Ballistic Energy Transport in Oligomers

Probing the Hydrophobic Region of a Lipid Bilayer at Specific Depths Using Vibrational Spectroscopy

A novel spectroscopic approach for studying the flexibility and mobility in the hydrophobic interior of lipid bilayers at specific depths is proposed. A set of test compounds featuring an azido moiety and a cyano or carboxylic acid moiety, connected by an alkyl chain of different lengths, was synthesized. FTIR data and molecular dynamics calculations indicated that the test compounds in a bilayer are oriented so that the cyano or carboxylic acid moiety is located in the lipid head-group region, while the azido group stays inside the bilayer at the depth determined by its alkyl chain length. We found that the asymmetric stretching mode of the azido group (νN3) can serve as a reporter of the membrane interior dynamics. FTIR and two-dimensional infrared (2DIR) studies were performed at different temperatures, ranging from 22 to 45 °C, covering the Lβ-Lα phase transition temperature of dipalmitoylphosphatidylcholine (∼41 °C). The width of the νN3 peak was found to be very sensitive to the phase transition and to the temperature in general. We introduced an order parameter, SN3, which characterizes restrictions to motion inside the bilayer. 2DIR spectra of νN3 showed different extents of inhomogeneity at different depths in the bilayer, with the smallest inhomogeneity in the middle of the leaflet. The spectral diffusion dynamics of the N3 peak was found to be dependent on the depth of the N3 group location in the bilayer. The obtained results enhance our understanding of the bilayer dynamics and can be extended to investigate membranes with more complex compositions.

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.

Molecular Vibrational Polariton Dynamics: What Can Polaritons Do?

ConspectusWhen molecular vibrational modes strongly couple to virtual states of photonic modes, new molecular vibrational polariton states are formed, along with a large population of dark reservoir modes. The polaritons are much like the bonding and antibonding molecular orbitals when atomic orbitals form molecular bonds, while the dark modes are like nonbonding orbitals. Because the polariton states are half-matter and half-light, whose energy is shifted from the parental states, polaritons are predicted to modify chemistry under thermally activated conditions, leading to an exciting and emerging field known as polariton chemistry that could potentially shift paradigms in chemistry. Despite several published results supporting this concept, the chemical physics and mechanism of polariton chemistry remain elusive. One reason for this challenge is that previous works cannot differentiate polaritons from dark modes. This limitation makes delineating the contributions to chemistry from polaritons and dark states difficult. However, this level of insight is critical for developing a solid mechanism for polariton chemistry to design and predict the outcome of strong coupling with any given reaction. My group addressed the challenge of differentiating the dynamics of polaritons and dark modes by ultrafast two-dimensional infrared (2D IR) spectroscopy. Specifically, (1) we found that polaritons can facilitate intra- and intermolecular vibrational energy transfer, opening a pathway to control vibrational energy flow in liquid-phase molecular systems, and (2) by studying a single-step isomerization event, we verified that indeed polaritons can modify chemical dynamics under strong coupling conditions, but in contrast, the dark modes behave like uncoupled molecules and do not change the dynamics. This finding confirmed the central concept of polariton chemistry: polaritons modify the potential energy landscape of reactions. The result also clarified the role of dark modes, which lays a critical foundation for designing cavities for future polariton chemistry. Aside from using 2D IR spectroscopy to study polariton chemistry, we also used the same technique to develop molecular polaritons into a potential quantum simulation platform. We demonstrated that polaritons have Rabi oscillations, and using a checkerboard cavity design, we showed that polaritons could have large nonlinearity across space. We further used the checkerboard polaritons to simulate coherence transfer and visualize it. A unidirectional coherence transfer was observed, indicating non-Hermitian dynamics. The highlighted efforts in this Account provide a solid understanding of the capability of polaritons for chemistry and quantum information science. I conclude this Account by discussing a few challenges for moving polariton chemistry toward being predictable and making the polariton quantum platform a complement to existing systems.

