Looking for synergies in solution chemistry between first-principles intermolecular potentials and exafs and xanes spectroscopies

UNIVERSIDAD DE SEVILLA FACULTAD DE QU´ IMICA DEPARTAMENTO DE QU´ IMICA F´ ISICA Looking for synergies in solution chemistry between first-principles intermolecular potentials and EXAFS and XANES spectroscopies Daniel Zein Caralampio M´ınguez Supervised by: Enrique S´anchez Marcos Jose Manuel Mart´ınez Fernandez DEPARTAMENTO DE QU´ IMICA F´ ISICA Thesis submitted for the degree of Doctor of Theoretical Chemistry and Molecular Modellization by the Universidad de Sevilla. Daniel Zein Caralampio M´ınguez Directores de la Tesis Dr. Enrique S´anchez Marcos Dr. Jose Manuel Mart´ınez Fernandez Contents Contents I List of Tables V List of Figures IX Abstract I 0.1 Bibliography .......................... V 1 Introduction 1 1.1 Bibliography .......................... 10 2 Methods 17 2.1 Quantum mechanics . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Moller-Plesset second order theory . . . . . . . . . . 18 2.1.2 Density functional theory . . . . . . . . . . . . . . . 19 2.1.2.1 B3LYP functional . . . . . . . . . . . . . . 20 2.1.2.2 M06 and M06-2X functionals . . . . . . . . 21 2.1.3 Basissets ........................ 22 2.1.4 Effective core potentials . . . . . . . . . . . . . . . . 22 2.1.5 Quantum approaches to the ion solvation . . . . . . 22 2.2 Molecular dynamics . . . . . . . . . . . . . . . . . . . . . . 23 2.3 X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . 25 2.4 Ab-initio intermolecular potentials . . . . . . . . . . . . . . 27 I II CONTENTS 2.4.1 Hydrated ion model . . . . . . . . . . . . . . . . . . 28 2.4.2 Watermodel ...................... 29 2.4.3 Ion-water model . . . . . . . . . . . . . . . . . . . . 34 2.4.4 Methodology . . . . . . . . . . . . . . . . . . . . . . 38 2.5 Bibliography .......................... 41 3 Intermolecular potentials 45 3.1 Alkalinegroup ......................... 46 3.1.1 Light alkalines . . . . . . . . . . . . . . . . . . . . . 46 3.1.2 Heavy alkalines . . . . . . . . . . . . . . . . . . . . . 47 3.2 Alkaline-earth.......................... 52 3.3 Transition metals cations . . . . . . . . . . . . . . . . . . . 54 3.4 Lanthanides........................... 59 3.5 Actinide............................. 62 3.5.1 Thorium......................... 62 3.6 Suplementary information . . . . . . . . . . . . . . . . . . . 64 3.6.1 Water model force field coefficients . . . . . . . . . . 64 3.6.2 Ion-water force field coefficients . . . . . . . . . . . . 65 3.6.3 Global energetic fitting comparison . . . . . . . . . . 67 3.7 Bibliography .......................... 76 4 System definition and analyzed properties 79 4.1 Bibliography .......................... 83 5 Alkalines 85 5.1 Lithium ............................. 85 5.2 Sodium ............................. 88 5.3 Potassium............................ 94 5.4 Rubidium ............................ 98 5.5 Caesium............................. 103 5.6 Global properties in solution . . . . . . . . . . . . . . . . . 106 5.6.1 Radial distribution function . . . . . . . . . . . . . . 106 5.6.2 Energetic properties . . . . . . . . . . . . . . . . . . 110 5.6.3 Hydrogen bonding . . . . . . . . . . . . . . . . . . . 111 CONTENTS III 5.6.4 Dynamic properties . . . . . . . . . . . . . . . . . . 116 5.6.5 Molecular asymmetry . . . . . . . . . . . . . . . . . 122 5.7 Global properties in gas phase . . . . . . . . . . . . . . . . . 125 5.7.1 Average dipole moment . . . . . . . . . . . . . . . . 125 5.8 Bibliography .......................... 127 6 Heavy alkaline-earths 133 6.1 Strontium............................ 133 6.2 Barium ............................. 138 6.3 Radium ............................. 140 6.4 Global properties in solution . . . . . . . . . . . . . . . . . 143 6.4.1 Radial distribution Function . . . . . . . . . . . . . 143 6.4.2 Energetic properties . . . . . . . . . . . . . . . . . . 146 6.4.3 Hydrogen bonding . . . . . . . . . . . . . . . . . . . 146 6.4.4 Dynamic properties . . . . . . . . . . . . . . . . . . 148 6.4.5 Molecular asymmetry . . . . . . . . . . . . . . . . . 151 6.5 Bibliography .......................... 151 7 Transition metals and rare earths 155 7.1 Transition metals . . . . . . . . . . . . . . . . . . . . . . . . 155 7.2 Scandium ............................ 155 7.3 Cobalt.............................. 162 7.4 Cadmium ............................ 165 7.5 Global properties in solution . . . . . . . . . . . . . . . . . 169 7.5.1 Radial distribution function . . . . . . . . . . . . . . 169 7.5.2 Energetic properties . . . . . . . . . . . . . . . . . . 171 7.5.3 Hydrogen bonding . . . . . . . . . . . . . . . . . . . 171 7.5.4 Dynamic properties . . . . . . . . . . . . . . . . . . 172 7.5.5 Molecular assymetry . . . . . . . . . . . . . . . . . . 176 7.6 Lanthanoids........................... 176 7.7 Lanthanum ........................... 176 7.8 Neodymium........................... 178 7.9 Thulium............................. 182 7.10 Global properties in solution . . . . . . . . . . . . . . . . . 186 IV CONTENTS 7.10.1 Radial distribution function . . . . . . . . . . . . . . 186 7.10.2 Energetic properties . . . . . . . . . . . . . . . . . . 189 7.10.3 Hydrogen bonding . . . . . . . . . . . . . . . . . . . 189 7.10.4 Dynamic properties . . . . . . . . . . . . . . . . . . 191 7.10.5 Molecular assymetry. . . . . . . . . . . . . . . . . . . 193 7.10.6 Second shell effects on XANES spectrum. . . . . . . 193 7.11 An actinide case: Th4+ .................... 196 7.12Bibliography .......................... 202 8 Born model 209 8.1 Bibliography .......................... 212 9 Conclusions 213 9.1 Bibliography .......................... 216 10 Appendix 221 10.1Scandium ............................ 221 10.2 XAS simulation. . . . . . . . . . . . . . . . . . . . . . . . . 222 List of Tables 2.1 Water model properties . . . . . . . . . . . . . . . . . . . . . . 29 2.2 MCDHO and MCDHO2 filter criteria . . . . . . . . . . . . . . 33 2.3 Spring constants based on experimental polarizability . . . . . 35 2.4 Non experimental spring constant . . . . . . . . . . . . . . . . 36 3.1 Energies (kcal/mol) and distances (˚ A) of Li+and Na+hydrates. 47 3.2 QM interaction energy for surface and inner minimum energy structures (kcal/mol) of heavy alkalines. . . . . . . . . . . . . . 49 3.3 Energies (kcal/mol) and distances (˚ A) of K+, Rb+and Cs+ inner cluster hydrates. . . . . . . . . . . . . . . . . . . . . . . . 52 3.4 Energies (kcal/mol) and distances (˚ A) of K+, Rb+and Cs+ surface cluster hydrates. . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Energies (kcal/mol) and distances (˚ A) of Sr2+, Ba2+ and Ra2+ hydrates. .............................. 54 3.6 Energies (kcal/mol) and distances (˚ A) of Co2+ hydrates. . . . . 55 3.7 Energies (kcal/mol) and distances (˚ A) of Cd2+ hydrates. . . . . 56 3.8 Energy (kcal/mol) comparison of water skeletons from optimized Sc3+ hydrates. ........................... 57 3.9 Energies (kcal/mol) and distances (˚ A) of Sc3+ hydrates. . . . . 59 3.10 Energies (kcal/mol) and distances (˚ A) of La3+, Nd3+ and Tm3+ hydrates. .............................. 62 3.11 Energies (kcal/mol) and distances (˚ A) of Th4+ hydrates. . . . . 