High accuracy exponential decomposition of bath correlation functions for arbitrary and structured spectral densities: Emerging methodologies and new approaches.

This study investigates the decomposition of bath correlation functions (BCFs) in terms of complex exponential functions, with an eye on the realistic modeling of open quantum systems based on the hierarchical equations of motion. We introduce the theoretical background of various decomposition schemes in both time and frequency domains and assess their efficiency and accuracy by demonstrating the decomposition of various BCFs. We further develop a new procedure for the decomposition of BCFs originating from highly structured spectral densities with a high accuracy and compare it with existing fitting techniques. Advantages and disadvantages of each methodology are discussed in detail with special attention to their application to the corresponding quantum dynamical problem. This work provides fundamental tools for choosing and using a variety of decomposition techniques of BCFs for the study of open quantum systems in structured environments.

Intramolecular singlet fission: Quantum dynamical simulations including the effect of the laser field.

In the previous work [Reddy et al., J. Chem. Phys. 151, 044307 (2019)], we have analyzed the dynamics of the intramolecular singlet fission process in a series of prototypical pentacene-based dimers, where the pentacene monomers are covalently bonded to a phenylene linker in ortho, meta, and para positions. The results obtained were qualitatively consistent with the experimental data available, showing an ultrafast population of the multiexcitonic state that mainly takes place via a mediated (superexchange-like) mechanism involving charge transfer and doubly excited states. Our results also highlighted the instrumental role of molecular vibrations in the process as a sizable population of the multiexcitonic state could only be obtained through vibronic coupling. Here, we extend these studies and investigate the effect of the laser field on the dynamics of intramolecular singlet fission by explicitly including the coupling to the laser field in our model. In this manner, and by selectively tuning the laser field to the different low-lying absorption bands of the systems investigated, we analyze the wavelength dependence of the intramolecular singlet fission process. In addition, we have also analyzed how the nature of the initially photoexcited electronic state (either localized or delocalized) affects its dynamics. Altogether, our results provide new insights into the design of intramolecular singlet fission-active molecules.

Nonadiabatic dynamics of molecules interacting with metal surfaces: A quantum-classical approach based on Langevin dynamics and the hierarchical equations of motion.

A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum-classical methods based on Langevin equations to models containing strong electron-electron or quantum electronic-vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule-metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions.

Protein charge transfer far from equilibrium: a theoretical perspective.

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

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.

Strong signature of electron-vibration coupling in molecules on Ag(111) triggered by tip-gated discharging.

Electron-vibration coupling is of critical importance for the development of molecular electronics, spintronics, and quantum technologies, as it affects transport properties and spin dynamics. The control over charge-state transitions and subsequent molecular vibrations using scanning tunneling microscopy typically requires the use of a decoupling layer. Here we show the vibronic excitations of tetrabromotetraazapyrene (TBTAP) molecules directly adsorbed on Ag(111) into an orientational glassy phase. The electron-deficient TBTAP is singly-occupied by an electron donated from the substrate, resulting in a spin 1/2 state, which is confirmed by a Kondo resonance. The TBTAP•- discharge is controlled by tip-gating and leads to a series of peaks in scanning tunneling spectroscopy. These occurrences are explained by combining a double-barrier tunneling junction with a Franck-Condon model including molecular vibrational modes. This work demonstrates that suitable precursor design enables gate-dependent vibrational excitations of molecules on a metal, thereby providing a method to investigate electron-vibration coupling in molecular assemblies without a decoupling layer.

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.

Incoherent nonadiabatic to coherent adiabatic transition of electron transfer in colloidal quantum dot molecules.

Electron transfer is a fundamental process in chemistry, biology, and physics. One of the most intriguing questions concerns the realization of the transitions between nonadiabatic and adiabatic regimes of electron transfer. Using colloidal quantum dot molecules, we computationally demonstrate how the hybridization energy (electronic coupling) can be tuned by changing the neck dimensions and/or the quantum dot sizes. This provides a handle to tune the electron transfer from the incoherent nonadiabatic regime to the coherent adiabatic regime in a single system. We develop an atomistic model to account for several states and couplings to the lattice vibrations and utilize the mean-field mixed quantum-classical method to describe the charge transfer dynamics. Here, we show that charge transfer rates increase by several orders of magnitude as the system is driven to the coherent, adiabatic limit, even at elevated temperatures, and delineate the inter-dot and torsional acoustic modes that couple most strongly to the charge transfer dynamics.

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.

Parallel versus Twisted Pentacenes: Conformational Impact on Singlet Fission.

