with N k the number of adsorbed molecules of adsorbate k, µ k the chemical potential, temperature T , (bulk) pressure p, composition of the bulk phase x i , and the number of components N c . The resulting evaluation of the enthalpy of adsorption is numerically robust and fast relative to the calculation of the density profile itself. Details on the derivation and the calculation of partial derivatives of density profiles are included in the Supplementary Material, Sec. S1C.