton-phonon couplings are explicitly included in a comprehensive model Hamiltonian, which is parameterized by first-principles calculations. The absorption spectral simulations clarify that the two absorption bands in the Q-band region observed in experiments can be assigned to the contribution from the CT-mediated interactions, rather than the mixtures of different-type aggregates, as prevailingly assumed. Furthermore, the relative intensities of the two bands are found to be closely related to the intermolecular distance and molecular number in a ZnPc aggregate. From the investigation of the decoherence process after optical excitation, it is found that CT states can induce coherence regeneration as the time scale of charge separation is much faster than that of the vibration-induced decoherence. However, they would instead boost the decoherence process as the two time scales become comparable. The two different effects of CT states may suggest a novel way to regulate the decoherence process in excitation energy relaxation.

Non-Markovian stochastic Schrödinger equation in k-space toward the calculation of carrier dynamics in organic semiconductors.

A non-Markovian stochastic Schrödinger equation developed in our former work [Y. Ke and Y. Zhao, J. Chem. Phys. 147, 184103 (2017)] is extended to the reciprocal (k-) space to calculate the carrier dynamics in organic semiconductors with both local and nonlocal carrier-phonon interactions taken into account. The validity of this approach is examined by comparing with numerically exact benchmark results. As an application, the carrier mobilities are calculated within a one-dimensional periodic lattice model. The results reveal an inversion in the magnitude of the mobility as the nonlocal carrier-phonon interaction varies from weak to strong strengths, indicating a transition of the transport mechanism. This is also demonstrated by a variation in the temperature dependence of the mobility. In addition, a transient localization diffusive behavior caused by intramolecular vibrations is also found.

Calculations of coherent two-dimensional electronic spectra using forward and backward stochastic wavefunctions.

Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schrödinger equations in a segmented way to accurately obtain the two-dimensional (2D) electronic spectrum is presented in this paper. Based on the simple excitonically coupled dimer model system, the validity and efficiency of the proposed schemes are demonstrated in detail, along with the comparison against the deterministic hierarchy equations of motion and perturbative second-order time-convolutionless quantum master equations. In addition, an important insight is provided in this paper that the characteristic frequency of the overdamped environment is an extremely crucial factor to regulate the lifetimes of the oscillating signals in 2D electronic spectra and of quantum coherence features of system dynamics. It is worth noting that the proposed scheme benefiting from its stochastic nature and wavefunction framework and many other advantages of substantially reducing the numerical cost has a great potential to systematically investigate various quantum effects observed in realistic large-scale natural and artificial photosynthetic systems.

Perturbation expansions of stochastic wavefunctions for open quantum systems.

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions.

A traditional stochastic hierarchy equations of motion method is extended into the correlated real-time and imaginary-time propagations, in this paper, for its applications in calculating the equilibrium correlation functions. The central idea is based on a combined employment of stochastic unravelling and hierarchical techniques for the temperature-dependent and temperature-free parts of the influence functional, respectively, in the path integral formalism of the open quantum systems coupled to a harmonic bath. The feasibility and validity of the proposed method are justified in the emission spectra of homodimer compared to those obtained through the deterministic hierarchy equations of motion. Besides, it is interesting to find that the complex noises generated from a small portion of real-time and imaginary-time cross terms can be safely dropped to produce the stable and accurate position and flux correlation functions in a broad parameter regime.

Hierarchy of stochastic Schrödinger equation towards the calculation of absorption and circular dichroism spectra.

A theoretically solid and numerically exact method is presented for the calculation of absorption and circular dichroism (CD) spectra of molecular aggregates immersed in a harmonic bath constituted as the combination of some prominent quantized vibrational modes and continuous overdamped Brownian oscillators. The feasibility and the validity of newly proposed method are affirmed in the analytical monomer spectra. To go beyond the independent local bath approximation, all the correlations of site energy fluctuations and excitonic coupling fluctuations are included in our strategy, and their influence on the absorption and CD spectra is investigated based on the Frenkel exciton model of homodimer. In the end, a good fit of the absorption and part of CD spectra for the entire B800-B850 ring in the light-harvesting complexes 2 of purple bacteria to the experimental data is given, and the simulation results suggest that the asymmetry in the 800 nm region of CD spectra is actually an indication of B800-B850 inter-ring coupling.

Hierarchy of forward-backward stochastic Schrödinger equation.

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

Visualization of Hot Exciton Energy Relaxation from Coherent to Diffusive Regimes in Conjugated Polymers: A Theoretical Analysis.

The unified coherent-to-diffusive energy relaxation of hot exciton in organic aggregates or polymers, which still remains largely unclear and is also a great challenge theoretically, is investigated from a time-dependent wavepacket diffusive approach. The results demonstrate that in the multiple time scale energy relaxation dynamics, the fast relaxation time essentially corresponds to the dephasing time of excitonic coherence motion, whereas the slow time is related to a hopping migration, and a suggested kinetic model successfully connects these two processes. The dependencies of those times on the initial energy and delocalization of exciton wavepacket as well as exciton-phonon interactions are further analyzed. The proposed method together with quantum chemistry calculations has explained an experimental observation of hot exciton energy relaxation in the low-bandgap copolymer PBDTTPD.