Adiabatic global potential energy surfaces, for singlet and triplet states of A′ and A″ symmetries, were computed for an extensive grid for a total of 8469 conformations of H3+ system at full configuration interaction ab initio level and using an extended basis set that has also been optimized for excited states. An accurate (root-mean-square error lower than 20 cm−1) global fit to the ground-state potential is obtained using a diatomics-in-molecules approach corrected by several symmetrized three-body terms with a total of 96 linear parameters and 3 nonlinear parameters. This produces an accurate global potential which represents all aspects of ground-state H3+ including the absolute minimum, the avoided crossing and dissociation limits, satisfying the correct symmetry properties of the system. The rovibrational eigenstates have been calculated up to total angular momentum J=20 using hyperspherical coordinates with symmetry adapted basis functions. The infrared spectra thus reproduced is within 1 cm−1 with respect to the experimental values for several transitions.

The adiabatic global potential energy surface of the ${\mathrm{H}}_3^{+}$ system for the lowest triplet excited state of $A^{\prime }$ symmetry was computed for an extensive grid of conformations around the minimum region at full configuration interaction ab initio level, using a much more extended basis set than in a previous paper from the same authors. An accurate global fit (rms error lower than 27 ${\mathrm{cm}}^{\text{−1}}$ for energies lower than dissociation into separated atoms and lower than 5 ${\mathrm{cm}}^{\text{−1}}$ for energies lower than the dissociation channel) to these ab initio points and also to part of the previous calculated points (for a total of 7689 energies in the data set) of the lowest triplet excited state of $A^{\prime }$ symmetry is obtained using a diatomics-in-molecules approach corrected by one symmetrized three-body term with a total of 109 linear parameters and 1 nonlinear parameter. This produces an accurate global potential which represents all aspects of the bound triplet excited state of ${\mathrm{H}}_3^{+}$ including the minima and dissociation limits, satisfying the correct symmetry properties of the system. The vibrational eigenstates have been calculated using hyperspherical coordinates with symmetry adapted basis functions with the proper regular behavior at the Eckart singularities. The accuracy of the vibrational levels thus obtained is expected to be better than 2 ${\mathrm{cm}}^{\text{−1}}$ with respect to unknown experimental values. Due to the presence of three equivalent minima at collinear geometries ${\mathrm{(D}}_{\mathrm{\infty h}})$ the lower vibrational levels are close to triple degenerate. Since the interconversion barrier between the three minima is about 2640 ${\mathrm{cm}}^{\text{−1}},$ these states split for the upper excited vibrational levels. Such splitting can provide a key feature to identifying the unassigned transitions amongst the many ${\mathrm{H}}_3^{+}$ lines that have been observed in hydrogen plasmas.

In this work the LiHF(A,B,B′←X) electronic spectrum is simulated and compared with the experimental one obtained by Hudson et al. [J. Chem. Phys. 113, 9897 (2000)]. High level ab initio calculations of three A′2 and one A″2 electronic states have been performed using a new atomic basis set and for a large number of nuclear configurations (about 6000). Four analytic global potential energy surfaces have been fitted. The spectrum involved very excited rovibrational states, close to the first dissociation limit, at high total angular momentum. Two different methods have been used, one based on bound state and the second one on wave packet calculations. Different alternatives have been used to simulate the relatively high temperatures involved. The agreement obtained with the experimental spectrum is very good allowing a very simple assignment of the peaks. They are due to bending progressions on the three excited electronic states. A simple model is used in which only rotational degrees of freedom are included, which simulates the spectrum in excellent agreement with the experimental one, providing a nice physical interpretation. Moreover, the remaining theoretical/experimental discrepancies have been attributed to nonadiabatic effects through the extension of this model to a diabatic representation of excited coupled electronic states.

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)10.1063/1.2430711]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of \documentclass[12pt]{minimal}\begin{document}${\rm H}_5^+$\end{document}H5+ complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the \documentclass[12pt]{minimal}\begin{document}${\rm H}_5^+$\end{document}H5+ complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice–Ramsperger–Kassel–Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)10.1063/1.3587246] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Analytical derivatives and non-adiabatic coupling matrix elements are derived for H${}_n^{+}$ systems (n = 3–5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H${}_3^{+}$ ) or triatomics-in-molecules (for H${}_4^{+}$ and H${}_5^{+}$ ) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate ${\mathrm{H}}_2(v^{\prime }=0,j^{\prime }=0)+{\mathrm{H}}_2^{+}(v,j=0)$ collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H${}_2^{+}$ are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H${}_2^{+}$ reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalism.