The HSAB principle from a finite-temperature grand-canonical perspective

We provide a new proof for Pearson’s hard/soft acid/base (HSAB) principle. Unlike alternative proofs, we do not presuppose a simplified parabolic dependence on the energy of the system with respect to changes in its number of electrons. Instead, we use the more physically grounded finite-temperature formulation of the grand-canonical ensemble. We show that under the usual assumptions regarding the chemical potentials and hardnesses of the involved species, the HSAB rule holds for a wide range of temperatures.