Trajectory simulations of collisional energy transfer in highly excited benzene and hexafluorobenzene

Collisional Relaxation of Highly Vibrationally Excited Acetylene Mediated by the Vinylidene Isomer

Collisional relaxation of highly vibrationally excited acetylene, generated from the 193 nm photolysis of vinyl bromide with roughly 23,000 cm-1 of nascent vibrational energy, is studied via submicrosecond time-resolved Fourier transform infrared (FTIR) emission spectroscopy. IR emission from vibrationally hot acetylene during collisional relaxation by helium, neon, argon, and krypton rare-gas colliders is recorded and analyzed to deduce the acetylene energy content as a function of time. The average energy lost per collision, ⟨ΔE⟩, is computed using the Lennard-Jones collision frequency. Two distinct vibrational-to-translational (V-T) energy transfer regimes in terms of the acetylene energy are identified. At vibrational energies below 10,000-14,000 cm-1, energy transfer efficiency increases linearly with molecular energy content and is in line with typical V-T behavior in quantity. In contrast, above 10,000-14,000 cm-1, the V-T energy transfer efficiency displays a dramatic and rapid increase. This increase is nearly coincident with the acetylene-vinylidene isomerization limit, which occurs nearly 15,000 cm-1 above the acetylene zero-point energy. Combined quasi-classical trajectory calculations and Schwartz-Slawsky-Herzfeld-Tanczos theory point to a vinylidene contribution being responsible for the large enhancement. This observation illustrates the influence of energetically accessible structural isomers to greatly enhance the energy transfer rates of highly vibrationally excited molecules.

High energy vibrational excitations of nitromethane in liquid water

The pathways and timescales of vibrational energy flow in nitromethane are investigated in both gas and condensed phases using classical molecular mechanics, with a particular focus on relaxation in liquid water. We monitor the flow of excess energy deposited in vibrational modes of nitromethane into the surrounding solvent. A marked energy flux anisotropy is found when nitromethane is immersed in liquid water, with a preferential flow to those water molecules in contact to the nitro group. The factors that permit such anisotropic energy relaxation are discussed, along with the potential implications on the molecule's non-equilibrium dynamics. In addition, the energy flux analysis allows us to identify the solvent motions responsible for the uptake of solute energy, confirming the crucial role of water librations. Finally, we also show that no anisotropic vibrational energy relaxation occurs when nitromethane is surrounded by argon gas.

Prediction of Kinetic Product Ratios: Investigation of a Dynamically Controlled Case

Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for "final" products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities.

An advanced bath model to simulate association followed by ensuing dissociation dynamics of benzene + benzene system: a comparative study of gas and condensed phase results

The role of the environment (N₂ molecules) on the association followed by the ensuing dissociation reaction of benzene + benzene system is studied here with the help of a new code setup. Chemical dynamics simulations are performed to investigate this reaction in vacuum as well as in a bath of 1000 N₂ molecules, equilibrated at 300 K. Bath densities of 20 and 324 kg m^-3 are considered with a few results from the latter density. The simulations are performed at three different excitation temperatures of benzene, namely, 1000, 1500, and 2000 K, with an impact parameter range of 0-12 Å for both vacuum and bath models. Higher association probabilities and hence, higher temperature dependent association rate constants are obtained in the condensed phase. In the condensed phase, when a trajectory takes a longer time for the monomers to associate, the associated complex is formed with a longer lifetime and provides a lower rate of ensuing dissociation. Higher association rate and lower dissociation rate in condensed phase dynamics are due to the energy transfer process. Hence, the energy transfer phenomenon plays a decisive role in the association/dissociation dynamics, which is completely ignored in the same reaction when studied in vacuum.

Predicting third-body collision efficiencies for water and other polyatomic baths

Low-pressure-limit microcanonical (collisional activation) and thermal rate constants are predicted using a combination of automated ab initio potential energy surface construction, classical trajectories, transition state theory, and a detailed kinetic...

