Reactive scattering with row-orthonormal hyperspherical coordinates. 4. Four-dimensional-space Wigner rotation function for pentaatomic systems.

The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles involved in 4-dimensional space.

Analytical derivation of row-orthonormal hyperspherical harmonics for triatomic systems.

Hyperspherical harmonics for triatomic systems as functions of row-orthonormal hyperspherical coordinates, (also called democratic hyperspherical harmonics) are obtained explicitly in terms of Jacobi polynomials and trigonometeric functions. These harmonics are regular at the poles of the triatomic kinetic energy operator, are complete, and are not highly oscillatory. They constitute an excellent basis set for calculating the local hyperspherical surface functions in the strong interaction region of nuclear configuration space.

Reactive scattering with row-orthonormal hyperspherical coordinates. 3. Hamiltonian and transformation properties for pentaatomic systems.

The Hamiltonian for triatomic and tetraatomic systems in row-orthonormal hyperspherical coordinates has been derived previously. However, for pentaatomic systems this derivation requires nontrivial generalizations. These are presented in this paper, together with the corresponding Hamiltonian.

Nonadiabatic effects in the H + H2 exchange reaction: accurate quantum dynamics calculations at a state-to-state level.

Real wave packet propagations were carried out on both a single ground electronic state and two-coupled-electronic states of the title reaction to investigate the extent of nonadiabatic effects on the distinguishable-atom reaction cross sections. The latest diabatic potential matrix of Abrol and Kuppermann [J. Chem.

Numerical generation of hyperspherical harmonics for tetra-atomic systems.

A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates-a hyper-radius and eight angles-is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles.