The He + H2+ → HeH+ + H reaction: ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

Improving potential energy surfaces using measured Feshbach resonance states

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

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.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Atom-Diatom Reactive Scattering Collisions in Protonated Rare Gas Systems

The study of the dynamics of atom-diatom reactions involving two rare gas (Rg) atoms and protons is of crucial importance given the astrophysical relevance of these processes. In a series of previous studies, we have been investigating a number of such Rg(1)+ Rg(2)H+→ Rg(2)+ Rg(1)H+ reactions by means of different numerical approaches. These investigations comprised the construction of accurate potential energy surfaces by means of ab initio calculations. In this work, we review the state-of-art of the study of these protonated Rg systems making special emphasis on the most relevant features regarding the dynamical mechanisms which govern these reactive collisions. The aim of this work therefore is to provide an as complete as possible description of the existing information regarding these processes.

Computational Characterization of Astrophysical Species: The Case of Noble Gas Hydride Cations

Theoretical-computational studies together with recent astronomical observations have shown that under extreme conditions in the interstellar medium (ISM), complexes of noble gases may be formed. Such observations have generated a wide range of possibilities. In order to identify new species containing such atoms, the present study gathers spectroscopic data for noble gas hydride cations, NgH+ (Ng = He, Ne, Ar) from high-level ab initio quantum chemistry computations, aiming to contribute in understanding the chemical bonding and electron sharing in these systems. The interaction potentials are obtained from CCSD(T)/CBS and MRCI+Q calculations using large basis sets, and then employed to compute vibrational levels and molecular spectroscopic constants for all known stable isotopologues of ground state NgH+ cations. Comparisons with previously reported values available are discussed, indicating that the present data could serve as a benchmark for future studies on these systems and on higher-order cationic noble gas hydrides of astrophysical interest.

Quantum and quasiclassical dynamical simulations for the Ar2H+ on a new global analytical potential energy surface

A new analytical potential energy surface (PES) has been constructed for the Ar₂H⁺ system from a dataset consisting of a large number of ab initio energies computed using the coupled-cluster singles, doubles and perturbative triples method and aug-cc-pVQZ basis set. The long-range interaction is added to the diatomic potentials using a standard long range expansion form to better describe the asymptotic regions. The vibrational states for the most stable structures of the Ar₂H⁺ system have been calculated, and few low lying states are assigned to quantum numbers. Reactive scattering studies have been performed for the Ar + Ar'H⁺ → Ar' + ArH⁺ proton exchange reaction on the newly generated PES. Reaction probability, cross sections, and rate constants are calculated for the Ar + Ar'H⁺(v = 0, j = 0) collisions within 0.01 eV-0.6 eV of relative translational energy using exact quantum dynamical simulations as well as quasiclassical trajectory (QCT) calculations. The effect of vibrational excitation of the reactants is also explored for the reaction. State averaged rate constants are calculated for the proton exchange reaction at different temperatures using the QCT method. The mechanistic pathways for the reaction are understood by analyzing the quasiclassical trajectories.

Experimental study of the proton-transfer reaction C + H2+ → CH+ + H and its isotopic variant (D2+)

We report absolute integral cross section (ICS) measurements using a dual-source merged-fast-beams apparatus to study the titular reactions over the relative translational energy range of Er ∼ 0.01-10 eV. We used photodetachment of C- to produce a pure beam of atomic C in the ground electronic 3P term, with statistically populated fine-structure levels. The H2+ and D2+ were formed in an electron impact ionization source, with well known vibrational and rotational distributions. The experimental work is complemented by a theoretical study of the CH2+ electronic system in the reactant and product channels, which helps to clarify the possible reaction mechanisms underlying the ICS measurements. Our measurements provide evidence that the reactions are barrierless and exoergic. They also indicate the apparent absence of an intermolecular isotope effect, to within the total experimental uncertainties. Capture models, taking into account either the charge-induced dipole interaction potential or the combined charge-quadrupole and charge-induced dipole interaction potentials, produce reaction cross sections that lie a factor of ∼4 above the experimental results. Based on our theoretical study, we hypothesize that the reaction is most likely to proceed adiabatically through the 14A' and 14A'' states of CH2+via the reaction C(3P) + H2+(2Σ+g) → CH+(3Π) + H(2S). We also hypothesize that at low collision energies only H2+(v ≤ 2) and D2+(v ≤ 3) contribute to the titular reactions, due to the onset of dissociative charge transfer for higher vibrational v levels. Incorporating these assumptions into the capture models brings them into better agreement with the experimental results. Still, for energies ⪅0.1 eV where capture models are most relevant, the modified charge-induced dipole model yields reaction cross sections with an incorrect energy dependence and lying ∼10% below the experimental results. The capture cross section obtained from the combined charge-quadrupole and charge-induced dipole model better matches the measured energy dependence but lies ∼30-50% above the experimental results. These findings provide important guidance for future quasiclassical trajectory and quantum mechanical treatments of this reaction.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

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.

Double resonance rotational spectroscopy of He-HCO. Phys Chem Chem Phys 2019;21:3440-3445. [PMID: 30191208 DOI: 10.1039/c8cp04532a]

The ground state of He-HCO+ is investigated using a recently developed double resonance technique, consisting of a rotational transition followed by a vibrational transition into a dissociative state. In order to derive precise predictions for the rotational states, the high resolution infrared predissociation spectroscopy of the v1 C-H stretching mode is revisited. Eleven pure rotational transitions are measured via the double resonance method. A least squares fit of these transitions to a standard linear rotor Hamiltonian reveals that the semirigid rotor model cannot fully describe the loosely bound He-HCO+ complex. The novel double resonance technique is compared with other action spectroscopic schemes, and some potential future applications are presented.

Near dissociation states for H2+–He on MRCI and FCI potential energy surfaces

Ro-vibrational states for H₂⁺–He on new kernel-based potential energy surfaces based on MRCI and FCI calculations.

Quantum state-to-state study for (H−(D−),HD) collisions on two potential energy surfaces

Revealing the reaction mechanisms of the H⁻/D⁻ + HD reaction – an exact quantum dynamics study on two potential energy surfaces.

A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2⋅CO systems

The quasi-variational quantum chemical protocol and code GENIUSH [E. Mátyus et al., J. Chem. Phys. 130, 134112 (2009) and C. Fábri et al., J. Chem. Phys. 134, 074105 (2011)] has been augmented with the complex absorbing potential (CAP) technique, yielding a method for the determination of rovibrational resonance states. Due to the effective implementation of the CAP technique within GENIUSH, the GENIUSH-CAP code is a powerful tool for the study of important dynamical features of arbitrary-sized molecular systems with arbitrary composition above their first dissociation limit. The GENIUSH-CAP code has been tested and validated on the H₂He⁺ cation: the computed resonance energies and lifetimes are compared to those obtained with a previously developed triatomic rovibrational resonance-computing code, D²FOPI-CCS [T. Szidarovszky and A. G. Császár Mol. Phys. 111, 2131 (2013)], utilizing the complex coordinate scaling method. A unique feature of the GENIUSH-CAP protocol is that it allows the simple implementation of reduced-dimensional dynamical models. To prove this, resonance energies and lifetimes of the H₂⋅CO van der Waals complex have been computed utilizing a four-dimensional model (freezing the two monomer stretches), and a related potential energy surface, of the complex.

Rovibrational Resonances in H2He. J Chem Theory Comput 2018;14:1523-1533. [PMID: 29390185 DOI: 10.1021/acs.jctc.7b01136]

The nuclear dynamics of the metastable H₂He⁺ complex is explored by symmetry considerations and angular momentum addition rules as well as by accurate quantum chemical computations with complex coordinate scaling, complex absorbing potential, and stabilization techniques. About 200 long-lived rovibrational resonance states of the complex are characterized and selected long-lived states are analyzed in detail. The stabilization mechanism of these long-lived resonance states is discussed on the basis of probability density plots of the wave functions. Overlaps of wave functions derived by a reduced-dimensional model with the full-dimensional wave functions reveal dissociation pathways for the long-lived resonance states and allow the calculation of their branching ratios.

On the Angular Distribution of the H+Li2 Cross Sections: a Converged Time-Independent Quantum Scattering Study

A thorough time-independent quantum scattering study is performed on a benchmark potential energy surface for the H+Li₂ reaction at the fundamental electronic state. Integral and differential cross sections are calculated along with thermal rate coefficients until convergence is reached. Our findings show that vibrational and rotational excitations of the reactant hinder reactivity, though for the latter a considerable reaction promotion was spotted as we increase the reactant rotational quantum number until the critical value of j = 4. Such a promotion then begins to retract, eventually becoming an actual inhibition for larger j. In a straightforward manner, the concept of time-independent methods implemented in this study allowed this accurate state-to-state analysis. Furthermore, a nearly isotropic behaviour of the scattering is noted to take place from the angular point of view. Remarkably, our computational protocol is ideally suited to yield converged thermal rate coefficients, revealing a non-Arrhenius pattern and showing that J-shifting approach fails to describe this particular reaction. Our results, when compared to previous and independent ones, reinforce the latest theoretical reference for future validation in the experimental field.

Scattering study of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction on an ab initio based analytical potential energy surface

Initial state selected dynamics of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction is investigated by quantum and statistical quantum mechanical (SQM) methods on the ground electronic state. The three-body ab initio energies on a set of suitably chosen grid points have been computed at CCSD(T)/aug-cc-PVQZ level and analytically fitted. The fitting of the diatomic potentials, computed at the same level of theory, is performed by spline interpolation. A collinear [NeHNe](+) structure lying 0.72 eV below the Ne + NeH(+) asymptote is found to be the most stable geometry for this system. Energies of low lying vibrational states have been computed for this stable complex. Reaction probabilities obtained from quantum calculations exhibit dense oscillatory structures, particularly in the low energy region and these get partially washed out in the integral cross section results. SQM predictions are devoid of oscillatory structures and remain close to 0.5 after the rise at the threshold thus giving a crude average description of the quantum probabilities. Statistical cross sections and rate constants are nevertheless in sufficiently good agreement with the quantum results to suggest an important role of a complex-forming dynamics for the title reaction.

