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The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier’s law. At molecular length scales, however, deviations from Fourier’s law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system’s thermal conductance commonly deviates from Fourier’s law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually contains some levels of perturbation theory, but under strong coupling conditions, other approximations are used. A common approximation is the 1-exciton model in which processes involving weak excitations are described using a basis comprising the ground state and singly excited states of the molecule cavity-mode system. In another frequently used approximation in numerical investigations, the electromagnetic field is described classically, and the quantum molecular subsystem is treated in the mean-field Hartree approximation with its wavefunction assumed to be a product of single molecules’ wavefunctions. The former disregards states that take long time to populate and is, therefore, essentially a short time approximation. The latter is not limited in this way, but by its nature, disregards some intermolecular and molecule-field correlations. In this work, we directly compare results obtained from these approximations when applied to several prototype problems involving the optical response of molecules-in-optical cavities systems. In particular, we show that our recent model investigation [J. Chem. Phys. 157, 114108 (2022)] of the interplay between the electronic strong coupling and molecular nuclear dynamics using the truncated 1-exciton approximation agrees very well with the semiclassical mean-field calculation.

As in the case of a free particle, the initial growth of a broad (relative to lattice spacing) wavepacket placed on an ordered lattice is slow (its time derivative has zero initial slope), and the spread (root mean square displacement) becomes linear in t at a long time. On a disordered lattice, the growth is inhibited for a long time (Anderson localization). We consider site disorder with nearest-neighbor hopping on one- and two-dimensional systems and show via numerical simulations supported by the analytical study that the short time growth of the particle distribution is faster on the disordered lattice than on the ordered one. Such faster spread takes place on time and length scales that may be relevant to the exciton motion in disordered systems.

We determine the zero-frequency charge current noise in a metal-molecule-metal junction embedded in a thermal environment, e.g., a solvent, dominated by sequential charge transmission described by a classical master equation, and study its dependence of specific model parameters, i.e., the environmental reorganization energy and relaxation behavior. Interestingly, the classical current noise term has the same structure as its quantum analog which reflects a charge correlation due to the bridging molecule. We further determine the thermodynamic uncertainty relation (TUR) which defines a bound on the relationship between the average charge current, its fluctuation and the entropy production in an electrochemical junction in the Marcus regime. In a second part, we use the same methodology to calculate the current noise and the TUR for a protoype photovoltaic cell in order to predict its upper bound for the efficiency of energy conversion into useful work., (in press)

We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell–Schrödinger equations with molecular rovibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissociation slowdown at polaritonic frequencies is proposed.

Controlling molecular spectroscopy and even chemical behavior in a cavity environment is a subject of intense experimental and theoretical interest. In Fabry-Pérot cavities, strong (radiation-matter) coupling phenomena without an intense radiation field often rely on the number of chromophore molecules collectively interacting with a cavity mode. For plasmonic cavities, the cavity field-matter coupling can be strong enough to manifest strong coupling involving even a single molecule. To this end, infrared plasmonic cavities can be particularly useful in understanding vibrational strong coupling. Here we present a procedure for estimating the radiation-matter coupling and, equivalently, the mode volume as well as the mode lifetime and quality factor for plasmonic cavities of arbitrary shapes and use it to estimate these quantities for infrared cavities of two particularly relevant geometries comprising several n-doped semiconductors. Our calculations demonstrate very high field confinement and low mode volumes of these cavities despite having relatively low quality factors, which is often the case for plasmonic cavities.

The interaction between excited states of a molecule and excited states of metal nanostructure (e.g. plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when $2|U|/{\hbar\Gamma}>1$, where $U$ and ${\Gamma}$ are the molecule-plasmon coupling and the spectral width of the optical transition respectively. Because both $U$ and ${\Gamma}$ strongly increase with decreasing distance between a molecule and a plasmonic structure it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work we investigate the behavior of $U$ and ${\Gamma}$ for several geometries. Surprisingly, we find that if the only contributions to ${\Gamma}$ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion $2|U|/{\hbar\Gamma}>1$ is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.