Time-resolved spectroscopic mapping of vibrational energy flow in proteins: Understanding thermal diffusion at the nanoscale

Vibrational energy exchange between various degrees of freedom is critical to barrier-crossing processes in proteins. Hemeproteins are well suited for studying vibrational energy exchange in proteins because the heme group is an efficient photothermal converter. The released energy by heme following photoexcitation shows migration in a protein moiety on a picosecond timescale, which is observed using time-resolved ultraviolet resonance Raman spectroscopy. The anti-Stokes ultraviolet resonance Raman intensity of a tryptophan residue is an excellent probe for the vibrational energy in proteins, allowing the mapping of energy flow with the spatial resolution of a single amino acid residue. This Perspective provides an overview of studies on vibrational energy flow in proteins, including future perspectives for both methodologies and applications.

Simulations of heat transport in single-molecule junctions: Investigations of the thermal diode effect

With the objective of understanding microscopic principles governing thermal energy flow in nanojunctions, we study phononic heat transport through metal-molecule-metal junctions using classical molecular dynamics (MD) simulations. Considering a single-molecule gold-alkanedithiol-gold junction, we first focus on aspects of method development and compare two techniques for calculating thermal conductance: (i) The Reverse Nonequilibrium MD (RNEMD) method, where heat is inputted and extracted at a constant rate from opposite metals. In this case, the thermal conductance is calculated from the nonequilibrium temperature profile that is created at the junction. (ii) The Approach-to-Equilibrium MD (AEMD) method, with the thermal conductance of the junction obtained from the equilibration dynamics of the metals. In both methods, simulations of alkane chains of a growing size display an approximate length-independence of the thermal conductance, with calculated values matching computational and experimental studies. The RNEMD and AEMD methods offer different insights, and we discuss their benefits and shortcomings. Assessing the potential application of molecular junctions as thermal diodes, alkane junctions are made spatially asymmetric by modifying their contact regions with the bulk, either by using distinct endgroups or by replacing one of the Au contacts with Ag. Anharmonicity is built into the system within the molecular force-field. We find that, while the temperature profile strongly varies (compared with the gold-alkanedithiol-gold junctions) due to these structural modifications, the thermal diode effect is inconsequential in these systems-unless one goes to very large thermal biases. This finding suggests that one should seek molecules with considerable internal anharmonic effects for developing nonlinear thermal devices.

Tracking Energy Transfer across a Platinum Center

Rigid, conjugated alkyne bridges serve as important components in various transition-metal complexes used for energy conversion, charge separation, sensing, and molecular electronics. Alkyne stretching modes have potential for modulating charge separation in donor–bridge–acceptor compounds. Understanding the rules of energy relaxation and energy transfer across the metal center in such compounds can help optimize their electron transfer switching properties. We used relaxation-assisted two-dimensional infrared spectroscopy to track energy transfer across metal centers in platinum complexes featuring a triazole-terminated alkyne ligand of two or six carbons, a perfluorophenyl ligand, and two tri(p-tolyl)phosphine ligands. Comprehensive analyses of waiting-time dynamics for numerous cross and diagonal peaks were performed, focusing on coherent oscillation, energy transfer, and cooling parameters. These observables augmented with density functional theory computations of vibrational frequencies and anharmonic force constants enabled identification of different functional groups of the compounds. Computations of vibrational relaxation pathways and mode couplings were performed, and two regimes of intramolecular energy redistribution are described. One involves energy transfer between ligands via high-frequency modes; the transfer is efficient only if the modes involved are delocalized over both ligands. The energy transport pathways between the ligands are identified. Another regime involves redistribution via low-frequency delocalized modes, which does not lead to interligand energy transport.

Competition of Several Energy-Transport Initiation Mechanisms Defines the Ballistic Transport Speed

