DFT calculations have been used to provide insights into the origin of the colossal positive and negative thermal expansion in Ag₃[Co(CN)₆]. The results confirm that the positive expansion within the trigonal basal plane and the negative expansion in the orthogonal direction are coupled due to the existence of a network defined by nearly rigid bonds within the chains of Co–C–N–Ag–N–C–Co linkages. The origin of the colossal values of the coefficients of thermal expansion arise from an extremely shallow energy surface that allows a flexing of the structure with small energy cost. The thermal expansion can be achieved with a modest value of the overall Grüneisen parameter. The energy surface is so shallow that we need to incorporate a small empirical dispersive interaction to give ground-state lattice parameters that match experimental values at low temperature. We compare the results with DFT calculations on two isostructural systems: H₃[Co(CN)₆], which is known to have much smaller values of the coefficients of thermal expansion, and Au₃[Co(CN)₆], which has not yet been synthesized but which is predicted by our calculations to be another candidate material for showing colossal positive and negative thermal expansion.