Vibrational Energy Transport Research Articles

The effect of echoes interference on phonon attenuation in a nanophononic membrane

Nanophononic materials are characterized by a periodic nanostructuration, which may lead to coherent scattering of phonons, enabling interference and resulting in modified phonon dispersions. We have used the extreme ultraviolet transient grating technique to measure phonon frequencies and lifetimes in a low-roughness nanoporous phononic membrane of SiN at wavelengths between 50 and 100 nm, comparable to the nanostructure lengthscale. Surprisingly, phonon frequencies are only slightly modified upon nanostructuration, while phonon lifetime is strongly reduced. Finite element calculations indicate that this is due to coherent phonon interference, which becomes dominant for wavelengths between ~ half and twice the inter-pores distance. Despite this, vibrational energy transport is ensured through an energy flow among the coherent modes created by reflections. This interference of phonon echos from periodic interfaces is likely another aspect of the mutual coherence effects recently highlighted in amorphous and complex crystalline materials and, in this context, could be used to tailor transport properties of nanostructured materials.

Ergodicity breaking in rapidly rotating C60 fullerenes.

Ergodicity, the central tenet of statistical mechanics, requires an isolated system to explore all available phase space constrained by energy and symmetry. Mechanisms for violating ergodicity are of interest for probing nonequilibrium matter and protecting quantum coherence in complex systems. Polyatomic molecules have long served as a platform for probing ergodicity breaking in vibrational energy transport. Here, we report the observation of rotational ergodicity breaking in an unprecedentedly large molecule, 12C60, determined from its icosahedral rovibrational fine structure. The ergodicity breaking occurs well below the vibrational ergodicity threshold and exhibits multiple transitions between ergodic and nonergodic regimes with increasing angular momentum. These peculiar dynamics result from the molecule's distinctive combination of symmetry, size, and rigidity, highlighting its relevance to emergent phenomena in mesoscopic quantum systems.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions.

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Collision-induced absorption spectra (CIA) for monatomic gas mixtures of Helium-Xenon

The lineshapes of collision-induced absorption (CIA) at room temperature are computed quantum mechanically for gaseous binary mixtures of helium with xenon using theoretical induced dipole moment and interatomic potentials. Empirical and literature models of the induced dipole moments which reproduce the experimental spectra and the first few spectral moments are given. Good agreement between the computed and experimental lineshapes of absorption is obtained when the potential parameters which are fitted well to the vibrational energy levels, thermophysical and transport properties are used.

Energy Transport and Its Function in Heptahelical Transmembrane Proteins.

Photoproteins such as bacteriorhodopsin (bR) and rhodopsin (Rho) need to effectively dissipate photoinduced excess energy to prevent themselves from damage. Another well-studied seven transmembrane (TM) helices protein is the β2 adrenergic receptor (β2AR), a G protein-coupled receptor for which energy dissipation paths have been linked with allosteric communication. To study the vibrational energy transport in the active and inactive states of these proteins, a master equation approach [J. Chem. Phys.2020, 152, 045103] is employed, which uses scaling rules that allow us to calculate energy transport rates solely based on the protein structure. Despite their overall structural similarity, the three 7TM proteins reveal quite different strategies to redistribute excess energy. While bR quickly removes the energy using the TM7 helix as a "lightning rod", Rho exhibits a rather poor energy dissipation, which might eventually require the hydrolysis of the Schiff base between the protein and the retinal chromophore to prevent overheating. Heating the ligand adrenaline of β2AR, the resulting energy transport network of the protein is found to change significantly upon switching from the active state to the inactive state. While the energy flow may highlight aspects of the inter-residue couplings of β2AR, it seems not particularly suited to explain allosteric phenomena.

DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach

Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed.

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 νN≡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 νN=N + νN–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 νN=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 νN≡N initiation: The νN=N mode relaxes efficiently into the twisting band states and low-frequency acoustic modes, and the νN–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 νN≡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 νN≡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.

Transporting and concentrating vibrational energy to promote isomerization.

Visible-light absorption and transport of the resultant electronic excitations to a reaction centre through Förster resonance energy transfer1-3 (FRET) are critical to the operation of biological light-harvesting systems4, and are used in various artificial systems made of synthetic dyes5, polymers6 or nanodots7,8. The fundamental equations describing FRET are similar to those describing vibration-to-vibration (V-V) energy transfer9, and suggest that transport and localization of vibrational energy should, in principle, also be possible. Although it is known that vibrational excitation can promote reactions10-16, transporting and concentrating vibrational energy has not yet been reported. We have recently demonstrated orientational isomerization enabled by vibrational energy pooling in a CO adsorbate layer on a NaCl(100) surface17. Here we build on that work to show that the isomerization reaction proceeds more efficiently with a thick 12C16O overlayer that absorbs more mid-infrared photons and transports the resultant vibrational excitations by V-V energy transfer to a 13C18O-NaCl interface. The vibrational energy density achieved at the interface is 30 times higher than that obtained with direct excitation of the interfacial CO. We anticipate that with careful system design, these concepts could be used to drive other chemical transformations, providing new approaches to condensed phase chemistry.

