The application of the Wigner R-matrix theory to molecular collisions

Abstract

The Wigner–Eisenbud R-matrix theory is applied to molecular collisions. Previous attempts required a Buttle correction to accelerate slow convergence. The present theory makes use of radial basis functions which satisfy arbitrary conditions at the R-matrix boundary. At the same time within the boundary, the basis functions are eigenfunctions of a realistic effective radial Hamiltonian. Consequently, the radial basis set is slightly nonorthogonal. It is shown that this is sufficient to afford a rapidly convergent expansion which remains reliable both in the neighborhood of and far from resonances. The Buttle correction is no longer needed. The method is applied to a problem of collinear collisions between an atom and a diatomic molecule. Results are in excellent agreement with previous calculations.

Low temperature scattering with the R-matrix method: argon-argon scattering

“…The Lobatto DVR method has boundary conditions that set the derivatives of the eigenfunctions at the boundary to zero, but the amplitudes themselves are allowed to take on non-zero values at a 0 . This is also in contrast to the method of Bocchetta and Gerratt [29], which used non-orthogonality and a grid that extended slightly beyond a 0 to produce arbitrary boundary conditions at a 0 . This approach was tested in earlier versions of this work (see [37]), but has since been supplanted by the Lobatto DVR methods.…”

“…The method is designed to study reactive and non-reactive, and elastic and inelastic collisions occurring over deep wells. With the exception of a single proof-of-principle study by Bocchetta and Gerratt [29], this method has not been applied to so-called heavy particle scattering before.…”

Low-temperature chemistry using the R-matrix method

“…Provided the wall is placed far enough out, the {ψ J i j } are effectively computational approximations of the eigenfunctions of ĤJ , with each basis function index j belonging to a channel i. Generally speaking, placing the wall such that a 0 was approximately ≈ 95% of the way to r wall was found to be appropriate 42 .…”

Low-temperature scattering with the R-matrix method: from nuclear scattering to atom-atom scattering and beyond

“…With the exception of a single proof-of-principle study by Bocchetta and Gerratt [14], the Calculable R-matrix method has not been applied to so-called heavy particle scattering before. Their work is unique because when heavy particle scattering is usually simulated using R-matrix methods, an alternate R-matrix method is used.…”

“…Within the standard Born-Oppenheimer approximation, which is the bedrock of molecular physics, there is a separation between electronic and nuclear motions. While the so-called calculable Rmatrix method has been very extensively applied to the electron collision problem, with one exception [14] discussed below, this method has not been applied to problems involving nuclear motion.…”