Suppose we consider the binding of a ligand L to a metal M, M+L=ML and M+2L=ML2 . We compute the Gibbs free energy change for two reaction using DFT. But can we compare this two free energies to conclude the most favourable pathway?
Yes for isomers. For other reactions, use equilibrium constant, K, (delta_rG = -RTlnK). For M+L=ML, K1 = [ML]/[M]/[L] where one meaning of K1 is K1=1/[L_1,(1/2)], where L_1,(1/2) is the activity (roughly concentration or partial pressure) at the half point reaction: the value of [L] when [M]=[ML]. You have similar meaning for M+2L=ML_2, alternatively you can consider the formation of ML_2 via the stepwise reaction ML+L=ML2. For very low values of [L] neither ML nor ML_2 are formed (actually they are always formed for entropy reason, but they are not predominating). At very high values of [L], ML2 is formed (actually predominating), and ML is eventually formed (actually predominating) for intermediary values of [L] depending on the values of the Gibbs reaction energies, and of course whether the values of [_i,(1/2)] can be reached experimentally
You need to consider the following 2 points:
1. Compare the gibbs energy change of M+2L->ML2 with M+2L-> ML+L
2. Negarive gibbs energy change shows the feasibility of a reaction (thermodynamics). For favorability you need to confirm if those reactions are elementary or not and conduct a complete simulation of reaction pathway, including energetics. If a conversion is more favorite or not also depends on the energetics (kinetics) and activation energies (barriers)
I advise some caution. First of all, the free energy (= Helmholtz energy) is minimal at equilibrium at constant temperature and volume. If the pressure is kept constant, the free enthalpy (= Gibbs energy) must be used.
Next, what is meant with “more favourable”? This only makes sense for similar reactions. For example, a comparison of
– the transformation of alpha-Fe to gamma-Fe
– and the reaction 4 alpha-Fe + 3 O2 → 2 Fe2O3
shows that the oxidation has a more negative standard Gibbs energy. But if no oxygen ist present, this reaction is not favoured. On the other hand, it makes sense to compare the Gibbs energies of reaction for the transformations of alpha-Fe to gamma-Fe, delta-Fe, and liquid Fe in order to find out which phase is stable at a given temperature (and pressure).
Finally, there may be kinetic aspects to consider. Even if a system goes to the thermodynamically most stable state in the end, it does not have to have a minimal Gibbs energy on its way to this end.
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