Accurate Calculation of Rate Constant and Isotope Effect for the F + H₂ Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

Abstract

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H2/D2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H2 and D2) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H2 and F + D2 reactions are presented along with previous theoretical and experimental results.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces

“…Total ICS for the product formation [F + H 2 ( v = 0, j = 0) → HF + H] reaction on the ground state (1 2 A ′) of diabatic calculation as a function of collision energy for without [-·-·- (black)] and with [-·-·-·- (red)] the inclusion of SO coupling in comparison with our previous adiabatic calculation [-·-·-·- (light blue)] as well as other theoretical results: TIQM by Aoiz et al on SW PES [···■···(green)] and HSW PES [·····(red)]; TIQM by Castillo et al on SW PES [–  - (pink)] and HSW PES [–  - (yellow)]; TDQM by Billing and Markovic [- ■- (light green)]; QM CS calculation by Baer and co-workers on SW PES [– – – (blue)]; TIQM by Alexander et al [---- (green)]; and TDWP by Zhang et al [–··–··– (purple)].…”

“…On the other hand, nonreactive probabilities obtained from diabatic calculation (see eq 15) on the ground state (1 2 A′) are depicted in Figures S2 and S3 of the Supporting Information for without and with SO coupling, respectively, which are discussed in detail later. The profiles for product (HF) formation obtained from diabatic calculation (see eq 15) are compared with our earlier single surface 77 and present SO coupled multiple surface (excluding nonadiabaticity) adiabatic calculation (see eq 12) as well as theoretical result by Alexander et al 49 These figures depict the following: (a) the present diabatic reaction probability profiles without and with the inclusion of SO coupling show similar thresholds for ground state product (HF + H [1 2 A′]) as well as excited state nonreactive species [F + H 2 [1 2 A″] (without SO) and F* + H 2 [1 2 A″] (with SO)]. Both the product formation probability profiles (without and with the inclusion of SO coupling) start at E tot ∼ 0.27 eV (E col ∼ 0.001 eV) depicting the exothermic nature of the reaction (see Figures 1 and 2) and thereafter, generally increase with the increase of total energy; (b) reaction probability for the product (HF) formation on the ground state (1 2 A′) including the SO coupling without the nonadiabatic interaction (see eq 12) show a similar profile as the single surface adiabatic one, 77 whereas the corresponding nonreactive species (F* + H 2 [1 2 A″]) on the excited state depict much less magnitude compared to the inclusion of nonadiabatic coupling; (c) for the ground state HF product, diabatic reaction probability (without or with the inclusion of SO coupling) subsides extensively compared to others 49,77 due to the competition between ground and excited state processes driven by nonadiabatic interaction; (d) the product (HF) reaction probability on the ground state (1 2 A′) and nonreactive probability [F + H 2 [1 2 A″] (without SO) and F* + H 2 [1 2 A″] (with SO)] on the excited state suddenly drops and increases near E tot ∼ 0.3137 eV (E col ∼ 0.0447 eV), respectively; (e) the present diabatic reaction probability profiles for the product formation show an oscillatory behavior at lower energies due to the reactive resonances in the title reaction, but the intensity of the resonance peaks are lower for the present case compared to the earlier calculations; 49,77 and (f) reaction probabilities calculated on diabatic surface for the product (HF) formation with the inclusion of SO coupling is higher in magnitude over the whole energy range compared to without SO cases, while such probabilities with the SO coupling for the nonreactive species on the excited state (F* + H 2 [1 2 A″]) depict less magnitude than that of without SO situation (F + H 2 [1 2 A″]).…”

“…Total reaction probability as a function of total energy for ground state (1 2 A ′) product, HF without ( J ) and with ( J ′ = J + 1 2 ) the inclusion of SO coupling at total angular momentum, J = 0 in comparison with previous theoretical calculations: three-surface diabatic calculation without [ (red)] and with [ (green)] SO coupling, three-surface adiabatic calculation with SO in the absence of nonadiabatic coupling [--- (yellow)] (see eq ), single-surface ground state adiabatic calculation [ (pink)], and theoretical result by Alexander et al [--- (blue)] …”

“…Over the last few decades, the development of accurate quantum dynamics algorithms 64−70 has led to the evaluation of precise cross sections and rate constants for atom−diatom collision processes, and the detailed literature survey can be found elsewhere. 71−76 In this current study, we extend our earlier scattering calculation 77 on ground adiabatic surface by employing the most recent and accurate three (3) state ab initio diabatic surfaces 31 of the FH 2 system without (J) and with (J′ = J + 1…”

“…Over the last few decades, the development of accurate quantum dynamics algorithms − has led to the evaluation of precise cross sections and rate constants for atom–diatom collision processes, and the detailed literature survey can be found elsewhere. − In this current study, we extend our earlier scattering calculation on ground adiabatic surface by employing the most recent and accurate three (3) state ab initio diabatic surfaces of the FH 2 system without ( J ) and with ( J ′ = J + 1 2 ) the inclusion of SO coupling over and above nonadiabatic interaction to carry out fully close coupled (FCC) 3D TDWP formalism for zero as well as nonzero total angular momentum, J situations on the F + H 2 reaction. Recently, Adhikari and Varandas have introduced OpenMP-MPI parallelized algorithm for TDWP formulation for any J ≠ 0 cases ,, with the inclusion of all helicity quantum numbers by FCC approach on the ground electronic PES as well as for diabatic calculation ,, on multisheeted PESs. , Such an “exact” and “accurate” methodology is employed for performing the scattering calculation on the nonadiabatically coupled diabatic surfaces for the title reaction without and with the inclusion of spin orbit corrected surfaces.…”