In standard molecular junctions, a molecular structure is placed between and connected to metal leads. Understanding how mechanical tuning in such molecular junctions can change heat conductance has interesting applications in nanoscale energy transport. In this work, we use nonequilibrium molecular dynamics simulations to address the effect of stretching on the phononic contribution to the heat conduction of molecular junctions consisting of single long-chain alkanes and various metal leads such as Ag, Au, Cu, Ni, and Pt. The thermal conductance of such junctions is found to be much smaller than the intrinsic thermal conductance of the polymer and significantly depends on the nature of metal leads as expressed by the metal-molecule coupling and metal vibrational density of states. This behavior is expected and reflects the mismatch of phonon spectra at the metal molecule interfaces. As a function of stretching, we find a behavior similar to what was observed earlier [J. Chem. Phys. 153, 164903 (2020)] for pure polymeric structures. At relatively short electrode distances, where the polyethylene chains are compressed, it is found that the thermal conductances of the molecular junctions remain almost constant as one stretches the polymer chains. At critical electrode distances, the thermal conductances start to increase, reaching the values of the fully-extended molecular junctions. Similar behaviors are observed for junctions in which several long-chain alkanes are sandwiched between various metal leads. These findings indicate that this behavior under stretching is an intrinsic property of the polymer chain and not significantly associated with the interfacial structures., 23 pages, 7 figures, 3 tables

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostatted ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that, as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic linewidths roughly by a factor of two. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside versus outside the cavity. This result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored., manuscript (18 pages) + supporting information (8 pages)

We simulate vibrational strong coupling (VSC) and vibrational ultrastrong coupling (V-USC) for liquid water with classical molecular dynamics simulations. When the cavity modes are resonantly coupled to the O−H stretch mode of liquid water, the infrared spectrum shows asymmetric Rabi splitting. The lower polariton (LP) may be suppressed or enhanced relative to the upper polariton (UP) depending on the frequency of the cavity mode. Moreover, although the static properties and the translational diffusion of water are not changed under VSC or V-USC, we do find the modification of the orientational autocorrelation function of H(2)O molecules especially under V-USC, which could play a role in ground-state chemistry.

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.

We consider a molecular junction immersed in a solvent where the electron transfer is dominated by Marcus-type steps. However, the successive nature of the charge transfer through the junction does not imply that the solvent reaches thermal equilibrium throughout the transport. In our previous work [Kirchberg et al., J. Phys. Chem. Lett. 11, 1729 (2020)], we have determined the nonequilibrium distribution of the solvent where its dynamics, expressed by a friction, is considered in two limiting regimes of fast and slow solvent relaxation. In dependence of the nonequilibrium solvent dynamics, we investigate now the electrical, thermal, and thermoelectric properties of the molecular junction. We show that by suitable tuning of the friction, we can reduce the heat dissipation into the solvent and enhance the heat transfer between the electrodes. Interestingly, we find that the Seebeck coefficient grows significantly by adapting the solvent friction in both regimes.

The interplay between static and dynamic disorder and collective optical response in molecular ensembles is an important characteristic of nanoplasmonic and nanophotonic molecular systems. Here we investigate the cooperative superradiant response of a molecular ensemble of quantum emitters under the influence of environmental disorder, including inhomogeneous broadening (as induced by static random distribution of the molecular transition frequencies) and motional narrowing (as induced by stochastic modulation of these excitation energies). The effect of inhomogeneous broadening is to destroy the coherence of the collective molecular excitation and suppress superradiant emission. However, fast stochastic modulation of the molecular excitation energy can effectively restore the coherence of the quantum emitters and lead to a recovery of superradiant emission, which is an unexpected manifestation of motional narrowing. For a light scattering process as induced by an off-resonant incident pulse, stochastic modulation leads to inelastic fluorescence emission at the average excitation energy at long times and suggests that dynamic disorder effects can actually lead to collective excitation of the molecular ensemble.

Nonequilibrium thermodynamics of the driven resonant-level model is studied using numerical simulations based on the driven Liouville von-Neumann formalism. The approach is first validated against recently obtained analytical results for quasistatic level shifts and the corresponding first-order corrections. The numerical approach is then used to study far-from-equilibrium thermodynamic properties of the system under finite level shift rates. The proposed methodology allows the study of unexplored nonequilibrium thermodynamic regimes in open quantum systems.

Zigzag edges in graphitic systems exhibit localized electronic states that drastically affect their properties. Here, room-temperature charge transport experiments across a single graphitic interface are reported, in which the interlayer current is confined to the contact edges. It is shown that the current exhibits pronounced oscillations of up to ≈40 µA with a dominant period of ≈5 Å with respect to lateral displacement that do not directly correspond to typical graphene lattice spacing. The origin of these features is computationally rationalized as quantum mechanical interference of localized edge states showing significant amplitude and interlayer coupling variations as a function of the interface stacking configuration. Such interference effects may therefore dominate the transport properties of low-dimensional graphitic interfaces.