Quasi-Classical Trajectory Study of Atom-Diatomic Molecule Collisions in Symmetric Hyperspherical Coordinates: The F + HCl Reaction as a Test Case

We investigate the reactive dynamics of the triatomic system F + HCl → HF + Cl for total angular momentum equal zero and for different low-lying rovibrational states of the diatomic molecule. For each of the initial vibrational quantum numbers, the time evolution of the atom-diatom collision process is investigated for a wide range of impact angles and collision energies. To this purpose, the Quasi-Classical Trajectories (QCT) method was implemented in a hyperspherical configuration space. The Hamilton equations of motion are solved numerically in an intermediate effective Cartesian space to exploit the relative simplicity of this intermediate representation. Interatomic interactions are described by a London-Eyring-Polanyi-Sato potential energy surface, specifically developed for the title reaction, and the results of the QCT simulations are discussed in terms of the time-evolution of the hyperangles. The analysis of the collision dynamics using symmetric hyperspherical coordinates provides, in addition to the description in terms of a natural reaction coordinate (the hyperradius), a more striking representation of the exchange dynamics, in terms of the time-dependent probability distribution along the kinematic rotation hyperangle, and a precise distinction between direct and indirect mechanisms of the reaction.

State-to-State Dynamics of the Ne + HeH(+) (v = 0, j = 0) → NeH(+)(v', j') + He Reaction

The dynamics of the Ne + HeH(+)(v = 0, j = 0) → NeH(+)(v', j') + He reaction was analyzed in detail at the state-to-state level. A time-independent quantum mechanical (TIQM) method was applied to calculate rovibrational distributions and differential cross sections (DCSs), in comparison with quasi-classical trajectory and statistical quantum predictions. Possible changes in the dynamical mechanisms that define the process were also investigated as a function of the collision energy. At the lowest energy regime, the TIQM results produce a noticeably different cross section in comparison with previously reported time-dependent wave packet results. Although the statistical methods reproduce some dynamical features, especially as the energy increases, the marked preference for the forward scattering direction on the DCSs suggests that the reaction mainly follows a direct mechanism.

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+.

Quantum, Statistical, and Quasiclassical Trajectory Studies For the Ne + HeH(+) → NeH(+) + He Reaction on the Ground Electronic State

Real wave packet, statistical quantum, and quasiclassical trajectory methods were employed to study the dynamics of Ne + HeH(+)(v0,j0) → He + NeH(+) reaction on an ab initio potential energy surface [J. Phys. Chem. A 2013, 117, 13070-13078]. Quantum and statistical quantum calculations were performed within the centrifugal sudden (CS) approximation as well as including the Coriolis coupling (CC). Dense oscillatory structures of the quantum reaction probabilities and fair agreement between quantum and statistical cross sections suggest a complex forming mechanism for the reaction. No significant differences between cross sections obtained within the CS and CC approaches are observed. Quasiclassical trajectory results give an excellent average description of the quantum CC results. At low collision energies, there is a substantial decrease in reactivity for the reaction upon rovibrational excitation. Initial state selected rate constants for the title reaction are calculated between 20 and 1000 K, and the calculated value at 300 K agrees quite well with the available experimental result. Reaction cross sections and rate constants are also compared with those calculated via the Langevin capture model for exothermic reactions.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

The H + HeH(+) → He + H2(+) reaction from the ultra-cold regime to the three-body breakup: exact quantum mechanical integral cross sections and rate constants

In this work, we present a quantum mechanical scattering study of the title reaction from 1 mK to 2000 K. Total integral cross sections and thermal rate constants are compared with previous theoretical and experimental data and with simpler theoretical models to understand the range of validity of the approximations used in the previous studies. The obtained quantum reactive observables have been found to be nearly insensitive to the roto-vibrational energy of the reactants at high temperatures. More sensitive to the reactant's roto-vibrational energy are the data in the cold and ultra-cold regimes. The implications of the new data presented here in the early universe scenario are also discussed and analyzed.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

The D(+) + H2 reaction: differential and integral cross sections at low energy and rate constants at low temperature

The D(+) + H2 reaction is investigated by means of a time independent quantum mechanical (TIQM) and statistical quantum mechanical (SQM) methods. Differential cross sections and product rotational distributions obtained with these two theoretical approaches for collision energies between 1 meV and 0.1 eV are compared to analyze the dynamics of the process. The agreement observed between the TIQM differential cross sections and the SQM predictions as the energy increases revealed the role played by the complex-forming mechanism. The importance of a good description of the asymptotic regions is also investigated by calculating rate constants for the title reaction at low temperature.