Intermode Energy Research Articles

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow.

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q1, the CO scissor mode Q10, and the OHO bending mode Q29. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q10 strongly modulates the donor-acceptor distance, it does not exchange energy with Q1. However, excitation in Q29 or Q1 does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

Origin of Nonlinear Damping Due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field orientation. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the crossover from linewidth narrowing to linewidth broadening in all individual modes. This indicates the activation of another relaxation process by nonlinear magnon-magnon scattering within the modes. We also find that both nonlinear damping and threshold current in the mode-interaction damping regime at high drive current after transition are temperature independent, suggesting that the mode coupling occurs dominantly through a non-thermal magnon scattering process via a dipole or exchange interaction rather than thermally excited magnon-mediated scattering. This finding presents a promising pathway to overcome the current limitations of efficiently controlling the interaction between two highly nonlinear magnetic oscillators to prevent mode crosstalk or inter-mode energy transfer and deepens understanding of complex nonlinear spin dynamics in multimode spin wave systems.

Hybrid approach to accurate modeling of coupled vibrational-chemical kinetics in carbon dioxide

In the present study, a new hybrid approach is proposed to modeling coupled vibrational and chemical kinetics in carbon dioxide (CO2) and products of its decomposition. The study develops and completes our previous work carried out for a single-component CO2 gas. The model is based on self-consistent implementation of state-to-state chemical and energy production rates into the equations of multi-temperature CO2 kinetics. It distinguishes vibrational temperatures of all CO2 modes and diatomic species and thus takes into account multiple relaxation mechanisms including intra-mode, inter-mode, and inter-molecular energy transitions as well as state-specific dissociation and exchange reactions. Other advantages of the proposed full multi-temperature approach are the possibility of capturing strong non-equilibrium effects in a flow, straightforward implementation of the chemical-vibrational coupling terms, easy update for new models of state-specific reaction rates. Comparisons with the results obtained in the frame of a detailed but numerically demanding state-to-state approach for the problem of spatially homogeneous relaxation showed good accuracy of the new model under the wide range of initial conditions; at the same time, traditional multi-temperature approaches failed to provide accurate predictions of non-equilibrium flow parameters under arbitrary deviations from equilibrium. Effects of chemical reaction models and selective mode excitation are assessed. The numerical efficiency of the developed model is found acceptable compared to that of the state-to-state approach.

Neural network approach in modelling vibrational kinetics of carbon dioxide

The study is devoted to modeling nonequilibrium vibrational kinetics of carbon dioxide taking into account complex mechanisms of relaxation and intermode energy exchanges. The possibilities of using machine learning methods to improve the performance of numerical simulation of non-equilibrium carbon dioxide flows are studied. Various strategies for increasing the efficiency of the hybrid four-temperature model of CO2 kinetics are considered. The neural network approach proposed by the authors to calculate the rate of vibrational relaxation in each mode turned out to be the most promising. For the problem of spatially homogeneous relaxation, estimates of the error and computational costs of the developed algorithm are carried out, and its high accuracy and efficiency are demonstrated. For the first time, the carbon dioxide flow behind a plane shock wave was simulated in a full state-to-state approximation. A comparison with the results obtained in the framework of the hybrid four-temperature approach is carried out, and the equivalence of the approaches is shown. This makes it possible to recommend developed multitemperature approxima tions as the main tool for solving problems of nonequilibrium kinetics and gas dynamics. The hybrid four-temperature approach using the neural network method for calculating relaxation terms showed the acceleration of numerical simulation in time by more than an order of magnitude, while maintaining accuracy. This technique can be recommended for solving complex multidimensional problems of nonequilibrium gas dynamics, including state-to-state chemical reactions.

Four-temperature kinetic model for CO2 vibrational relaxation

A four-temperature kinetic-theory approach for modeling vibrationally non-equilibrium carbon dioxide flows is developed. The model takes into account all kinds of vibrational–translational energy transitions and inter-mode vibrational energy exchange between symmetric, bending, and asymmetric CO2 modes. The key feature of the model is using the averaged state-resolved relaxation rates instead of conventional Landau–Teller expressions. Spatially homogeneous CO2 vibrational relaxation is studied using the state-to-state, new four-temperature and commonly used three-temperature models. Excellent agreement between four-temperature and state-to-state solutions is found, whereas using the three-temperature model with the Landau–Teller production rates leads to significant loss of accuracy. Numerical efficiency of various approaches is discussed as well as the ways for its improvement.

