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We study the statistical properties of the potential energy landscape of asystem of particles interacting via a very short-range square-well potential(of depth $-u_0$), as a function of the range of attraction $\Delta$ to providethermodynamic insights of the Noro and Frenkel [ M.G. Noro and D. Frenkel,J.Chem.Phys. {\bf 113}, 2941 (2000)] scaling. We exactly evaluate the basinfree energy and show that it can be separated into a {\it vibrational}($\Delta$-dependent) and a {\it floppy} ($\Delta$-independent) component. Wealso show that the partition function is a function of $\Delta e^{\beta u_o}$,explaining the equivalence of the thermodynamics for systems characterized bythe same second virial coefficient. An outcome of our approach is thepossibility of counting the number of floppy modes (and their entropy).Comment: 4 pages, 4 figures accepted for publication on PR

Extended law of corresponding states in short-range square wells: A potential energy landscape study