63 3.12 MCDHO2 coefficients. . . . . . . . . . . . . . . . . . . . . . . . 64 V XII List of Figures 5.24 Average number of hydrogen bonds for first-shell water molecules. Black dots: average number of hydrogen bonds per molecule. Red dots: average number of hydrogen bonds between first-shell watermolecules. .......................... 113 5.25 Average hydrogen bond interaction energy (kcal/mol). Black dots: average interaction energy per hydrogen bond between a molecule of the first-shell and a molecule of the second shell. Red dots: average interaction energy per hydrogen bonds between first-shell molecules. Blue line: MCDHO2 bulk water value. . . 114 5.26 Mean residence time of first-shell molecules computed by the Impey method. Black dots: MRT using t* = 0 ps. Red dots: MRTusingt*=2ps. ....................... 116 5.27 τ2,µ and τ2,OH correlational functions. . . . . . . . . . . . . . . 120 5.28 Self-diffusion coefficient (top), self-diffusion coefficient relative to the bulk water diffusion coefficient (bottom). . . . . . . . . . 121 5.29 Eccentricity, (˚ A), and eccentricity reorientational time, τ1, (ps). Standard deviation defined by error bars. . . . . . . . . . 123 5.30 Two views of a representative structure and its first hydration shell containing ten solvent molecules taken from the MD simulation. ............................... 124 5.31 Average dipole moment of the water molecules. . . . . . . . . . 126 5.32 Lithium (left) and caesium hydrates (right) with 25 water molecules.126 6.1 Time evolution of Sr2+ coordination number in aqueous solution. 136 6.2 Coordination number histogram of Sr2+ on aqueous solution. . 136 6.3 k2-weighted Sr2+ K-edge EXAFS. . . . . . . . . . . . . . . . . 137 6.4 Sr2+ K-edgeXANES. ....................... 137 6.5 Time evolution of Ba2+ coordination number in aqueous solution.139 6.6 Coordination number histogram of Ba2+ in aqueous solution. . 139 6.7 k2-weighted Ba2+ K-edge EXAFS. . . . . . . . . . . . . . . . . 141 6.8 Time evolution of Ra2+ coordination number aqueous solution. 142 6.9 Coordination number histogram of Ra2+ in aqueous solution. . 142 6.10 Metal-oxygen radial distribution function. . . . . . . . . . . . . 145 List of Figures XIII 6.11 Metal-hydrogen radial distribution function for the heavy alkalineearthscations. ........................... 145 6.12 Hydration enthalpy (kcal/mol). Red dots: experimental values.23 Black dots calculated values from simulations with error bars defining its mean error. . . . . . . . . . . . . . . . . . . . . 146 6.13 Mean residence times of first-shell molecules computed by the Impey method. Black dots: MRT using t* = 0 ps. Red dots: MRTusingt*=2.......................... 149 6.14 Self-diffusion coefficients (top), self-diffusion coefficient relative to bulk water (down). . . . . . . . . . . . . . . . . . . . . . . . 150 7.1 k2-weighted Sc3+ K-edge EXAFS. . . . . . . . . . . . . . . . . 160 7.2 Sc3+ K-edgeXANES. ....................... 160 7.3 Sc3+ K-edge XANES of QM clusters of [Sc(H2O)n]3+. . . . . . 161 7.4 FT-VAC of Sc3+ aqua ion in the gas phase (left) and solution (right)................................. 161 7.5 k2-weighted Co2+ K-edge EXAFS. . . . . . . . . . . . . . . . . 164 7.6 Co2+ K-edgeXANES........................ 164 7.7 FT-VAC of Co2+ aqua ion in gas phase (left) and in solution (right)................................. 165 7.8 Time evolution of Cd2+ coordination number. . . . . . . . . . . 167 7.9 Coordination number histogram of Cd2+ in aqueous solution. . 167 7.10 k2-weighted Cd2+ K-edge EXAFS. . . . . . . . . . . . . . . . . 168 7.11 Cd2+ K-edgeXANES........................ 