Multi-temperature vibrational energy relaxation rates in CO2

Rates of vibrational energy relaxation in carbon dioxide are studied in the framework of the three-temperature kinetic-theory approach. Vibrational–translational transitions in the bending mode and inter-mode exchange of vibrational quanta are considered. In the zero-order approximation of the generalized Chapman–Enskog method, the energy relaxation rates in the coupled symmetric–bending and asymmetric modes are expressed in terms of thermodynamic forces similar to chemical reaction affinities, and a compact representation for the vibrational energy production rates is proposed. Linearized theory is developed, and analytical ratios of linearized relaxation rates to those defined by the original Landau–Teller (LT) theory are obtained. The relaxation rates are calculated using the Schwartz–Slawsky–Herzfeld (SSH) and forced harmonic oscillator models for the vibrational energy transition probabilities in the temperature range 200 K–10 000 K. For inter-mode exchanges, using the SSH theory yields significantly underpredicted relaxation rates. The ranges of applicability for the LT formula and linearized theory are estimated; the original LT formula for inter-mode vibrational energy exchanges is not capable of accounting for the excitation of both vibrational modes; linearized models yield better results. Possible steps for improving the numerically efficient LT model are proposed.

On the roles of baroclinic modes in eddy-resolving midlatitude ocean dynamics

This work concerns how different baroclinic modes interact and influence solutions of the midlatitude ocean dynamics described by the eddy-resolving quasi-geostrophic model of wind-driven gyres. We developed multi-modal energetics analysis to illuminate dynamical roles of the vertical modes, carried out a systematic analysis of modal energetics and found that the eddy-resolving dynamics of the eastward jet extension of the western boundary currents, such as the Gulf Stream or Kuroshio, is dominated by the barotropic, and the first and second baroclinic modes, which become more energized with smaller eddy viscosity. In the absence of high baroclinic modes, the energy input from the wind is more efficiently focused onto the lower modes, therefore, the eddy backscatter maintaining the eastward jet and its adjacent recirculation zones is the strongest and overestimated with respect to cases including higher baroclinic modes. In the presence of high baroclinic modes, the eddy backscatter effect on the eastward jet is much weaker. Thus, the higher baroclinic modes play effectively the inhibiting role in the backscatter, which is opposite to what has been previously thought. The higher baroclinic modes are less energetic and have progressively decreasing effect on the flow dynamics; nevertheless, they still play important roles in inter-mode energy transfers (by injecting energy into the region of the most intensive eddy forcing, in the neighborhood of the eastward jet) that have to be taken into account for correct representation of the backscatter and, thus, for determining the eastward jet extension.

Optical Control of Mechanical Mode-Coupling within a MoS2 Resonator in the Strong-Coupling Regime.

Two-dimensional (2-D) materials including graphene and transition metal dichalcogenides (TMDs) are an exciting platform for ultrasensitive force and displacement detection in which the strong light-matter coupling is exploited in the optical control of nanomechanical motion. Here we report the optical excitation and displacement detection of a ∼ 3 nm thick MoS2 resonator in the strong-coupling regime, which has not previously been achieved in 2-D materials. Mechanical mode frequencies can be tuned by more than 12% by optical heating, and they exhibit avoided crossings indicative of strong intermode coupling. When the membrane is optically excited at the frequency difference between vibrational modes, normal mode splitting is observed, and the intermode energy exchange rate exceeds the mode decay rate by a factor of 15. Finite element and analytical modeling quantifies the extent of mode softening necessary to control intermode energy exchange in the strong coupling regime.

