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

y We study the statistical properties of the potential energy landscape of a system 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 provide thermodynamic insights of the Noro and Frenkel [M. G. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a vibrational (Delta dependent) and a floppy (Delta independent) component. We also show that the partition function is a function of Delta e(o)(beta u), explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).