Cluster-continuum quasichemical theory calculation of the lithium ion solvation in water, acetonitrile and dimethyl sulfoxide: an absolute single-ion solvation free energy scale

Abstract

Absolute single-ion solvation free energy is a very useful property for understanding solution phase chemistry. The real solvation free energy of an ion depends on its interaction with the solvent molecules and on the net potential inside the solute cavity. The tetraphenyl arsonium–tetraphenyl borate (TATB) assumption as well as the cluster-continuum quasichemical theory (CC-QCT) approach for Li⁺ solvation allows access to a solvation scale excluding the net potential. We have determined this free energy scale investigating the solvation of the lithium ion in water (H₂O), acetonitrile (CH₃CN) and dimethyl sulfoxide (DMSO) solvents via the CC-QCT approach. Our calculations at the MP2 and MP4 levels with basis sets up to the QZVPP+diff quality, and including solvation of the clusters and solvent molecules by the dielectric continuum SMD method, predict the solvation free energy of Li⁺ as −116.1, −120.6 and −123.6 kcal mol⁻¹ in H₂O, CH₃CN and DMSO solvents, respectively (1 mol L⁻¹ standard state). These values are compatible with the solvation free energy of the proton of −253.4, −253.2 and −261.1 kcal mol⁻¹ in H₂O, CH₃CN and DMSO solvents, respectively. Deviations from the experimental TATB scale are only 1.3 kcal mol⁻¹ in H₂O and 1.8 kcal mol⁻¹ in DMSO solvents. However, in the case of CH₃CN, the deviation reaches a value of 9.2 kcal mol⁻¹. The present study suggests that the experimental TATB scale is inconsistent for CH₃CN. A total of 125 values of the solvation free energy of ions in these three solvents were obtained. These new data should be useful for the development of theoretical solvation models.