Régimes of sloping thermal convection in a rotating liquid “annulus”

Wide-ranging laboratory investigations of thermally-driven flows in a baroclinic liquid of low viscosity and thermal conductivity in apparatus bounded by concentric cylindrical side-walls have (a) identified the dynamically-significant dimensionless parameters in terms of which the impressed conditions can be expressed, (b) stimulated advances in theoretical research on nonlinear dynamical systems, (c) established that under most (mechanical and thermal) boundary conditions, the action of gyroscopic (Coriolis) forces ensures that the dominant mode of heat transfer is “sloping thermal convection” (STC), and (d) provided insights into flows occurring in natural rotating fluid systems on length-scales up to thousands of kilometres. STC is characterised by relative flow that is nearly horizontal nearly everywhere, in wide-ranging patterns of waves and eddies which exhibit jet streams and fronts and which in some cases are spatially and temporally highly regular and in others are highly irregular (“chaotic”). Some of these manifold laboratory flows have their counterparts in the gaseous atmospheres of the Earth, Jupiter, Saturn and other spinning planets. When Coriolis forces are not quite strong enough to promote baroclinic instability leading to STC, heat transfer and associated generation of kinetic energy by buoyancy forces is effected by axisymmetric meridional overturning involving inter alia radial flow in end-wall Ekman boundary layers and vertical flow in side-wall boundary layers. Otherwise Coriolis forces promote quasi-geostrophic non-axisymmetric STC in the main body of the fluid. “Barotropic stability” due to enstrophy constraints renders this STC regular (i.e. spatially and temporally periodic) when the azimuthal scale of the flow exceeds a critical value found to satisfy a remarkably simple criterion. At shorter scales, enstrophy constraints weaken and no longer suffice to prevent inter-mode kinetic energy exchanges characteristic of “geostrophic turbulence”. The present article on rôle of boundary layers and on other aspects of annulus flows is largely intended to guide future investigations of crucial details of the dynamical processes that underlie fully-developed STC, some made possible by the ever-improving techniques of computational fluid dynamics.

Bond connectivity measured via relaxation-assisted two-dimensional infrared spectroscopy

The relaxation-assisted two-dimensional infrared (RA 2DIR) method is a novel technique for probing structures of molecules, which relies on vibrational energy transport in molecules. In this article we demonstrate the ability of RA 2DIR to detect the bond connectivity patterns in molecules using two parameters, a characteristic intermode energy transport time (arrival time) and a cross-peak amplification coefficient. A correlation of the arrival time with the distance between the modes is demonstrated. An 18-fold amplification of the cross-peak amplitude for the modes separated by approximately 11 A is shown using RA 2DIR; larger cross-peak amplifications are expected for the modes separated by larger distances. The RA 2DIR method enhances the applicability of 2DIR spectroscopy by making practical the long-range measurements using a variety of structural reporters, including weak IR modes. The data presented demonstrate the analytical power of RA 2DIR which permits the speedy structural assessments of the bond connectivity patterns.

Stochastic differential equation analysis for sound scattering by random internal waves in the ocean

The scattering of a weakly divergent narrow sound beam by random inhomogeneities of a fluctuating ocean is considered in the coupled-mode approximation. The random index of sound refraction is described using the Garrett-Munk internal wave spectrum. The problem is solved using the stochastic differential equations for the first-and second-order statistical moments of the acoustic field. The equations are formulated according to the cumulant expansion method. The existence of weakly divergent narrow sound beams in long-range sound propagation was one of the last discoveries of L.M. Brekhovskikh, to which he attached much importance. The concentration of sound into narrow beams away from the axis of the underwater sound channel was first observed experimentally and then explained by Brekhovskikh and his former students Goncharov, Kurtepov, and Petukhov. In the present paper, the scattered field intensity of a sound beam is calculated for different frequencies and source depths. Analytical expressions are obtained for the coefficients of the differential equation. The intermode energy transfer that accompanies the long-range propagation of a weakly divergent sound beam is analyzed. A comparison with the conventionally used Monte Carlo simulation in the parabolic equation approximation is performed.

