Mikhail B. Sevryuk

Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy

Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.

A wave packet propagation study of inelastic and reactive F+D2 scattering

We compute the rotationally resolved differential cross sections for F(2P3/2)+D2(v=0,j) inelastic scattering as well as opacity functions for D2 rotational excitation and the reaction F+D2→D+DF. Two values of the collision energy (89.7 and 187 meV) and two initial D2 rotational states (j=0 and j=1) are probed. Four calculation techniques have been compared: the quasiclassical trajectory approach and the Wigner method on the ground state (12A′) surface, wave packet propagation (with the D2 vibrational degree of freedom treated quantum mechanically) on the 12A′ surface, and wave packet propagation on the two coupled surfaces 12A′ and 22A′. The effect of the nonadiabatic spin–orbit coupling on the nonreactive F+D2 scattering is almost negligible, whereas the reaction cross sections in the two‐surface wave packet propagation treatment are considerably smaller than those in the calculations taking into account the ground state surface only.

A TEST OF THE SEMICLASSICAL WIGNER METHOD FOR THE REACTION F + H2 H + HF

Abstract We compute the vibrationally resolved integral cross sections σ R (ν′), differential cross sections, and opacity functions for the reaction F + H 2 ( ν = 0, j = 0, 1) → H + HF( ν ′, j ′) on the 6SEC potential energy surface by the quasiclassical trajectory technique as well as the Wigner method. In both cases, the Langer correction of the initial H 2 rotational energy is implemented. The results are compared with the recent quasiclassical trajectory calculations on the same surface without the Langer correction and quantum mechanical calculations. It is shown that use of the Wigner phase space functions to describe the H 2 and HF vibrational degrees of freedom reduces the total integral cross sections, smooths the selective HF( ν ′ = 3) forward peak in the HF center-of-mass angular distributions, and dramatically increases the σ R ( ν ′ = 3)/ σ R ( ν ′ = 2) vibrational branching ratio. These results indicate that the disagreements between the quasiclassical trajectory cross sections and the quantum mechanical ones observed in the previous works cannot be minimized by just a proper choice and weighting of the initial conditions in the quasiclassical trajectory calculations.

Dynamical mechanisms of direct three-body recombination.

Despite the ubiquity of recombination processes in nature and various technologies, presently little is known about the dynamics of these processes. This article reports on a quasi-classical trajectory study of the dynamics of the direct three-body recombination of Cs(+) and Br(-) ions in the presence of a Xe atom at energies of the ion encounter and that of the third body ranging from 0.2 to 10 eV. Several dynamical mechanisms of stabilization of the recombining ion pair have been found. Head-on ion encounters are characterized by two mechanisms of removing the energy from the recombining pair. In the case of nonzero impact parameters of ion encounters, the dynamics leading to the stabilization of the nascent CsBr molecule becomes much more complicated and three new mechanisms appear. They depend mainly on the energy of the ion encounter, on the energy of the collision of the ion pair with the third body, and on the impact parameter of the ion encounter and the impact parameter of the third body. The common feature of all the three mechanisms is the transfer of a fraction of the rotational energy of the recombining pair to the third body. This transfer plays a key role in the stabilization of the molecule. The dynamical peculiarities observed are expected to be common for the recombination of the charged and neutral particles.

Vibrational transition probabilities for the CO molecule trapped in an argon cluster : a semiclassical simulation

Abstract We calculate the 0→1, 1→0, 1→2, 2→1, and 2→3 vibrational transition probabilities of the CO molecule trapped in the center of icosahedral argon clusters with 12, 54, and 146 Ar atoms at various cluster temperatures. The semiclassical scheme has been employed, where the impurity vibrations are quantized while all the other degrees of freedom are treated classically. The transition probabilities increase with the cluster size but exhibit an inverse temperature dependence.

A hard-sphere model for the reactions of two diatomic molecules with ionic bond

Abstract We propose an impulsive model for the interaction between two alkali halide molecules. The excitation functions for various channels of the reactions RbBr+RbBr, CsBr+CsBr, RbCl+CsI, and RbI+CsCl obtained within this model exhibit a qualitative agreement with the results of exact quasiclassical trajectory calculations.

Post-adiabatic approach to atomic and molecular processes: The van der Waals interactions of some open shell systems

SummaryVarious properties of post-adiabatic representations of multichannel Schrödinger equations are described in the general context of adiabatic and classical path approximations as used in atomic and molecular physics. The van der Waals interactions of fluorine, chlorine, and oxygen atoms with rare gases, hydrogen, methane, and hydrogen halides are considered: it is found that in some of these systems, the first-order post-adiabatic scheme exhibits a smaller coupling than the adiabatic representation, thus providing an appropriate choice of the basis functions for a decoupling approximation.

The complete T→V,R energy conversion in three-body collisions within the hard sphere model

It is shown that in hard sphere (impulsive) collisions of atoms with diatomic molecules, complete conversion of the collision energy into the internal energy of the diatomic partner is possible for any number of impacts between the elastic balls representing the particles. The corresponding collision geometries and relations between the masses of the particles are described in detail.

Multiple impacts and energy transfer in a three-body system for noncollinear collisions

SummaryWithin the impulsive framework, the energy transfer processes in collisions of atoms with diatomic molecules are considered. In the case of noncollinear collisions involving multiple impacts between the particles, analytic expressions for the amount of the collision energy transferred to the internal degrees of freedom of the molecule have been derived. The limiting cases of these expressions are the well-known Mahan (a single impact) and Mahan-Shin (collinear collisions) formulas. The efficiency of energy transfer in collisions of cesium halide molecules with xenon atoms has been computed as an example; the results obtained agree well with the data of accurate trajectory calculations.

Simulation of the reactive scattering of F+D2 on a model family of potential energy surfaces with various topographies: The correlation approach

The connection between the salient features of the potential energy surface (PES) and the dynamical characteristics of the elementary collision process is studied using a correlation approach based on quasiclassical trajectory simulations. The method is demonstrated for the reaction F + D2 --> D + DF for which the scattering characteristics were calculated on a model family of PESs based on a London-Eyring-Polanyi-Sato-type five-parameter equation. The correlations between the reactive cross section and the vibrational and rotational quantum numbers and the scattering angle of the DF product, and the various parameters of the collinear and noncollinear PESs, such as the location and height of the minimal barrier and the Sato coefficients, are reported. Although usually correlations between two variables suffice, in some cases coefficients of correlation among three variables are required. The role of nonlinear parameter dependencies in computing the correlation coefficients is also considered. The correlation approach makes it possible to examine a large set of potential surfaces without intermediate human control and obtain quantitative information.