We identified a transversing physical connection between kinetic, exchange, and correlation functionals by using parameter-free (Pfree) exchange and one-parameter progressive (OP) correlation. On the basis of this connection, we investigated how the calculated energies and chemical properties depend on the shape of the functional in the Kohn–Sham scheme. We found that the fundamental conditions of the functionals are connected through Pfree and OP functionals with the exception of a rapidly varying density limit. We also found that the calculated properties are highly affected by the exchange functional shape in particular regions of xσ=|∇ρσ|/ρσ4/3.