Quantum reactive scattering in three dimensions: Using tangent-sphere coordinates to smoothly transform from hyperspherical to Jacobi regions

Interaction-Asymptotic Region Decomposition Method for an Insertion Reaction: Application to the S(1D) + H2 Reaction

With adjusting principal axes hyperspherical (APH) coordinate in the interaction region, and the Jacobi coordinates in the asymptotic regions, an efficient multidomain interaction-asymptotic region decomposition (IARD) method has been developed to solve the "coordinate problem" in a product-state-resolved reactive scattering calculation using the quantum wave packet method. Although the APH coordinate treats with all three channels equally, and is efficient for describing the interaction region for some direct reactions, it is inefficient for describing the insertion-type reaction due to the singularity problem, such as the S(¹D) + H₂ reaction. To deal with this issue, in this work, the channel-dependent Delves hyperspherical (DH) coordinate is proposed to describe the interaction region using the IARD method. The proposed DH-IARD method was applied to calculate the product-state-resolved reaction probabilities of the H + HD reaction, and the differential and integral cross sections of the typical insertion reaction S(¹D) + H₂. It is found that the new DH-IARD method is much more efficient than the previous APH-IARD method for dealing with insertion reactions. The partial wave resonance structures were observed in the integral cross section. It is found that at a low collision energy, the position of the initial wave packet has to be put far away. Otherwise, the partial wave resonance structures could not be correctly reproduced due to the reef well arising with a large total angular momentum J.

Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets

Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known "symmetric" and "asymmetric" parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems.