What's the Gibbs free energy of a reaction at zero temperature and pressure? I heard that Gibbs free energy changes with temperature and pressure as

$$ \Delta G_1 = \Delta G_0 + R T \ln Q $$

But this makes no sense when pressure is zero or temperature is zero.
$G^\circ = U(0K) = E^{ele}+ZPE$, i.e. the sum of the electronic energy (electrons and nuclei interacting) and the zero point vibrational energy.

You can't use $K=e^{-\Delta G^\circ/RT}$ at 0K because the derivation assumes that a certain amount of thermal energy is available. But you don't need the equation to figure out the relative amount of two molecules. At equilibrium at 0K all molecules are in the lowest possible state.