Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The role of intersystem crossing in the reactive collision of S+(4S) with H2

We report a study on the reactive collision of S+(4S) with H2, HD, and D2 combining guided ion beam experiments and quantum-mechanical calculations. It is found that the reactive cross sections reflect the existence of two different mechanisms, one being spin-forbidden. Using different models, we demonstrate that the spin-forbidden pathway follows a complex mechanism involving three electronic states instead of two as previously thought. The good agreement between theory and experiment validates the methodology employed and allows us to fully understand the reaction mechanism. This study also provides new fundamental insights into the intersystem crossing process.

Quantum study of the CH3+ photodissociation in full-dimensional neural network potential energy surfaces

C H 3 + , a cornerstone intermediate in interstellar chemistry, has recently been detected for the first time by using the James Webb Space Telescope. The photodissociation of this ion is studied here. Accurate explicitly correlated multi-reference configuration interaction ab initio calculations are done, and full-dimensional potential energy surfaces are developed for the three lower electronic states, with a fundamental invariant neural network method. The photodissociation cross section is calculated using a full-dimensional quantum wave packet method in heliocentric Radau coordinates. The wave packet is represented in angular and radial grids, allowing us to reduce the number of points physically accessible, requiring to push up the spurious states appearing when evaluating the angular kinetic terms, through projection technique. The photodissociation spectra, when employed in astrochemical models to simulate the conditions of the Orion bar, result in a lesser destruction of CH3+ compared to that obtained when utilizing the recommended values in the kinetic database for astrochemistry.

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

Spin-orbit transitions in the N+(3PJA) + H2 → NH+(X2 Π, 4Σ-)+ H(2S) reaction, using adiabatic and mixed quantum-adiabatic statistical approaches

The cross section and rate constants for the title reaction are calculated for all the spin-orbit states of N+(3PJA) using two statistical approaches, one purely adiabatic and the other one mixing quantum capture for the entrance channel and adiabatic treatment for the products channel. This is made by using a symmetry adapted basis set combining electronic (spin and orbital) and nuclear angular momenta in the reactants channel. To this aim, accurate ab initio calculations are performed separately for reactants and products. In the reactants channel, the three lowest electronic states (without spin-orbit couplings) have been diabatized, and the spin-orbit couplings have been introduced through a model localizing the spin-orbit interactions in the N+ atom, which yields accurate results as compared to ab initio calculations including spin-orbit couplings. For the products, eleven purely adiabatic spin-orbit states have been determined with ab initio calculations. The reactive rate constants thus obtained are in very good agreement with the available experimental data for several ortho-H2 fractions, assuming a thermal initial distribution of spin-orbit states. The rate constants for selected spin-orbit JA states are obtained, to provide a proper validation of the spin-orbit effects to obtain the experimental rate constants.

HD-H+ collisions: statistical and quantum state-to-state studies

In the early Universe, the cooling mechanisms of the gas significantly rely on the HD abundance and excitation conditions. A proper modeling of its formation and destruction paths as well as its excitation by both radiative and collisional processes is then required to accurately describe the cooling mechanisms of the pristine gas. In such media, ion-molecule reactions are dominant. Their theoretical study is challenging and state-of-the-art quantum time-independent methods are computationally limited to collisions involving light molecules. Here, we report a state-to-state scattering study of the HD-H⁺ collisional system using two different methods: an exact quantum time-independent approach and a recently developed fast and efficient statistical method. Reactive and inelastic rate coefficients were obtained for temperatures up to 300 K. The statistical method is able to reproduce exact calculations with an accuracy reaching the astrophysical needs while drastically reducing the computational resources requirements. Such results suggest that this new statistical method should be considered to provide the astrophysical community collisional data for which quantum calculations are impossible.

