How to connect the results of the pair entropy values to free energy?

Dear all
I would like to calculate the free energy needed for adsorption of O2 on the surface of ZrO2 using COMB3 potential.
This system consistent of one O2 molecule in the solution above the surface of ZrO2.
I employed compute 1 all entropy/atom 0.25 11. to calculate the pair entropy values. My question is that how I can connect the values of the pair entropy to free energy?
I would be appreciated it if you give your recommendations.

You cannot. This compute serves a very specific purpose, but that is different from what you want to compute.

What you want to do is a very well understood problem and there are several possible approaches to do this, e.g. umbrella sampling, steered MD, metadynamics, adaptive biasing force. There also also plenty of review articles and some text books on such free energy methods (I recall one edited by Chris Chipot that seemed pretty comprehensive). LAMMPS has provisions to support either of these methods. There are even two competing packages, COLVARS and PLUMED that offer independent implementations in addition to doing umbrella sampling and steered MD “manually” with individual fixes in LAMMPS instead of going through the colvars/plumed wrapper.

Dear Akohlmey
Thanks for your reply
Using the results of these calculations ( compute entropy/atom), is it possible to make a thermodynamic interpretation on the system and conclude that a system with less entropy/atom has more order and can be done less spontaneously?

I already answered this.

You only have to look at the documentation of the command that it is completely unsuitable for your purpose:

Define a computation that calculates the pair entropy fingerprint for each atom in the group. The fingerprint is useful to distinguish between ordered and disordered environments, for instance liquid and solid-like environments, or glassy and crystalline-like environments. Some applications could be the identification of grain boundaries, a melt-solid interface, or a solid cluster emerging from the melt.

How could this ever be converted into a free energy of adsorption?

In general, free energy differences are defined by the process that takes you from one state to the other and to do that efficiently, you need to define one or a few “reaction coordinates” or “collective variables” that span the phase space of the transition process. In you case a simple distance between two groups of atoms should suffice, which makes it easily treatable. However, there is no escape from first learning the necessary statistical mechanics and thermodynamics fundamental to apply the method correctly and interpreting the results correctly.