168 7.12 Metal-oxygen radial distribution function. Distances in ˚ A. . . . 170 7.13 Metal-hydrogen radial distribution function. Distances in ˚ A. . 170 7.14 Self-diffusion coefficient (top), self-diffusion coefficient relative to the bulk water diffusion coefficient (bottom). . . . . . . . . . 175 7.15 k2-weighted La L3-edgeEXAFS. ................. 179 7.16 Time evolution of Nd3+ coordination number in aqueous solution.181 7.17 Coordination number histogram of Nd3+ in aqueous solution. . 181 7.18 k2-weighted Nd3+ L3-edge EXAFS. . . . . . . . . . . . . . . . . 183 7.19 Coordination number evolution of Tm3+ aqueous solution. . . . 185 7.20 Coordination number histogram of Tm3+ aqueous solution. . . 185 XIV List of Figures 7.21 k2-weighted Tm3+ L3-edge EXAFS. . . . . . . . . . . . . . . . 186 7.22 Metal-oxygen radial distribution function. . . . . . . . . . . . . 187 7.23 Metal-hydrogen radial distribution function. . . . . . . . . . . . 188 7.24 Hydration enthalpy. . . . . . . . . . . . . . . . . . . . . . . . . 189 7.25 Self-diffusion coefficient (top), self-diffusion coefficient relative to the bulk water diffusion coefficient (bottom). . . . . . . . . . 192 7.26 La3+ L3-edgeXANES........................ 194 7.27 Nd3+ L3-edgeXANES........................ 195 7.28 Tm3+ L3-edgeXANES. ...................... 195 7.29 k2-weighted Th L3-edge EXAFS. . . . . . . . . . . . . . . . . . 199 7.30 Th L3-edgeXANES......................... 199 7.31 Thorium-oxygen and thorium-hydrogen radial distribution function.................................. 201 8.1 Hydration enthalpy versus the effective ionic radii. Dashed lines are the fits of the experimental and theoretical values. . . . . . 210 8.2 Hydration enthalpy of the hydrated ion. Dashed line is the fit of theoretical values. . . . . . . . . . . . . . . . . . . . . . . . . 212 Abstract Physicochemical properties of aqueous solutions containing a broad spectrum of metal cations have been studied by means of Molecular Dynamic (MD) simulations employing classic ion-water intermolecular potentials based on ab initio potential energy surfaces. A polarizable ion and a flexible and polarizable water model, the MCDHO2,1were chosen. The aquaions were described by the Hydrated Ion Model, based on the idea of the concentric shells model of Frank and Evans.2This model was implemented in computer simulations in the mid 90‘s by this research group.3–5 The ions considered in this work have covered a wide range of the Periodic Table. Thus, the alkalines series, some alkaline-earths (Sr2+, Ba2+ and Ra2+), some d metals (Sc3+, Cd2+ and Co2+), some Lanthanoids (La3+, Nd3+ and Tm3+) and an actinoid (Th4+) have been studied by means of MD simulations of systems formed by 1 cation and 1000 water molecules at 300K in the NVT ensemble using the DLPOLY code.6 The x-ray absorption spectroscopy (XAS) was used as the main method to asses the quality of the results derived from the developed intermolecular potentials. This was based on the comparison of the experimental EXAFS and XANES spectra with the simulated ones. Theoretical spectra computed using an ab-initio FEFF multiscattering formalism, as implemented in FEFF code,7employing an statistically significant number of structures provided by the MD simulations. I II Abstract The obtained coordination numbers in aqueous solutions for Li+, Na+, K+, Rb+and Cs+cations were 4.0, 5.8, 7.2, 7.9 and 9.9 with the metaloxygen peak distances at 1.91, 2.34, 2.72, 2.87 and 3.12 ˚ A, respectively. For the heavy alkaline cations, surface cluster structures are lower in energy than the inner ones. Then, the range