How Intramolecular Vibrational Energy Transport Changes with Rigidity and Polarity of the Environment?

Vibrational energy transport through oligomeric polyethylene glycol (PEG) chains can occur ballistically via optical vibrational chain bands, showing fast and constant transport speed and high efficiency of the transport, thus offering means to transfer significant quanta of energy, exceeding 1000 cm–1, to large distances exceeding 60 A. We report how the intramolecular energy transport time, through-chain transport speed, and end-group cooling rate depend on the rigidity and polarity of the environment. The experiments were performed with end-group labeled PEG oligomers using two-dimensional infrared (2DIR) spectroscopy. The ballistic energy transport was initiated at one end of the chain by exciting an azido moiety at ca. 2100 cm–1 and recorded at another end of the chain by probing the carbonyl stretching mode of succinimide ester. We found that the rigidity of the environment, polystyrene (PS) matrix vs. a solution of similar polarity, did not change the energy transport times much, nor the through-chain transport speed. These results suggest that in mildly polar media, dynamic fluctuations, occurring in solution but largely frozen in a solid matrix, are not the dominant cause of the dephasing of the chain states, despite the presence of fast relaxation components in the solution. The similarity of the transport times in different media suggests that the secondary chain structure does not affect much the transport in PEG chains. The solvent polarity affected the intramolecular transport significantly: the transport efficiency in polar DMSO is ca. 1.6 fold smaller than that in nonpolar CCl4 or PS. The cooling time of the succinimide ester end group is reduced in more polar solvents affecting the waiting time dependence shape and thus the energy arrival time to the reporter. The analysis of different ways of extracting the energy arrival time from the data is presented. The observed dependences of the through-chain transport time on the solvent polarity suggests the presence of multiple wavepackets propagating in the PEG chain with different group velocities.

Collective excitations in α-helical protein structures interacting with the water environment

ABSTRACT Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon–phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.

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 ∝ T3/4 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.

Topology, landscapes, and biomolecular energy transport

While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior that diverges from the macroscale. Here, we show that transient thermal transport reflects macromolecular energy landscape architecture through the topological characteristics of molecular contacts and the nonlinear processes that mediate dynamics. While the former determines transport pathways via pairwise interactions, the latter reflects frustration within the landscape for local conformational rearrangements. Unlike transport through small-molecule systems, such as alkanes, nonlinearity dominates over coherent processes at even quite short time- and length-scales. Our exhaustive all-atom simulations and novel local-in-time and space analysis, applicable to both theory and experiment, permit dissection of energy migration in biomolecules. The approach demonstrates that vibrational energy transport can probe otherwise inaccessible aspects of macromolecular dynamics and interactions that underly biological function.

Energy Transport across Interfaces in Biomolecular Systems.

Energy transport during chemical reactions or following photoexcitation in systems of biological molecules is mediated by numerous interfaces that separate chemical groups and molecules. Describing and predicting energy transport has been complicated by the inhomogeneous environment through which it occurs, and general rules are still lacking. We discuss recent work on identification of networks for vibrational energy transport in biomolecules and their environment, with focus on the nature of energy transfer across interfaces. Energy transport is influenced both by structure of the biomolecular system as well as by equilibrium fluctuations of nonbonded contacts between chemical groups, biomolecules, and water along the network. We also discuss recent theoretical and computational work on the related topic of thermal transport through molecular interfaces, with focus on systems important in biology as well as relevant experimental studies.

Ballistic Transport of Vibrational Energy through an Amide Group Bridging Alkyl Chains

Transport of vibrational energy via linear alkyl molecular chains can occur efficiently and with a high speed. This study addresses the question of how such transport is changed if an amide group is incorporated in the middle of such chain. A set of four compounds, Amn-4, was synthesized such that an amide group is connected to two alkyl chains. The alkyl chain on one side of the amide, featuring 4, 7, 11, or 15 CH2 units, is terminated by an azido group, while the alkyl chain on another side is of fixed length with four methylene groups terminated with a methyl ester group. The energy transport in Amn-4 in CD3CN solution, measured by relaxation-assisted two-dimensional infrared spectroscopy, was initiated and recorded using various combinations of tags and reporters, which included N3 and C═O stretching modes of the end groups and amide-I and amide-II modes at the amide. It was found that the transport initiated by the amide-I mode in the alkyl chain attached to C═O side of the amide proceeds with a cons...

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.

Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. II. Application to vibrational energy transport in a molecular chain

We report on first applications of the Two-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (2L-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] for high-dimensional quantum propagation using variational Gaussian basis sets. This method circumvents the limitations of conventional variational Gaussian wavepacket (GWP) methods by introducing a hierarchical wavefunction representation with a fully flexible first layer composed of orthogonal single-particle functions, which are in turn expressed as superpositions of GWPs of fixed width. The method is applied to a model Hamiltonian describing vibrational energy transport through a molecular chain. The model combines bilinear site-to-site couplings with site-local couplings induced by cubic anharmonicities. We report on simulation results for realizations comprising 5 sites with 35 vibrational modes and 18 sites with 90 vibrational modes, which are shown to be in excellent agreement with reference calculations by the Multi-Layer MCTDH method.