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

Comparison of intermolecular energy transfer from vibrationally excited benzene in mixed nitrogen-benzene baths at 140 K and 300 K

Gas phase intermolecular energy transfer (IET) is a fundamental component of accurately explaining the behavior of gas phase systems in which the internal energy of particular modes of molecules is greatly out of equilibrium. In this work, chemical dynamics simulations of mixed benzene/N₂ baths with one highly vibrationally excited benzene molecule (Bz^*) are compared to experimental results at 140 K. Two mixed bath models are considered. In one, the bath consists of 190 N₂ and 10 Bz, whereas in the other bath, 396 N₂ and 4 Bz are utilized. The results are compared to results from 300 K simulations and experiments, revealing that Bz^*-Bz vibration-vibration IET efficiency increased at low temperatures consistent with longer lived "chattering" collisions at lower temperatures. In the simulations, at the Bz^* excitation energy of 150 kcal/mol, the averaged energy transferred per collision, ⟨ΔE_c⟩, for Bz^*-Bz collisions is found to be ∼2.4 times larger in 140 K than in 300 K bath, whereas this value is ∼1.3 times lower for Bz^*-N₂ collisions. The overall ⟨ΔE_c⟩, for all collisions, is found to be almost two times larger at 140 K compared to the one obtained from the 300 K bath. Such an enhancement of IET efficiency at 140 K is qualitatively consistent with the experimental observation. However, the possible reasons for not attaining a quantitative agreement are discussed. These results imply that the bath temperature and molecular composition as well as the magnitude of vibrational energy of a highly vibrationally excited molecule can shift the overall timescale of rethermalization.

A Competition between Dissociation Pathway and Energy Transfer Pathway: Unimolecular Dissociation of a Benzene-Hexafluorobenzene Complex in Nitrogen Bath

The unimolecular dissociation of a benzene-hexafluorobenzene complex at 1000, 1500, and 2000 K is studied inside a bath of 1000 N₂ molecules kept at 300 K using chemical dynamics simulation. Three bath densities of 20, 324, and 750 kg/m³ are considered. The dissociation dynamics of the complex at a 20 kg/m³ bath density is found to be similar to that in the gas phase, whereas the dynamics is drastically different at higher bath densities. The microcanonical/canonical dissociation rate constants for the three bath densities are calculated and fitted to the Arrhenius equation. The activation energies are found to be similar to the gas-phase one. However, the pre-exponential factor is lower and decreases with the increase in bath density. The vibrational degree of freedom of the complex more effectively participates in the collisional energy transfer to the N₂ bath, whereas the translational and rotational degrees of freedom of N₂ receive the transferred energy. The energy transfer efficiency increases with the increase in bath density. The time scale of the energy transfer pathway is more than that of the dissociation pathway, and negligible direct dissociation of the complex is observed from the simulation at the highest bath density.

Collisional Energy Transfer from Vibrationally Excited Hydrogen Isocyanide

Collisional deactivation of vibrationally excited hydrogen isocyanide (HNC) by inert gas atoms was characterized using nanosecond time-resolved Fourier transform infrared emission spectroscopy. HNC, with an average nascent internal energy of 25.9 ± 1.4 kcal mol^-1, was generated following the 193 nm photolysis of vinyl cyanide (CH₂CHCN) and collisionally deactivated with the series of inert atomic gases: He, Ar, Kr, and Xe. Time-dependent IR emission allows simultaneous experimental observation of the ν₁ NH and ν₃ NC stretch emissions from vibrationally excited HNC. Subsequent spectral fit analysis enables direct determination of the average energy of HNC in each spectrum and therefore a measure of the average energy lost per collision, ⟨ΔE⟩, as a function of internal energy. Collisional deactivation of excited HNC is shown to be relatively efficient, exhibiting ⟨ΔE⟩ values more than an order of magnitude larger than comparably sized molecules at similar internal energies. Furthermore, the lighter inert gases are shown to be more efficient quenchers. Both observations can be qualitatively explained by the momentum gap law modeled through the repulsive force dominated vibration-to-translation energy transfer mechanism. The feasibility of efficient collisional deactivation as a contributing factor to the observed overabundance of astrophysical HNC is discussed.

Energy transfer in intermolecular collisions of polycyclic aromatic hydrocarbons with bath gases He and Ar

Classical trajectory simulations of intermolecular collisions were performed for a series of polycyclic aromatic hydrocarbons interacting with the bath gases helium and argon for bath gas temperature from 300 to 2500 K. The phase-space average energy transferred per deactivating collision, ⟨∆E_down⟩, was obtained. The Buckingham pairwise intermolecular potentials were validated against high-level quantum chemistry calculations and used in the simulations. The reactive force-field was used to describe intramolecular potentials. The dependence of ⟨∆E_down⟩ on initial vibrational energy is discussed. A canonical sampling method was compared with a microcanonical sampling method for selecting initial vibrational energy at high bath gas temperatures. Uncertainties introduced by the initial angular momentum distribution were identified. The dependence of the collisional energy transfer parameters on the type of bath gas and the molecular structure of polycyclic aromatic hydrocarbons was examined.