of structures to be included in the fitting was extended to arrangements where the metal cation is not longer in the middle of a water cluster, but on the top. An specific method8was applied to the multi-electron excitation (MEE) of the experimental EXAFS spectra. The signal treactement, that removes multi-electron excitations, allows to analyze a larger k-range, improving the comparison between the theoretical and experimental data. The solvation structure obtained for the Sr2+, Ba2+ and Ra2+ is composed by 8.0, 9.4 and 9.8 water molecules with peak distances at 2.57, 2.81 and 2.93 ˚ A, respectively. For Sc3+, Co2+ and Cd2+ coordination numbers of 6.0, 6.0 and 6.6 with peak distances at 2.15, 2.29 and 2.09 ˚ A were found. X-ray absorption measurements, EXAFS and XANES, were carried out at the SOLEIL synchrotron for the Co2+ aqueous solution. A very good agreement between the simulated and the experimental EXAFS spectra is obtained in all cases. For the Lanthanoid cations studied: La3+, Nd3+ and Tm3+, coordination numbers of 9.0, 8.7 and 7.7 with a peak distance of 2.58, 2.50 and 2.33 ˚ A, respectively, were found. In the case of the actinoid thorium cation coordination number of 9.0 and a peak distance of 2.47 ˚ A was obtained. Additional structural, energetical and dynamical properties have been calculated for the ions in solution. Thus, mean residence times and selfdiffusion coefficient at 300 K, reorientational properties and hydrogen bond characterization. The comparison of the results obtained in this work with raw experimental data supports the generation of ab initio potentials combined with MD-XAS to study the ion hydration. This shows that the computational techniques can be used to provide accurate properties of the system when experimental data are not available. 0.1. BIBLIOGRAPHY V 0.1 Bibliography [1] Villa, A.; Hess, B.; Saint-Martin, H. J. Phys. Chem. B 2009,113, 7270–7281. [2] Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945,13, 507–532. [3] Pappalardo, R.; S´anchez-Marcos, E. J. Phys. Chem. 1993,97, 4500– 4504. [4] Mart´ınez, J. M.; Pappalardo, R. R.; S´anchez Marcos, E. J. Chem. Phys. 1998,109, 1445–1455. [5] Mart´ınez, J.; Pappalardo, R.; S´anchez Marcos, E. J. Am. Chem. Soc. 1999,121, 3175–3184. [6] Smith, W.; Forester, T.; Todorov, I. T. The DL POLY Classic. 2012; STFC Daresbury Laboratory, Daresbury (UK). [7] Rehr, J. J.; Kas, J. J.; Vila, F. D.; Prange, M. P.; Jorissen, K. Phys. Chem. Chem. Phys. 2010,12, 5503–5513. [8] Ohta, A.; Kagi, H.; Tsuno, H.; Nomura, M.; Kawabe, I. Am. Mineralogist 2008,93, 1384–1392. Chapter 1 Introduction The aqua ions are the common speciation of the charged ions in aqueous solutions at acidic and dilute conditions. They have long been studied due to their abundance and importance in many fields.1 A good starting point to describe the aqua ion structure is the concentric shell model of Frank and Evans,2where up to three solvation regionsmaybe defined around the ion. The first solvation region is composed by the nearest water molecules,that are the most affected by the cation charge. The second hydration shell water molecules are less affected by the ion and are forming hydrogen bonds with those of the first-shell. The third shell water molecules behaves like bulk water molecules, except for the cases of highly charged cations. The water molecules in the first-shell are assigned to the aqua ion entity, [M(H2O)m]n+, because some properties as diffusion are explained by the consideration of the hydrated ion as the most representative chemical species.1The first-shell water molecules of highly charged cations (+3 or +4) are strongly polarized by the ion and even a partial charge transfer takes place. The water molecules are affected structurally both intra and intermolecularly by modifying their O-H distances, H-O-H bond angle, as 1 2CHAPTER 1. INTRODUCTION well as arranged orientation towards the ion. But in the case of a low polarizing ion, such as large monovalent cations water molecules are not strongly polarized, and the ion-dipole orientation is lost, becoming a disordered aqua ion where the water structure is partially retained. Figure 1.1: Scheme of the concentric shell model The main parameters to define the structure of an aqua ion are the average number of water molecules in the first and second hydration shells, their orientation, the average distance between the ion and the hydration shells and the thermal disorder of the hydration shells. Other relevant properties of an aqua ion are its diffusion properties, mean residence time of the water molecules in the hydration shells, coordination geometry, water exchange mechanism, reorientational properties and its hydration enthalpy. Based on the ion capability to order water molecules around it, ions are classified as structure maker or breaker.3A structure maker ion is able to create structure around it whereas a breaker one is unable to do it. For a structure maker ion the first-shell water molecules are polarized and ori- 3 entated by the ion interacting through a double hydrogen bond with the oxygen atoms of a second shell of water molecules. Several theoretical approaches have been employed to study the ions in solution; from QM calculations to Monte-carlo simulations to know the most probable conformation or MD, QM/MM and AIMD simulations to get insight into dynamic processes and the disorder of the system.1,4,5 Several experimental techniques as x-ray absorption spectroscopy, neutron diffraction, x-ray diffraction, nuclear magnetic resonance or raman spectroscopy are used to study the local structure of aqua ions.1,3,5–8 In this thesis, we have employed ab initio intermolecular potentials in classical MD simulations. The statistical information produced is used to generate EXAFS and XANES spectra to compare with experimental spectra in order to validate the structural information coming from the simulation. The combination of MD simulations and XAS spectroscopy has been proved to be a robust methodology in determining structural properties of solvated ions.9,10 This thesis has explored the new exchangeable-HIW intermolecular potential strategy11 on a wide set of metal cations covering the Periodic Table, from alkalines to heavy actinoid cations, including d-transition metal ones. The great difference among these ions is a demanding test to our methodology, an interesting source of new simulations to get a deeper insight into their physicochemical properties, as well as sources of challenges to improve the interaction potential building. In addition, the set of potentials presented in this thesis establishes a kind of database for future investigations involving aqueous solutions of salts. The group has previously worked on the development of interaction potentials for anions such halide.12–15 Now, the option to include cations and anions in the simulation cell bring us closer to a wide range of salts that become accesible to the MD simulations with sophisticated models like the one here developed. Diffraction techniques studies of the lighter alkalines, Li+and Na+, provided consistently hydration numbers of 416–18 and above 5,19,20 respectively. Some authors found higher coordination numbers for lithium21,22 10 CHAPTER 1. INTRODUCTION •To make a systematic characterization of the hydrogen bond network in the hydration structure around the whole set of metal cations studied, to stablish the similarities and differences of their hydration, finding, if possible a rational pattern. 