The redcution of CO₂ into acetic acid (CH₃COOH) on the greigite Fe₃S₄{111} surface has been investigated using density functional theory (DFT) calculations. CH₃COOH is an important commodity chemical widely used in a myriad of industrial processes, whose production still largely depends on homogeneous catalysts based on expensive rare metals. Fe₃S₄ is an iron sulfide phase ubiquitous in several types of environments, where it has been linked to the catalytic conversion of CO₂ into the first organic molecules. The work involved studying three mechanistic pathways to account for the formation of CH₃COOH on the two catalytic sites of the Fe₃S₄{111} surface. The data described here are ASCII files containing the vibrational frequencies of the glyoxalate intermediates adsorbed on the Fe₃S₄{111} surface. Calculations were carried out using the Vienna Ab-initio Simulation Package (VASP).