We placed two pentacene chromophores at the termini of a diacetylene linker to investigate the impact of excitation wavelength, conformational flexibility, and vibronic coupling on singlet fission. Photoexcitation of the low-energy absorption results in a superposed mixture of states, which transform on an ultrafast time-scale into a spin-correlated and vibronically coupled/hot delocalized triplet pair 1(T1T1)deloc. Regardless of temperature, the lifetime for 1(T1T1)deloc is less than 2 ps. In contrast, photoexcitation of the high-energy absorption results in the formation of 1(T1T1)deloc lasting 1.0 ps, which then decays at room temperature within 4 ps via triplet-triplet annihilation. Lowering the temperature enables 1(T1T1)deloc to delocalize and vibronically decouple, in turn affording 1(T1T1)loc. In addition, our results suggest that the quasi-free rotation at the diacetylene spacer may lead to twisted conformations with very low SF quantum yields, highlighting the need of controlling this structural aspect in the design of new singlet fission active molecules.

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.

Theory of Chirality Induced Spin Selectivity: Progress and Challenges.

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.

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.

Quantum dynamical simulation of intramolecular singlet fission in covalently coupled pentacene dimers.

We analyze the dynamics of intramolecular singlet fission in a series of pentacene-based dimers consisting of two pentacene-like chromophores covalently bonded to a phenylene linker in ortho, meta, and para positions. The study uses a quantum dynamical approach that employs a model vibronic Hamiltonian whose parameters are obtained using multireference perturbation theory methods. The results highlight the different role of the direct and mediated mechanism in these systems, showing that the population of the multiexcitonic state, corresponding to the first step of the intramolecular singlet fission process, occurs mainly through a superexchange-like mechanism involving doubly excited or charge transfer states that participate in the process in a virtual way. In addition, the systems investigated provide insight into the roles that built-in geometrical constraints and the electronic structure of the spacer play in the intramolecular singlet fission process.

On the memory kernel and the reduced system propagator.

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables, thus streamlining the use of numerically exact solvers for calculating the memory kernel. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations.

We investigate the dynamics of intramolecular singlet fission in a dimer consisting of two pentacene-based chromophores covalently bonded to a phenylene spacer using an approach that combines high-level ab initio multireference perturbation theory methods and quantum dynamical simulations. The results show that the population of the multiexcitonic state, corresponding to the first step of singlet fission, is facilitated by the existence of higher-lying doubly excited and charge transfer states that participate in a superexchange-like way. The important role played by high-frequency ring-breathing molecular vibrations in the process is also discussed.

High-Voltage-Assisted Mechanical Stabilization of Single-Molecule Junctions.

Resonant tunneling is an efficient mechanism for charge transport through nanoscale conductance junctions due to the relatively high currents involved. However, continuous charging and discharging cycles of the nanoconductor during resonant tunneling often lead to mechanical instability. The realization of efficient nanoscale electronic components therefore depends to a large extent on the ability to mechanically stabilize them during resonant transport. In this work, we focus on single-molecule junctions, demonstrating that their mechanical stability during resonant transport can be increased by increasing the bias voltage. This counter-intuitive effect is attributed to the energy dependence of the molecule-lead coupling densities, which promote the rate of transport-induced cooling of molecular vibrations at higher voltages. The required energy dependence is characteristic of realistic electrodes (such as graphene), which cannot be modeled within the commonly invoked wide-band approximation. Our research provides new guidelines for the design of mechanically stable molecular devices operating in the regime of resonant charge transport and demonstrates these guidelines while considering realistic features of single-molecule junctions.

A broadened classical master equation approach for treating electron-nuclear coupling in non-equilibrium transport.

We extend the broadened classical master equation (bCME) approach [W. Dou and J. E. Subotnik, J. Chem. Phys. 144, 024116 (2016)] to the case of two electrodes, such that we may now calculate non-equilibrium transport properties when molecules come near metal surfaces and there is both strong electron-nuclear and strong metal-molecule coupling. By comparing against a numerically exact solution, we show that the bCME usually works very well, provided that the temperature is high enough that a classical treatment of nuclear motion is valid. Finally, in the low temperature (quantum) regime, we suggest a means to incorporate broadening effects in the quantum master equation (QME). This bQME works well for fairly low temperatures.

Perspective: Theory of quantum transport in molecular junctions.

Molecular junctions, where single molecules are bound to metal or semiconductor electrodes, represent a unique architecture to investigate molecules in a distinct nonequilibrium situation and, in a broader context, to study basic mechanisms of charge and energy transport in a many-body quantum system at the nanoscale. Experimental studies of molecular junctions have revealed a wealth of interesting transport phenomena, the understanding of which necessitates theoretical modeling. The accurate theoretical description of quantum transport in molecular junctions is challenging because it requires methods that are capable to describe the electronic structure and dynamics of molecules in a condensed phase environment out of equilibrium, in some cases with strong electron-electron and/or electronic-vibrational interaction. This perspective discusses recent progress in the theory and simulation of quantum transport in molecular junctions. Furthermore, challenges are identified, which appear crucial to achieve a comprehensive and quantitative understanding of transport in these systems.