R. Shannon and C. Prewitt, Effective Ionic Radii in Oxides and Fluorides, Acta Cryst, vol.25, p.925, 1969.

Y. Marcus, Thermodynamics of Solvation of Ions. Part 5. Gibbs Free Energy of Hydration at 298.15 K, J. Chem. Soc. Faraday Trans, vol.87, pp.2995-2999, 1991.

H. Friedman and C. Krishnan, Thermodynamics of Ion Hydration in Water: A Comprehensive Treatise, vol.3, 1973.

D. Powell, P. Gullidge, G. Neilson, and M. Bellissent-funel, Zn 2+ Hydration and Complexation in Aqueous Electrolyte Solutions, Mol. Phys, vol.71, pp.1107-1116, 1990.

M. Q. Fatmi, T. S. Hofer, B. R. Randolf, and B. M. Rode, Extended Ab-Initio QM/MM MD Approach to Structure and Dynamics of Zn(II) in Aqueous Solution, J. Chem. Phys, p.54514, 2005.

G. Brancato, N. Rega, and V. Barone, Microsolvation of the Zn(II) Ion in Aqueous Solution: A Hybrid QM/MM MD Approach Using Non-Periodic Boundary Conditions, Chem. Phys. Lett, vol.451, pp.53-57, 2008.

C. W. Bock, A. K. Katz, and J. P. Glusker, Hydration of Zinc Ions: A Comparison with Magnesium and Beryllium Ions, J. Am. Chem. Soc, vol.117, pp.3754-3765, 1995.

M. Biesaga, K. Pyrzynska, and M. Trojanowicz, Porphyrins in Analytical Chemistry. A Review. Talanta, vol.51, pp.209-224, 2000.

Y. H. Ko, S. Hong, and P. L. Pedersen, Chemical Mechanism of ATP Synthase, J. Bio, vol.274, pp.28853-28856, 1999.

A. L. Buchachenko, D. A. Kouznetsov, N. N. Breslavskaya, and M. A. Orlova, Magnesium Isotope Effects in Enzymatic Phosphorylation, J. Phys. Chem. B, vol.112, pp.2548-2556, 2008.

K. Pasternak, J. Kocot, and A. Horecka, Biochemistry of Magnesium. J. Elementol, vol.15, pp.601-616, 2010.

T. Kambe, T. Fukada, and S. Toyokuni, The Cutting Edge of Zinc Biology, Arch. Biochem. Biophys, vol.611, pp.1-2, 2016.

W. N. Lipscomb and N. Sträter, Recent Advances in Zinc Enzymology, Chem. Rev, vol.96, pp.2375-2434, 1996.

S. O. Emdin, G. G. Dodson, J. M. Cutfield, and S. M. Cutfield, Role of Zinc in Insulin Biosynthesis, Diabetologia, vol.19, pp.174-182, 1980.

D. V. Sakharov and C. Lim, Zn Protein Simulations Including Charge Transfer and Local Polarization Effects, J. Am. Chem. Soc, vol.127, pp.4921-4929, 2005.

M. Kohagen, P. E. Mason, and P. Jungwirth, Accurate Description of Calcium Solvation in Concentrated Aqueous Solutions, J. Phys. Chem. B, vol.118, pp.7902-7909, 2014.

M. Soniat, L. Hartman, and S. W. Rick, Charge Transfer Models of Zinc and Magnesium in Water, J. Chem. Theory Comput, vol.11, pp.1658-1667, 2015.

T. Martinek, E. Duboué-dijon, S. Timr, P. E. Mason, K. Boxova et al., Calcium Dications in Aqueous Solutions: Accurate Force Field Description Aided by Ab Initio Molecular Dynamics Simulations and Neutron Scattering Experiments, 2017.

S. Mamatkulov, M. Fyta, and R. R. Netz, Force Fields for Divalent Cations Based on Single-Ion and Ion-Pair Properties, J. Chem. Phys, p.24505, 2013.

I. Leontyev and A. Stuchebrukhov, Accounting for Electronic Polarization in Non-Polarizable Force Fields, Phys. Chem. Chem. Phys, vol.13, pp.2613-2626, 2011.

J. E. Enderby, Ion Solvation Via Neutron Scattering, Chem. Soc. Rev, vol.24, pp.159-168, 1995.

J. L. Finney and A. K. Soper, Solvent Structure and Perturbation in Solutions of Chemical and Biological Importance, Chem. Soc. Rev, vol.23, pp.1-10, 1994.

G. W. Neilson and R. H. Tromp, Neutron and X-Ray Diffraction on Aqueous Solutions, Ann. Rep. Chem., Sect. C, vol.88, pp.45-75, 1991.

B. G. Neilson, P. E. Mason, S. Ramos, and D. Sullivan, Neutron and X-Ray Scattering Studies of Hydration in Aqueous Solutions, Phil. Trans. R. Soc. Lond. A, vol.359, pp.1575-1591, 2001.

