Molecular chirality quantification: Tools and benchmarks.

Molecular chirality has traditionally been viewed as a binary property where a molecule is classified as either chiral or achiral, yet in recent decades, mathematical methods for quantifying chirality have been explored. Here, we use toy molecular systems to systematically compare the performance of two state-of-the-art chirality measures: (1) the Continuous Chirality Measure (CCM) and (2) the Chirality Characteristic (χ). We find that both methods exhibit qualitatively similar behavior when applied to simple molecular systems such as a four-site molecule or the polymer double-helix, but we show that the CCM may be more suitable for evaluating the chirality of arbitrary molecules or abstract structures such as normal vibrational modes. We discuss a range of considerations for applying these methods to molecular systems in general, and we provide links to user-friendly codes for both methods. We aim for this paper to serve as a concise resource for scientists attempting to familiarize themselves with these chirality measures or attempting to implement chirality measures in their own work.

On the nature of two-photon transitions for a collection of molecules in a Fabry-Perot cavity.

We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and we analyze how such an effect depends on the cavity quality factor, the field enhancement, and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with a variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical level description of the radiation field (i.e., we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in the past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing.

Heat transport with a twist.

Despite the desirability of polymers for use in many products due to their flexibility, light weight, and durability, their status as thermal insulators has precluded their use in applications where thermal conductors are required. However, recent results suggest that the thermal conductance of polymers can be enhanced and that their heat transport behaviors may be highly sensitive to nanoscale control. Here we use non-equilibrium molecular dynamics simulations to study the effect of mechanical twist on the steady-state thermal conductance across multi-stranded polyethylene wires. We find that a highly twisted double-helical polyethylene wire can display a thermal conductance up to three times that of its untwisted form, an effect which can be attributed to a structural transition in the strands of the double helix. We also find that in thicker wires composed of many parallel strands, adding just one twist can increase its thermal conductance by over 30%. However, we find that unlike stretching a polymer wire, which causes a monotonic increase in thermal conductance, the effect of twist is highly non-monotonic, and certain amounts of twist can actually decrease the thermal conductance. Finally, we apply the Continuous Chirality Measure (CCM) in an attempt to explore the correlation between heat conductance and chirality. The CCM is found to correlate with twist as expected, but we attribute the observed heat transport behaviors to structural factors other than chirality.

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction.

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.

Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory.

A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.

Energy Conversion and Entropy Production in Biased Random Walk Processes-From Discrete Modeling to the Continuous Limit.

We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete model, the limit in which the motion becomes continuous in space and time (N→∞) is not unique and depends on what physical observables are assumed to be unchanged in the process. In particular, one may (as usually done) choose to keep the speed and diffusion coefficient fixed during this limiting process, in which case, the entropy production is affected. In addition, we also studied processes in which the entropy production is kept constant as N→∞ at the cost of a modified speed or diffusion coefficient. Furthermore, we also combined this dynamics with work against an opposing force, which made it possible to study the effect of discretization of the process on the thermodynamic efficiency of transferring the power input to the power output. Interestingly, we found that the efficiency was increased in the limit of N→∞. Finally, we investigated the same process when transitions between sites can only happen at finite time intervals and studied the impact of this time discretization on the thermodynamic variables as the continuous limit is approached.

Phonon transport along long polymer chains with varying configurations: Effects of phonon scattering.

Following recent molecular dynamic simulations [M. Dinpajooh and A. Nitzan, J. Chem. Phys. 153, 164903 (2020)], we theoretically analyze how the phonon heat transport along a single polymer chain may be affected by varying the chain configuration. We suggest that phonon scattering controls the phonon heat conduction in strongly compressed (and tangled) chain when multiple random bends act as scattering centers for vibrational phonon modes, which results in the diffusive character of heat transport. As the chain is straightening up, the number of scatterers decreases, and the heat transport acquires nearly ballistic character. To analyze these effects, we introduce a model of a long atomic chain made out of identical atoms where some atoms are put in contact with scatterers and treat the phonon heat transfer through such a system as a multichannel scattering problem. We simulate the changes in the chain configurations by varying the number of the scatterers and mimic a gradual straightening of the chain by a gradual reducing of the number of scatterers attached to the chain atoms. It is demonstrated, in agreement with recently published simulation results, that the phonon thermal conductance shows a threshold-like transition from the limit where nearly all atoms are attached to the scatterers to the opposite limit where the scatterers vanish, which corresponds to a transition from the diffusive to the ballistic phonon transport.

Electron hopping heat transport in molecules.

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.

Comparing semiclassical mean-field and 1-exciton approximations in evaluating optical response under strong light-matter coupling conditions.

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.

Short-time particle motion in one and two-dimensional lattices with site disorder.

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.

Dissociation slowdown by collective optical response under strong coupling conditions.

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.

Noise and thermodynamic uncertainty relation in "underwater" molecular junctions.

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 we study the 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) defininig 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 the 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.

Strong Coupling in Infrared Plasmonic Cavities.

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.

Energy-efficient pathway for selectively exciting solute molecules to high vibrational states via solvent vibration-polariton pumping.

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.

Coupling, lifetimes, and "strong coupling" maps for single molecules at plasmonic interfaces.

The interaction between excited states of a molecule and excited states of a 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⟩|/â„Γ > 1, where ⟨U⟩ and Γ are the molecule-plasmon coupling and the spectral width of the optical transition, respectively. Because both ⟨U⟩ and Γ 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 Γ for several geometries. Surprisingly, we find that if the only contributions to Γ 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⟩|/â„Γ > 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.

Quantum Simulations of Vibrational Strong Coupling via Path Integrals.

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated 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 line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs 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.

Heat conduction in polymer chains: Effect of substrate on the thermal conductance.

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 [M. Dinpajooh and A. Nitzan, 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.

Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi's golden rule rate.

Under vibrational strong coupling (VSC), the formation of molecular polaritons may significantly modify the photo-induced or thermal properties of molecules. In an effort to understand these intriguing modifications, both experimental and theoretical studies have focused on the ultrafast dynamics of vibrational polaritons. Here, following our recent work [Li et al., J. Chem. Phys. 154, 094124 (2021)], we systematically study the mechanism of polariton relaxation for liquid CO2 under a weak external pumping. Classical cavity molecular dynamics (CavMD) simulations confirm that polariton relaxation results from the combined effects of (i) cavity loss through the photonic component and (ii) dephasing of the bright-mode component to vibrational dark modes as mediated by intermolecular interactions. The latter polaritonic dephasing rate is proportional to the product of the weight of the bright mode in the polariton wave function and the spectral overlap between the polariton and dark modes. Both these factors are sensitive to parameters such as the Rabi splitting and cavity mode detuning. Compared to a Fermi's golden rule calculation based on a tight-binding harmonic model, CavMD yields a similar parameter dependence for the upper polariton relaxation lifetime but sometimes a modest disagreement for the lower polariton. We suggest that this disagreement results from polariton-enhanced molecular nonlinear absorption due to molecular anharmonicity, which is not included in our analytical model. We also summarize recent progress on probing nonreactive VSC dynamics with CavMD.

Energy transfer and thermoelectricity in molecular junctions in non-equilibrated solvents.

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.

Edge State Quantum Interference in Twisted Graphitic Interfaces.

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.