Classical Trajectory Study Research Articles

Quantum capture, adiabatic channel, and classical trajectory study of the high pressure rate constant of the reaction H+O2→HO2 between 0 and 5000K

Limiting high pressure rate constants for the recombination reaction H+O(2)-->HO(2) are modeled between 0 and 5000 K on an ab initio potential. Quantum capture theory is employed for the temperature range from 0 to about 1 K, while classical trajectory calculations are suitable for covering temperatures above about 200 K. The intermediate temperature range is analyzed by adiabatic channel capture theory. The system is characterized by transition-state switching from outer transition states in the long-range-C(6)R(6) potential to inner transition states in the range of a "shoulder" of the potential. The limiting high pressure rate constants from the trajectory calculations are sufficient for comparison with the experimental data which are available over the range from 300 to 900 K. Specific rate constants k(E,J) for HO(2) dissociation are also given and analyzed with respect to internal consistency with capture cross sections.

Theoretical study of the dynamics of hyperthermal collisions of Ar with a fluorinated alkanethiolate self-assembled monolayer

We present a classical-trajectory study of the dynamics of energy exchange in collisions between hyperthermal Ar (6-12 eV collision energy) and a fluorinated self-assembled monolayer (SAM). Product translational-energy, polar-angle, and azimuthal-angle distributions as a function of collision energy and incidence angle are presented to provide a detailed description of the gas/surface energy exchange dynamics. Our results indicate that while the properties of the scattered Ar atom at normal and 30 degrees incidence are notably similar and essentially independent of collision energy in the 6-12 eV range, the dynamics of energy exchange when Ar impinges at 60 degrees are remarkably different and depend on collision energy. This behavior is understood via analysis of the microscopic mechanism of the collisions. Three main collision mechanisms-direct collisions without surface penetration, direct collisions involving surface penetration, and surface-penetrating non-direct collisions-are found to govern the dynamics, and the ratio of these mechanisms determines the properties of the scattered Ar atom. Our study also reveals that the Ar atoms that penetrate the organic monolayer do not desorb following a direct-ejection mechanism proposed in recent studies of Xe collisions with a hydrogenated SAM. The vast amount of energy transferred to the surface found in the calculations lends support to recent experiments showing degradation of fluorinated surfaces in collisions with hyperthermal Ar.

Classical trajectory study of the formation of XeH+ and XeCl+ in the Xe++HCl collision

The collision-induced reaction of Xe+ with HCl has been studied by use of classical dynamics procedures at collision energies 2-20 eV using empirical potential parameters. The principal reaction pathway on the potential energy surface is the formation of XeH+ with the maximum reaction cross section, 1.2 A2, occurring at E=9 eV. At lower energies, the cross section for the charge transfer process Xe++HCl-->Xe+HCl+ is comparable to that for XeH+ formation, but at higher energies, it is larger by a factor of 2. The cross section of the XeCl+ formation is an order of magnitude smaller than that of XeH+. For both XeH+ and XeCl+ formations, the reaction threshold is approximately 2 eV. The XeH+ formation takes place immediately following the turning point in a direct-mode mechanism, whereas an indirect-mode mechanism operates in the formation of XeCl+. Both XeH+ and XeCl+ formations come mainly from the perpendicular configuration, Xe+...HCl, at the turning point. Product vibrational excitation is found to be strong in both XeH+ and XeCl+.

Generalization of Classical Mechanics for Nuclear Motions on Nonadiabatically Coupled Potential Energy Surfaces in Chemical Reactions

Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.

Theoretical Study of the Dynamics of Ar Collisions with C2H6 and C2F6 at Hyperthermal Energy

We present a classical-trajectory study of the dynamics of high-energy (5-12 eV) collisions between Ar atoms and the C2H6 and C2F6 molecules. We have constructed the potential-energy surfaces for these systems considering separately the Ar-molecule interactions (intermolecular potential) and the interactions within the molecule (intramolecular potential). The intermolecular surfaces consist of pairwise empirical potentials derived from high-accuracy ab initio calculations. The intramolecular potentials for C2H6 and C2F6 are described using specific-reaction-parameters semiempirical Hamiltonians and are calculated "on the fly", i.e., while the trajectories are evolving. Trajectory analysis shows that C2F6 absorbs more energy than C2H6 and is more susceptible to collision-induced dissociation (CID). C-C bond-breakage processes are more important than C-H or C-F bond breakage at the energies explored in this work. Analysis of the reaction mechanism for CID processes indicates that, although C-C breakage is mostly produced by side-on collisions, head-on collisions are more efficient in producing C-F or C-H dissociation. Our results suggest that high-energy collisions between closed-shell species of the natural low-Earth-orbit environment and spacecraft can contribute to the observed degradation of polymers that coat spacecraft surfaces.