Near-resonant effects in the quantum dynamics of the H + H2 + → H2 + H+ charge transfer reaction and isotopic variants

The non-adiabatic quantum dynamics of the H + H₂ ⁺ → H₂ + H⁺ charge transfer reactions, and some isotopic variants, is studied with an accurate wave packet method. A recently developed 3 × 3 diabatic potential model is used, which is based on very accurate ab initio calculations and includes the long-range interactions for ground and excited states. It is found that for initial H₂ ⁺(v = 0), the quasi-degenerate H₂(v' = 4) non-reactive charge transfer product is enhanced, producing an increase in the reaction probability and cross section. It becomes the dominant channel from collision energies above 0.2 eV, producing a ratio between v' = 4 and the rest of v's, which that increase up to 1 eV. The H + H₂ ⁺ → H₂ ⁺ + H exchange reaction channel is nearly negligible, while the reactive and non-reactive charge transfer reaction channels are of the same order, except that corresponding to H₂(v' = 4), and the two charge transfer processes compete below 0.2 eV. This enhancement is expected to play an important vibrational and isotopic effect that needs to be evaluated. For the three proton case, the problem of the permutation symmetry is discussed when using reactant Jacobi coordinates.

Rate constants for the H+ + H2 reaction from 5 K to 3000 K with a statistical quantum method

An exhaustive investigation of state-to-state H⁺ + H₂(v, j) → H⁺ + H₂(v', j') transitions for rovibrational levels of molecular hydrogen below 1.3 eV from the bottom of the H₂ well is carried out by means of a statistical quantum method, which assumes the complex-forming nature of the process. Integral cross sections for transitions involving states H₂(v = 0, j = 0-12), H₂(v = 1, j = 0-8), and H₂(v = 2, j = 0-3) are obtained for collision energies within a range of E_min = 10^-5 eV and E_max = 2 eV. Rate constants are then calculated between T = 5 K and 3000 K, and they are compared, when possible, with previous values reported in the literature. As a first application, the cooling rate coefficient of H₂ excited by protons is determined and compared with a recent estimate.

Origin band of the first photoionizing transition of hydrogen isocyanide

The photoelectron spectrum of the X1Σ+ → X+2Σ+ ionizing transition of hydrogen isocyanide (HNC) is measured for the first time at a fixed photon energy (13 eV). The assignment of the spectrum is supported by wave-packet calculations simulating the photoionization transition spectrum and using ab initio calculations of the potential energy surfaces for the three lowest electronic states of the cation. The photoelectron spectrum allows the retrieval of the fundamental of the CN stretching mode of the cationic ground state ([small nu, Greek, tilde]3 = 2260 ± 80 cm-1) and the adiabatic ionization energy of hydrogen isocyanide: IE(HNC) = 12.011 ± 0.010 eV, which is far below that of HCN (IE(HCN) = 13.607 eV). In light of this latter result, the thermodynamics of the HCN+/HNC+ isomers is discussed and a short summary of the values available in the literature is given.

The low temperature D+ + H2→ HD + H+ reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study

The reaction between D⁺ and H₂ plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]¹A' state has a very small thermodynamic barrier (up to 1.8 × 10^-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10^-9 cm³ s^-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.

The Photodissociation of HCN and HNC: Effects on the HNC/HCN Abundance Ratio in the Interstellar Medium

The impact of the photodissociation of HCN and HNC isomers is analyzed in different astrophysical environments. For this purpose, the individual photodissociation cross section of HCN and HNC isomers have been calculated in the 7-13.6 eV photon energy range for a temperature of 10 K. These calculations are based on the ab initio calculation of three-dimensional adiabatic potential energy surfaces of the 21 lower electronic states. The cross sections are then obtained using a quantum wave packet calculation of the rotational transitions needed to simulate a rotational temperature of 10 K. The cross section calculated for HCN shows significant differences with respect to the experimental one, and this is attributed to the need of considering non-adiabatic transitions. Ratios between the photodissociation rates of HCN and HNC under different ultraviolet radiation fields have been computed by renormalizing the rates to the experimental one. It is found that HNC is photodissociated faster than HCN by a factor of 2.2, for the local interstellar radiation field, and 9.2, for the solar radiation field at 1 au. We conclude that to properly describe the HNC/HCN abundance ratio in astronomical environments illuminated by an intense ultraviolet radiation field it is necessary to use different photodissociation rates for each of the two isomers, obtained by integrating the product of the photodissociation cross sections and ultraviolet radiation field over the relevant wavelength range.

