Coupled 3D Time-Dependent Wave-Packet Approach in Hyperspherical Coordinates: Application to the Adiabatic Singlet-State(1¹A′) D⁺ + H₂ Reaction

Abstract

We explore a coupled three-dimensional (3D) time-dependent wave packet formalism in hyperspherical coordinates for a 4D reactive scattering problem on the lowest adiabatic singlet surface (1(1)A') of the D(+) + H2 reaction. The coupling among the wavepackets arises through quantization of the rotation matrix, which represents the orientation of the three particles in space. The required transformation from Jacobi to hyperspherical coordinates and vice versa during initialization and projection of the wave packet on the asymptotic state(s), and the coupled equations of motion, are briefly discussed. With the long-range potential known to contribute significantly on the D(+) + H2 system, we demonstrate the workability of our approach, where the convergence profiles of the reaction probability for the reactive noncharge transfer (RNCT) process [D(+) + H2(v=0, j=0,1) → HD(v',j') + H(+)] are shown for three different collisional energies (1.7, 2.1, and 2.5 eV) with respect to the helicity (K) and total angular momentum (J) quantum numbers. The calculated reactive cross-section is presented as a function of the collision energy for two different initial states of the diatom (v = 0, j = 0, 1).

Quantum mechanical study of the high-temperature H+ + HD → D+ + H2 reaction for the primordial universe chemistry

“…In the literature, the scarce results given on the H + + HD → D + + H 2 reaction (Henchman et al 1981;Smith et al 1982;Millar et al 1989;Gerlich & Schlemmer 2002;Jambrina et al 2012) generally belong to articles focused on the inverse reaction D + + H 2 → H + + HD (Fehsenfeld et al 1974;Gerlich 1992;Jambrina et al 2009;González-Lezana et al 2013;Sahoo et al 2014Sahoo et al , 2015Lara et al 2015;Bhowmick et al 2018). In Refs (Henchman et al 1981;Smith et al 1982), thermal rates of 1.1 ± 0.2 and 1.7 ± 0.2 × 10 −10 cm 3 .s −1 are measured at 205 and 295 K respectively using the selected ion flow tube (SIFT) technique.…”

Near-resonant effects in the quantum dynamics of the H+H$_2^+$ $\rightarrow$ H$_2$+ H$^+$ charge transfer reaction and isotopic variants

“…The H + + H 2 exchange reaction has been the subject of many experimental [36][37][38][39][40][41][42][43][44][45] and theoretical 41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] studies. This reaction governs the ortho/para transitions of H 2 and is also responsible of the H 2 deuteration.…”

“…In the ground H + 3 electronic state there is a deep insertion well, of ≈ 4.6 eV, and the dynamics is mediated by a dense manifold of resonances, and exact calculations show that the reaction proceeds through a statistical mechanism [57][58][59] . Above 1.82 eV collision energy, the H + 2 + H channel becomes accessible, opening the charge transfer process, inverse to the reaction 2, and has been studied in a broad energy range 40,41,[45][46][47][48][49][50][51][52][53][54][55][56]61,62 . Furthermore, the non-adiabatic transitions in H + 3 were studied recently in photodissociation experiments by Urbain et al 63 .…”

Exploring the reaction dynamics of O(3P)+ (X2)→OH+(X3Σ−)+ H(2S) reaction with time‐dependent wave packet method

“…As we all know, some reactions, such as He + , N + , H/D + , S + HD/ are influenced by the reactants vibrational and rotational level changing. Sahoo et al explored reactive scattering problem of the D + + in various initial states, which used a coupled three‐dimensional time‐dependent wave packet formalism in hyperspherical coordinates. In addition, De Fazio et al presented a dynamical study of the H + HeH + reaction, which have been found to be nearly insensitive to the roto‐vibrational energy of the reactants.…”