Chemical manifestations of strong light–matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light–matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light–matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor.

Methodological aspects of using the driven Liouville-von Neumann (DLvN) approach for simulating dynamical properties of molecular junctions are discussed. As a model system we consider a non-interacting resonant level uniformly coupled to a single Fermionic bath. We demonstrate how a finite system can mimic the depopulation dynamics of the dot into an infinite band bath of continuous and uniform density of states. We further show how the effects of spurious energy resolved currents, appearing due to the approximate nature of the equilibrium state obtained in DLvN calculations, can be avoided. Several ways to approach the wide band limit that is often adopted in analytical treatments, using a finite numerical model system are discussed including brute-force increase of the lead model bandwidth as well as efficient cancellation or direct subtraction of finite-bandwidth effect. These methodological considerations may be relevant also for other numerical schemes that aim to study non-equilibrium thermodynamics via simulations of open quantum systems., 30 pages, 6 figures

For a small fraction of hot CO2 molecules immersed in a liquid-phase CO2 thermal bath, classical cavity molecular dynamics simulations show that forming collective vibrational strong coupling (VSC) between the C=O asymmetric stretch of CO2 molecules and a cavity mode accelerates hot-molecule relaxation. The physical mechanism underlying this acceleration is the fact that polaritons, especially the lower polariton, can be transiently excited during the nonequilibrium process, which facilitates intermolecular vibrational energy transfer. The VSC effects on these rates (i) resonantly depend on the cavity mode detuning, (ii) cooperatively depend on molecular concentration or Rabi splitting, and (iii) collectively scale with the number of hot molecules, which is similar to Dicke's superradiance. For larger cavity volumes, due to a balance between this superradiant-like behavior and a smaller light-matter coupling, the total VSC effect on relaxation rates can scale slower than $1/N$, and the average VSC effect per molecule can remain meaningful for up to $N \sim10^4$ molecules forming VSC. Moreover, we find that the transiently excited lower polariton prefers to relax by transferring its energy to the tail of the molecular energy distribution rather than equally distributing it to all thermal molecules. Finally, we highlight the similarities of parameter dependence between the current finding with VSC catalysis observed in Fabry-Perot microcavities., Comment: 10 pages, 7 figures

Selectively exciting target molecules to high vibrational states is inefficient in the liquid phase, which restricts the use of IR pumping to catalyze ground-state chemical reactions. Here, we demonstrate that this inefficiency can sometimes be solved by confining the liquid to an optical cavity under vibrational strong coupling conditions. For a liquid solution of 13CO2 solute in a 12CO2 solvent, cavity molecular dynamics simulations show that exciting a polariton (hybrid light-matter state) of the solvent with an intense laser pulse, under suitable resonant conditions, may lead to a very strong (> 3 quanta) and ultrafast (< 1 ps) excitation of the solute, even though the solvent ends up being barely excited. By contrast, outside a cavity the same input pulse fluence can excite the solute by only half a vibrational quantum and the selectivity of excitation is low. Our finding is robust under different cavity volumes, which may lead to observable cavity enhancement on IR photochemical reactions in Fabry-Pérot cavities., 10 pages of manuscript + 23 pages of SI

We present a consistent theory of energy balance and conversion in a single-molecule junction with strong interactions between electrons on the molecular linker (dot) and phonons in the nuclear environment where the Marcus-type electron hopping processes predominate in the electron transport. It is shown that the environmental reorganization and relaxation that accompany electron hopping energy exchange between the electrodes and the nuclear (molecular and solvent) environment may bring a moderate local cooling of the latter in biased systems. The effect of a periodically driven dot level on the heat transport and power generated in the system is analyzed, and energy conservation is demonstrated both within and beyond the quasistatic regime. Finally, a simple model of atomic scale engine based on a Marcus single-molecule junction with a driven electron level is suggested and discussed.

