Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

Classical model for electronically non-adiabatic collision processes resonance effects in electronic-vibrational energy transfer

A classical model for electronically non-adiabatic collision processes is applied to E → V energy transfer in a collinear system, A + BC (v = 1) → A¹ + BC (v = 0), resembling Br-H₂.The model, which treats electronic as well as translational, rotational, and vibrational degrees of freedom by classical mechanics, describes the resonance features in this process reasonably well.     

Ultrafast many-body energy transfer in the frequency domain

In this paper, we consider the response of many-body systems to ultrashort time scale impulsive perturbations. We focus on the interplay between the characteristic frequencies and time scales of the interacting degrees of freedom, and develop both a qualitative picture and a simple analytic theory in terms of a frequency domain perspective. We illustrate the general approach by considering a model many-body problem consisting of the impulsive collision of an atom with a harmonic chain, and treat the dynamics using classical mechanics. An analytic expression for the energy uptake of the chain is derived, and its predictions are compared with classical molecular dynamics simulations on a one-dimensional model of rare gas scattering from a Pt surface. Our approach highlights the importance of the overlap in frequency between the phonon spectrum of the solid, weighted by each mode's contribution to the surface atom displacement, and the power spectrum of the impulsive force felt by the surface during the collision. The analytic theory reproduces the high energy kinematic limit of binary atom–atom collisional energy transfer, and emphasizes the adiabatic “freezing out” of high frequency phonons as the collision energy is decreased.     

Role of projectile and surface temperatures in the energy transfer dynamics of protonated peptide ion collisions with the diamond {111} surface

The effects of temperature on energy transfer during collisions of protonated diglycine ions, Gly(2)-H(+), with a diamond {111} surface were investigated by chemical dynamics simulations. The simulations were performed for a collision energy of 70 eV and angle of 0 degrees with respect to the surface normal. In one set of simulations the initial surface temperature, T(surf), was varied from 300 to 2000 K, while the Gly(2)-H(+) vibrational and rotational temperatures were maintained at 300 K. For the second set of simulations the Gly(2)-H(+) vibrational temperature, T(vib), was varied from 300 to 2000 K, keeping both the Gly(2)-H(+) rotational and surface temperatures at 300 K. Increasing either the surface temperature or Gly(2)-H(+) vibrational temperature to values as high as 2000 K has, at most, only a negligible effect on the partitioning of the incident collision energy to the surface and to the vibrational and rotational modes of Gly(2)-H(+). To a good approximation, the initial surface and peptide ion energies are nearly adiabatic during the collisional energy transfer. This adiabaticity of the initial peptide ion energy agrees with experiments (J. Phys. Chem. A 2004, 108, 1). A more quantitative analysis of the effects of T(vib) and T(surf) shows there are small, but noticeable, effects on the energy transfer efficiencies. Namely, increasing the vibrational or surface temperature results in a near-linear decrease in the energy transfer to the degrees of freedom associated with this temperature.     

Dynamics of energy transfer in peptide-surface collisions

Classical trajectory simulations are performed to study energy transfer in collisions of protonated triglycine (Gly)(3) and pentaglycine (Gly)(5) ions with n-hexyl thiolate self-assembled monolayer (SAM) and diamond [111] surfaces, for a collision energy E(i) in the range of 10-110 eV and a collision angle of 45 degrees. Energy transfer to the peptide ions' internal degrees of freedom is more efficient for collision with the diamond surface; i.e., 20% transfer to peptide vibration/rotation at E(i) = 30 eV. For collision with diamond, the majority of E(i) remains in peptide translation, while the majority of the energy transfer is to surface vibrations for collision with the softer SAM surface. The energy-transfer efficiencies are very similar for (Gly)(3) and (Gly)(5). Constraining various modes of (Gly)(3) shows that the peptide torsional modes absorb approximately 80% of the energy transfer to the peptide's internal modes. The energy-transfer efficiencies depend on E(i). These simulations are compared with recent experiments of peptide SID and simulations of energy transfer in Cr(CO)(6)(+) collisions with the SAM and diamond surfaces.     

