Gas phase computations

The CP-PAW calculations of the isolated compounds were performed in a cubic periodic unit cell of size $L=10$ Å. A rectangular periodic unit cell of size 10x10x18 Å was used for the isolated (gas phase) reaction. These sizes are sufficiently large to ensure negligible overlap of the wave functions of the periodic images. To suppress the electrostatic interaction among the periodic images, we used the method of electrostatic decoupling of ref PAWdecouple.

For the ADF calculations, the finite-temperature reaction enthalpies at $T=300$ K and the entropies were estimated using

$$\Delta H_{300K} = \Delta E_0 + \Delta E_{\rm ZPE} + \Delta E^\mathrm{v}_T + \Delta E^\mathrm{t} + \Delta E^\mathrm{r} + \Delta(PV)$$ (49)

$$\Delta S = R \ln(Q^{\mathrm{t}}Q^{\mathrm{r}}Q^{\mathrm{v}})$$ (50)

with $E_0$ the sum of the electronic energy in a static nuclear field (Born-Oppenheimer approximation) and the nuclear electrostatic repulsion. The zero-point vibrational energy $E_{\rm ZPE}$ and the temperature dependent vibrational energy $E^\mathrm{v}_T$ were calculated from the unscaled DFT-BP frequencies, within the harmonic approximation. The change in translational energy $\Delta E^\mathrm{t}$, rotational energy $\Delta E^\mathrm{r}$, and $PV$ were obtained using the ideal gas law, associating $\frac{1}{2}k_BT$ to each degree of freedom. The partition function $Q$ is the product of translational, rotational and vibrational contributions (see e.g. chapter 20 in reference atkins).