Molecular conduction operating in dielectric solvent environments is often described using kinetic rates based on the Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer in such a system implies that the solvent does not necessarily reach equilibrium in such processes. Here we generalize the theory to account for solvent nonequilibrium and consider a molecular junction consisting of an electronic donor-acceptor system coupled to two metallic electrodes and placed in a polarizable solvent. We determine the nonequilbrium distribution of the solvent by solving diffusion equations in the strong- and weak-friction limits and calculate the charge current and its fluctuating behavior. In extreme limits, the absence of the solvent or fast solvent relaxation, the charge-transfer statistics is Poissonian, while it becomes correlated by the dynamic solvent between these limits. A Kramers-like turnover of the nonequilibrium current as a function of the solvent damping is found. Finally, we propose a way to tune the solvent-induced damping using geometrical control of the solvent dielectric response in nanostructured solvent channels.

The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant origin of energy conversion in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear temperature dependence of their ratio as expressed in the standard WF law is replaced by a linear dependence on the nuclear reorganization energy associated with the electron hopping process. The robustness of the molecular WF relation is confirmed by examining the conductance properties of a paradigmatic molecular junction. This result opens a new way to analyze conductivity in molecular systems, with possible applications advancing the design of molecular technologies that derive their function from electrical and/or thermal conductance.

Recent experiments suggest that vibrational strong coupling (VSC) may significantly modify ground-state chemical reactions and their rates even without external pumping. The intrinsic mechanism of this "vacuum-field catalysis" remains largely unclear. Generally, modifications of thermal reactions in the ground electronic states can be caused by equilibrium or non-equilibrium effects. The former are associated with modifications of the reactant equilibrium distribution as expressed by the transition state theory of chemical reaction rates, while the latter stem from the dynamics of reaching and leaving transition state configurations. Here, we examine how VSC can affect chemical reactions rates in a cavity environment according to transition state theory. Our approach is to examine the effect of coupling to cavity mode(s) on the potential of mean force (PMF) associated with the reaction coordinate. Within the context of classical nuclei and classical photons and also assuming no charge overlap between molecules, we find that while the PMF can be affected by the cavity environment, this effect is negligible for the usual micron-length cavities used to examine VSC situations.

Recent experiments have observed that the chemical and photophysical properties of molecules can be modified inside an optical Fabry-Perot microcavity under collective vibrational strong coupling (VSC) conditions, and such modification is currently not well understood by theory. In an effort to understand the origin of such cavity induced phenomena, some recent studies have focused on the effect of the cavity environment on the nonlinear optical response of the molecular subsystem. Here, we use a recently proposed protocol for classical cavity molecular dynamics (CavMD) simulations to numerically investigate the linear and nonlinear response of liquid carbon dioxide under such VSC conditions following an optical pulse excitation. We find that applying a strong pulse of excitation to the lower hybrid light-matter state, i.e., the lower polariton (LP), can lead to an overall molecular nonlinear absorption which is enhanced by up to two orders of magnitude relative to the excitation outside the cavity. This polariton-enhanced multiphoton absorption also causes an ultrashort LP lifetime (0.2 ps) under strong illumination. Unlike usual polariton relaxation processes -- whereby polaritonic energy transfers directly to the manifold of singly excited vibrational dark states -- under the present mechanism, the LP transfers energy directly to the manifold of higher vibrationally excited dark states; these highly excited dark states subsequently relax to the manifold of singly excited states with a lifetime of tens of ps. Because the present mechanism is generic in nature, we expect these numerical predictions to be experimentally observed in different molecular systems and in cavities with different volumes.

The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions for the rate constant and the electronic contribution to a heat transfer mechanism which is induced by the temperature gradient between molecule and metal are constructed. The system of coupled dynamical equations describing the electronic and thermal currents are derived and examined over diverse ranges of reaction geometries and temperature gradients. It is shown that electron transfer across the molecule-metal interface is associated with heat transfer and that the electron exchange between metal and molecule makes a distinct contribution to the interfacial heat conduction even when the net electronic current vanishes.

The physics of collective optical response of molecular assemblies, pioneered by Dicke in 1954, has long been at the center of theoretical and experimental scrutiny. The influence of the environment on such phenomena is also of great interest due to various important applications in, e.g., energy conversion devices. In this Letter, we demonstrate both experimentally and theoretically the spatial modulations of the collective decay rates of molecules placed in proximity to a metal interface. We show in a very simple framework how the cooperative optical response can be analyzed in terms of intermolecular correlations causing interference between the response of different molecules and the polarization induced on a nearby metallic boundary and predict similar collective interference phenomena in excitation energy transfer between molecular aggregates.