A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures

A phase-space boundary integral method is developed for modelling stochastic high-frequency acoustic and vibrational energy transport in both single and multi-domain problems. The numerical implementation is carried out using the collocation method in both the position and momentum phase-space variables. One of the major developments of this work is the systematic convergence study, which demonstrates that the proposed numerical schemes exhibit convergence rates that could be expected from theoretical estimates under the right conditions. For the discretisation with respect to the momentum variable, we employ spectrally convergent basis approximations using both Legendre polynomials and Gaussian radial basis functions. The former have the advantage of being simpler to apply in general without the need for preconditioning techniques. The Gaussian basis is introduced with the aim of achieving more efficient computations in the weak noise case with near-deterministic dynamics. Numerical results for a series of coupled domain problems are presented, and demonstrate the potential for future applications to larger scale problems from industry.

Vibrational Energy Transport in Hybrid Ordered/Disordered Nanocomposites: Hybridization and Avoided Crossings of Localized and Delocalized Modes

AbstractVibrational energy transport in disordered media is of fundamental importance to several fields spanning from sustainable energy to biomedicine to thermal management. This work investigates hybrid ordered/disordered nanocomposites that consist of crystalline membranes decorated by regularly patterned disordered regions formed by ion beam irradiation. The presence of the disordered regions results in reduced thermal conductivity, rendering these systems of interest for use as nanostructured thermoelectrics and thermal device components, yet their vibrational properties are not well understood. Here, the mechanism of vibrational transport and the reason underlying the observed reduction is established in detail. The hybrid systems are found to exhibit glass‐crystal duality in vibrational transport. Lattice dynamics reveals substantial hybridization between the localized and delocalized modes, which induces avoided crossings and harmonic broadening in the dispersion. Allen/Feldman theory shows that the hybridization and avoided crossings are the dominant drivers of the reduction. Anharmonic scattering is also enhanced in the patterned nanocomposites, further contributing to the reduction. The systems exhibit features reminiscent of both nanophononic materials and locally resonant nanophononic metamaterials, but operate in a manner distinct to both. These findings indicate that such “patterned disorder” can be a promising strategy to tailor vibrational transport through hybrid nanostructures.

Influence of thermalization on thermal conduction through molecular junctions: Computational study of PEG oligomers.

Thermalization in molecular junctions and the extent to which it mediates thermal transport through the junction are explored and illustrated with computational modeling of polyethylene glycol (PEG) oligomer junctions. We calculate rates of thermalization in the PEG oligomers from 100 K to 600 K and thermal conduction through PEG oligomer interfaces between gold and other materials, including water, motivated in part by photothermal applications of gold nanoparticles capped by PEG oligomers in aqueous and cellular environments. Variation of thermalization rates over a range of oligomer lengths and temperatures reveals striking effects of thermalization on thermal conduction through the junction. The calculated thermalization rates help clarify the scope of applicability of approaches that can be used to predict thermal conduction, e.g., where Fourier's law breaks down and where a Landauer approach is suitable. The rates and nature of vibrational energy transport computed for PEG oligomers are compared with available experimental results.

Importance of eigenvector sign consistency in computations of expectation values via mixed quantum-classical surface-hopping dynamics

For simulations of systems undergoing nonadiabatic dynamics between multiple quantum states, one must often compute nonadiabatic coupling vectors, which involve the overlap of one adiabatic state with the gradient (with respect to the nuclear positions) of another. Because these states are usually computed numerically using a matrix diagonalization routine, the signs of the eigenvectors and the resulting nonadiabatic coupling vectors can change erratically over the course of a trajectory. To ensure a smooth evolution of the eigenvectors, one usually tracks the sign of the overlap of the current eigenvector with that of the previous time step and corrects the sign if needed. However, when computing time-dependent expectation values based on an ensemble of trajectories (which are typically initialized at different points in configuration space), one now has to ensure eigenvector sign continuity across the entire ensemble. In this work, we present a simple procedure for accomplishing this in mixed quantum-classical surface-hopping dynamics. The utility of this procedure is demonstrated by calculating both adiabatic state populations in a reduced model of a condensed phase proton-coupled electron transfer (PCET) reaction and subsystem state populations in an excitonic model of an alpha-helical chain undergoing vibrational energy transport (VET), using mixed quantum-classical Liouville surface-hopping dynamics. Our results show that when eigenvector sign continuity across the ensemble is neglected, as is commonly done, one can obtain large deviations from the correct values. However, after implementing this procedure, the results agree better with the exact results in the case of the PCET model and behave physically in the case of the VET model. These results illustrate the importance of a careful treatment of the signs in mixed quantum-classical dynamics calculations of expectation values in the adiabatic representation.