Photodissociation of HCN and HNC isomers in the 7-10 eV energy range

The ultraviolet photoabsorption spectra of the HCN and HNC isomers have been simulated in the 7-10 eV photon energy range. For this purpose, the three-dimensional adiabatic potential energy surfaces of the 7 lowest electronic states, and the corresponding transition dipole moments, have been calculated, at multireference configuration interaction level. The spectra are calculated with a quantum wave packet method on these adiabatic potential energy surfaces. The spectra for the 3 lower excited states, the dissociative electronic states, correspond essentially to predissociation peaks, most of them through tunneling on the same adiabatic state. The 3 higher electronic states are bound, hereafter electronic bound states, and their spectra consist of delta lines, in the adiabatic approximation. The radiative lifetime towards the ground electronic states of these bound states has been calculated, being longer than 10 ns in all cases, much longer that the characteristic predissociation lifetimes. The spectra of HCN is compared with the available experimental and previous theoretical simulations, while in the case of HNC there are no previous studies to our knowledge. The spectrum for HNC is considerably more intense than that of HCN in the 7-10 eV photon energy range, which points to a higher photodissociation rate for HNC, compared to HCN, in astrophysical environments illuminated by ultraviolet radiation.

Exchange and Inelastic OH(+) + H Collisions on the Doublet and Quartet Electronic States

The exchange and inelastic state-to-state cross sections for the OH(+) + H collisions are computed from wave packet calculations using the doublet and quartet ground electronic potential energy surface (PES) correlating to the open shell reactants, for collision energies in the range of 1 meV to 0.7 eV. The doublet PES presents a deep insertion well, of ≈6 eV, but the exchange reaction has a rather low probability, showing that the mechanism is not statistical. This well is also responsible of a rather high rotational energy transfer, which makes the rigid-rotor approach overestimate the cross section for low Δj transitions and for high collisonal energies. The quartet PES, with a much shallower well, also presents a low exchange reaction cross section, but the inelastic state-to-state cross sections are very well reproduced by rigid-rotor calculations. When the electronic partition is used to obtain the total state-to-state cross section, the contribution of the doublet state becomes small, and the resulting total cross sections become close to those obtained for the quartet state. Thus, the total (quartet and doublet) cross sections for this open shell system can be reproduced rather satisfactorily by those obtained with the rigid-rotor approximation on the quartet state. Finally, we compare the new OH(+)-H cross sections with OH(+)-He ones recently computed. We found significant differences, especially for transitions with large Δj showing that specific OH(+)-H calculations had to be performed to accurately analyze the OH(+) emission from interstellar molecular clouds.

Quantum mechanical calculations of state-to-state cross sections and rate constants for the F + DCl → Cl + DF reaction

We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 - 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.

A comparative account of quantum dynamics of the H⁺ + H₂ reaction at low temperature on two different potential energy surfaces

Rotationally resolved reaction probabilities, integral cross sections, and rate constant for the H(+) + H2 (v = 0, j = 0 or 1) → H2 (v' = 0, j') + H(+) reaction are calculated using a time-independent quantum mechanical method and the potential energy surface of Kamisaka et al. [J. Chem. Phys. 116, 654 (2002)] (say KBNN PES). All partial wave contributions of the total angular momentum, J, are included to obtain converged cross sections at low collision energies and rate constants at low temperatures. In order to test the accuracy of the KBNN PES, the results obtained here are compared with those obtained in our earlier work [P. Honvault et al., Phys. Rev. Lett. 107, 023201 (2011)] using the accurate potential energy surface of Velilla et al. [J. Chem. Phys. 129, 084307 (2008)]. Integral cross sections and rate constants obtained on the two potential energy surfaces considered here show remarkable differences in terms of magnitude and dependence on collision energy (or temperature) which can be attributed to the differences observed in the topography of the surfaces near to the entrance channel. This clearly shows the inadequacy of the KBNN PES for calculations at low collision energies.

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 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.