Classical Trajectory Study of the Reaction between H and HCO

The thermal reaction between H and HCO was studied by classical trajectory calculations on an ab initio potential. The formation of H2+CO, the exchange of hydrogen atoms, and nonreactive encounters, proceeding either via direct or via complex-forming pathways, were separated. The reaction H+HCO-->H2+CO, with direct and complex-forming components, was found to have a low-pressure rate coefficient of 2.0(+/-0.15)x10(-10) cm3 molecule(-1) s(-1), being nearly independent of temperature between 200 and 1000 K. This value is in agreement with the recent experimental value of 1.83(+/-0.4)x10(-10) cm3 molecule(-1) s(-1). Thermal lifetime distributions of H2CO* complexes formed in the reaction are only weakly temperature dependent due to a compensation of energy and angular momentum effects.

A classical trajectory study of the photodissociation of T1 acetaldehyde: The transition from impulsive to statistical dynamics

Previous experimental and theoretical studies of the radical dissociation channel of T(1) acetaldehyde show conflicting behavior in the HCO and CH(3) product distributions. To resolve these conflicts, a full-dimensional potential-energy surface for the dissociation of CH(3)CHO into HCO and CH(3) fragments over the barrier on the T(1) surface is developed based on RO-CCSD(T)/cc-pVTZ(DZ) ab initio calculations. 20,000 classical trajectories are calculated on this surface at each of five initial excess energies, spanning the excitation energies used in previous experimental studies, and translational, vibrational, and rotational distributions of the radical products are determined. For excess energies near the dissociation threshold, both the HCO and CH(3) products are vibrationally cold; there is a small amount of HCO rotational excitation and little CH(3) rotational excitation, and the reaction energy is partitioned dominantly (>90% at threshold) into relative translational motion. Close to threshold the HCO and CH(3) rotational distributions are symmetrically shaped, resembling a Gaussian function, in agreement with observed experimental HCO rotational distributions. As the excess energy increases the calculated HCO and CH(3) rotational distributions are observed to change from a Gaussian shape at threshold to one more resembling a Boltzmann distribution, a behavior also seen by various experimental groups. Thus the distribution of energy in these rotational degrees of freedom is observed to change from nonstatistical to apparently statistical, as excess energy increases. As the energy above threshold increases all the internal and external degrees of freedom are observed to gain population at a similar rate, broadly consistent with equipartitioning of the available energy at the transition state. These observations generally support the practice of separating the reaction dynamics into two reservoirs: an impulsive reservoir, fed by the exit channel dynamics, and a statistical reservoir, supported by the random distribution of excess energy above the barrier. The HCO rotation, however, is favored by approximately a factor of 3 over the statistical prediction. Thus, at sufficiently high excess energies, although the HCO rotational distribution may be considered statistical, the partitioning of energy into HCO rotation is not.

Theoretical Study of the Effect of Surface Density on the Dynamics of Ar + Alkanethiolate Self-Assembled Monolayer Collisions

We present a classical-trajectory study of energy transfer in collisions of Ar atoms with alkanethiolate self-assembled monolayers (SAMs) of different densities. The density of the SAMs is varied by changing the distance between the alkanethiolate chains in the organic monolayers. Our calculations indicate that SAMs with smaller packing densities absorb more energy from the impinging Ar atoms, in agreement with recent molecular-beam scattering experiments. We find that energy transfer is enhanced by a decrease in the SAM density because (1) less dense SAMs increase the probability of multiple encounters between Ar and the SAM, (2) the vibrational frequencies of large-amplitude motions of the SAM chains decrease for less dense SAMs, which makes energy transfer more efficient in single-encounter collisions, and (3) increases in the distance between chains promote surface penetration of the Ar atom. Analysis of angular distributions reveals that the polar-angle distributions do not have a cosine shape in trapping-desorption processes involving penetration of the Ar atom into the alkanethiolate self-assembled monolayers. Instead, there is a preference for Ar atoms that penetrate the surface to desorb along the chain-tilt direction.

Classical trajectory study of collisions of Ar with alkanethiolate self-assembled monolayers: Potential-energy surface effects on dynamics

We have investigated collisions between Ar and alkanethiolate self-assembled monolayers (SAMs) using classical trajectory calculations with several potential-energy surfaces. The legitimacy of the potential-energy surfaces is established through comparison with molecular-beam data and ab initio calculations. Potential-energy surfaces used in previous work overestimate the binding of Ar to the SAM, leading to larger energy transfer than found in the experiments. New calculations, based on empirical force fields that better reproduce ab initio calculations, exhibit improved agreement with the experiments. In particular, polar-angle-dependent average energies calculated with explicit-atom potential-energy surfaces are in excellent agreement with the experiments. Polar- and azimuthal-angle-dependent product translational energies are examined to gain deeper insight into the dynamics of Ar+SAM collisions.

The effect of zero-point energy differences on the isotope dependence of the formation of ozone: A classical trajectory study

The effect of zero-point energy differences (DeltaZPE) between the possible fragmentation channels of highly excited O(3) complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. DeltaZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions omega and an energy dependent parameter Delta(damp), which favors the lower energies in the Maxwell-Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Delta(damp) is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on DeltaZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter eta approximately 1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed.

Collisional Energy Transfer between Hot Pyrazine and Cold CO: A Classical Trajectory Study

Vibrational energy transfer from hot pyrazine (E‘ = 40 322 cm-1) to cold CO is modeled using classical trajectories. Collisional energy transfer properties are studied as a function of the initial rotational state J‘ of the CO, the length of the CO, the energy E‘ in pyrazine, the relative kinetic energy, the temperature, isotopic substitution on pyrazine, and the intermolecular potential. The energy transfer probability function P(E,E‘) exhibits distinct deviation from single exponential behavior. Collisions that transfer particularly large energy are associated with large amplitude out-of-plane motion of a C−H bond, imparting a kick to the departing CO. Slower collisions are particularly effective in relaxing pyrazine; faster collisions can add energy as often as they remove it. Energy transfer properties also depend on the initial rotational state of the CO. Temperature effects on 〈E − E‘〉 are weak in the 200−500 K range; this results from an increase in the magnitudes of both 〈ΔE〉down and 〈ΔE〉up. The f...

Rotamer Dynamics of Substituted Simple Alkanes. 1. A Classical Trajectory Study of Collisional Orientation and Alignment of 1-Bromo-2-Chloroethane with Argon

The 1-bromo-2-chloroethane molecule could exist in T, G, and G‘ rotamer forms. The collisional orientation and alignment of these rotamers in colliding with the Ar atom were studied by classical trajectory method. With the initial translational collision energies and rotational energies being selected in the main energy range covered by room temperatures to around 1000 K, the collisional orientation and alignment moments of the rotamers of the title molecule were calculated as a function of the impact parameter and the rotational angular momentum along the molecular z axis. As far as the collisional orientation and alignment behaviors are concerned, the calculations show that there are similarities as well as differences between these rotamers. Following the generally accepted physical models developed for the collisional alignment of diatomic molecules, model mechanisms for the collisional orientation and alignment of the present system were proposed and discussed.

A classical trajectory study of bond dissociation in HONO and HOOH

Dissociations of the O–N bond in trans-HONO and O–O bond in HOOH are studied using the quasiclassical trajectory approach. Despite their similarities, the results are quite different. The method seems to work well for HONO, giving results in accord with experiment. On the other hand, the classical trajectory approximation breaks down for HOOH near the reaction threshold due to the aphysical zero-point energy flow, although it is better for the higher energy states. These results show that the intramolecular couplings are quite different for the two seemingly similar systems.

A direct classical trajectory study of the acetone photodissociation on the triplet surface

Product energy distributions (PEDs) for the photodissociation of acetone at 266, 248, and 193 nm were evaluated by direct classical trajectory calculations on the lowest triplet potential energy surface. CASSCF(8,7) and MRCI+Q calculations were first performed to obtain a set of high-level ab initio data with which the semiempirical parameters were refined. The trajectories were initiated at the barrier, using two different microcanonical sampling methods. The results obtained for the excess energies corresponding to excitation at 266 and 248 nm are in good agreement with the experimental product energy partitioning, supporting a dissociation event taking place on the T1 surface after intersystem crossing from the initially exited S1 state. At 193 nm, the results obtained with the two sampling methods show significant discrepancies. The PEDs calculated with the anharmonic sampling procedure appear to be consistent with the experimental data.

A Direct Classical Trajectory Study of HCl Elimination from the 193 nm Photodissociation of Vinyl Chloride

Direct AM1 with specific reaction parameters (AM1-SRP) trajectory calculations were performed to investigate the photodissociation of vinyl chloride at 193 nm. Marked differences were found between the trajectories run from the transition states to the products for the four-center (4C) and three-center (3C) dissociation channels. The average internal energy of HCl is found to be about 2.5 times larger for the 4C channel. The calculated translational and HCl vibrational distributions, especially those obtained with a quasi-classical normal-mode sampling method, are in good agreement with the experimental data. The results are consistent with a concerted but nonsynchronous 3C mechanism, producing a lifetime for vinylidene to acetylene isomerization in line with the experimental observations. The theoretical HCl rotational distributions are in reasonable agreement with experiment, although they do not support the experimental interpretation of Lin et al. [J. Chem. Phys. 2001, 114, 160], who attributed low-J and high-J components to the 4C and 3C channels, respectively.

