  In this work, the effect of the range of the dispersive interactions in the
determination of the three-phase coexistence line of the CO$_2$ and CH$_4$
hydrates has been studied. In particular, the temperature ($T_3$) at which
solid hydrate, water, and liquid CO$_2$/gas CH$_4$ coexist has been determined
through molecular dynamics simulations using different cut-off values (from 0.9
to 1.6 nm) for the dispersive interactions. The $T_3$ of both hydrates has been
determined using the direct coexistence simulation technique. Following this
method, the three phases in equilibrium are put together in the same simulation
box, the pressure is fixed, and simulations are performed at different
temperatures $T$. If the hydrate melts, then $T>T_3$. Contrary, if the hydrate
grows, then $T<T_3$. The effect of the cut-off distance on the dissociation
temperature has been analyzed at three different pressures for CO$_{2}$
hydrate, namely, $100$, $400$, and $1000\,\text{bar}$. Then, we have changed
the guest and studied the effect of the cut-off distance on the dissociation
temperature of the CH$_{4}$ hydrate at $400\,\text{bar}$. Also, the effect of
long-range corrections for dispersive interactions has been analyzed by running
simulations with homo- and inhomogeneous corrections and a cut-off value of 0.9
nm. The results obtained in this work highlight that the cut-off distance for
the dispersive interactions affects the stability conditions of these hydrates.
This effect is enhanced when the pressure is decreased, displacing the $T_{3}$
about $2-4\,\text{K}$ depending on the system and the pressure.