The ballistic regime of vibrational energy transport in oligomeric molecular chains occurs with a constant, often high, transport speed and high efficiency. Such a transport regime can be initiated by exciting a chain end group with a mid-infrared (IR) photon. To better understand the wavepacket formation process, two chemically identical end groups, azido groups with normal, ¹⁴N₃-, and isotopically substituted, ¹⁵N₃-, nitrogen atoms, were tested for wavepacket initiation in compounds with alkyl chains of n = 5, 10, and 15 methylene units terminated with a carboxylic acid (-a) group, denoted as ¹⁴N₃Cn-a and ¹⁵N₃Cn-a. The transport was initiated by exciting the azido moiety stretching mode, the ν_N≡N tag, at 2100 cm^–1 (¹⁴N₃Cn-a) or 2031 cm^–1 (¹⁵N₃Cn-a). Opposite to the expectation, the ballistic transport speed was found to decrease upon ¹⁴N₃ → ¹⁵N₃ isotope editing. Three mechanisms of the transport initiation of a vibrational wavepacket are described and analyzed. The first mechanism involves the direct formation of a wavepacket via excitation with IR photons of several strong Fermi resonances of the tag mode with the ν_N=N + ν_N–C combination state while each of the combination state components is mixed with delocalized chain states. The second mechanism relies on the vibrational relaxation of an end-group-localized tag into a mostly localized end-group state that is strongly coupled to multiple delocalized states of a chain band. Harmonic mixing of ν_N=N of the azido group with CH₂ wagging states of the chain permits a wavepacket formation within a portion of the wagging band, suggesting a fast transport speed. The third mechanism involves the vibrational relaxation of an end-group-localized mode into chain states. Two such pathways were found for the ν_N≡N initiation: The ν_N=N mode relaxes efficiently into the twisting band states and low-frequency acoustic modes, and the ν_N–C mode relaxes into the rocking band states and low-frequency acoustic modes. The contributions of the three initiation mechanisms in the ballistic energy transport initiated by ν_N≡N tag are quantitatively evaluated and related to the experiment. We conclude that the third mechanism dominates the transport in alkane chains of 5–15 methylene units initiated with the ν_N≡N tag and the wavepacket generated predominantly at the CH₂ twisting band. The isotope effect of the transport speed is attributed to a larger contribution of the faster wavepackets for ¹⁴N₃Cn-a or to the different breadth of the wavepacket within the twisting band. The study offers a systematic description of different transport initiation mechanisms and discusses the requirements and features of each mechanism. Such analysis will be useful for designing novel materials for energy management.

Through bonds or contacts? Mapping protein vibrational energy transfer using non-canonical amino acids

Vibrational energy transfer (VET) is essential for protein function. It is responsible for efficient energy dissipation in reaction sites, and has been linked to pathways of allosteric communication. While it is understood that VET occurs via backbone as well as via non-covalent contacts, little is known about the competition of these two transport channels, which determines the VET pathways. To tackle this problem, we equipped the β-hairpin fold of a tryptophan zipper with pairs of non-canonical amino acids, one serving as a VET injector and one as a VET sensor in a femtosecond pump probe experiment. Accompanying extensive non-equilibrium molecular dynamics simulations combined with a master equation analysis unravel the VET pathways. Our joint experimental/computational endeavor reveals the efficiency of backbone vs. contact transport, showing that even if cutting short backbone stretches of only 3 to 4 amino acids in a protein, hydrogen bonds are the dominant VET pathway.

Unidirectional coherent energy transport via conjugated oligo(p-phenylene) chains

We discovered a way to funnel high-frequency vibrational quanta rapidly and unidirectionally over large distances using oligo(p-phenylene) chains. After mid-IR photon photoexcitation of a -COOH end group, the excess energy is injected efficiently into the chain, forming vibrational wavepackets that propagate freely along the chain. The transport delivers high-energy vibrational quanta with a range of transport speeds reaching 8.6 km/s, which exceeds the speed of sound in common metals (∼5 km/s) and polymers (∼2 km/s). Efficiencies of energy injection into the chain and transport along the chain are found to be very high and dependent on the extent of conjugation across the structure. By tuning the degree of conjugation via electronic doping of the chain, the transport speed and efficiency can be controlled. The study opens avenues for developing materials with controllable energy transport properties for heat management, schemes with efficient energy delivery to hard-to-reach regions, including transport against thermal gradients, and ways for initiating chemical reactions remotely.

Stochastic simulation of nonequilibrium heat conduction in extended molecular junctions

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.

