Collision theory treatment of monomolecular and bimolecular gas reactions

An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).     

Effects of classical nonlinear resonances in grazing diatom-surface collisions

Energy transfer between vibrational, rotational, and translational degrees of freedom of a molecule during a collision process is enhanced when the classical frequencies associated with the initial state are in the proximity of nonlinear resonance conditions. We present an analysis of the classical resonant effects in the collisions of light diatoms with periodic surfaces, and discuss the initial conditions in which these effects can be observed. In particular, we find that for grazing incidence and resonant initial values of the classical frequencies, corresponding to specific vibro-rotational molecular states and translational energies, an efficient energy transfer between the intramolecular vibro-rotational degrees of freedom and the translational degree of freedom along a symmetry direction on the surface can be found. This efficient energy transfer manifests itself in the emergence of specific peaks in the molecular diffraction patterns. The predictions of the resonance analysis are contrasted with the results of classical trajectory calculations obtained in a diatom-rigid surface collision model.     

Classical theory of collisional entropy production

A classical dynamical theory of elementary collision processes is formulated in analogy to the quantum theory of the dynamical scattering matrix, which can be defined for a pure quantum stationary scattering state. The elements of this matrix are probability amplitudes for transitions between internal states defined for given values of a reaction coordinate. The squared magnitudes of these amplitudes, modeled in the proposed classical theory, define normalized internal state population distributions suitable for information theoretical analysis. Statistical entropy and surprisal are defined as dynamical functions of a reaction coordinate. This formalism differs fundamentally from concepts based on the classical Liouville equation.     

Collision dynamics of non-integrable systems: Validity of classical scaling

The classical collision dynamics of a model atom—molecule non-integrable collision system is studied, and the energy transfer (ET) moment is examined as a function of the initial semiclassical level of the molecule. A recently derived classical scaling theory is shown to be valid in the case when the molecular motion remains regular throughout the collision, and the ET variation is then characterized by a polynomial dependence on the initial (semiclassical) quantum numbers. When chaotic motions participate, the ET no longer follows the scaling law. The utility of the scaling theory in providing the proper interpolation form for extending classical trajectory data in non-integrable collision systems is discussed.     

A new approximation for atom-diatom rotational-relaxation cross sections

A semiclassical approximation to the S matrix of the infinite-order-sudden approximation is introduced. This is employed to yield for the energy-transfer effective cross section a purely classical approximation, analogous to the Mason-Monchick approximation [J. Chem. Phys. 36, 1622 (1962)] for traditional collision integrals. Constraints on energy and on angular momentum transfer are included. Numerical evaluation of this new approximation can readily be performed alongside that for traditional collision integrals. The new result is tested against full classical trajectory calculations for six potential energy surfaces for the collision systems H-N(2), He-N(2), He-CO, and Ar-CO(2). Differences of no more than 15% from the classical trajectory calculations have been obtained.     

Classical formalism for a translational—rotational energy transfer mechanism in atom—diatom collisions

The role of the time-varying torque in rotationally inelastic atom—diatom collisions is explored through a simple classical formalism. The classical collision mechanism is discussed in terms of the time variation of the projection of the torque vector along a unique direction. The formalism is applied to LiH-He collision.     

Classical trajectory analysis in atom—triatom collisions: Continuous quantization and scaling behaviour

A method of analysing classical trajectory data, based on recently derived scaling principles, is applied to a model atom-triatom collinear collision system. Apart from the utility of the scaling idea in extending trajectory computations, the analysis of the scaling coefficients in terms of transition probabilities increases the scope of the classical scaling theory as a means of obtaining (at the very least) qualitative quantum-mechanical information from classical trajectories. As an useful adjunct, the method of continuous quantization is applied to generate approximate transition probabilities. These results are semiquantitative; thus a combination of classical scaling and continuous quantization affords a powerful means of modeling complex collision cases with a minimum of computational effort.     

