Cross sections for the dissociative recombination of ${\mathrm{N}}_2^{+}$ for $v_i^{+}=0–3$ are computed using multichannel quantum defect theory with molecular data generated using the $R$-matrix method. The calculation is completely ab initio and includes three electronic cores of the ion. Extensive comparisons are made with previous experimental and theoretical studies. Our cross section is in excellent agreement with experimental results and other theoretical results. Cross sections and isotropic rate coefficients are provided for all computed vibrational levels.

Our approach to the dissociative recombination and competitive processes based on the multichannel quantum defect theory is extended to the full account of the dissociative excitation, including the electronic excitation of the molecular ion. Compared to other existing modelings, ours relies on a simpler and less-time-consuming discretization of the vibrational continua of the target ion and to a more accurate account of the Rydberg-valence interactions via a second-order solution of the Lippman-Schwinger equation. A thorough study of the competition among the dissociative recombination, vibrational excitation, and dissociative excitation is performed, including a detailed analysis of the two different mechanisms governing the ion dissociation. The application of our method to the high-energy electron collisions with ${{\mathrm{H}}_2}^{+}$ and ${\mathrm{HD}}^{+}$ ions results in a cross section in good agreement with the best previous modeling and with the most recent measurements performed in the Test Storage Ring of the Max-Planck-Institut für Kernphysik in Heidelberg.

Cross sections and thermal rate coefficients are computed for electron-impact dissociative recombination and vibrational excitation/de-excitation of the N${}_2^{+}$ molecular ion in its lowest six vibrational levels, for collision energies/temperatures up to 2.3 eV/5000 K.

A quantitative theoretical study of the dissociative recombination of SH⁺ with electrons has been carried out. Multireference, configuration interaction calculations were used to determine accurate potential energy curves for SH⁺ and SH. The block diagonalization method was used to disentangle strongly interacting SH valence and Rydberg states and to construct a diabatic Hamiltonian whose diagonal matrix elements provide the diabatic potential energy curves. The off-diagonal elements are related to the electronic valence-Rydberg couplings. Cross sections and rate coefficients for the dissociative recombination reaction were calculated with a stepwise version of the multichannel quantum defect theory, using the molecular data provided by the block diagonalization method. The calculated rates are compared with the most recent measurements performed on the ion Test Storage Ring (TSR) in Heidelberg, Germany.