Beyond Born–Oppenheimer Constructed Diabatic Potential Energy Surfaces for HeH₂⁺

Abstract

First-principles based beyond Born−Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH 2 + system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (1 2 A′, 2 2 A′, 3 2 A′ and 4 2 A′) are evaluated as functions of hyperangles for a grid of fixed values of the hyperradius in hyperspherical coordinates. Conical intersection between different states are validated by integrating the NACTs along appropriately chosen contours. Subsequently, adiabatic-to-diabatic (ADT) transformation angles are determined by solving the ADT equations to construct the diabatic potential matrix for the HeH 2 + system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

Curl condition: Existence of sub‐Hilbert space for molecular species or chemical processes

“…Since the lowest four electronic states (, , and ) of HeH are strongly coupled with each other through “1–2”, “2–3” and “3–4” JT type accidental seams, the titled system can be considered as a representative reactive species with four coupled electronic manifold. [37] Figure S10a–c of SI represent the components of ab initio NACTs (, and ). On the other hand, Figure S10d depicts 1D curves of ADT angles, namely, , and at Bohr and .…”

“…In the present investigation, the calculated ADT angles are used to Since the lowest four electronic states (1 2 A 0 , 2 2 A 0 , 3 2 A 0 and 4 2 A 0 ) of HeH þ 2 are strongly coupled with each other through "1-2", "2-3" and "3-4" JT type accidental seams, the titled system can be considered as a representative reactive species with four coupled electronic manifold. [37] Figure S10a-c and ADT Curls (Subsections S3.3.3 and S3.2.3 of SI) with the explicit expressions of NACTs and Mathematical Curls. It is evident from Figure 8 that profiles of both the Curls are almost close to each other for all the three cases ("1-2", "2-3", and "3-4") and therefore, the Curl Condition (F ij ρϕ ) acquire very small nonzero values ( < 10 À12 Bohr À2 ) affirming the existence of the four state SHS.…”

“…In addition, their workability have been demonstrated on several molecules of spectroscopic interest [29,30,[32][33][34][35], various triatomic scattering processes [35][36][37] and phase transitions in perovskite solids [38]. A program package, 'ADT' [31] has been developed for formulation of ADT equations through symbolic manipulations as well as numerical solutions of those equations for N coupled electronic states and K nuclear degrees of freedom.…”

“…[25,26] Later on, such theory has been generalized by Adhikari and coworkers [27–31] for three to six electronic states by formulating explicit forms of various ADT quantities (ADT equations, NACTs, Curl‐divergence equations and diabatic PESs matrix elements). In addition, their workability have been demonstrated on several molecules of spectroscopic interest [29,30,32–35], various triatomic scattering processes [35–37] and phase transitions in perovskite solids [38]. A program package, ‘ADT’ [31] has been developed for formulation of ADT equations through symbolic manipulations as well as numerical solutions of those equations for coupled electronic states and nuclear degrees of freedom.…”

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

“…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. State-to-state as well as total reaction probabilities, cross sections, and rate coefficients are calculated for various reactive as well as nonreactive channels and are compared with previous theoretical calculations and experimental measurements.…”