## 1 Introduction  
Hybrid ion-neutral systems have been the subject of intense research [1], offering the possibility to prepare highly refined molecular systems, study their dynamics in the quantum regime and possibly utilize them for quantum technological applications. As charged particles are easy to manipulate and to address with external fields, an especially promising research direction is the study of cold quantum chemistry involving ions, granting the opportunity to prepare the reactants in a well defined quantum state as well as the access to some of the reaction products. Various experimental protocols have been developed in order to bring the system to the low temperature regime, where quantum effects such as resonances can become relevant. The simplest idea relies on sympathetic cooling of the ion placed in an external trap by already ultracold atoms, which requires sufficiently large ion-to-atom mass ratio to be fully effective. Multiple experiments have been performed using this technique for an ion in a time-dependent Paul trap (see [1] and references therein), allowing for valuable insight in the collisional dynamics of ions in a buffer gas, including inelastic three-body recombination [2]. A related study used the ion trap to capture the reaction products of the recombination of three neutral atoms [3]. Recently, cooling of the system down to the \(s\)-wave regime where the ion-atom interaction is taking place in a single partial wave has been demonstrated [4]. Furthermore, it has become possible to sympathetically cool ions which are placed in a static optical trap [5], which in principle allows for reaching even lower temperatures. Another recently developed method is to produce an already cold ion directly from the ultracold gas with a carefully designed excitation scheme involving highly excited Rydberg states [6; 7]. Reactive molecular collisions in the ultracold domain are very appealing from the theoretical point of view [8; 9]. Initial preparation of the collision partners with very low kinetic energy and well defined internal states restricts the initially available phase space. However, formation of the collision complex opens up the possibility to rearrange the constituents and, for exoergic reactions, can lead to multiple open exit channels. In such a case, one can employ statistical methods [10; 11; 12; 13; 14] to obtain some insight into the product distribution. The validity of statistical approaches relies on the assumption of the complex formation and subsequent ergodicity, which can fail for long-range processes in which the reactants do not combine into a complex, as well as for light particles for which the density of states is low. Another possibility is to disregard the quantum aspects of the process and use classical trajectory methods [15; 16], which proved to be accurate for ion-atom systems, as the collision partners acquire large kinetic energy while approaching each other in the presence of the attractive polarization potential. Full quantum scattering calculations are computationally very costly for multiple bodies and often have to be performed on simplified potential surfaces, but can in principle provide more complete information and test the validity of approximate methods [17; 18; 19; 20; 21]. In this work, we study the collisional dynamics of a homonuclear molecular ion placed in a dilute bosonic gas of the same species. This setting is particularly relevant for experiments in which the ion is directly produced from the ultracold gas. Due to the low anisotropy of the potential surface and the lack of possible products with different nuclear arrangement, the dominant reactive process is the vibrationally inelastic collision. It turns out that the vibrational quenching is governed by long-range terms in the effective Hamiltonian, allowing for changing the internal state of the molecule without forming a three-body collision complex.