###### Abstract  
Complexes formed by sulfuric acid (H\({}_{2}\)SO\({}_{4}\)) with HX (X = OH, Cl, Br) are critical in various chemical processes. In this work, we theoretically investigated the isomerization pathways of these complexes, analyzing their structures, energies, and reaction mechanisms. We identified eight, eight, and nine isomers for the H\({}_{2}\)SO\({}_{4}\) + HX systems with X = OH, Cl, and Br, respectively, including mirror-symmetrized structures. The most stable complexes in each system are cyclic, stabilized by double hydrogen bonds forming six-membered rings. We discovered 7, 10, and 10 new transition states for the reaction involving X = OH, Cl, and Br, respectively. Isomer rearrangements primarily involve the hydrogen bond dynamics, hydrogen atom exchange, and cis-trans isomerization of H\({}_{2}\)SO\({}_{4}\) due to wagging of its non-interacting O-H bond. Our findings underscore the dominance of hydrogen bonding in these intermolecular interactions and provide fresh insights into the nature and reactivity of these complexes. sultiric acid; hydrogen bonding; isomerization pathways; binary complex; transition states 20251576420251576  
The formation of sulfuric acid hydrates and complexes with these molecules is fundamental to atmospheric nucleation, particularly in the stratosphere, where H\({}_{2}\)SO\({}_{4}\) and H\({}_{2}\)O molecules play a key role in particle nucleation and growth [20; 21; 22; 23; 24; 25]. Experimentally, [PERSON] et al. used rotational spectroscopy to identify the minimum-energy structure of the H\({}_{2}\)SO\({}_{4}\) + H\({}_{2}\)O complex, which was found to adopt a twisted six-membered ring structure, with both H\({}_{2}\)O and H\({}_{2}\)SO\({}_{4}\) acting as proton acceptors and donors [26]. Theoretical studies, such as those by [PERSON] et al., have also identified strong hydrogen bonds between H\({}_{2}\)SO\({}_{4}\) and H\({}_{2}\)O, with HCl showing similar interactions in H\({}_{2}\)SO\({}_{4}\)-based complexes [25]. [PERSON] et al. investigated the complexes of H\({}_{2}\)SO\({}_{4}\) (H\({}_{2}\)O)\({}_{n}\) (\(n\) = 1-5) and showed that all stable structures tend to form polycyclic forms [27]. Additionally, [PERSON] et al. explored the vibrational frequencies of the H\({}_{2}\)SO\({}_{4}\) + H\({}_{2}\)O system using ab initio calculations [28]. [PERSON] et al. systematically investigated the interaction of H\({}_{2}\)SO\({}_{4}\) with HOO and H\({}_{2}\)O using density functional theory (DFT) and atoms in molecules (AIM) [23] and pointed out that H\({}_{2}\)SO\({}_{4}\) aerosol actively participates in the absorption of HOO. Research on the gas-phase interactions between H\({}_{2}\)SO\({}_{4}\) and hydrogen halides has provided critical insights into the formation of pre-nucleation complexes, which are essential for understanding aerosol chemistry in the atmosphere [29; 30; 31]. For the H\({}_{2}\)SO\({}_{4}\)-HCl system, studies have demonstrated that the formation of hydrogen-bonded adducts plays a pivotal role in stratospheric nucleation processes [29; 32; 33]. For example, DFT calculations at the \(\omega\)B97X-D/6-311++(2d,2p) level have revealed that these complexes exhibit binding energies closely associated with the electron density at the hydrogen bond critical points [29]. Observable shifts in the vibrational frequencies of H\({}_{2}\)SO\({}_{4}\)'s OH bonds upon complexation further underscore the directional and strong nature of the hydrogen bonds involving HCl [29]. These findings confirm that HCl acts effectively as both a hydrogen bond donor and acceptor, thereby stabilizing the complexes under atmospheric conditions. While the H\({}_{2}\)SO\({}_{4}\)-HCl interactions are relatively well-characterized, the gas-phase reaction between H\({}_{2}\)SO\({}_{4}\) and HBr remains less explored. Notably, despite the chemical similarities between HCl and HBr--both being hydrogen halides capable of participating in robust hydrogen bonding--the two systems exhibit important differences in reactivity and molecular properties.