On a correct description of a multi-temperature dissociating CO 2 flow

In the present paper, a strongly non-equilibrium reacting CO 2 flow is studied on the basis of the kinetic theory methods. An accurate description of kinetics, gas dynamics and transport properties taking into account complex internal structure of carbon dioxide molecules as well as different rates of vibrational energy exchanges and dissociation is proposed. The expressions for all transport coefficients are derived in the final form. The model, while taking into account multiple CO 2 vibrational modes and main features of intra- and inter-mode energy transitions, is sufficiently simple and suitable for practical realization.

Current-driven dynamics in quantum electronics

We suggest that inelastic electron tunnelling via molecular-scale electronics can induce a variety of fascinating dynamic processes in the molecular moiety. These include vibration, rotation, intermode energy flow and reaction. Potential applications of current-induced dynamics in molecular-scale devices range from new forms of molecular machines and approaches to enhancing the conductivity of molecular wires, to new directions in nanochemistry and nanolithography. Understanding the molecular properties that encourage current-triggered dynamics is relevant also to the design of devices that would be guaranteed to remain stable under current. We discuss the qualitative physics underlying current-driven dynamics, briefly sketch a theory developed to explore these dynamics, describe a few examples from recent and ongoing numerical work and note avenues for future research.

Current-driven dynamics in quantum electronics

Abstract We suggest that inelastic electron tunnelling via molecular-scale electronics can induce a variety of fascinating dynamic processes in the molecular moiety. These include vibration, rotation, intermode energy flow and reaction. Potential applications of current-induced dynamics in molecular-scale devices range from new forms of molecular machines and approaches to enhancing the conductivity of molecular wires, to new directions in nanochemistry and nanolithography. Understanding the molecular properties that encourage current-triggered dynamics is relevant also to the design of devices that would be guaranteed to remain stable under current. We discuss the qualitative physics underlying current-driven dynamics, briefly sketch a theory developed to explore these dynamics, describe a few examples from recent and ongoing numerical work and note avenues for future research.

Extension of quantized Hamilton dynamics to higher orders

The quantized Hamilton dynamics (QHD) method, which was introduced and developed in J. Chem. Phys. 113, 6557 (2000) to the second order, is extended to the third and fourth orders. The QHD formalism represents an extension of classical mechanics and allows for the derivation of a hierarchy of equations of motion which converge with the quantum-mechanical limit. Here, the second, third, and fourth order QHD approximations are applied to two model problems: the decay of a particle in a metastable cubic potential and the intermode energy exchange observed in the Henon–Heiles system. The QHD results exhibit good convergence with the quantum data with increasing order yet preserve the computational efficiency of classical calculations. The second order QHD approximation already does an excellent job in maintaining the zero-point energy in the Henon–Heiles system and describing moderate tunneling events in the metastable potential. Extensions to higher orders substantially improve the QHD results for deep tunneling and are capable of describing the finer details of energy exchange.

Molecular dynamics simulation of vibrational relaxation of highly excited molecules in fluids. II. Nonequilibrium simulation of azulene in CO2 and Xe

Results of nonequilibrium molecular dynamics simulations of vibrational energy relaxation of azulene in carbon dioxide and xenon at low and high pressure are presented and analyzed. Simulated relaxation times are in good agreement with experimental data for all systems considered. The contribution of vibration–rotation coupling to vibrational energy relaxation is shown to be negligible. A normal mode analysis of solute-to-solvent energy flux reveals an important role of high-frequency modes in the process of vibrational energy relaxation. Under all thermodynamic conditions considered they take part in solvent-assisted intramolecular energy redistribution and, moreover, at high pressure they considerably contribute to azulene-to-carbon dioxide energy flux. Solvent-assisted (or collision-induced) intermode energy exchange seems to be the main channel, ensuring fast intramolecular energy redistribution. For isolated azulene intramolecular energy redistribution is characterized by time scales from several to hundreds of ps and even longer, depending on initial excitation. The major part of solute vibrational energy is transferred to the solvent via solute out-of-plane vibrational modes. In-plane vibrational modes are of minor importance in this process. However, their contribution grows with solvent density. The distribution of energy fluxes via azulene normal modes strongly depends on thermodynamic conditions. The contribution of hydrogen atoms to the overall solute-to-solvent energy flux is approximately two to three times higher than of carbon atoms depending on the system and thermodynamic conditions as well. Carbon atoms transfer energy only in the direction perpendicular to the molecular plane of azulene, whereas hydrogen atoms show more isotropic behavior, especially at high pressure.

