Accurate fit of the two lowest excited‐state potential‐energy surfaces for doublet HeH2+

Potential energy surfaces for singlet and triplet states of the LiH2+ system and quasi-classical trajectory cross sections for H + LiH+ and H+ + LiH

A new set of six accurate ab initio potential energy surfaces (PESs) is presented for the first three singlet and triplet states of LiH2+ (1,21A', 11A'', 1,23A', and 13A'' states, where four of them are investigated for the first time), which have allowed new detailed studies gaining a global view on this interesting system. These states are relevant for the study of the most important reactions of lithium chemistry in the early universe. More than 45 000 energy points were calculated using the multi-reference configuration interaction level of theory using explicitly correlated methods (ic-MRCI-F12), and the results obtained for each individual electronic state were fitted to an analytical function. Using quasiclassical trajectories and considering the initial diatomic fragment in the ground rovibrational state, we have determined the integral cross sections for the H + LiH+(X2Σ+, C2Π) and H+ + LiH(X1Σ+, B1Π) reactions. In these calculations all available reaction channels were considered: the chemically most important H or H+ transfer/abstraction as well as atom exchange and collision induced dissociation for up to 1.0 eV of collision energy.

Beyond Born-Oppenheimer Constructed Diabatic Potential Energy Surfaces for HeH2. J Phys Chem A 2023;127:3832-3847. [PMID: 37098130 DOI: 10.1021/acs.jpca.3c01047]

First-principles based beyond Born-Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH₂⁺ system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (1²A', 2²A', 3²A' and 4²A') 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 HeH₂⁺ system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

Globally Accurate Potential Energy Surface for BH2+2(13A') Using the Switching Function Formalism

A great number of ab initio energy points are calculated using the aug-cc-pV(Q,5)Z basis sets at the multireference configuration interaction level and extrapolated to the complete basis set limit. An exact three-dimensional potential energy surface of the ground-state BH₂⁺ is obtained. A switching function is developed to model the transition of B⁺(³P) to B⁺(¹S) to guarantee the reliable behavior at B⁺(³P) + H₂(X¹∑_g⁺) and BH⁺(X²∑⁺) + H(²S) dissociation limits. The various topographic features of the new global potential energy surface are discussed in detail, showing a good agreement with the previous results from the theory. The quasi-classical trajectory method is utilized to calculate the integral cross sections of the B⁺(³P) + H₂(X¹∑_g⁺) (v = 0, j = 0) → BH⁺(X²∑⁺) + H(²S) reaction, which can provide another support for reliability of the title potential energy surface.

A new global potential energy surface of the SH2+(X4A'') system and quantum calculations for the S+ + H2(v = 0-3, j = 0) reaction

A new global potential energy surface (PES) for the ground state of the SH2+(X4A'') system is constructed using a permutation invariant polynomial neural network method. In ab initio calculations, the MRCI-F12 method with the AVTZ basis set is used. Furthermore, the dynamics calculations of the S+ + H2(v = 0-3, j = 0) → SH+ + H reaction are carried out based on the new PES. The reaction probabilities and integral cross sections are compared with available theoretical calculations. Present values are in general good agreement with the previous theoretical studies. However, some discrepancies can still be found due to different PESs used in the calculation. Furthermore, the vibrational energy of the reactant molecule can significantly enhance the reactivity compared to the translational energy. The differential cross sections indicated that the reaction mechanism is changed from the "head-on" rebound mechanism to the tripping mechanism with the increasing number of initial vibrational excitation state.

Dynamics of H + HeH+(v = 0, j = 0) → H2+ + He: Insight on the Possible Complex-Forming Behavior of the Reaction

The H + HeH⁺→ He + H₂⁺ reaction has been studied by means of a combination of theoretical approaches: a statistical quantum method (SQM), ring polymer molecular dynamics (RPMD), and the quasiclassical trajectory (QCT) method. Cross sections and rate constants have been calculated in an attempt to investigate the dynamics of the process. The comparison with previous calculations and experimental results reveals that despite the fact that statistical predictions seem to reproduce some of the overall observed features, the analysis at a more detailed state-to-state level shows noticeable deviations from a complex-forming dynamics. We find some differences in cross sections and rate constants obtained in the QCT calculation with a Gaussian binning procedure with respect to previous works in which the standard histogram binning was employed.

