Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li^sup +^ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy ΔsGM+,wat◦ of the Li+ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy of the proton, the surface electric potential jump χwat◦ upon entering bulk water, and the absolute single-electrode potential of the reference hydrogen electrode are calculated to be −1099.9 ± 4.2 kJ·mol–1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (−1100 ± 5 kJ·mol–1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li+ are also compared to those for Na+ and K+ from a previous study in terms of relative hydration free energies ΔΔsGM+,wat◦ and relative electrode potentials . The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔsGM+,wat• and redox potentials . The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller–Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li+ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.