Crucial effect of transverse vibrations on the transport through polymer chains

The low temperature transport of electron, or vibrational or electronic exciton toward polymer chains, turns out to be dramatically sensitive to its interaction with transverse acoustic vibrations. We show that this interaction leads to a substantial polaron effect and decoherence, which are generally stronger than those associated with longitudinal vibrations. For site-dependent interactions, transverse phonons form subohmic bath leading to the quantum phase transition accompanied by full suppression of the transport at zero temperature and fast decoherence characterized by temperature dependent rate k₂ ∝ T^3/4 at low temperature, while k₂ ∝ T² for site-independent interactions. The latter dependence was used to interpret recent measurements of temperature dependent vibrational energy transport in polyethylene glycol oligomers.

Low-Temperature Vibrational Energy Transport via PEG Chains

We used relaxation-assisted two-dimensional infrared spectroscopy to study the temperature dependence (10-295 K) of end-to-end energy transport across end-decorated PEG oligomers of various chain lengths. The excess energy was introduced by exciting the azido end-group stretching mode at 2100 cm^-1 (tag); the transport was recorded by observing the asymmetric C═O stretching mode of the succinimide ester end group at 1740 cm^-1. The overall transport involves diffusive steps at the end groups and a ballistic step through the PEG chain. We found that at lower temperatures the through-chain energy transport became faster, while the end-group diffusive transport time and the tag lifetime increase. The modeling of the transport using a quantum Liouville equation linked the observations to the reduction of decoherence rate and an increase of the mean-free-path for the vibrational wavepacket. The energy transport at the end groups slowed down at low temperatures due to the decreased number and efficiency of the anharmonic energy redistribution pathways.

Vibrational Cooling in Oligomeric Viologens of Different Sizes and Topologies

Vibrational cooling was investigated in a set of homologous dimers and trimers with methyl viologen repeat units (MV²⁺). The rapid, <500 fs decay of the D₁ excited state of monoreduced viologen (MV^+•) via a conical intersection allows the preparation of a vibrationally hot D₀ ground state with a large excess energy of 1.7 eV, which is equivalent to the initial effective temperature of ∼800 K. Pump-probe spectroscopy was used to monitor the disappearance of the characteristic D₀ → D₁ hot absorption band, which appears at longer wavelengths than the steady-state spectrum of "cold" MV^+• in equilibrium with the solvent. It is assumed that the vibrational excitation of the ground is initially confined to the same monoreduced viologen repeat unit, which was optically excited to the localized electronic D₁ state, although some degree of redistribution may occur already in the excited state. The observed cooling rates depend on the size and topology of the oligomer, with the linear trimer exhibiting significantly faster thermalization than the branched one. The experimental results were corroborated by molecular dynamics simulations carried out in the harmonic approximation. The dynamics of the thermal equilibration in these systems appears to be consistent with primarily ballistic initial propagation of the vibrational excess energy over distances as large as ∼4 nm and suggests the presence of interference between the equivalent pathways in the branched trimer.

Ballistic and diffusive vibrational energy transport in molecules

Energy transport in molecules is essential for many areas of science and technology. Strong covalent bonds of a molecular backbone can facilitate the involvement of the molecule's high-frequency modes in energy transport, which, under certain conditions, makes the transport fast and efficient. We discuss such conditions and describe various transport regimes in molecules, including ballistic, diffusive, directed diffusion, and intermediate regime cases, in light of recently developed experimental and theoretical approaches.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Failure and Redemption of Statistical and Nonstatistical Rate Theories in the Hydroboration of Alkenes

Our previous work found that canonical forms of transition state theory incorrectly predict the regioselectivity of the hydroboration of propene with BH3 in solution. In response, it has been suggested that alternative statistical and nonstatistical rate theories can adequately account for the selectivity. This paper uses a combination of experimental and theoretical studies to critically evaluate the ability of these rate theories, as well as dynamic trajectories and newly developed localized statistical models, to predict quantitative selectivities and qualitative trends in hydroborations on a broader scale. The hydroboration of a series of terminally substituted alkenes with BH3 was examined experimentally, and a classically unexpected trend is that the selectivity increases as the alkyl chain is lengthened far from the reactive centers. Conventional and variational transition state theories can predict neither the selectivities nor the trends. The canonical competitive nonstatistical model makes somewhat better predictions for some alkenes but fails to predict trends, and it performs poorly with an alkene chosen to test a specific prediction of the model. Added nonstatistical corrections to this model make the predictions worse. Parametrized Rice-Ramsperger-Kassel-Marcus (RRKM)-master equation calculations correctly predict the direction of the trend in selectivity versus alkene size but overpredict its magnitude, and the selectivity with large alkenes remains unpredictable with any parametrization. Trajectory studies in explicit solvent can predict selectivities without parametrization but are impractical for predicting small changes in selectivity. From a lifetime and energy analysis of the trajectories, "localized RRKM-ME" and "competitive localized noncanonical" rate models are suggested as steps toward a general model. These provide the best predictions of the experimental observations and insight into the selectivities.

