Nonequilibrium Vibrational Distribution Research Articles

Charge-State Dependent Vibrational Relaxation in a Single-Molecule Junction.

The outcome of an electron-transfer process is determined by the quantum-mechanical interplay between electronic and vibrational degrees of freedom. Nonequilibrium vibrational dynamics are known to direct electron-transfer mechanisms in molecular systems; however, the structural features of a molecule that lead to certain modes being pushed out of equilibrium are not well understood. Herein, we report on electron transport through a porphyrin dimer molecule, weakly coupled to graphene electrodes, that displays sequential tunneling within the Coulomb-blockade regime. The sequential transport is initiated by current-induced phonon absorption and proceeds by rapid sequential transport via a nonequilibrium vibrational distribution of low-energy modes, likely related to torsional molecular motions. We demonstrate that this is an experimental signature of slow vibrational dissipation, and obtain a lower bound for the vibrational relaxation time of 8ns, a value dependent on the molecular charge state.

Non-Boltzmann vibrational energy distributions and coupling to dissociation rate.

In this article, we propose a generalized model for nonequilibrium vibrational energy distribution functions. The model can be used, in place of equilibrium (Boltzmann) distribution functions, when deriving reaction rate constants for high-temperature nonequilibrium flows. The distribution model is derived based on the recent ab initio calculations, carried out using potential energy surfaces developed using accurate computational quantum chemistry techniques for the purpose of studying air chemistry at high temperatures. Immediately behind a strong shock wave, the vibrational energy distribution is non-Boltzmann. Specifically, as the gas internal energy rapidly excites to a high temperature, overpopulation of the high-energy tail (relative to a corresponding Boltzmann distribution) is observed in ab initio simulations. As the gas excites further and begins to dissociate, a depletion of the high-energy tail is observed, during a time-invariant quasi-steady state. Since the probability of dissociation is exponentially related to the vibrational energy of the dissociating molecule, the overall dissociation rate is sensitive to the populations of these high vibrational energy states. The non-Boltzmann effects captured by the new model either enhance or reduce the dissociation rate relative to that obtained assuming a Boltzmann distribution. This article proposes a simple model that is demonstrated to reproduce these non-Boltzmann effects quantitatively when compared to ab initio simulations.

Franck-Condon Theory of Quantum Mechanochemistry.

The spectroscopic Franck-Condon (FC) principle is extended to mechanochemistry. If the external force is applied rapidly (the sudden-force regime), then the transition between the potential energy surface and the force-modified potential energy surface is analogous to the optical electronic transition. Such a transition produces a nonequilibrium ensemble of vibrationally excited molecules. This excess of vibrational energy is another activation source in addition to the well-known reaction barrier modulation by the external force. In the same time, the nonequilibrium vibrational distribution implies nonstatistical kinetics of a mechanochemical transformation. Mechanochemical FC principle thus provides a conceptual picture for the sudden-force mechanochemistry and opens possibilities for quantitative calculations of the mechanochemical rates and mechanisms. Here we use it to compute the dissociation rates of a model diatomic molecule and to explain the selectivity in mechanochemical bond breaking in n-butane. The approach is predicted to be relevant for large-magnitude external forces, applied instantaneously. Otherwise, the excess vibrational energy will dissipate due to intramolecular vibrational redistribution and interaction with environment.

Pooling through cooling: creating optimal vibrational non-equilibrium in CO2 by supersonic expansion

We present a quasi-1D model to study the influence of supersonic expansion on the non-equilibrium vibrational distribution function in CO2, relevant for the energy efficient splitting of CO2. The model includes 21 vibrational levels and state-to-state vibrational kinetics. It is found that the amount of non-equilibrium after the expansion is strongly dependent on the nozzle geometry. The highest degree of non-equilibrium is found for moderate Mach numbers. The inflow pressure appears to have a negligible effect on the degree of non-equilibrium. Lowering the inflow temperature has a beneficial effect on the vibrational distribution function.

Relaxation of vibrational nonequilibrium distributions: the effect of multiphoton excitation on relaxation behavior

A theoretical study has been made on the non-stationary relaxation of highly vibrationally excited molecules in the presence of a source, producing these molecules. Initially, the nonequilibrium vibrational distribution is created using multiphoton absorption of laser radiation. An exact, analytical solution to the master equation is derived in terms of Meixner polynomials with regard to VV- and VT-processes. The time-dependent distribution of the system “molecule + field” is used to give explicit expressions for the mean number of photons distributed among vibrational and translational degrees of freedom and for the time dependence of average energy transferred per collision.

Spectrum of sprite halos

[1] Spectra of sprite halos in the spectral ranges 200–500 nm and 640–1065 nm are calculated for different spectral resolutions (between 2 nm and 10 nm), rotational temperatures (220 K and 1000 K) and observation altitudes corresponding to mountain (3 km and 4.3 km), airplane (14 km), balloon (35 km) and space observation platforms. We have calculated the non-equilibrium vibrational distribution functions (VDF) of different excited electronic states of molecular nitrogen (N2) associated to sprite halo optical emissions in the ultraviolet (UV), due to the N2 Lyman-Birge-Hopfield (LBH) and Vegard-Kaplan (VK) band systems, and near UV, visible and near infrared (NIR) due to the first (1PG) and second positive (2PG) bands of N2. Comparison of synthetic sprite halo spectra with the single sprite halo spectrum existing to date shows reasonable agreement after the observed sprite halo spectra was corrected for instrument sensitivity response. Calculated VDFs of the N2(B3Πg) and N2(C3Πu) states of sprite halos show that the blue and NIR emissions produced through strong N2-1PG (B3Πg → A3Σu+) and N2-2PG (C3Πu → B3Πg) transitions are generally similar to those of known sprite spectral emission patterns, but differences may be observable at some vibrational levels. The calculated sprite halo spectra can be used as a predictive tool for the expected spectral emissions of sprite halos in different possible scenarios.

Counting statistics of tunneling through a single molecule: Effect of distortion and displacement of vibrational potential surface

We analyze the effects of a distortion of the nuclear potential of a molecular quantum dot (QD) as well as a shift in its equilibrium position on nonequilibrium-vibration-assisted tunneling through the QD with a single level (εd) coupled to the vibrational mode. For this purpose, we derive an explicit analytical expression for the Franck–Condon (FC) factor for a displaced-distorted oscillator surface of the molecule and establish rate equations in the joint electron-phonon representation to examine the current-voltage characteristics and zero-frequency shot noise and skewness as well. Our numerical analysis shows that the distortion has two important effects. The first one is that it breaks the symmetry between the excitation spectra of the charge states, leading to asymmetric tunneling properties with respect to εd>0 and εd<0. Second, distortion (frequency change in the oscillator) significantly changes the voltage-activated cascaded transition mechanism and consequently gives rise to a different nonequilibrium vibrational distribution from that of the case without distortion. Taken in conjunction with strongly modified FC factors due to distortion, this results in some new transport features: the appearance of strong negative differential conductance even for a single-level QD with symmetric tunnel couplings, a giant Fano factor even for a molecule with an extremely weak electron-phonon interaction, and enhanced skewness that can have a large negative value under certain conditions.

Quantum-state resolved reactive scattering at the gas-liquid interface: F+squalane (C30H62) dynamics via high-resolution infrared absorption of nascent HF(v,J)

Exothermic chemical reaction dynamics at the gas-liquid interface have been investigated by colliding a supersonic beam of F atoms [E(com)=0.7(3) kcalmol] with a continuously refreshed liquid hydrocarbon (squalane) surface under high vacuum conditions. Absolute HF(v,J) product densities are determined by infrared laser absorption spectroscopy, with velocity distributions along the probe axis derived from high resolution Dopplerimetry. Nascent HF(v<or=3) products are formed in a highly nonequilibrium (inverted) vibrational distribution [E(vib)=13.2(2) kcalmol], reflecting insufficient time for complete thermal accommodation with the surface prior to desorption. Colder, but still non-Boltzmann, rotational state populations [E(rot)=1.0(1) kcalmol] indicate that some fraction of molecules directly scatter into the gas phase without rotationally equilibrating with the surface. Nascent HF also recoils from the liquid surface with excess translational energy, resulting in Doppler broadened linewidths that increase systematically with internal HF excitation. The data are consistent with microscopic branching in HF-surface dynamics following the reactive event, with (i) a direct reactive scattering fraction of newly formed product molecules leaving the surface promptly and (ii) a trapping desorption fraction that accommodates rotationally (though still not vibrationally) with the bulk liquid. Comparison with analogous gas phase F+hydrocarbon processes reveals that the liquid acts as a partial "heat sink" for vibrational energy flow on the time scale of the chemical reaction event.

Time-resolved Fourier transform infrared emission spectroscopy of laser ablation products

Time-resolved Fourier transform infrared spectroscopy was applied for observations of emission spectra from ablation products induced by a Nd:YLF laser with a 2.5 kHz repletion rate. The infrared emission spectra from Fe, Cu, Zn, and Al atoms were observed in the 2.5–5 μm region. The observed emission spectrum from iron ablation in the 2500 cm −1 region agrees very well with solar absorption spectrum, where new lines have been detected in the present experiment in addition to the lines observed from a hollow cathode discharge. When O 2 was added to the carbon ablation, emissions from vibrationally excited CO were observed with non-equilibrium vibrational distribution.

The dynamics of direct three-body recombination of ions

The trajectory simulation of the direct recombination of the Cs+ and Br− heavy ions in the presence of third-body atoms R = Kr, Xe, Hg was performed on the potential energy surface that controlled the dissociation of CsBr induced by collisions with the same R. The results showed that the probability of recombination decreased as the energy of the approach of ions to each other and the energy of a third body with respect to the center of mass of the ion pair increased. Direct recombination proceeds according to at least two mechanisms of the stabilization of the molecule formed. The first mechanism involves the collision of the R atom with both ions at low impact parameters with respect to the center of gravity of the ion pair. In the second mechanism, impact parameters are large, and energy is removed through a collision with one of the ions of the pair. The products formed have a strongly nonequilibrium vibrational distribution and almost equilibrium rotational energy distribution.

An evaluation of the effect of the dissociative attachment of vibrationally excited H2on primordial universe chemistry

Aims. We study the relevance of including vibrational levels of molecular hydrogen in one of the processes taking place in the primordial Universe: the dissociative attachment of H2. Methods. We calculated the rate of dissociative attachment of H2, covering the contribution of all vibrational levels in standard conditions for primordial Universe chemistry. We then compared this rate to the rates of other chemical processes relevant for H2 balance as a function of z. Results. It is shown that vibrationally excited levels of molecular hydrogen cannot be neglected in evaluating the rate of dissociative attachment in early Universe conditions and that this process is one of the most relevant channels for destruction of H2 molecules at z ≈ 10 3 . We also propose a preliminary estimation of the effect of a possible non-equilibrium vibrational distribution on the results.

Vibrational relaxation of CO2(ν2) by atomic oxygen

In the Earth's upper atmosphere, collisions with ambient O atoms efficiently excite the CO2 [0000] vibrational ground‐state population to the first excited, [0110] or ν2, vibrational bend state. Subsequent relaxation of the ν2 population occurs through spontaneous emission of 15‐μm radiation. Much of this radiation escapes into space, thereby removing ambient kinetic energy from the atmosphere. This cooling mechanism is especially important at altitudes between the mesopause and the lower thermosphere, approximately 80–120 km, where the O‐atom density is relatively high and the kinetic temperature is rising. Laboratory measurements have been performed to better characterize the CO2(ν2)‐O vibrational relaxation rate coefficient kO(ν2). A 266‐nm laser pulse photolyzed trace amounts of O3 in a CO2‐O3‐rare gas mixture, simultaneously creating O atoms and raising the gas temperature to create a nonequilibrium CO2 vibrational distribution. Transient diode laser absorption spectroscopy was used to monitor CO2 vibrational level population reequilibration. A global nonlinear least squares fitting technique was used to interpret the kinetic data, yielding kO(ν2) = (1.8 ± 0.3) × 10−12 cm3s−1. The result is in good agreement with previous laboratory measurements, with published kO(ν2) values in the (1.2–1.5) × 10−12 cm3s−1 range and at the low end of the (2–6) × 10−12 cm3s−1 range estimated from the analysis of upper atmospheric data.

Reduction of State-to-State Kinetics to Macroscopic Models in Hypersonic Flows

The state-to-state chemical kinetic model, which considers a kinetic equation for each vibrational state of diatomic molecules, has been applied to some supersonic flow regimes and in particular in boundary layer, nozzle expansion, and shock wave. Nonequilibrium vibrational distribution obtained in the calculations shows strong departure from equilibrium-inducing non-Arrhenius global chemical rates, which differ substantially from macroscopic rates commonly used in fluid-dynamic codes. The evolution properties of the distribution have been investigated by a zero-dimensional numerical code in controlled conditions. We are trying to obtain from zero-dimensional results the approach to find appropriate macroscopic rate models to be used in fluid-dynamic codes accounting for the vibrational nonequilibrium. A comparison of analytical fitting of the zero-dimensional data and fluid dynamic global rates has been performed. Nomenclature ci = coefficients for the solution of the master equation Ev = energy of the vth vibrational level k = Boltzmann constant k d = dissociation rate constant k p = rates of the process p

Nuclear wavefunction interference in single-molecule electron transport

It is demonstrated that non-equilibrium vibrational effects are enhanced in molecular devices for which the effective potential for vibrations is sensitive to the charge state of the device. We calculate the electron tunnelling current through a molecule accounting for the two simplest qualitative effects of the charging on the nuclear potential for vibrational motion: a shift (change in the equilibrium position) and a distortion (change in the vibrational frequency). The distortion has two important effects: firstly, it breaks the symmetry between the excitation spectra of the two charge states. This gives rise to new transport effects which map out changes in the current-induced non-equilibrium vibrational distribution with increasing bias voltage. Secondly, the distortion modifies the Franck–Condon factors for electron tunnelling. Together with the spectral asymmetry this gives rise to pronounced nuclear wavefunction interference effects on the electron transport. For instance nuclear-parity forbidden transitions lead to differential conductance anti-resonances, which are stronger than those due to allowed transitions. For special distortion and shift combinations a coherent suppression of transport beyond a bias voltage threshold is possible.