H. Powell, A. C. Barnes, J. E. Enderby, G. W. Neilson, and P. S. Salmon, The Hydration Structure Around Chloride Ions in Aqueous Solution, Faraday Discuss. Chem. Soc, vol.85, pp.137-146, 1988.

Y. S. Badyal, A. C. Barnes, G. J. Cuello, and J. Simonson, Understanding the Effects of Concentration on the Solvation Structure of Ca 2+ in Aqueous Solution. II: Insights into Longer Range Order from Neutron Diffraction Isotope Substitution, J. Phys. Chem. A, vol.108, pp.11819-11827, 2004.

P. E. Mason, S. Ansell, and G. W. Neilson, Neutron Diffraction Studies of Electrolytes in Null Water: A Direct Determination of the First Hydration Zone of Ions, J. Phys. Condens. Matter, vol.18, pp.8437-8447, 2006.

H. E. Fischer, G. J. Cuello, P. Palleau, D. Feltin, A. C. Barnes et al., D4C: A Very High Precision Diffractometer for Disordered Materials, Appl. Phys. A: Mater, vol.74, pp.160-162, 2002.

P. Mason, K. Boxova, E. Duboué-dijon, H. E. Fischer, and P. Jungwirth, Towards a Faithful Descripion of Biologically Relevant Dications. Institut Laue-Langevin, 2016.

A. C. Barnes, S. B. Lague, P. S. Salmon, and H. E. Fischer, A Determination of the Structure of Liquid Ag 2 Se Using Neutron Diffraction and Isotopic Substitution, J. Phys.: Condens. Matt, vol.9, pp.6159-6173, 1997.

G. Placzek, the Scattering of Neutrons by Systems of Heavy Nuclei, Phys. Rev, vol.86, pp.377-388, 1952.

D. Van-der-spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark et al., GROMACS: Fast, Flexible, and Free, J. Comput. Chem, p.26, 2005.

M. Parrinello and A. Rahman, Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method, J. Appl. Phys, vol.52, pp.7182-7190, 1981.

T. Darden, D. York, and L. Pedersen, Particle Mesh Ewald: An Nlog(N) Method for Ewald Sums in Large Systems, J. Chem. Phys, p.10089, 1993.

B. Hess, H. Bekker, H. J. Berendsen, and J. G. Fraaije, LINCS: A Linear Constraint Solver for Molecular Simulations, J. Comput. Chem, vol.18, pp.1463-1472, 1997.

H. J. Berendsen, J. R. Grigera, and T. P. Straatsma, The Missing Term in Effective Pair Potentials, J. Phys. Chem, vol.91, pp.6269-6271, 1987.

J. Chandrasekhar, D. C. Spellmeyer, and W. L. Jorgensen, Energy Component Analysis for Dilute Aqueous Solutions of Li + , Na + , F ? , and Cl ? Ions, J. Am. Chem. Soc, vol.106, pp.903-910, 1984.

K. M. Callahan, N. N. Casillas-ituarte, M. Roeselová, H. C. Allen, and D. J. Tobias, Solvation of Magnesium Dication: Molecular Dynamics Simulation and Vibrational Spectroscopic Study of Magnesium Chloride in Aqueous Solutions, J. Phys. Chem. A, vol.114, pp.5141-5148, 2010.

R. H. Stote and M. Karplus, Zinc Binding in Proteins and Solution: A Simple but Accurate Nonbonded Representation, Proteins, vol.23, pp.12-31, 1995.

E. Pluharova, P. E. Mason, and P. Jungwirth, Ion Pairing in Aqueous Lithium Salt Solutions with Monovalent and Divalent Counter-Anions, J. Phys. Chem. A, vol.117, pp.11766-11773, 2013.

E. Pluharova, H. E. Fischer, P. E. Mason, and P. Jungwirth, Hydration of the Chloride Ion in Concentrated Aqueous Solutions Using Neutron Scattering and Molecular Dynamics, Mol. Phys, vol.8976, pp.1-11, 2014.

R. Caminiti, G. Licheri, G. Piccaluga, and G. Pinna, X-Ray Diffraction Study of MgCl 2 Aqueous Solutions, J. Appl. Cryst, vol.12, pp.34-38, 1979.

G. Palinkas, T. Radnai, W. Dietz, G. I. Szasz, and K. Heinzinger, Hydration Shell Structures in an MgCl 2 Solution from X-Ray and MD Studies, Z. Naturforsch, vol.37, pp.1049-1060, 1982.

F. Bruni, S. Imberti, R. Mancinelli, and M. A. Ricci, Aqueous Solutions of Divalent Chlorides: Ions Hydration Shell and Water Structure, J. Chem. Phys, vol.136, p.64520, 2012.

J. Vandevondele, M. Krack, F. Mohamed, M. Parrinello, T. Chassaing et al., QUICK-STEP: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach, Comput. Phys. Comm, vol.167, pp.103-128, 2005.

G. Bussi, D. Donadio, and M. Parrinello, Canonical Sampling Through Velocity Rescaling, J. Chem. Phys, p.14101, 2007.

A. D. Becke, Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior, Phys. Rev. A, vol.38, pp.3098-3100, 1988.

C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density, Phys. Rev. B, vol.37, pp.785-789, 1988.