Dynamics of the D(+) + H2 → HD + H(+) reaction at the low energy regime by means of a statistical quantum method

The D(+) +H2(v = 0, j = 0, 1) → HD+H(+) reaction has been investigated at the low energy regime by means of a statistical quantum mechanical (SQM) method. Reaction probabilities and integral cross sections (ICSs) between a collisional energy of 10(-4) eV and 0.1 eV have been calculated and compared with previously reported results of a time independent quantum mechanical (TIQM) approach. The TIQM results exhibit a dense profile with numerous narrow resonances down to Ec ~ 10(-2) eV and for the case of H2(v = 0, j = 0) a prominent peak is found at ~2.5 × 10(-4) eV. The analysis at the state-to-state level reveals that this feature is originated in those processes which yield the formation of rotationally excited HD(v' = 0, j' > 0). The statistical predictions reproduce reasonably well the overall behaviour of the TIQM ICSs at the larger energy range (Ec ≥ 10(-3) eV). Thermal rate constants are in qualitative agreement for the whole range of temperatures investigated in this work, 10-100 K, although the SQM values remain above the TIQM results for both initial H2 rotational states, j = 0 and 1. The enlargement of the asymptotic region for the statistical approach is crucial for a proper description at low energies. In particular, we find that the SQM method leads to rate coefficients in terms of the energy in perfect agreement with previously reported measurements if the maximum distance at which the calculation is performed increases noticeably with respect to the value employed to reproduce the TIQM results.

State-to-state quantum mechanical calculations of rate coefficients for the D+ + H2 → HD + H+ reaction at low temperature

The dynamics of the D(+) + H2 → HD + H(+) reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models.

Accurate study on the quantum dynamics of the He + HeH(+) (X1Σ+) reaction on a new ab initio potential energy surface for the lowest 1(1)A' electronic singlet state

A time-dependent quantum wave packet method is used to investigate the dynamics of the He + HeH(+)(X(1)Σ(+)) reaction based on a new potential energy surface [Liang et al., J. Chem. Phys.2012, 136, 094307]. The coupled channel (CC) and centrifugal-sudden (CS) reaction probabilities as well as the total integral cross sections are calculated. A comparison of the results with and without Coriolis coupling revealed that the number of K states N(K) (K is the projection of the total angular momentum J on the body-fixed z axis) significantly influences the reaction threshold. The effective potential energy profiles of each N(K) for the He + HeH(+) reaction in a collinear geometry indicate that the barrier height gradually decreased with increased N(K). The calculated time evolution of CC and CS probability density distribution over the collision energy of 0.27-0.36 eV at total angular momentum J = 50 clearly suggests a lower reaction threshold of CC probabilities. The CC cross sections are larger than the CS results within the entire energy range, demonstrating that the Coriolis coupling effect can effectively promote the He + HeH(+) reaction.

THEORETICAL STUDIES OF STEREODYNAMICS FOR THE H+ + H2 (ν = 0–3, j = 0) → H2 + H+ REACTION

The stereodynamics calculation was carried out for the title reaction by quasiclassical trajectory method on the ground surface of KBNN potential energy surface. The vector correlations are determined at initial ground state and vibrational excitation of the reagent H 2. The results show that the rotational polarization is affected lightly by collision energy and strongly by reagent excitation for title reaction. The rotational alignments are almost isotropic at several collision energies on initial ground state of the reagent H 2, which means that the product rotational angular momentum is weakly polarized (or no polarized). Nevertheless, the polarization of product rotational angular momentum is enhanced remarkably at the vibrational excitations of the reagent H 2 in collision energy of 0.524 eV.

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Nonadiabatic state-to-state reactive collisions among open shell reactants with conical intersections: the OH((2)Pi) + F((2)P) example

Accurate wave packet calculations on the OH((2)Pi) + F((2)P) → O((3)P) + HF((1)Sigma(+)) reactive collisions are performed using a recently proposed coupled diabatic states. Adiabatic and nonadiabatic dynamics are compared in detail, analyzing the final state distribution of products. It is found that with the new surfaces a significant increase of the rate constant is obtained, with noticeable nonadiabatic effects. The inclusion of the spin-orbit splittings for the calculation of the electronic partition function produces an important increase of the reaction rate constants, yielding a rather good agreement with the experimental results. It is also concluded that spin-orbit couplings are also necessary in the entrance channel to describe this reaction.

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.

Cumulative reaction probabilities and transition state properties: a study of the H+ + H2 and H+ + D2 proton exchange reactions

Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H(+) + H(2) and H(+) + D(2) reactions at collision energies up to 1.2 eV and total angular momentum J = 0-4. A marked resonance structure is found in the QM CRP, most especially for the H(3)(+) system and J = 0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H(+) + D(2) isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H(+) + D(2) reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by the dynamical and statistical trajectory methods.