We report for the first time an accurate ab initio potential energy surface for the HeH+–H2 system in four dimensions (4D) treating both diatomic species as rigid rotors. The computed ab initio potential energy point values are fitted using an artificial neural network method and used in quantum close coupling calculations for different initial states of both rotors, in their ground electronic states, over a range of collision energies. The state-to-state cross section results are used to compute the rate coefficients over a range of temperatures relevant to interstellar conditions. By comparing the four dimensional quantum results with those obtained by a reduced-dimensions approach that treats the H2 molecule as an averaged, nonrotating target, it is shown that the reduced dimensionality results are in good accord with the four dimensional results as long as the HeH+ molecule is not initially rotationally excited. By further comparing the present rate coefficients with those for HeH+–H and for HeH+–He, we demonstrate that H2 molecules are the most effective collision partners in inducing rotational excitation in HeH+ cation at interstellar temperatures. The rotationally inelastic rates involving o-H2 and p-H2 excitations are also obtained and they turn out to be, as in previous systems, orders of magnitude smaller than those involving the cation. The results for the H2 molecular partner clearly indicate its large energy-transfer efficiency to the HeH+ system, thereby confirming its expected importance within the kinetics networks involving HeH+ in interstellar environments.

https://cdm21054.contentdm.oclc.org/digital/api/collection/IR/id/10503/download

HeH+ Collisions with H2: Rotationally Inelastic Cross Sections and Rate Coefficients from Quantum Dynamics at Interstellar Temperatures

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

The transition state, a first-order saddle point on the potential energy surface, plays a central role in understanding the mechanism, dynamics, and rate of chemical reactions. However, we recently identified energetically accessible second-order saddles (SOS) in certain reactions and showed that the SOS plays a crucial role in the dynamics of the reactions [Pradhan et al., Phys. Chem. Chem. Phys., 2019, 21, 12837; Rashmi et al., Regul. Chaotic Dyn., 2021, 26, 119]. In the present work, we investigated the role of second-order saddle points on the dynamics of the thermal denitrogenation of 1-pyrazoline using ab initio classical trajectory simulations at the CASSCF(4,4)/6-31+G* level of theory, for total energies of 130, 140, and 150 kcal mol-1 available to the system. In this unimolecular dissociation reaction, the SOS point is 4 kcal mol-1 higher in energy than the synchronous bond-breaking transition state and opens up an additional reaction pathway. We found that the fraction of molecules following the synchronous bond-breaking pathway decreased with an increase in the total available energy in the reaction, accompanied by an increase in the fraction following the asynchronous pathway. To further understand the competition between the transition state and the SOS pathways, we investigated the mechanism of halogen-substituted 1-pyrazolines where the SOS energies are comparable to that of the transition states.

Influence of second-order saddles on reaction mechanisms.

Prediction of interaction energy for rare gas dimers using machine learning approaches

We analyze the classical phase space dynamics of a three degree of freedom Hamiltonian that models multiple bond breaking and forming reactions. The model Hamiltonian, inspired from studies on double proton transfer reactions, allows for exploring the dynamical consequences of higher index saddles on multidimensional potential energy surfaces. Studies have shown that coupling of low frequency transverse modes to the reaction coordinate can significantly influence the reaction mechanism, concerted or sequential, as inferred from a reduced dimensional analysis. Using the notion of dynamically concerted and sequential pathways, we provide insights into the role of the transverse modes by studying the delay times between the formation of two bonds. The delay time distribution, used extensively in earlier studies, is placed on a firm dynamical footing by correlating it with the phase space manifolds, determined using the technique of Lagrangian descriptors. We establish the utility of Lagrangian descriptors in identifying the phase space manifolds responsible for the dynamically concerted and dynamically sequential pathways.

Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics

The role of second-order saddle in the isomerization dynamics was investigated by considering the $$E-Z$$
 isomerization of guanidine. The potential energy profile for the reaction was mapped using the ab initio wavefunction method. The isomerization path involved a torsional motion about the imine (C-N) bond in a clockwise or an anticlockwise fashion resulting in two degenerate transition states corresponding to a barrier of 23.67 kcal/mol.
An alternative energetically favorable path (
 $$\sim$$
 1 kcal/mol higher than the transition states) by an in-plane motion of the imine (N-H) bond via a second-order saddle point on the potential energy surface was also obtained. The dynamics of the isomerization was investigated by ab initio classical trajectory simulations. The trajectories reveal that isomerization happens via the transition states as well as the second-order saddle. The dynamics was found to be nonstatistical with trajectories exhibiting recrossing and the higher energy second-order saddle pathway preferred over the traditional transition state pathway. Wavelet based time-frequency analysis of internal coordinates indicate regular dynamics and existence of long-lived quasi-periodic trajectories in the phase space.

Second-order Saddle Dynamics in Isomerization Reaction

Machine learning has been applied to various fields and is envisaged as the technology of the future. We discuss here, the applications of machine learning methods to represent potential energy surfaces - an important aspect of chemical dynamics. We illustrate the process of machine learning using simple examples, and demonstrate how it can be extended to complicated problems.

Machine Learning in Chemical Dynamics

Our recent work on the E - Z isomerization reaction of guanidine using ab initio chemical dynamics simulations [Rashmi et al, Regul. Chaotic Dyn. 2021, 26, 119] emphasized the role of second-order saddle (SOS) in the isomerization reaction; however we could not unequivocally establish the non-statistical nature of the dynamics followed in the reaction. In the present study, we performed thousands of on-the-fly trajectories using forces computed at the MNDO level to investigate the influence of second-order saddle in the E - Z isomerization reaction of guanidine and the role of intramolecular vibrational energy redistribution (IVR) on the reaction dynamics. The simulations reveal that while majority of the trajectories follow the traditional transition state pathways, 15% of the trajectories follow the SOS path. The dynamics was found to be highly non-statistical with the survival probabilities of the reactants showing large deviations from those obtained within the RRKM assumptions. In addition, a detailed analysis of the dynamics using time-dependent frequencies and the frequency ratio spaces reveal the existence of multiple resonance junctions that indicate the existence of regular dynamics and long-lived quasi-periodic trajectories in the phase space associated with non-RRKM behavior.

Richa Rashmi

Papers

Second-order Saddle Dynamics in Isomerization Reaction

Machine Learning in Chemical Dynamics

E-Z Isomerization in Guanidine: Second-order Saddle Dynamics, Non-statisticality, and Time-frequency Analysis.