S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu, J. Chem. Phys, p.154104, 2010.

D. G. Smith, L. A. Burns, K. Patkowski, and C. D. Sherrill, Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory, J. Phys. Chem. Lett, vol.7, pp.2197-2203, 2016.

A. D. Becke and E. R. Johnson, A Density-Functional Model of the Dispersion Interaction, J. Chem. Phys, p.154101, 2005.

S. Grimme and . Semiempirical, GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction, J. Comput. Chem, vol.27, pp.1787-1799, 2006.

J. Vandevondele and J. Hutter, Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases, J. Chem. Phys, p.114105, 2007.

S. Goedecker, M. Teter, and J. Hutter, Separable Dual-Space Gaussian Pseudopotentials, Phys. Rev. B, vol.54, pp.1703-1710, 1996.

A. Bleuzen, L. Helm, and E. Merbach, Water Exchange on Magnesium(II) in Aqueous Solution: A Variable Temperature and Pressure, Magn. Reson. Chem, vol.35, pp.765-773, 1997.

S. Kumar, J. M. Rosenberg, D. Bouzida, R. H. Swendsen, and P. A. Kollman, Multidimensional Free-Energy Calculations Using the Weighted Histogram Analysis Method, J. Comput. Chem, vol.16, pp.1339-1350, 1995.

G. Paschina, G. Piccaluga, G. Pinna, and M. Magini, Chloro-Complexes Formation in a ZnCl 2 -CdCl 2 Aqueous Solution: An X-Ray Diffraction Study, J. Chem. Phys, p.5745, 1983.

D. E. Irish, B. Mccarroll, T. F. Young, and . Raman, Study of Zinc Chloride Solutions, J. Chem. Phys, vol.39, pp.3436-3444, 1963.

R. Caminiti, G. Licheri, G. Piccalljga, G. Pinna, and . X-ray, Diffraction Study of a Three-Ion Aqueous Solution, Chem. Phys. Lett, vol.47, pp.275-278, 1977.

A. K. Dorosh and A. F. Skryshevskii, The Structural Characteristics of the Immediate Environment of Cations in Aqueous Solutions, Zh. Strukt. Khim, vol.5, pp.911-913, 1964.

P. D'angelo, V. Barone, G. Chillemi, N. Sanna, W. Meyer-klaucke et al., Hydrogen and Higher Shell Contributions in Zn 2+ , Ni 2+ , and Co 2+ Aqueous Solutions: An X-Ray Absorption Fine Structure and Molecular Dynamics Study, J. Am. Chem. Soc, vol.124, pp.1958-1967, 2002.

A. Kuzmin, S. Obst, J. Purans, and . X-ray, Absorption Spectroscopy and Molecular Dynamics Studies of Zn2+ Hydration in Aqueous Solutions, J. Phys. Condens. Matter, vol.9, pp.10065-10078, 1997.

F. C. Lightstone, E. Schwegler, R. Q. Hood, F. Gygi, and G. Galli, A First Principles Molecular Dynamics Simulation of the Hydrated Magnesium Ion, Chem. Phys. Lett, vol.343, pp.549-555, 2001.

S. Riahi, B. Roux, and C. N. Rowley, QM/MM Molecular Dynamics Simulations of the Hydration of Mg(II) and Zn(II) Ions, Can. J. Chem, vol.99, pp.1-9, 2013.

D. D. Tommaso and N. H. De-leeuw, Structure and Dynamics of the Hydrated Magnesium Ion and of the Solvated Magnesium Carbonates: Insights from First Principles Simulations, Phys. Chem. Chem. Phys, vol.12, pp.894-901, 2010.

T. Ikeda, M. Boero, and K. Terakura, Hydration Properties of Magnesium and Calcium Ions from Constrained First Principles Molecular Dynamics, J. Chem. Phys, p.74503, 2007.

J. C. Wu, J. Piquemal, R. Chaudret, P. Reinhardt, and P. Ren, Polarizable Molecular Dynamics Simulation of Zn(II) in Water Using the AMOEBa Force Field, J. Chem. Theory Comput, vol.6, pp.2059-2070, 2010.
URL : https://hal.archives-ouvertes.fr/hal-02126833

J. P. Piquemal, L. Perera, G. A. Cisneros, P. Ren, L. G. Pedersen et al., Towards Accurate Solvation Dynamics of Divalent Cations in Water Using the Polarizable AMOEBA Force Field: From Energetics to Structure, J. Chem. Phys, p.54511, 2006.
URL : https://hal.archives-ouvertes.fr/hal-02126806

J. W. Ponder, C. Wu, V. S. Pande, J. D. Chodera, M. J. Schnieders et al., Current Status of the AMOEBA Polarizable Force Field, J. Phys. Chem. B, vol.114, pp.2549-2564, 2010.

N. Marzari and D. Vanderbilt, Maximally Localized Generalized Wannier Functions for Composite Energy Bands, Phys. Rev. B, p.22, 1997.