State‐to‐state quantum reactive scattering in four‐atom systems

Abstract

The recent advances in quantum mechanical studies of four-atom reactions at the state-to-state level are reviewed. With six internal degrees of freedom, such reactions offer richer chemistry than the much studied atom-diatom reactions, but also pose challenges to the quantum mechanical treatment of the state-tostate scattering process. Several approaches that are capable of providing a complete solution to the problem have recently been suggested and a brief description and comparison of these approaches are given here. In addition, recent quantum mechanical state-to-state results for tetratomic reactions are discussed and a simple transition-state-based model is shown to provide useful insights into the correlation between reactant and product quantum states during a reaction. , for useful discussions. FIGURE 7 | Three-dimensional polar plots of differential cross sections (DCSs) for the D 2 + OH(v) ! D + DOH(v OD v b v OH ) reaction with the OH reactant in the v = 0 (a) and v = 1 (b) vibrational states at the collision energies of E c = 0.25 eV. The 3D DCSs show the product angular distributions with respect to the incoming direction of the OH reactant, i.e., the forward direction of DOH product corresponds to 0 while backward direction to 180 . The radius of the plot represents the product translational energy and arcs with shorter radius correspond to product states with higher internal energies and vice versa. Reproduced from Ref 46 with permission. WIREs Computational Molecular ScienceState-to-state quantum reactive scattering in four-atom systems Volume 7,

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

“…Quantum dynamic (QD) studies of reactive scattering are currently restricted to lowdimensional systems because of the so-called "dimensionality curse", namely the fact that the size of the problem (N) increases exponentially with the number of DOFs. Time-independent quantum mechanical (TIQM) approaches solve the timeindependent Schrodinger equation as a boundary value problem, thus scale steeply with the problem size (∝N 3 30 supplemented by some further improvements. 78,79 For atom− diatom problems, the hyperspherical coordinates allow three arrangement channels to be treated equally, which is particularly important for X 3 type systems where the three channels are identical.…”

“…This intuitive picture of nuclear motion on a multidimensional PES benefits from the natural separation of the electronic motion from that of nuclei, although it can break down near electronic degeneracies . Recent advances in both electronic structure theory and fitting techniques have perfected our ability to map out global PESs with high accuracy and efficiency for not just simple A + BC type reactions, but also for systems involving many nuclear degrees of freedom (DOFs). − These advances enabled quantum and classical investigations of scattering dynamics of polyatomic reactions, ,− which might have multiple channels leading to different products. Direct dynamics studies, which compute the forces on the fly without analytical PESs, provide an alternative means to explore chemical dynamics in even larger systems .…”

Nonequilibrium internal energy distributions during dissociation

“…Apart from QCT, purely quantum dynamics approaches (27)(28)(29) can also be used to obtain thermal rate constants, as done by Meuwly and coworkers (29) to study the NO(2Π) + N(4S) interaction for conditions relevant to hypersonic flows. However, to compute the evolution of a reacting gas, including non-Boltzmann internal energy distributions, the set of state-specific transition rates must be incorporated into master equation analysis.…”

Classification of Shapes and Deformations of Large Systems by Invariant Coordinates

“…The hyperspherical approach to molecular dynamics is well suited for quantum reactive scattering calculations and has been extensively adopted during the last decades, when efforts have been dedicated to the definition of sets of hyperspherical functions [ 1 – 3 ] for three and four-body collision dynamics (see e.g. [ 4 – 9 ]).…”