Theory of inelastic tunneling and its relation to vibrational excitation in ladder climbing processes of single adsorbates

A relation between inelastic electron tunneling (IET) current and vibrational generation rate, a key source of vibrational heating, is studied on the basis of the adsorbate-induced resonance model for inelastic electron tunneling using the coupled Dyson and kinetic equations of phonon number for the causal and statistical Keldysh–Green functions. The self-consistent solution of the kinetic equation gives the stationary nonequilibrium vibrational distribution function, from which a general formula for the vibrational heating is derived. A physical explanation of a relation between the elementary processes for inelastic electron tunneling and vibrational excitation is demonstrated. Based on the numerical calculations including the self-consistently determined vibrational distribution function and the vibrational density of states, the influence of vibrational relaxation due to electron–hole pair excitations and sample temperature on the IET current and on the vibrational generation rate is discussed with a primary attention to a possible deviation from a simple power-law dependence of the reaction rate in the vicinity of the threshold for the adsorbate motion. It is found that the temperature broadening appears to be confined near the threshold voltage, whereas the lifetime broadening manifests itself in a much wider region of applied voltage below the threshold.

Spectral–kinetic characteristics of the F2 laser transition

A theoretical model for the F2(D′–A′) laser transitions is built. The model includes a scheme of the main laser transitions proposed. A value of the radiative lifetime of the upper laser level in the conventional kinetic models of the F2 laser is proved to be underestimated by one order of magnitude. A general theory of steady-state light amplification in a molecular laser with non-equilibrium vibrational distribution is developed. Relations of the small-signal gain and the saturating energy flux with parameters of molecular electronic–vibrational kinetics are established. The theory is applied to explain properties of F2 laser amplifiers.

Possibility of revealing the role of nonresonant energy exchange between electrons and CO molecules at high vibrational levels

An experimental method providing information about the interaction of electrons with excited CO molecules at high vibrational levels is proposed and justified theoretically. The suggested experimental scheme is based on the use of two successive discharge pulses under the conditions prevailing in an electroionization CO laser. The first pulse should ensure a sufficiently high energy input in order for a nonequilibrium vibrational distribution function to form. The second pulse serves to study the effect of the electric current on the vibrational distribution function of excited molecules at high vibrational levels. The theoretical analysis is based on the simultaneous solution of the Boltzmann equation for the electron energy distribution function and the vibrational kinetic equations realistically describing the multiquantum vibrational-vibrational exchange processes. The calculated results show that the sensitivity of the proposed measurement technique promises to be high.

Vibrational non-equilibrium and `hot atoms' in the oxidation of carbon monoxide on catalytic surfaces

Non-equilibrium vibrational kinetics, as recently developed for adlayers, is applied to the catalytic oxidation of CO by either molecular or atomic oxygen. This model allows one to fit experimental distribution functions of the product CO 2(g) molecules leaving the surface with hyperthermal energies. An LH * mechanism involving non-equilibrium vibrational distribution functions (vdfs) of the relevant adspecies is presented showing the basic consequences of non-equilibrium at the catalytic surface. In this picture `hot atoms' are seen as mobile, vibrationally excited adspecies with their vibrational ladders populated according to non-equilibrium Treanor distribution functions.

Vibrational Non-Equilibrium at Catalytic Surfaces

Inclusion in a surface reaction scheme of fast V-V up-pumping processes, bound to the anharmonicity of the vibrational levels of mobile surface species, can lead to quasi-steady states characterized by non-equilibrium Treanor vibrational distribution functions, with ν > 0 levels over-populated with respect to Boltzmann equilibrium. Non-equilibrium distributions are shown to depend on the intensity of the chemisorption processes active under the working conditions of the catalyst. The shape of these distributions determines the surface reaction rate, and reactions with widely different “true” activation energies can proceed at comparable speeds at finite surface temperatures. This provides an interpretation of the isokinetic relationship in heterogeneous catalysis based on a non-Boltzmann picture of the catalytic surface.

AIO VIBRATIONAL TEMPERATURE MEASUREMENTS FROM BURNING ALUMINUM PARTICLES AT ELEVATED PRESSURE

A streak camera is used to obtain time-resolved AIO emission spectra from burning 10 micron aluminum particles in a C02/Ar mixture at 8.6 atmospheres in a shock tube. Digital spectra are obtained with a temporal resolution of 16 microseconds over the entire 180 microsecond combustion event. These spectra are fit to vibrational temperatures in the range of 4225 to 5900 K, with uncertainties ranging from 500 to 1400 K. The estimated temperatures are in agreement to within experimental uncertainty with the predicted aluminum combustion temperatures under these conditions. The spectra show some evidence of a non-equilibrium vibrational population distribution during peak of the combustion event.