Molecule-specific interactions of diatomic adsorbates at metal-liquid interfaces

Ultrafast vibrational dynamics of small molecules on platinum (Pt) layers in water are investigated using 2D attenuated total reflectance IR spectroscopy. Isotope combinations of carbon monoxide and cyanide are used to elucidate inter-adsorbate and substrate-adsorbate interactions. Despite observed cross-peaks in the CO spectra, we conclude that the molecules are not vibrationally coupled. Rather, strong substrate-adsorbate interactions evoke rapid (∼2 ps) vibrational relaxation from the adsorbate into the Pt layer, leading to thermal cross-peaks. In the case of CN, vibrational relaxation is significantly slower (∼10 ps) and dominated by adsorbate-solvent interactions, while the coupling to the substrate is negligible.

Experimental Evidence of Long-Range Intramolecular Vibrational Energy Redistribution through Eight Covalent Bonds: NIR Irradiation Induced Conformational Transformation of E-Glutaconic Acid

Long-range intramolecular vibrational energy redistribution (IVR) driven conformational changes were investigated in a matrix-isolated open-chain, asymmetrical dicarboxylic acid, E-glutaconic acid. Although the analysis was challenging due to the presence of multiple backbone conformers and short lifetimes of the prepared higher energy cis conformers, it was shown that the selective excitation of the O-H stretching overtone of one of the carboxylic groups can induce the conformational change (trans to cis) of the other carboxylic group, located at the other end of the E-glutaconic acid molecule. This is a direct proof that the IVR process can act through eight covalent bonds in a flexible molecule before the excess energy completely dissipates into the matrix. The lifetime of the prepared higher energy conformers (averaged over the different backbones) was measured to be 12 s.

Thermalization and Thermal Transport in Molecules

The nature and rate of thermal transport through molecular junctions depend on the length over which thermalization occurs. For junctions formed by alkane chains, in which thermalization occurs only slowly, measurements reveal that thermal resistance is controlled by bonding with the substrates, whereas fluorination can introduce thermal resistance within the molecules themselves, although the mechanism remains unclear. Here we present results of quantum-mechanical calculations of elastic and inelastic scattering rates, the length over which thermalization occurs, and thermal conductance in alkane and perfluoroalkane junctions. The contribution to thermalization of quantum effects that give rise to many-body localization (MBL) in isolated molecules is examined. While MBL does not occur due to dephasing, thermalization is typically too slow to establish local temperature if the same molecule in isolation exhibits MBL. The results indicate limitations on the applicability of classical molecular simulations in modeling thermal transport in molecular junctions.

Electron transfer across a thermal gradient

Charge transfer is a fundamental process that underlies a multitude of phenomena in chemistry and biology. Recent advances in observing and manipulating charge and heat transport at the nanoscale, and recently developed techniques for monitoring temperature at high temporal and spatial resolution, imply the need for considering electron transfer across thermal gradients. Here, a theory is developed for the rate of electron transfer and the associated heat transport between donor-acceptor pairs located at sites of different temperatures. To this end, through application of a generalized multidimensional transition state theory, the traditional Arrhenius picture of activation energy as a single point on a free energy surface is replaced with a bithermal property that is derived from statistical weighting over all configurations where the reactant and product states are equienergetic. The flow of energy associated with the electron transfer process is also examined, leading to relations between the rate of heat exchange among the donor and acceptor sites as functions of the temperature difference and the electronic driving bias. In particular, we find that an open electron transfer channel contributes to enhanced heat transport between sites even when they are in electronic equilibrium. The presented results provide a unified theory for charge transport and the associated heat conduction between sites at different temperatures.