Product energy distributions from ethylene photodissociation at 193 nm: a DFT direct classical trajectory study

The photodissociation of ethylene at 193 nm was studied by a B3LYP/6-31G(d) direct trajectory method, in which the trajectories were initialized from the two exit barriers associated to molecular hydrogen formation. The calculated translational energies and the H 2 rotational and vibrational states distributions are in good agreement with the experimental data. Our results, together with those obtained in a previous trajectory study [A. Peña-Gallego, E. Martı́nez-Núñez, S.A. Vázquez, Chem. Phys. Lett. 353 (2002) 418], are in line with the conclusion that the dissociation dynamics is statistical in the reactant phase space, although the product energy distributions for both channels are nonstatistical.

Translational energy dependence of NO+NO/N 2+O 2 product branching in the [formula omitted] reaction: a classical trajectory study on a new global potential energy surface for the lowest [formula omitted] state

An analytical potential energy surface of the lowest singlet 1 A ′ state for the O( 1 D)+ N 2 O→ NO+ NO/ N 2+ O 2 reaction has been developed on the basis of extensive ab initio electronic structure calculations at the CASPT2/cc-pVDZ level of theory within C s constraint. A many-body expansion type function was employed to fit the calculated ab initio points. Classical trajectory calculations have been carried out using the newly developed potential energy surface. We found that the initial orientation angle significantly affects the NO+NO/N 2+O 2 product branching and the branching ratio decreases as the relative translational energy increases.

Classical trajectory and statistical adiabatic channel study of the dynamics of capture and unimolecular bond fission. VI. Properties of transitional modes and specific rate constants k(E,J)

Transitional modes in simple unimolecular bond fission and in the reverse recombination reactions are characterized quantitatively by statistical adiabatic channel (SACM) and classical trajectory (CT) calculations. Energy E- and angular momentum J-specific numbers of open channels (or activated complex states) W(E,J) and capture probabilities w(E,J) are determined for a series of potentials such as ion—dipole, dipole–dipole, and various model valence potentials. SACM and CT treatments are shown to coincide under classical conditions. Adiabatic as well as nonadiabatic dynamics are considered. The dominant importance of angular momentum couplings is elaborated. A sequence of successive approximations, from phase space theory neglecting centrifugal barriers E0(J), via phase space theory accounting for centrifugal barriers E0(J), toward the final result, expressing the effects of the anisotropy of the potentials by specific rigidity factors frigid(E,J), is described. This approach emphasizes the importance to characterize the employed potentials by their centrifugal barriers E0(J). The derived specific rigidity factors frigid(E,J) are consistent with previously calculated thermal rigidity factors frigid(T). The present approach properly accounts for angular momentum conservation and, at the same time, facilitates the calculation of specific rate constants k(E,J) and falloff curves for unimolecular bond fission and the reverse radical recombination reactions.

Checking the influence of numerically induced chaos in the computational study of intramolecular dynamics using trajectory equivalence

Influence of the numerical chaos induced by the numerical round-off errors in the classical trajectory study of intramolecular dynamics has been investigated using HOD as an example. Calculation of the trajectory equivalence based on the scaling theorem for classical dynamics has been found useful to check the onset of the numerically induced chaos. It has also been found that the use of higher precision arithmetic is not very effective to delay this onset.

Classical Trajectory Study of the HFCO → HF + CO Reaction. II. Mode Specificity, DFCO Dissociation Dynamics, Effects of Rotational Energy

AbstractClassical trajectories have been calculated for the unimolecular dissociation reaction H(D)FCO → H(D)F + CO over a modified form of the electronic ground state potential surface of Wei and Wyatt [J. Phys. Chem. 1993, 97, 13580]. The modifications of the potential energy surface and the method of calculating the trajectories are de scribed in an earlier publication from our laboratory [J. Phys. Chem. A. 1998, 102, 947]. Trajectories were initiated with the classical zero point energy distributed randomly in the six normal modes of the molecule and an additional approximately 60 kcal/mol distributed in one of the six normal modes. Clear evidence of mode specificity was found in that the excitation of the six different modes leads to significantly different rates of reaction: CH stretch > CH bend ≅ CF stretch ≥ CO stretch ≅ FCO bend > out of plane bend. For DFCO, mode specificity is considerably less apparent in that the range of life times for the six normal modes is less than half that for HFCO. Average product CO and HF distributions were also determined for both HFCO and DFCO dissociation. To investigate the degree of IVR between various modes, trajectories were calculated with the same initial energy approximately equally divided between two different initial modes. Finally, trajectories were calculated to study the effect of increasing rotational energy on the rate of HFCO dissociation. These results are discussed in terms of general theories of reaction rates, recent theoretical treatments of HFCO dissociation and experimental results.