Attack and Recoil Angle Dependence of the Li + HF → LiF + H Reaction at J = 0

Abstract

This article presents a quantum theoretical study of the attack-angle dependence and the recoil-angle selectivity in the title reaction. Two complementary approaches were used: the preferred attack angle method and the examination of spatial distributions of molecular axes associated with either minimal- or maximal-probability reactions. These approaches were extended so that recoil angles could be included in the stereodynamical analysis. Our results were compared to those obtained by Alvariño et al. with the stereodirected representation (J. Phys. Chem. A 1998, 102, 9638). This allowed for an assessment of the advantages and disavantages of each method. The reaction was confirmed to be highly dependent on the attack angle and highly selective with regard to the recoil angle. The attack angle dependence is itself highly dependent on the total energy and on the product vibrational state, but the recoil angle selectivity is not.

Correlation of attack and recoil angles for the Li+HF reaction: An exact quantum mechanical study at low and high total angular momentum

“…Our aim is to compare the predictions of the two methods as the energy of the collisional process increases (and higher total angular momenta come into play) not only to compare the relative accuracy of the two approaches, but also to understand the validity of those approximations which estimate higher J contributions to reaction cross sections by shifting in energy the J = 0 ones. The S matrix elements needed for our study have been partly obtained from both time independent [16,17] and time-dependent calculations [18,19] previously published and already used to investigate angular correlation effects [10] and partly produced for the present paper. These S matrices have been transformed into both the SDR and the DVR representations which essentially constitute linear combinations of reactant and product rotational states.…”

Li + HF: A Case Study to Develop Novel Computational Technologies for Reactive Scattering

“…Sometimes, the limitation is given by the large amount of computing time associated with the calculations. Our work has also progressed along the 3D QM time dependent line , and along the appropriate transformation of the S matrix to evaluate stereodynamical properties. − …”

“…Our work has also progressed along the 3D QM time dependent line 16,32 and along the appropriate transformation of the S matrix to evaluate stereodynamical properties. [33][34][35] The work reported here focuses on the effect of increasing J on the dynamical outcome in order to provide useful hints to evaluate the efficacy of some popular approximations. The related formalism has been developed by expanding, as usual, the partial wave functions Ψ JMpn (F,θ,χ) (where J is the total angular momentum quantum number, M is its space fixed projection on the reference axis, p is the parity of the function, n is the numbering index of the partial waves, F is the hyperradius, θ and χ are the two internal hyperangles) expanded in terms of products of the Wigner rotation functions D ˆΛM Jp (R,β,γ) times the corresponding surface functions Φ tΛ Jp (where Λ is the projection of the total angular momentum on the body fixed reference axis, t is the expansion index, R, β, and γ are the three Euler angles) calculated at fixed (F ξ ) value of F. 36 The key scattering information is carried by the expansion coefficients ψ tΛ Jpn (F), which are functions of the hyperradius and whose asymptotic values can be obtained by integrating the coupled differential equations:…”

Collisional and photoinitiated reaction dynamics in the ground electronic state of Ca–HCl

“…123, 064301 ͑2005͒ representation 57 or from the preferred attack angle method. 58 These methods use the complete S matrix for J = 0 and were applied to Li+ HF reactive collisions. The reaction probability obtained for Ca+ HCl collisions behaves oppositely to the reaction probability in the Li + HF system, in spite of the fact that the saddle points in both systems have a similar configuration, 57°for CaHCl and 75.5°for LiHF.…”