Thermal energy charge transfer reactions of acetone and biacetyl

Rate coefficients up to a factor of 2.5 times larger than the capture collision rate are reported for a series of thermal energy, positive ion-molecule reactions of acetone and biacetyl. These rapid rates are interpreted in tems of a dissociative charge transfer process in which an electron is transferred in a non-spiralling collision from outside the classical capture limit. The factor which lead to this type of mechanism are discussed briefly.     

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission

The classical theory of collision induced emission (CIE) from pairs of dissimilar atoms is studied. This radiation emitted by accelerating dipoles is produced essentially by their overlap and exchange interaction at short range. This classical calculation is based on exact collinear solutions of the trajectories of two spherical particles in a head-on collision under the influence of a Morse potential with a well of arbitrary depth. Without too restrictive conditions a variety of simple solutions in closed form is obtained that illustrates the connection between collision dynamics and CIE. Depending on the well depth and energy of the particles, they may radiate in the far infrared to infrared or visible and shorter wavelength regions. The results are characterized by a fixed total energy. Nevertheless, a connection is demonstrated between the line shape in CIE computed through the trajectory and that based on the emission of a thermally equilibrated system.     

Vibrational exchange in high-energy linear collisions

Over a wide interval for the energy of relative motion, we have considered the problems of linear collision of a classical oscillator (anharmonic in the general case) with a structureless particle for an arbitrary mass ratio, and the collision of two classical harmonic oscillators with close frequencies. Results of the analytical solutions in the adiabatic and the impulse limits are given in comparison with the results of the corresponding numerical calculations.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 21, No. 2, pp. 129–137, March–April, 1985.     

A quantum-mechanical explanation of vibronic phenomena in atom-molecule collisions

The quantum-mechanical equivalent of a classically vibrating molecular ion during an ion-pair formation collision is presented. The classical vibration in the quantal representation is explained as an interference between partial waves which evolve along neighbouring vibronic states during the collision.     

Extended diffusion in a double well potential: Transition from classical to quantum regime

The transition between the classical and quantum regimes in the diffusion of a particle in a 2-4 double-well potential is treated via the strong collision model in the high-temperature limit. Both the classical and semiclassical position correlation functions, their spectra, and correlation times are evaluated using the memory function formalism. It is shown that even in the high temperature limit, marked classical-quantum transition effects appear in the observables when collisions are rare.     

Bi-modal hetero-aggregation rate response to particle dosage

The rate of flocculation of cationic polystyrene latex (PSL) particles by smaller, anionic PSL particles has been measured using a low-angle static light scattering technique. The rate of aggregate growth has been investigated as a function of particle size ratio and relative concentration of each particle species (for a constant dose of cationic particles). Contrary to many previous reports, two peaks in the flocculation rate were observed as a function of dose. It is speculated that the peak observed at the lower particle concentration coincides with the dose yielding maximum constant collision efficiency in the steady-state regime, a condition which is attained only after complete adsorption of the smaller particles onto the larger particle species. The peak at the higher particle concentration is believed to be related to the maximum collision rate constant upon reaching the steady-state regime, the value of which corresponds to maximum degree of aggregation and therefore the maximum mean collision efficiency prior to reaching this condition. From classical collision kinetics, the rate of aggregate growth may be represented as being proportional to the product of the collision rate constant and collision efficiency at any given time. Given then that the maximum value of these two variables coincides with different particle concentrations, the product of the response of each to particle dosage can in some cases yield a net bi-modal aggregation rate response to particle dosage.     

Quasiclassical trajectory study of reactive and dissociative processes in H2+H2: comparison with quantum-mechanical calculations

Quasiclassical trajectory calculations have been carried out for H(2)(v(1)=high)+H(2)(v(2)=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v(1)'s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H(2)(v(1)=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined.     

