Abstract: The n_TOF Total Absorption Calorimeter (TAC) is a 4 pi BaF2 segmented detector used at CERN for measuring neutron capture cross-sections of importance for the design of advanced nuclear reactors. This work presents the simulation code that has been developed in GEANT4 for the accurate determination of the detection efficiency of the TAC for neutron capture events. The code allows to calculate the efficiency of the TAC for every neutron capture state, as a function of energy, crystal multiplicity, and counting rate. The code includes all instrumental effects such as the single crystal detection threshold and energy resolution, finite size of the coincidence time window, and signal pile-up. The results from the simulation have been validated with experimental data for a large set of electromagnetic de-excitation patterns: beta-decay of well known calibration sources, neutron capture reactions in light nuclei with well known level schemes like Ti-nat, reference samples used in (n,gamma) measurements like Au-197 and experimental data from an actinide sample like Pu-240. The systematic uncertainty in the determination of the detection efficiency has been estimated for all the cases. As a representative example, the accuracy reached for the case of Au-197(n,gamma) ranges between 0.5% and 2%, depending on the experimental and analysis conditions. Such a value matches the high accuracy required for the nuclear cross-section data needed in advanced reactor design.