Abstract. DFT calculations have been used to provide insights into the origin of the colossal positive and negative thermal expansion in Ag 3 [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: H 3 [Co(CN) 6 ], which is known to have much smaller values of the coefficients of thermal expansion, and Au 3 [Co(CN) 6 ], which has not yet been synthesised but which is predicted by our calculations to be another candidate material for showing colossal positive and negative thermal expansion.