Chemical Dynamics Simulations on Association and Ensuing Dissociation of a Benzene-Hexafluorobenzene Molecular System

Chemical dynamics simulations are performed to study the association of benzene (Bz) and hexafluorobenzene (HFB) followed by the ensuing dissociation of the Bz-HFB complex. The calculations are done for 1000, 1500, and 2000 K with an impact parameter ( b) range of 0-10 Å at each temperature. Almost no complexes are observed to form at b = 8 and 10 Å. Following three different methods of calculation of the temperature-dependent association rate constant k_asso( T), the values obtained are 1.67 × 10^-10, 1.86 × 10^-10, and 2.05 × 10^-10 cm³/molecule·s with a standard deviation of approximately 0.1 × 10^-10 cm³/molecule·s for T = 1500 K. Among those values of k_asso( T), the middle one is obtained by considering a relative translational energy of 3 RT/2 at T = 1500 K, and the same is followed to calculate k_asso( T) at 1000 and 2000 K. The Arrhenius parameters, using the k_asso( T) values at three temperatures, are 0.203 × 10^-10 cm³/molecule·s for the pre-exponential factor and -5.79 kcal/mol for the activation energy. The absolute value of the latter is similar to the Bz + HFB association energy of 5.93 kcal/mol. The ensuing dissociation dynamics of the complex is significantly different from the unimolecular dissociation dynamics, and an exponential function fits the N( t - t₀)/ N( t₀) curves comparatively well. The ensuing dissociation is also observed to be independent of time for a statistically large sample size.

A Better Understanding of the Unimolecular Dissociation Dynamics of Weakly Bound Aromatic Compounds at High Temperature: A Study on C6H6-C6F6 and Comparison with C6H6 Dimer

Chemical dynamics simulations are performed to study the unimolecular dissociation of the benzene (Bz)-hexafluorobenzene (HFB) complex at five different temperatures ranging from 1000 to 2000 K, and the results are compared with that of the Bz dimer at common simulation temperatures. Bz-HFB, in comparison with Bz dimer, possesses a much attractive intermolecular interaction, a very different equilibrium geometry, and a lower average quantum vibrational excitation energy at a given temperature. Six low-frequency modes of Bz-HFB are formed by Bz + HFB association which are weakly coupled with the vibrational modes of Bz and HFB. However, this coupling is found much stronger in Bz-HFB compared to the same in the Bz dimer. The simulations are done with very good potential energy parameters taken from the literature. Considering the canonical (TST) model, the unimolecular dissociation rate constant at each temperature is calculated and fitted to the Arrhenius equation. An activation energy of 5.0 kcal/mol and a pre-exponential factor of 2.39 × 10¹² s^-1 are obtained, which are of expected magnitudes. The responsible vibrational mode for dissociation is identified by performing normal-mode analysis. Simulations with random excitations of high-frequency Bz and HFB modes and low-frequency inter-Bz-HFB vibrational modes of the Bz-HFB complex are also performed. The intramolecular vibrational energy redistribution (IVR) time and the unimolecular dissociation rate constants are calculated from these simulations. The latter shows good agreement with the same obtained from simulation with random excitation of all vibrational modes.

A theoretical study of energy transfer in Ar(1S) + SO2( X ̃ 1 A ') collisions: Cross sections and rate coefficients for vibrational transitions

