###### Abstract
The relatively limited direct studies on the H\({}_{2}\)SO\({}_{4}\)-HBr system necessitate a distinct focus on it. Although direct computational analyses of H\({}_{2}\)SO\({}_{4}\)-HBr clusters are scarce, indirect evidence from related systems, such as investigations on HBr solubility in H\({}_{2}\)SO\({}_{4}\)/H\({}_{2}\)O mixtures [34], supports the plausibility of hydrogen-bonded interactions between H\({}_{2}\)SO\({}_{4}\) and HBr. The high acidity of H\({}_{2}\)SO\({}_{4}\) and its dual capacity to donate and accept protons remain crucial factors that drive the stabilization of these binary complexes, emphasizing the need for dedicated studies on the H\({}_{2}\)SO\({}_{4}\)-HBr system in atmospheric environments. In the broader context of atmospheric aerosol science, the role of ternary complexes involving three of H\({}_{2}\)SO\({}_{4}\), HCl, HNO\({}_{3}\), HBr, and H\({}_{2}\)O has been extensively investigated [9; 14; 16; 32; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48]. For example, [PERSON] et al. developed a multicomponent thermodynamic model to estimate the solubility of HNO\({}_{3}\), HCl, and HBr in stratospheric H\({}_{2}\)SO\({}_{4}\) aerosols, contributing to our understanding of the dynamics of particle formation in the stratosphere [48]. Similarly, studies by [PERSON] and [PERSON] on the HNO\({}_{3}\)-HCl-H\({}_{2}\)O ternary system showed how the aggregation energy of clusters increases with the addition of water molecules, providing important insights into the role of water in atmospheric nucleation processes [37; 38]. These works indicate that H\({}_{2}\)SO\({}_{4}\) can form stable complexes with other molecules, with interactions dominated by hydrogen bonding, a key factor in aerosol formation. However, despite the significant body of research on the interactions between H\({}_{2}\)SO\({}_{4}\) and other atmospheric molecules, the isomerization mechanisms of these complexes, par ticularly those involving H\({}_{2}\)O, HCl, and HBr, still remain inadequately explored. [PERSON] et al. briefly investigated the potential energy surface of the H\({}_{2}\)SO\({}_{4}\) + H\({}_{2}\)O system but did not provide an in-depth analysis of the structural rearrangement mechanisms [24]. In this study, we address this gap by investigating the isomerization mechanisms of the binary complexes between H\({}_{2}\)SO\({}_{4}\) and H\({}_{2}\)O, HCl, and HBr in the gas phase. We focus on the structural rearrangement mechanisms and transition states connecting the isomers of these binary complexes. The isomerization reaction pathways identified in this work are expected to provide valuable insights into the behavior of ternary systems involving these molecules, such as H\({}_{2}\)SO\({}_{4}\)/H\({}_{2}\)O/HCl or H\({}_{2}\)SO\({}_{4}\)/H\({}_{2}\)O/HBr. Using high-level quantum chemical calculations, we identify potential isomers and transition states in the H\({}_{2}\)SO\({}_{4}\) + HX (X = OH, Cl, Br) systems and analyze the hydrogen bonding interactions responsible for their stability and interconversion. This study aims to deepen our understanding of the intermolecular forces governing the isomerization of sulfuric acid-based aerosols and their potential role in atmospheric chemistry.