We investigate detailed balance for a quantum system interacting with thermal radiation within mixed quantum-classical theory. For a two-level system coupled to classical radiation fields, three semiclassical methods are benchmarked: (1) Ehrenfest dynamics overestimate the excited-state population at equilibrium due to the failure of capturing vacuum fluctuations. (2) The coupled Maxwell-Bloch equations, which supplement Ehrenfest dynamics by damping at the full golden rule rate, underestimate the excited state population due to double-counting of the self-interaction effect. (3) $\mathrm{Ehrenfest}+\mathrm{R}$ dynamics recover detailed balance and the correct thermal equilibrium by enforcing the correct balance between the optical excitation and spontaneous emission of the quantum system. These results highlight the fact that, when properly designed, mixed quantum-classical electrodynamics can simulate thermal equilibrium in the field of nanoplasmonics.

We re-investigate the famous Mollow triplet and show that most of the well-known quantum characteristics of the Mollow triplet--including incoherent emission and a non-standard dependence of the sidebands on detuning--can be recovered quantitatively using semiclassical dynamics with a classical light field. In fact, by not relying on the rotating wave approximation, a semiclassical model predicts some quantum effects beyond the quantum optical Bloch equation, including higher order scattering and asymmetric sideband features. This letter highlights the fact that, with strong intensities, many putatively quantum features of light-matter interactions arise from a simple balance of mean-field electrodynamics and elementary spontaneous emission which requires minimal computational cost. Our results suggest that the application of semiclassical electrodynamics to problems with strong light-matter coupling in the fields of nanophotonics and superradiance are likely to yield a plethora of new information., 3 figures

The dynamics of an electronic system interacting with an electromagnetic field is investigated within mixed quantum–classical theory. Beyond the classical path approximation (where we ignore all feedback from the electronic system on the photon field), we consider all electron–photon interactions explicitly according to Ehrenfest (i.e., mean-field) dynamics and a set of coupled Maxwell–Liouville equations. Because Ehrenfest dynamics cannot capture certain quantum features of the photon field correctly, we propose a new Ehrenfest+R method that can recover (by construction) spontaneous emission while also distinguishing between electromagnetic fluctuations and coherent emission.

Semiclassical electrodynamics is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting different molecules plus a classical transverse E-field; we will call this Hamiltonian #I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body E-field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian #II. Moreover, one can also mix these two Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a pair of identical two-level systems (TLSs) undergoing either resonance energy transfer (RET) or collectively driven dynamics. While all approaches perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions. Each method has its own distinct problems: Hamiltonian #I performs best for RET but behaves in a complicated manner for driven dynamics. Hamiltonian #II is always stable, but obviously fails for RET at short distances. One key finding is that, under externally driving, a full configuration interaction description of Hamiltonian #I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field treatment., Comment: 17 pages, 7 figures

The low thermal conductance of polymers is one of the major drawbacks for many polymer-based products. However, a single polymer chain when stretched can have high thermal conductivities. We use non-equilibrium molecular dynamics simulations to study the steady-state thermal conductance along finite macromolecules under mechanical control of the end-to-end distance. We find that the nature of heat transport along such chains strongly depends on mechanical tuning, leading to significantly different heat conductions and temperature profiles along the chain in the compressed-chain and stretched-chain limits. This transition between modes of behaviors appears to be a threshold phenomenon: at relatively small end-to-end distances, the thermal conductance remains almost constant as one stretches the polymer chain. At given critical end-to-end distances, thermal conductances start to increase, reaching the fully extended chain values. Correlated with this behavior are two observations: first, the temperature bias falls mostly at contacts in the fully stretched chain, while part of it falls along the molecule in the compressed limit. Second, the heat conduction does not change significantly with the chain length in the stretched-chain limit but decreases dramatically when this length increases in the compressed molecule. This suggests that heat transfer along stretched chains is mostly ballistic, while in the compressed chain, heat is transferred by diffusive mechanisms. Significantly, these trends persist also for a large range of molecular structures and force fields, and the changing behavior correlates well with mode localization properties. Similar studies conducted with disordered chains and bundles of several chains show remnants of the same behavior.

Understanding phononic heat transport processes in molecular junctions is a central issue in the developing field of nanoscale heat conduction. Here, we present a Langevin dynamics simulation framework to investigate heat transport processes in molecular junctions at and beyond the linear response regime and apply it to saturated and unsaturated linear hydrocarbon chains connecting two gold substrates. Thermal boundary conditions represented by Markovian noise and damping are filtered through several (up to four) gold layers to provide a realistic and controllable bath spectral density. Classical simulations using the full universal force field are compared with quantum calculations that use only the harmonic part of this field. The close agreement found at about room temperature between these very different calculations suggests that heat transport at such temperatures is dominated by lower frequency vibrations whose dynamics is described well by classical mechanics. The results obtained for alkanedithiol molecules connecting gold substrates agree with previous quantum calculations based on the Landauer formula and match recent experimental measurements [e.g., thermal conductance around 20 pW/K for alkanedithiols in single-molecule junctions (SMJs)]. Heat conductance simulations on polyynes of different lengths illuminate the effects of molecular conjugation on thermal transport. The difference between alkanes and polyynes is not large but correlates with the larger rigidity and stronger mode localization that characterize the polyyne structure. This computational approach has been recently used [R. Chen, I. Sharony, and A. Nitzan, J. Phys. Chem. Lett. 11, 4261-4268 (2020)] to unveil local atomic heat currents and phononic interference effect in aromatic-ring based SMJs.

We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for quantum transport and reproduces recently obtained results for the quantum thermodynamic of slowly driven systems. Using this approach, new results have been obtained. First, we derived of a general explicit expression for non-equilibrium steady state density matrix of a system compromised of multiple infinite baths coupled through a general interaction. Then, we obtained a general expression for the dissipated power for the driven non-interacting resonant level to first order in the driving speeds, where both the dot energy level and its couplings are changing, without invoking the wide band approximation. In addition, we also showed that the symmetric splitting of system bath interaction, employed for the case of a system coupled to one bath to determine the effective system Hamiltonian [Phys. Rev. B 93, 115318 (2016)] is valid for the multiple baths case as well. Finally, we demonstrated an equivalence of our method to the Landauer-Buttiker formalism and its extension to slowly driven systems developed by von Oppen and co-workers [Phys. Rev. Lett. 120, 107701 (2018)]. To demonstrate the use of this formalism we analyze the operation a device in which the dot is driven cyclically between two leads under strong coupling conditions. We also generalize the previously obtained expression for entropy production in such driven processes to the many-bath case., 86 pages, 2 figures

In contrast to a projective quantum measurement in which the system is projected onto an eigenstate of the measured operator, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A full description of such measurement should describe the measurement protocol and provide an explicit form of the measurement operator that transform the quantum state to its post measurement form. A simultaneous measurement of non-commuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator often used to model a weak measurement of a single observable is obtained by projecting a na\"ive extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened. published

We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat, and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is positive and is found to be related to the excess work dissipated by friction, at least up to second order in the driving speed. As an example of the present methodology, we reproduce the results for the quantum thermodynamics of the driven resonance level model. We also emphasize that our formalism is quite general and allows for electron-electron interactions, which can give rise to exotic Kondo resonances appearing in thermodynamic quantities.

The energy partitioning during activation and relaxation events under steady-state conditions for a Brownian particle driven by multiple thermal reservoirs of different local temperatures is investigated. Specifically, we apply the formalism derived in a previous article [G. T. Craven and A. Nitzan, J. Chem. Phys. 148, 044101 (2018)] to examine the thermal transport properties of two sub-ensembles of Brownian processes, distinguished at any given time by the specification that all the trajectories in each group have, at that time, energy either above (upside) or below (downside) a preselected energy threshold. Dynamical properties describing energy accumulation and release during activation/relaxation events and relations for upside/downside energy partitioning between thermal reservoirs are derived. The implications for heat transport induced by upside and downside events are discussed.

We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of timescale separation between system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green's function (NEGF) analysis, is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling., Comment: 22 pages, 4 figures

Controlling the direction and magnitude of both heat and electronic currents using rectifiers has significant implications for the advancement of molecular circuit design. In order to facilitate the implementation of new transport phenomena in such molecular structures, we examine thermal and thermoelectric rectification effects that are induced by an electron transfer process that occurs across a temperature gradient between molecules. Historically, the only known heat conduction mechanism able to generate thermal rectification in purely molecular environments is phononic heat transport. Here, we show that electron transfer between molecular sites with different local temperatures can also generate a thermal rectification effect and that electron hopping through molecular bridges connecting metal leads at different temperatures gives rise to asymmetric Seebeck effects, that is, thermoelectric rectification, in molecular junctions.