Phase space bottlenecks and rates of no-barrier fragmentation reactions into polyatomic molecules

An expression of the microcanonical unimolecular rate for an arbitrary transition state surface in phase space is derived and applied to fragmentation reactions into polyatomic molecules without potential barrier. The transition state which has a ‘‘point of no return’’ property in unimolecular dissociation is defined as an interfragment bottleneck in phase space. The fragmentation rate based on the interfragment bottleneck in phase space is compared with the rate based on the transition state defined in configuration space. The rate derived from the flux which crosses the interfragment bottleneck by intermode energy transfer is found to be smaller than the rate derived from the Rice–Ramsperger–Kassel–Marcus or phase space theory by an approximate factor (s+r/2)|W̃|/E, where E is the total energy and |W̃| is the magnitude of the coupling energy between the reaction coordinate and the s-dimensional vibrational and r-dimensional rotational modes of the fragments. Phase space theory grossly overestimates the rate of fragmentation of small molecules with small |W̃| in the high energy range, because the theory does not take into account the slow process of intramolecular energy redistribution.

Ultrafast infrared spectroscopy of vibrational CO-stretch up-pumping and relaxation dynamics of W(CO) 6

The ultrafast infrared (IR) vibrational up-pumping and energy relaxation dynamics are reported of the T 1u CO-stretching manifold of W(CO) 6 in room temperature n-hexane solution. The frequency and energy content of the tunable 2 ps IR pump pulse strongly influences the distribution of vibrational level population. With broadband transient IR absorption spectroscopy, vibrational T 1 lifetimes of the overtone states of W(CO) 6 were directly determined to be 140 ± 20 (1 σ) ps for ν = 1, 75 ± 20 ps for ν = 2 and 30 ± 15 ps for ν = 3. T 1u to E g intermode energy transfer occurs on the 10–20 ps timescale.

Infrared fluorescence from CO2 laser-pumped CF2HCl: collision dynamics of intermode energy flow

Infrared fluorescence (IRF) has been observed from 2ν3, 2ν2 and ν1 modes of CF2HCl following CO2laser excitation. The IRF signal was studied as a function of parent and buffer gas pressure. From the kinetic analysis, the decay rate constant for the 2ν3 mode was calculated to be (4.2 ± 1.0)× 104s–1 Torr–1[1 Torr =(101 325/760) Pa], which is assigned to the outflow of vibrationally excited population from the ν3 mode. The rise and decay rate constants for the v1 mode were estimated to be (1.2 ± 0.3)× 105 and (3.9 ± 0.9)× 104s–1 Torr–1, respectively. The ν1 decay rate constant was assigned to the intermode vibrational–vibrational (V–V) relaxation process from the ν1 mode.

Theoretical studies of vibrationally assisted reactions of the O3 ⋅ NO van der Waals complex

The exchange reaction and dissociation dynamics of two O3 ⋅ NO van der Waals complexes upon vibrational excitation has been determined at two different internal energies from the results of quasiclassical trajectories. The dynamics for such complexes is found to resemble that for chemical reactions occurring under matrix isolation conditions and to be significantly different from the O3+NO bimolecular collision dynamics. Mode specificity is found for reaction, vibrational predissociation, and intermode energy transfer. Structure specificity is also observed for the van der Waals complexes. In most cases, the asymmetric stretching mode of O3 is found to be the most effective in promoting reaction. For predissociation and intermode energy transfer, the O3 bending mode is usually the most effective. We find that a five-step mechanism consisting of two non-RRKM reactions, a non-RRKM energy transfer step, and two RRKM steps is required to explain the overall reaction. Excitation of the hindered rotational of NO about the O3 symmetry axis is found to significantly influence the dynamics in that partitioning of less than 2% of the energy into such motion dramatically increases the predissociation rate and, by inference, the intermode energy transfer rate. Excitation of the NO vibrational mode is found to be much less effective in promoting reaction or vibrational predissociation on this potential-energy surface.