Atom probe tomography allows us to measure the three-dimensional composition of materials with up to atomic resolution by evaporating the material using high electric fields. Initially developed for metals, it is increasingly used for covalently bound structures. To aid the interpretation of the obtained fragmentation pattern, we modeled the fragmentation and desorption of self-assembled monolayers of thiolate molecules on a gold surface in strong electrostatic fields using density functional theory. We used a cluster model and a periodic model of amino-undecanethiolate, NH2(CH2)11S, and fluoro-decanethiolate, CF3(CF2)7(CH2)2S. In the former molecule, the fragment CH2NH2+ was found to evaporate at fields of 5.4-7.7 V/nm. It was followed by different hydrocarbon fragments. Fluoro-decanethiolate evaporates CF3+ at fields of 5.7-6.7 V/nm in the cluster model and at 15.4-23.1 V/nm in the periodic model, followed by CF2+ and C2F42+. Detailed analysis of the electronic structure during the evaporation process revealed a stepwise accumulation of the charge in the head groups exposed to the strongest fields, followed by dissociation of covalent bonds. These observations will facilitate the analysis of atom probe experiments of covalently bound structures.