New, unexpected, and dominant mechanisms in the hydrogen exchange reaction

A quasiclassical trajectory study of the state specific H+D(2)(upsilon = 0,j = 0) --> HD(upsilon' = 0,j' = 0) + D reaction at a collision energy of 1.85 eV (total energy of 2.04 eV) found that the scattering is governed by two unexpected and dominant new mechanisms, and not by direct recoil as is generally assumed. The new mechanisms involve strong interaction with the sloping potential around the conical intersection, an area of the potential energy surface not previously considered to have much effect upon reactive scattering. Initial investigations indicate that more than 50% of reactive scattering could be the result of these new mechanisms at this collision energy. Features in the corresponding quantum mechanical results can be attributed to these new (classical) reaction mechanisms.     

转动取向影响因素的多元非线性分析

在不同拓扑特征的London-Eying-Polanyi-Sato(LEPS)型势能面上，应用经典轨线法计算了不同动态条件下的58个样本，应用多元非线性分析方法研究了势能面及动态条件对转动取向的影响.结果表明, 对于A＋BC→AB＋C类反应, 反应物分子的质量比、势能面出口处的宽度和相对平动能对产物分子的转动取向有重要作用，且发现不同影响因素之间的乘积对产物的转动取向具有更重要的作用.     

Classical probability matrix: Prediction of quantum-state distributions by a moment analysis of classical trajectories

A new method is presented for extracting approximate quantum mechanical state-to-state transition probabilities from the results of classical trajectory calculations. The method recognizes quantum discreteness by dealing with the quantum mechanical probability matrix, but all dynamical quantities are evaluated by classical mechanics. It is illustrated by application to the linear atom-diatom collision (vibrational excitation); it is capable of treating both classically allowed and classically forbidden processes.     

Restoring detailed balance in the Landau-Teller probabilities for collision-induced vibrational transitions

The general quasi-classical treatment for collision-induced vibrational transitions in diatomic molecules, under near-adiabatic conditions, is used to derive quantum corrections for probabilities, calculated in the external field approximation originally used by Landau and Teller. The quantum corrections are expressed through the Landau-Teller classical collision time. The first-order correction to the classical exponent restores detailed balance for up- and down-transitions and does not depend on the properties of the bath except for its temperature. The limits of applicability of the first-order correction are discussed.     

Potential surfaces and dynamics of the O(3P)+H2O(X1A1)-->OH(X2pi)+OH(X2pi) reaction

We present global potential energy surfaces for the three lowest triplet states in O(3P)+H2O(X1A1) collisions and present results of classical dynamics calculations on the O(3P)+H2O(X1A1)-->OH(X2pi)+OH(X2pi) reaction using these surfaces. The surfaces are spline-based fits of approximately 20,000 fixed geometry ab initio calculations at the complete-active-space self-consistent field+second-order perturbation theory (CASSCF+MP2) level with a O(4s3p2d1f)/H(3s2p) one electron basis set. Computed rate constants compare well to measurements in the 1000-2500 K range using these surfaces. We also compute the total, rovibrationally resolved, and differential angular cross sections at fixed collision velocities from near threshold at approximately 4 km s(-1) (16.9 kcal mol(-1) collision energy) to 11 km s(-1) (122.5 kcal mol(-1) collision energy), and we compare these computed cross sections to available space-based and laboratory data. A major finding of the present work is that above approximately 40 kcal mol(-1) collision energy rovibrationally excited OH(X2pi) products are a significant and perhaps dominant contributor to the observed 1-5 micro spectral emission from O(3P)+H2O(X1A1) collisions. Another important result is that OH(X2pi) products are formed in two distinct rovibrational distributions. The "active" OH products are formed with the reagent O atom, and their rovibrational distributions are extremely hot. The remaining "spectator" OH is relatively rovibrationally cold. For the active OH, rotational energy is dominant at all collision velocities, but the opposite holds for the spectator OH. Summed over both OH products, below approximately 50 kcal mol(-1) collision energy, vibration dominates the OH internal energy, and above approximately 50 kcal mol(-1) rotation is greater than vibrational energy. As the collision energy increases, energy is diverted from vibration to mostly translational energy. We note that the present fitted surfaces can also be used to investigate direct collisional excitation of H2O(X1A1) by O(3P) and also OH(X2pi)+OH(X2pi) collisions.