Based on a systematic investigation of trajectories of ab initio quantum mechanical/molecular mechanical simulations of numerous cations in water a standardized procedure for the evaluation of mean ligand residence times is proposed. For the characterization of reactivity and structure-breaking/structure-forming properties of the ions a measure is derived from the mean residence times calculated with different time limits. It is shown that ab initio simulations can provide much insight into ultrafast dynamics that are presently not easily accessible by experiment.

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Despite the large number of experimental as well as theoretical investigations available in the literature, some properties of the hydration structure of Sr(II), for example, the coordination number, are still ambiguous. The presented molecular dynamics study based on a most suitable ab initio QM/MM protocol allowed a detailed investigation of structural and dynamical properties of this hydrate, which shows a considerable degree of internal flexebility as well as ligand mobility within the first shell. Despite the high computational effort an exceptionally long QM/MM simulation had to be carried out to obtain sufficient information to investigate first shell ligand exchange reactions.

Structural and dynamical properties of the hydrated Cs + ion have been investigated by performing ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations at different quantum mechanical levels (HF, B3LYP and BP86). The first shell coordination number was found to be ∼8 in the HF and ∼9 in the B3LYP and BP86 case and several other structural parameters such as angular distribution functions, radial distribution functions, and tilt-and θ-angle distributions allowed to fully characterize the hydration structure of the Cs + ion. Velocity autocorrelation functions were used to calculate librational and vibrational motions, ion-ligand motions, as well as reorientation times. The strong "structure breaking" effect of Cs + can be interpreted on the basis of different dynamical parameters such as accelerated water reorientation, mean ligand residence time, and the number of ligand exchange processes.

A simulation of phosphate in aqueous solution was carried out employing the new QMCF MD approach which offers the possibility to investigate composite systems with the accuracy of a QMMM method but without the time consuming creation of solute-solvent potential functions. The data of the simulations give a clear picture of the hydration shells of the phosphate anion. The first shell consists of 13 water molecules and each oxygen of the phosphate forms in average three hydrogens bonds to different solvent molecules. Several structural parameters such as radial distribution functions and coordination number distributions allow to fully characterize the embedding of the highly charged phosphate ion in the solvent water. The dynamics of the hydration structure of phosphate are described by mean residence times of the solvent molecules in the first hydration shell and the water exchange rate.

The absolute intrinsic hydration free energy G • H + ,wat of the proton, the surface electric potential jump χ • wat upon entering bulk water, and the absolute redox potential V • H + ,wat of the reference hydrogen electrode are cornerstone quantities for formulating single-ion thermodynamics on absolute scales. They can be easily calculated from each other but remain fundamentally elusive, i.e., they cannot be determined experimentally without invoking some extra-thermodynamic assumption (ETA). The Born model provides a natural framework to formulate such an assumption (Born ETA), as it automatically factors out the contribution of crossing the water surface from the hydration free energy. However, this model describes the short-range solvation inaccurately and relies on the choice of arbitrary ion-size parameters. In the present study, both shortcomings are alleviated by performing first-principle calculations of the hydration free energies of the sodium (Na + ) and potassium (K + ) ions. The calculations rely on thermodynamic integration based on quantum-mechanical molecular-mechanical (QM/MM) molecular dynamics (MD) simulations involving the ion and 2000 water molecules. The ion and its first hydration shell are described using a correlated ab initio method, namely resolution-of-identity second-order Møller-Plesset perturbation (RIMP2). The next hydration shells are described using the extended simple point charge water model (SPC/E). The hydration free energy is first calculated at the MM level and subsequently increased by a quantization term accounting for the transformation to a QM/MM description. It is also corrected for finite-size, approximate-electrostatics, and potentialsummation errors, as well as standard-state definition. These computationally intensive simulations provide accurate first-principle estimates for G • H + ,wat , χ • wat , and V • H + ,wat , reported with statistical errors based on a confidence interval of 99%. The values obtained from the independent Na + and K + simulations are in excellent agreement. In particular, the difference between the two hydration free energies, which is not an elusive quantity, is 73.9 ± 5.4 kJ mol 1 (K + minus Na + ), to be compared with the experimental value of 71.7 ± 2.8 kJ mol 1 . The calculated values of G • H + ,wat , χ • wat , and V • H + ,wat ( 1096.7 ± 6.1 kJ mol 1 , 0.10 ± 0.10 V, and 4.32 ± 0.06 V, respectively, averaging over the two ions) are also in remarkable agreement with the values recommended by Reif and Hünenberger based on a thorough analysis of the experimental literature ( 1100 ± 5 kJ mol 1 , 0.13 ± 0.10 V, and 4.28 ± 0.13 V, respectively). The QM/MM MD simulations are also shown to provide an accurate description of the hydration structure, dynamics, and energetics. Published by AIP Publishing.

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