 Adsorption-site grand partition function

An independent site has one empty state and an occupied set with binding energy $-ϵ$ and vibrational partition function $z_s$. Its occupied probability is $\theta =z_s{e}^{\beta (\mu +ϵ)}/[1+z_s{e}^{\beta (\mu +ϵ)}]$. The denominator enforces the one-molecule-per-site constraint even though the vapour may obey classical statistics. Multiple occupancy or lateral interactions require a different model.