The mechanisms of chemical reactions, including the transformation pathways of the electronic and geometric structures of molecules, are crucial for comprehending the essence and developing new chemistry. However, it is extremely difficult to realize at the single-molecule level. Here, we report a single-molecule approach capable of electrically probing stochastic fluctuations under equilibrium conditions and elucidating time trajectories of single species in non-equilibrated systems. Through molecular engineering, a single molecular wire containing a functional center of 9-phenyl-9-fluorenol was covalently wired into nanogapped graphene electrodes to form stable single-molecule junctions. Both experimental and theoretical studies consistently demonstrate and interpret the direct measurement of the formation dynamics of individual carbocation intermediates with a strong solvent dependence in a nucleophilic-substitution reaction. We also show the kinetic process of competitive transitions between acetate and bromide species, which is inevitable through a carbocation intermediate, confirming the classical mechanism. This unique method creates plenty of opportunities for carrying out single-molecule dynamics or biophysics investigations in broad fields beyond reaction chemistry through molecular design and engineering.

Since the discovery a century ago1–3 of electronic thermal noise and shot noise, these forms of fundamental noise have had an enormous impact on science and technology research and applications. They can be used to probe quantum effects and thermodynamic quantities4–11, but they are also regarded as undesirable in electronic devices because they obscure the target signal. Electronic thermal noise is generated at equilibrium at finite (non-zero) temperature, whereas electronic shot noise is a non-equilibrium current noise that is generated by partial transmission and reflection (partition) of the incoming electrons8. Until now, shot noise has been stimulated by a voltage, either applied directly8 or activated by radiation12,13. Here we report measurements of a fundamental electronic noise that is generated by temperature differences across nanoscale conductors, which we term ‘delta-T noise’. We experimentally demonstrate this noise in atomic and molecular junctions, and analyse it theoretically using the Landauer formalism8,14. Our findings show that delta-T noise is distinct from thermal noise and voltage-activated shot noise8. Like thermal noise, it has a purely thermal origin, but delta-T noise is generated only out of equilibrium. Delta-T noise and standard shot noise have the same partition origin, but are activated by different stimuli. We infer that delta-T noise in combination with thermal noise can be used to detect temperature differences across nanoscale conductors without the need to fabricate sophisticated local probes. Thus it can greatly facilitate the study of heat transport at the nanoscale. In the context of modern electronics, temperature differences are often generated unintentionally across electronic components. Taking into account the contribution of delta-T noise in these cases is likely to be essential for the design of efficient nanoscale electronics at the quantum limit. A fundamental electronic noise—beyond electronic thermal noise and voltage-activated shot noise—that is generated by temperature differences across nanoscale conductors is demonstrated, with possible implications for thermometry and electronics.

This corrects the article DOI: 10.1103/PhysRevLett.114.126803.

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one and three dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: the classical path approximation (CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics. The CPA fails to recover a consistent description of spontaneous emission. A consistent "spontaneous" emission can be obtained from Ehrenfest dynamics--provided that one starts in an electronic superposition state. Spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by W. Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights new possibilities for studying light-matter interactions with semiclassical mechanics., 15 figures

We study the dynamics of charge separation in bulk heterojunction organic photovoltaic systems in light of recent experimental observations that this process is characterized by multiple time scales in the range of 10 fs to 100 ps. Coherent evolution of the excitonic state has been suggested to dominate the early stages of the charge separation process and diffusion of localized excitons to be dominant at longer times. Both of these processes obviously depend on the system morphology, in particular on the grain sizes of the donor and acceptor phases. Here we analyze these mechanisms and their characteristic time scales, aiming to verify the consistency of the proposed mechanisms with the experimentally observed time scales of charge separation. We suggest that the coherent mechanism that dominates the early stage of charge separation involves delocalized excitons. These excitons are formed by optical excitation of clusters of strongly interacting donor sites, and the charge separation rate is determined by the probability that such sites lie at the donor-acceptor interface. The (relatively) slow diffusive rate is estimated from the mean first passage time for a diffusing exciton to reach the donor grain surface. Our estimates, based on available exciton diffusion rates and morphology data, are consistent with experimental observations. (Figure Presented).