A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies

A new model for energy exchange between translational and internal degrees of freedom in atom-molecule collisions has been developed. It is suitable for both steady state conditions (e.g., a large number of collisions with thermal kinetic energies) and non-steady state conditions with an arbitrary distribution of collision energies (e.g., single high-energy collisions). In particular, it does not require that the collision energies be characterized by a quasi-thermal distribution, but nevertheless it is capable of producing a Boltzmann distribution of internal energies with the correct internal temperature under quasi-thermal conditions. The energy exchange is described by a transfer probability density that depends on the initial relative kinetic energy, the internal energy of the molecule, and the amount of energy transferred. The probability density for collisions that lead to excitation is assumed to decrease exponentially with the amount of transferred energy. The probability density for de-excitation is obtained from microscopic reversibility. The model has been implemented in the ion trap simulation program ITSIM and coupled with an Rice-Rampsberger-Kassel-Marcus (RRKM) algorithm to describe the unimolecular dissociation of populations of ions. Monte Carlo simulations of collisional energy transfer are presented. The model is validated for non-steady state conditions and for steady state conditions, and the effect of the kinetic energy dependence of the collision cross-section on internal temperature is discussed. Applications of the model to the problem of chemical mass shifts in RF ion trap mass spectrometry are shown.     

Dissociative chemisorption and energy transfer for methane on Ir(111)

A 3-parameter local hot spot model of gas-surface reactivity is employed to analyze and predict dissociative sticking coefficients for CH(4) incident on Ir(111) under varied nonequilibrium and equilibrium conditions. One Ir surface oscillator and the molecular vibrations, rotations, and translational energy directed along the surface normal are treated as active degrees of freedom in the 14 dimensional microcanonical kinetics. The threshold energy for CH(4) dissociative chemisorption on Ir(111) derived from modeling molecular beam experiments is E(0) = 39 kJ/mol. Over more than 4 orders of magnitude of variation in sticking, the average relative discrepancy between the beam and theoretically derived sticking coefficients is 88%. The experimentally observed enhancement in dissociative sticking as beam translational energies decrease below approximately 10 kJ/mol is consistent with a parallel dynamical trapping/energy transfer channel that likely fails to completely thermalize the molecules to the surface temperature. This trapping-mediated sticking, indicative of specific energy transfer pathways from the surface under nonequilibrium conditions, should be a minor contributor to the overall dissociative sticking at thermal equilibrium. Surprisingly, the CH(4) dissociative sticking coefficient predicted for Ir(111) surfaces at thermal equilibrium, based on the molecular beam experiments, is roughly 4 orders of magnitude higher than recent measurements on supported nanoscale Ir catalysts at 1 bar pressure, which suggests that substantial improvements in catalyst turnover rates may be possible.     

Application of the Monte Carlo method to modeling of kinetic processes with the participation of polyatomic molecules and clusters: 1. Kinetics of energy transfer during collisions of polyatomic molecules

The Monte Carlo method was used to model the collisional energy transfer for polyatomic molecules within the framework of the statistical theory of reactions. A model describing energy transfer through the formation of a statistical collisional complex was suggested. It was assumed that the total energy of the complex was randomized in the course of collisions and statistically distributed among the internal and translational degrees of freedom. The method was verified by comparing the equilibrium distribution functions for the vibrational, rotational, and total energies of the molecule. The mean energy portion and the root-mean-square energy portion transferred per collision, as functions of the total molecular energy, were determined. The relaxation parameters of the population distribution over energy after a sharp increase in the bath-gas temperature were calculated.     

Dynamically biased RRKM model of activated gas-surface reactivity: vibrational efficacy and rotation as a spectator in the dissociative chemisorption of CH4 on Pt(111)

The reactivity of CH(4) impinging on a Pt(111) surface was examined using a precursor-mediated microcanonical trapping model of dissociative chemisorption wherein the effects of rotational and vibrational energy could be explored. Dissociative sticking coefficients for a diverse range of non-equilibrium effusive beam, supersonic beam, and eigenstate-resolved experiments were simulated and an average relative discrepancy between theory and experiment of better than 50% was achieved by treating molecular rotations and translation parallel to the surface as spectator degrees of freedom, and introducing a dynamically-biased vibrational efficacy. The model parameters are {E(0) = 57.9 kJ mol(-1), s = 2, η(v) = 0.40} where E(0) is the apparent threshold energy for reaction, s is the number of surface oscillators participating in energy exchange within each gas-surface collision complex formed, and η(v) is the mean vibrational efficacy for reaction relative to normal translational energy which figures in the assembly of the active exchangeable energy which is available to surmount the activation barrier to dissociative chemisorption. GGA-DFT electronic structure calculations provided vibrational frequencies for the transition state for dissociative chemisorption. The asymmetry of the rotational state populations in supersonic and effusive molecular beam experiments allowed kinetic analysis to establish that taking rotation as a spectator degree of freedom is a good approximation. Surface phonons, rather than the incident molecules, are calculated to play the dominant role in supplying the energy required to overcome the activation barrier for dissociative chemisorption under the thermal equilibrium conditions relevant to high pressure catalysis. Over the temperature range 300 K ≤T≤ 1000 K, the thermal dissociative sticking coefficient is predicted to be well described by S(T) = S(0) exp(-E(a)/RT) where S(0) = 0.62 and E(a) = 62.6 kJ mol(-1).     