Non-adiabatic Quantum Dynamics of the Dissociative Charge Transfer He++H2 → He+H+H. Front Chem 2019;7:249. [PMID: 31041310 PMCID: PMC6477054 DOI: 10.3389/fchem.2019.00249]

We present the non-adiabatic, conical-intersection quantum dynamics of the title collision where reactants and products are in the ground electronic states. Initial-state-resolved reaction probabilities, total integral cross sections, and rate constants of two H₂ vibrational states, v₀ = 0 and 1, in the ground rotational state (j₀ = 0) are obtained at collision energies E_coll ≤ 3 eV. We employ the lowest two excited diabatic electronic states of HeH2+ and their electronic coupling, a coupled-channel time-dependent real wavepacket method, and a flux analysis. Both probabilities and cross sections present a few groups of resonances at low E_coll, whose amplitudes decrease with the energy, due to an ion-induced dipole interaction in the entrance channel. At higher E_coll, reaction probabilities and cross sections increase monotonically up to 3 eV, remaining however quite small. When H₂ is in the v₀ = 1 state, the reactivity increases by ~2 orders of magnitude at the lowest energies and by ~1 order at the highest ones. Initial-state resolved rate constants at room temperature are equal to 1.74 × 10⁻¹⁴ and to 1.98 × 10⁻¹² cm³s⁻¹ at v₀ = 0 and 1, respectively. Test calculations for H₂ at j₀ = 1 show that the probabilities can be enhanced by a factor of ~1/3, that is ortho-H₂ seems ~4 times more reactive than para-H₂.

Accurate potential energy surface of H2S+(X 2 A″) via extrapolation to the complete basis set limit and its use in dynamics study of S + ( D 2 ) + H 2 ( X 1 Σ g + ) reaction

The single-sheeted potential energy surface (PES) of H 2 S + ( X   2 A ' ' ) is developed based on the ab initio energies calculated by the multi-reference configuration interaction method including the Davidson correction. All the ab initio energies are first calculated using aug-cc-pVQdZ and aug-cc-pV5dZ basis sets, which are then extrapolated to the complete basis set (CBS) limit. A switching function is developed to model the transition of S + D 2 to S + S 4 . The many-body expansion formalism is employed to obtain the H 2 S + ( X   2 A ' ' ) PES by fitting such CBS energies and the root-mean square derivation is 0.0367 eV. The topographical features of the present PES are examined in detail, which are well consistent with previous studies. The quasiclassical trajectory method is subsequently utilized to study the S + D 2 + H 2 ( X 1 Σ g + )   →   S H + ( X   3 Σ - ) + H ( S 2 ) reaction. The capture time, integral cross sections, and rovibrational distributions are calculated. By examining the capture time, it can be concluded that the title reaction is mainly controlled by the indirect mechanism for lower collision energies, while the direct and indirect mechanisms coexist and the latter plays a dominant role for higher collision energies.

Product lambda-doublet ratios as an imprint of chemical reaction mechanism

In the last decade, the development of theoretical methods has allowed chemists to reproduce and explain almost all of the experimental data associated with elementary atom plus diatom collisions. However, there are still a few examples where theory cannot account yet for experimental results. This is the case for the preferential population of one of the Λ-doublet states produced by chemical reactions. In particular, recent measurements of the OD(²Π) product of the O(³P)+D₂ reaction have shown a clear preference for the Π(A′) Λ-doublet states, in apparent contradiction with ab initio calculations, which predict a larger reactivity on the A′′ potential energy surface. Here we present a method to calculate the Λ-doublet ratio when concurrent potential energy surfaces participate in the reaction. It accounts for the experimental Λ-doublet populations via explicit consideration of the stereodynamics of the process. Furthermore, our results demonstrate that the propensity of the Π(A′) state is a consequence of the different mechanisms of the reaction on the two concurrent potential energy surfaces

Propensity for a given Λ-doublet level is a common feature in many chemical reactions, but has so far remained unexplained. Here, the authors show how to predict computationally those propensities and relate them to the reaction mechanism on concurrent potential energy surfaces.

Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2 + + He Reaction: A Rigourous Test for Reaction Dynamics Methods

In this work we present a dynamical study of the H + HeH+ → H2+ + He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models. The paper extends and complements a recent work [ Phys. Chem. Chem. Phys. 2014, 16, 11662] devoted to the characterization of the reactivity from the ultracold regime up to the three-body dissociation breakup. In particular, the accuracy of the quasi-classical trajectory method below the three-body dissociation threshold has been assessed by a detailed comparison with previous calculations performed with different reaction dynamics methods, whereas the reliability of the results in the high energy range has been checked by a direct comparison with the available experimental data. Integral cross sections for several HeH+ roto-vibrational states have been analyzed and used to understand the extent of quantum effects in the reaction dynamics. By using the quasi-classical trajectory method and quantum mechanical close coupling data, respectively, in the high and low collision energy ranges, we obtain highly accurate thermal rate costants until 15 000 K including all (178) the roto-vibrational bound and quasi-bound states of HeH+. The role of the collision-induced dissociation is also discussed and explicitly calculated for the ground roto-vibrational state of HeH+.

A comparative study of the Au + H₂, Au⁺ + H₂, and Au⁻ + H₂ systems: Potential energy surfaces and dynamics of reactive collisions

In order to study the Au(-) + H2 collision, a new global potential energy surface (PES) describing the ground electronic state of AuH2(-) system is developed and compared with the PESs of the neutral [Zanchet et al., J. Chem. Phys. 132, 034301 (2010)] and cationic systems [Anaís et al., J. Chem. Phys. 135, 091102 (2011)]. We found that Au(-) - H2 presents a H-Au-H insertion minimum attributed to the stabilization of the LUMO 3b2 orbital, which can be considered as the preamble of the chemisorption well appearing in larger gold clusters. While the LUMO orbital is stabilized, the HOMO 6a1 is destabilized, creating a barrier at the geometry where the energy orbitals' curves are crossing. In the anion, this HOMO is doubly occupied, while in the neutral system is half-filled and completely empty in the cation, explaining the gradual disappearance of the well and the barrier as the number of electrons decreases. The cation presents a well in the entrance channel partially explained by electrostatic interactions. The three systems' reactions are highly endothermic, by 1.66, 2.79, and 3.23 eV for AuH, AuH(+), and AuH(-) products, respectively. The reaction dynamics is studied using quasi-classical trajectory method for the three systems. The one corresponding to the anionic system is new in this work. Collision energies between 1.00 and 8.00 eV, measured for the cation, are in good agreement with the simulated cross section for the AuH(+). It was also found that the total fragmentation, in three atoms, competes becoming dominant at sufficiently high energy. Here, we study the competition between the two different reaction pathways for the anionic, cationic, and neutral species, explaining the differences using a simple model based on the topology of the potential energy surfaces.

Potential energy surface and reactive collisions for the Au+H(2) system

A global potential energy surface is obtained for the ground state of the endoergic Au((2)S)+H(2)(X (1)Sigma(g) (+))-->AuH((1)Sigma(+))+H((2)S) reaction. The global potential is obtained by fitting highly correlated ab initio calculations on the system, using relativistic pseudopotential for the gold atom. Several electronic states are calculated correlating with Au((2)S)+H(2), Au((2)D)+H(2), and H(2), Au((2)P)+H(2) asymptotes. These states show several conical intersections and curve crossings along the minimum energy reaction path which are analyzed in detail. One of them gives rise to an insertion well in which there are important contributions from the Au((2)D) and Au((2)P) states of gold, which is interesting because it is analog to the deep chemisorption well appearing in larger gold clusters. Quantum wave packet and quasiclassical trajectory dynamical calculations performed for the reaction at zero total angular momentum are in good agreement, provided that a Gaussian binning method is used to account for the zero-point energy of products. Finally, integral and differential cross sections are calculated for the reaction with quasiclassical trajectories. Two different reaction mechanisms are found, one direct and the second indirect, in which the Au atom inserts in between the two hydrogen atoms because of the existence of the insertion well discussed above.

Conical intersections and semiclassical trajectories: Comparison to accurate quantum dynamics and analyses of the trajectories

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.