Asymptotic analysis of state-to-state tetraatomic reactions using row-orthonormal hyperspherical coordinates

Rotational effects in complex-forming bimolecular substitution reactions: A quantum-mechanical approach

The quantum dynamics of the complex-forming S(N)2 reaction Cl(-)+CH(3)Br-->ClCH(3)+Br(-) is studied with emphasis on rotational effects. The pseudotriatomic system Cl-Me-Br is treated with a corresponding three-dimensional (3D) potential energy surface as a function of the two scattering coordinates and the enclosed angle where the geometry of the methyl group Me is optimized at each point. The 3D space is divided into three different parts, the interaction region, an intermediate region, and the asymptotic region. In line with simple classical-mechanical arguments and previous classical trajectory calculations, initial rotational motion of CH(3)Br seemingly decreases the reaction probability. However, the dynamical inclusion of the rotational degree of freedom and the presence of the many rovibrational product states overall lead to a large increase in reactivity compared to our previous collinear study on this reaction. If the reactant is rotationally excited, the higher vibrational product states are depleted in favor of lower-lying levels. Starting the reaction with rotationless reactants may end up in significant rotational excitation in the product molecules (translation-to-rotation energy transfer). On the other hand, initial rotational energy in rotationally highly excited reactants is to a large amount converted into translational and vibrational energy. The average amount of rotational energy in the products shows a twofold vibrational excitation-independent saturation (i.e., memorylessness), with respect to both initial rotational excitation and translational energy. Since only about one-half of all reactant states end in rotationless products, the reaction probability should be increased by a factor of 2; the actually larger reactivity points to other dynamical effects that play an important role in the reaction.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.

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.

Body frames in the separation of collective angles in quantum N-body problems

The application of the concept of body-fixed reference frames, proposed by C. Eckart [Phys. Rev. 47, 552 (1935)], to the problem of the separation of three collective angles in quantum N-body problems is analyzed based on the technique recently developed by Meremianin and Briggs [Phys. Rep. 384, 121 (2003)]. Special attention is paid to the body frame defined by the "second Eckart condition" which minimizes vibro-rotational couplings near the equilibrium position. The important case of the Eckart frame for three-body systems is considered in detail. The connection of the basis vectors of the Eckart frame with Jacobi vectors is derived. All results of this work are valid for an arbitrary choice of internal (body-frame) coordinates.