Multichannel quantum defect studies of e$^-$ + LiH$_2^+$ and e$^-$ + NO$_2^+$

We present the results of calculations on electron-molecule scattering involving the molecules LiH$_2^+$ and NO$_2^+$. We focus on dissociative recombination (DR), vibrational excitation, and vibrational autoionization. Our treatment involves the \textit{ab initio} calculation of quantum defect matrices using the UK R-matrix codes of Tennyson, Morgan, and co-workers. We employ rovibrational frame-transformation techniques of multichannel quantum defect theory to calculate cross sections and rates for these processes. In the case of the LiH$_2^+$ system, we calculate the DR rate using an exact Born-Oppenheimer rovibrational Hamiltonian. We provide comparisons with recent experiment. In the case of NO$_2^+$, we analyze the effect of several Feshbach resonances upon vibrational excitation and autoionization. Our MQDT treatment of this system incorporates these doubly excited valence states of neutral NO$_2$ and the valence-rydberg coupling that is known to be significant in this system. We compare our results with prior theory and with the experimental results of Grant.