The Hessian dataset for Optimizing Reactive MLIP (HORM) comprising 1.84 million Hessian matrices computed at the ωB97x/6-31G(d) level of theory. The geometries in the HORM dataset are sampled from two reactive datasets, Transition1x and RGD1. To ensure consistency in the level of theory, all sampled geometries were recomputed by GPU4PYSCF at the ω B97X/6-31G* level of theory to obtain energies, forces, and Hessian matrices. The usage of the datasets and data types are shown in the file 'how-to-load-the-lmdb-files.ipynb'.