Molecular dynamics with quantum transitions study of the vibrational relaxation of the HOD bend fundamental in liquid D2O

The molecular dynamics with quantum transitions method is used to study the vibrational relaxation of the HOD bend fundamental in liquid D(2)O. All of the vibrational bending degrees of freedom of the HOD and D(2)O molecules are described by quantum mechanics, while the remaining translational and rotational degrees of freedom are described classically. The effect of the coupling between the rotational and vibrational degrees of freedom of the deuterated water molecules is analyzed. A kinetic mechanism based on three steps is proposed in order to interpret the dynamics of the system. It is shown that intermolecular vibrational energy transfer plays an important role in the relaxation process and also that the transfer of energy into the rotational degrees of freedom is favored over the transfer of energy into the translational motions. The thermalization of the system after the relaxation is reached in a shorter time scale than that of the recovery of the hydrogen bond network. The relaxation and equilibration times obtained compare well with experimental and previous theoretical results.     

Controlling an Electron‐Transfer Reaction at a Metal Surface by Manipulating Reactant Motion and Orientation

The loss or gain of vibrational energy in collisions of an NO molecule with the surface of a gold single crystal proceeds by electron transfer. With the advent of new optical pumping and orientation methods, we can now control all molecular degrees of freedom important to this electron‐transfer‐mediated process, providing the most detailed look yet into the inner workings of an electron‐transfer reaction and showing how to control its outcome. We find the probability of electron transfer increases with increasing translational and vibrational energy as well as with proper orientation of the reactant. However, as the vibrational energy increases, translational excitation becomes unimportant and proper orientation becomes less critical. One can understand the interplay of all three control parameters from simple model potentials.     

Microcanonical unimolecular rate theory at surfaces. II. Vibrational state resolved dissociative chemisorption of methane on Ni(100)

A three-parameter microcanonical theory of gas-surface reactivity is used to investigate the dissociative chemisorption of methane impinging on a Ni(100) surface. Assuming an apparent threshold energy for dissociative chemisorption of E(0)=65 kJ/mol, contributions to the dissociative sticking coefficient from individual methane vibrational states are calculated: (i) as a function of molecular translational energy to model nonequilibrium molecular beam experiments and (ii) as a function of temperature to model thermal equilibrium mbar pressure bulb experiments. Under fairly typical molecular beam conditions (e.g., E(t)>/=25 kJ mol(-1), T(s)>/=475 K, T(n)/=100 K the dissociative sticking is dominated by methane in vibrationally excited states, particularly those involving excitation of the nu(4) bending mode. Fractional energy uptakes f(j) defined as the fraction of the mean energy of the reacting gas-surface collision complexes that derives from specific degrees of freedom of the reactants (i.e., molecular translation, rotation, vibration, and surface) are calculated for thermal dissociative chemisorption. At 500 K, the fractional energy uptakes are calculated to be f(t)=14%, f(r)=21%, f(v)=40%, and f(s)=25%. Over the temperature range from 500 K to 1500 K relevant to thermal catalysis, the incident gas-phase molecules supply the preponderance of energy used to surmount the barrier to dissociative chemisorption, f(g)=f(t)+f(r)+f(v) approximately 75%, with the highest energy uptake always coming from the molecular vibrational degrees of freedom. The predictions of the statistical, mode-nonspecific microcanonical theory are compared to those of other dynamical theories and to recent experimental data.     

Energy transfer of highly vibrationally excited naphthalene. III. Rotational effects

The rotational effects in the energy transfer between Kr atoms and highly vibrationally excited naphthalene in the triplet state were investigated using crossed-beam/time-sliced velocity map ion imaging at various translational collision energies. As the initial rotational temperature changes from less than 10 to approximately 350 K, the ratio of vibrational to translational (V-->T) energy transfer cross section to translational to vibrational/rotational (T-->VR) energy transfer cross section increases, but the probability of forming a complex during the collisions decreases. Significant increases in the large V-->T energy transfer probabilities, termed supercollisions, at high initial rotational temperature were observed.     