Vibrational transitions, induced by collisions between rare-gas atoms and molecules, play a key role in many problems of interest in physics and chemistry. A theoretical investigation of the translation-to-vibration (T-V) energy transfer process in argon atom and sulfur dioxide molecule collisions is presented here. For such a purpose, the framework of the quasi-classical trajectory (QCT) methodology was followed over the range of translational energies 2 ≤ E_tr/kcal mol^-1 ≤ 100. A new realistic potential energy surface (PES) for the ArSO₂ system was developed using pairwise addition for the four-body energy term within the double many-body expansion. The topological features of the obtained function are compared with a previous one reported by Hippler et al. [J. Phys. Chem. 90, 6158 (1986)]. To test the accuracy of the PES, additional coupled cluster singles and doubles method with a perturbative contribution of connected triples calculations were carried out for the global minimum configuration. From dynamical calculations, the cross sections for the T-V excitation process indicate a barrier-type mechanism due to strong repulsive interactions between SO₂ molecules and the Ar atom. Corrections to zero-point energy leakage in QCT were carried out using vibrational energy quantum mechanical threshold of the complex and variations. Rate coefficients and cross sections are calculated for some vibrational transitions using pseudo-quantization approaches of the vibrational energy of products. Main attributes of the title molecular collision are discussed and compared with available information in the literature.

Collision Frequency for Energy Transfer in Unimolecular Reactions

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

Collisional Intermolecular Energy Transfer from a N2 Bath at Room Temperature to a Vibrationlly "Cold" C6F6 Molecule Using Chemical Dynamics Simulations

Chemical dynamics simulations were performed to study collisional intermolecular energy transfer from a thermalized N₂ bath at 300 K to vibrationally "cold" C₆F₆. The vibrational temperature of C₆F₆ is taken as 50 K, which corresponds to a classical vibrational energy of 2.98 kcal/mol. The temperature ratio between C₆F₆ and the bath is 1/6, the reciprocal of the same ratio for previous "hot" C₆F₆ simulations (J. Chem. Phys. 2014, 140, 194103). Simulations were also done for a C₆F₆ vibrational temperature of 0 K. The average energy of C₆F₆ versus time is well fit by a biexponential function which gives a slightly larger short time rate component, k₁, but a four times smaller long time rate component, k₂, compared to those obtained from the "hot" C₆F₆ simulations. The average energy transferred per collision depends on the difference between the average energy of C₆F₆ and the final C₆F₆ energy after equilibration with the bath, but not on the temperature ratio of C₆F₆ and the bath. The translational and rotational degrees of freedom of the N₂ bath transfer their energies to the vibrational degrees of freedom of C₆F₆. The energies of the N₂ vibrational mode and translational and rotational modes of C₆F₆ remain unchanged during the energy transfer. It is also found that the energy distribution of C₆F₆ broadens as energy is transferred from the bath, with an almost linear increase in the deviation of the C₆F₆ energies from the average C₆F₆ energy as the average energy of C₆F₆ increases.

Chemical Dynamics Simulations of Intermolecular Energy Transfer: Azulene + N2 Collisions

Chemical dynamics simulations were performed to investigate collisional energy transfer from highly vibrationally excited azulene (Az*) in a N2 bath. The intermolecular potential between Az and N2, used for the simulations, was determined from MP2/6-31+G* ab initio calculations. Az* is prepared with an 87.5 kcal/mol excitation energy by using quantum microcanonical sampling, including its 95.7 kcal/mol zero-point energy. The average energy of Az* versus time, obtained from the simulations, shows different rates of Az* deactivation depending on the N2 bath density. Using the N2 bath density and Lennard-Jones collision number, the average energy transfer per collision ⟨ΔEc⟩ was obtained for Az* as it is collisionally relaxed. By comparing ⟨ΔEc⟩ versus the bath density, the single collision limiting density was found for energy transfer. The resulting ⟨ΔEc⟩, for an 87.5 kcal/mol excitation energy, is 0.30 ± 0.01 and 0.32 ± 0.01 kcal/mol for harmonic and anharmonic Az potentials, respectively. For comparison, the experimental value is 0.57 ± 0.11 kcal/mol. During Az* relaxation there is no appreciable energy transfer to Az translation and rotation, and the energy transfer is to the N2 bath.

Pressure effects on the relaxation of an excited nitromethane molecule in an argon bath

Classical molecular dynamics simulations were performed to study the relaxation of nitromethane in an Ar bath (of 1000 atoms) at 300 K and pressures 10, 50, 75, 100, 125, 150, 300, and 400 atm. The molecule was instantaneously excited by statistically distributing 50 kcal/mol among the internal degrees of freedom. At each pressure, 1000 trajectories were integrated for 1000 ps, except for 10 atm, for which the integration time was 5000 ps. The computed ensemble-averaged rotational energy decay is ∼100 times faster than the vibrational energy decay. Both rotational and vibrational decay curves can be satisfactorily fit with the Lendvay-Schatz function, which involves two parameters: one for the initial rate and one for the curvature of the decay curve. The decay curves for all pressures exhibit positive curvature implying the rate slows as the molecule loses energy. The initial rotational relaxation rate is directly proportional to density over the interval of simulated densities, but the initial vibrational relaxation rate decreases with increasing density relative to the extrapolation of the limiting low-pressure proportionality to density. The initial vibrational relaxation rate and curvature are fit as functions of density. For the initial vibrational relaxation rate, the functional form of the fit arises from a combinatorial model for the frequency of nitromethane "simultaneously" colliding with multiple Ar atoms. Roll-off of the initial rate from its low-density extrapolation occurs because the cross section for collision events with L Ar atoms increases with L more slowly than L times the cross section for collision events with one Ar atom. The resulting density-dependent functions of the initial rate and curvature represent, reasonably well, all the vibrational decay curves except at the lowest density for which the functions overestimate the rate of decay. The decay over all gas phase densities is predicted by extrapolating the fits to condensed-phase densities.

High resolution IR diode laser study of collisional energy transfer between highly vibrationally excited monofluorobenzene and CO2: the effect of donor fluorination on strong collision energy transfer

Collisional energy transfer between vibrational ground state CO2 and highly vibrationally excited monofluorobenzene (MFB) was studied using narrow bandwidth (0.0003 cm(-1)) IR diode laser absorption spectroscopy. Highly vibrationally excited MFB with E' = ∼41,000 cm(-1) was prepared by 248 nm UV excitation followed by rapid radiationless internal conversion to the electronic ground state (S1→S0*). The amount of vibrational energy transferred from hot MFB into rotations and translations of CO2 via collisions was measured by probing the scattered CO2 using the IR diode laser. The absolute state specific energy transfer rate constants and scattering probabilities for single collisions between hot MFB and CO2 were measured and used to determine the energy transfer probability distribution function, P(E,E'), in the large ΔE region. P(E,E') was then fit to a bi-exponential function and extrapolated to the low ΔE region. P(E,E') and the biexponential fit data were used to determine the partitioning between weak and strong collisions as well as investigate molecular properties responsible for large collisional energy transfer events. Fermi's Golden rule was used to model the shape of P(E,E') and identify which donor vibrational motions are primarily responsible for energy transfer. In general, the results suggest that low-frequency MFB vibrational modes are primarily responsible for strong collisions, and govern the shape and magnitude of P(E,E'). Where deviations from this general trend occur, vibrational modes with large negative anharmonicity constants are more efficient energy gateways than modes with similar frequency, while vibrational modes with large positive anharmonicity constants are less efficient at energy transfer than modes of similar frequency.

Predictive a priori pressure-dependent kinetics

The ability to predict the pressure dependence of chemical reaction rates would be a great boon to kinetic modeling of processes such as combustion and atmospheric chemistry. This pressure dependence is intimately related to the rate of collision-induced transitions in energy E and angular momentum J. We present a scheme for predicting this pressure dependence based on coupling trajectory-based determinations of moments of the E,J-resolved collisional transfer rates with the two-dimensional master equation. This completely a priori procedure provides a means for proceeding beyond the empiricism of prior work. The requisite microcanonical dissociation rates are obtained from ab initio transition state theory. Predictions for the CH4 = CH3 + H and C2H3 = C2H2 + H reaction systems are in excellent agreement with experiment.

Kinematics and dynamics of atomic-beam scattering on liquid and self-assembled monolayer surfaces

We have conducted investigations of the energy transfer dynamics of atomic oxygen and argon scattering from hydrocarbon and fluorocarbon surfaces. In light of these results, we appraise the applicability and value of a kinematic scattering model, which views a gas-surface interaction as a gas-phase-like collision between an incident atom or molecule and a localized region of the surface with an effective mass. We have applied this model to interpret the effective surface mass and energy transfer when atoms strike two different surfaces under identical bombardment conditions. To this end, we have collected new data, and we have re-examined existing data sets from both molecular-beam experiments and molecular dynamics simulations. We seek to identify trends that could lead to a robust general understanding of energy transfer processes induced by collisions of gas-phase species with liquid and semi-solid surfaces.