Crystalline hydrates of calix[4]arene-para-sulfonic acid with n (n = 6–16) water molecules: a structure modeling

Abstract

The structures of crystalline hydrates of calix[4]arene-para-sulfonic acid with n (n = 6–16) water molecules and the activation barriers to surface proton migration were calculated within the framework of the density functional theory (DFT) using the PBE gradient-corrected functional, the "hard" basis set of projector-augmented waves (PAW), a corresponding pseudopotential, periodic boundary conditions, and the VASP program package. The energies of formation of crystalline hydrates from calix[4]arene-para-sulfonic acid and n water molecules calculated per water molecule are in the range of 0.4–0.9 eV and depend on n. The adsorption energy of water on the surface is in the range of 0.5–0.7 eV. The activation barriers to proton transfer across the surface calculated for the most stable crystal (n = 8) are close to experimental data and depend on the number of superstoihiometric water molecules, being equal to ~0.2 eV provided three superstoihiometric water molecules per surface SO₃H group.