Energy transfer of highly vibrationally excited azulene: collisions between azulene and krypton

The energy-transfer dynamics between highly vibrationally excited azulene molecules and Kr atoms in a series of collision energies (i.e., relative translational energies 170, 410, and 780 cm(-1)) was studied using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. "Hot" azulene (4.66 eV internal energy) was formed via the rapid internal conversion of azulene initially excited to the S4 state by 266-nm photons. The shapes of the collisional energy-transfer probability density functions were measured directly from the scattering results of highly vibrationally excited or hot azulene. At low enough collision energies an azulene-Kr complex was observed, resulting from small amounts of translational to vibrational-rotational (T-VR) energy transfer. T-VR energy transfer was found to be quite efficient. In some instances, nearly all of the translational energy is transferred to vibrational-rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy (V-T). The shapes of V-T energy-transfer probability density functions were best fit by multiexponential functions. We find that substantial amounts of energy are transferred in the backward scattering direction due to supercollisions at high collision energies. The probability for supercollisions, defined arbitrarily as the scattered azulene in the region 160 degrees 2000 cm(-1) is 1% and 0.3% of all other collisions at collision energies 410 and 780 cm(-1), respectively.     

A microscopic model of chemical reactions with reorganization. High-energy approximation

A dynamical model of a chemical reaction, accompanied by reorganization of the immediate environment of the isolated chemical subsystem, is proposed. The model enables studying the emergence of nonequilibrium distribution functions as a combined result of the interaction within the dynamical subsystem and the energy exchange with a subsystem of inactive degrees of freedom (thermal bath). The study is based on the quasiclassical high-energy approximation for nonadiabatic effects in the energy exchange within the dynamical subsystem, for strong and weak coupling of the oscillator mode with the thermal bath. Such an approximation allows for the important statement that nonequilibrium effects in thermal reactions are absent if the initial translational distribution along the reaction coordinate and the initial vibrational distribution in transversal degrees of freedom are Boltzmann-like with the same temperature. The results obtained in the absence of the initial equilibrium distribution have been used for interpreting the kinetics of endothermic plasmochemical reactions proceeding under nonequilibrium conditions.     

Energy transfer of highly vibrationally excited naphthalene. I. Translational collision energy dependence

Energy transfer between highly vibrationally excited naphthalene and Kr atom in a series of translational collision energies (108-847 cm(-1)) was studied separately using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. Highly vibrationally excited naphthalene in the triplet state (vibrational energy: 16,194 cm(-1); electronic energy: 21,400 cm(-1)) was formed via the rapid intersystem crossing of naphthalene initially excited to the S(2) state by 266 nm photons. The collisional energy transfer probability density functions were measured directly from the scattering results of highly vibrationally excited naphthalene. At low collision energies a short-lived naphthalene-Kr complex was observed, resulting in small amounts of translational to vibrational-rotational (T-->VR) energy transfer. The complex formation probability decreases as the collision energy increases. T-->VR energy transfer was found to be quite efficient at all collision energies. In some instances, nearly all of the translational energy is transferred to vibrational-rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy. The translational energy gained from vibrational energy extend to large energy transfer (up to 3000 cm(-1)) as the collision energy increases to 847 cm(-1). Substantial amounts of large V-->T energy transfer were observed in the forward and backward directions at large collision energies.     

A linearized path integral description of the collision process between a water molecule and a graphite surface

Quantum effects in the scattering and desorption process of a water molecule from a graphite surface are investigated using the linearized path integral model. The graphite surface is quantized rigorously using the fully quantum many-body Wigner transform of the surface Boltzmann operator, while the water molecule is treated as rigid. Classical dynamics with these quantized initial conditions show that quantizing the surface at 100 and 300 K results in markedly different results, compared to a fully classical analysis. The trapping probability (defined as the probability of multiple encounters with the surface) is not sensitive to the choice of dynamical treatment, but the residence time on the surface is much shorter in the quantum case. At 300 K the transiently trapped molecules desorb from the surface with a rate constant which is 60-70% larger than the corresponding classical value. Lowering the surface temperature to 100 K decreases the quantum rate constant by approximately a factor of 3 while all trapped molecules stick to the surface in the classical case. The stability of the quantum initial state for the highly anisotropic graphite crystal is discussed in detail as well as the dynamical consequences of energy redistribution during the scattering process. The graphite surface application demonstrates that the Boltzmann operator Wigner transform for a system with 900 degrees of freedom can be obtained by the so-called gradient implementation [Poulsen et al. J. Chem. Theory Comput. 2006, 2, 1482] of the underlying Feynman-Kleinert effective frequency theory, an implementation that only requires a force and potential routine for the system at hand, and hence is applicable to any molecule-surface collision problem.     

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.