1.1 Bibliography [1] Richens, D. T. The Chemistry of Aqua Ions; John Wiley: Chichester, 1997. [2] Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945,13, 507–532. [3] Marcus, Y. Ion properties; Markel Dekker, Inc, 1997. [4] Allen, M. P.; Tidesley, D. J. Computer simulation of liquids; Oxford University Press, 1989. [5] Ohtaki, H.; Radnai, T. Chem. rev. 1993,83, 1157–1204. [6] Mu˜noz-Paez, A.; Marcos, E. S. En Molecular structure of solvates and coordination complexes in solution as determined with EXAFS and XANES.; Reedik, J., Poeppelmeier, K., Eds.; Comprehensive Inorganic Chemisry II, 2013; Vol. 9. [7] Marx, D.; Hutter, J. Ab initio molecular dynamics: Basic Theory and Advanced Methods.; Cambridge: Cambridge University Press, 2009. [8] Magini, M. X-ray diffraction of ions in aqueous solutions: hydration and complex formation; CRC Press., 1988. [9] Merkling, P. J.; Mu˜noz-P´aez, A.; S´anchez Marcos, E. J. Am. Chem. Soc. 2002,124, 10911–10920. [10] Galbis, E.; Hern´andez-Cobos, J.; den Auwer, C.; Naour, C. L.; Guillaumont, D.; Simoni, E.; Pappalardo, R. R.; S´anchez Marcos, E. Angew. Chem. Int. Ed. 2010,22, 3811–3815. 1.1. BIBLIOGRAPHY 11 [11] Galbis, E.; Hern´andez-Cobos, J.; Pappalardo, R. R.; S´anchez Marcos, E. J. Chem. Phys. 2014,140, 214104. [12] Ayala, R.; Mart´ınez, J. M.; Pappalardo, R.; Marcos, E. S. J. Chem. Phys. 2004,15, 7269–75. [13] Ayala, R.; Mart´ınez, J. M.; Pappalardo, R.; Marcos, E. S. J Chem. Phys. 2003,119, 9538. [14] Ayala, R.; Mart´ınez, J. M.; Pappalardo, R.; Marcos, E. S. J. Phys. Chem. A 2000,104, 2799–2807. [15] Ayala, R.; Mart´ınez, J. M.; Pappalardo, R. R. J. Chem. Phys. 2002, 117, 10512. [16] Bouazizi, S.; Nasr, S. J. Mol. Struct. 2007,837, 206–213. [17] Rudolph, W.; Brooker, M. H.; Pye, C. C. J. Phys. Chem. 1995,99, 3793–3797. [18] Palinkas, G.; Radnai, T.; Hajdu, F. Z. Naturforsch 1979,35a, 107– 114. [19] Mancinelli, R.; Boti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. J. Phys. Chem. B 2007,11, 13570–13577. [20] Galib, M.; Baer, M.; Skinner, L.; Mundy, C.; Huthwelker, T.; Schenter, G.; Benmore, C.; Govind, N.; Fulton, J. J. Chem. Phys. 2017, 146, 084504. [21] Mason, E.; Anell, S.; Neilson, G.; Rempe, S. B. J. Phys. Chem. B 2015,119, 2003–2009. [22] Szasz, G.; Heinzinger, K.; Palinkas, G. Chem. Phys. Lett. 1981,78, 194–196. [23] Glezaku, V.; Chen, Y.; Fulton, J.; Schenter, G.; Dang, L. Theor. Chem. Acc. 2006,115, 86–99. 12 CHAPTER 1. INTRODUCTION [24] Vao-Soongnern, V.; Pipatpanukul, C.; Horpibulsuk, S. J. Mater. Sci. 2015,50, 7126–7136. [25] Lee, S. H.; Rasaiah, J. Y. J. Phys. Chem. 1996,100, 1420–1425. [26] San-Rom´an, M. L.; Carrillo-Tripp, M.; Saint-Martin, H.; Cobos, J. H.; Ortega-Blake, I. Theor. Chem. Acc. 2006,115, 177–189. [27] Loeffler, H. H.; Rode, B. M. J. Chem. Phys. 2002,117, 110–116. [28] Lyubartsev, A. P.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 2001, 114, 3120–3126. [29] Tongraar, A.; Liedl, K. R.; Rode, B. M. Chem. Phys. Lett. 1998,286, 56–64. [30] Sripa, P.; Tongraar, A.; Kerdcharoen, T. J. Mol. Liq. 2015,208, 280– 285. [31] Sripa, P.; Tongraar, A.; Kerdcharoen, T. J. Phys. Chem. A 2013,117, 1826–1833. [32] Tongraar, A.; Liedl, K. R.; Rode, B. M. J. Phys. Chem. A 1998,102, 10340–10346. [33] Carrillo-Tripp, M.; Saint-Martin, H.; Ortega-Blake, I. The J. Chem. Phys. 2003,118, 7062–7073. [34] Ma, H. Int. J. Quantum Chem. 2014,114, 1006–1011. [35] Chandrasekhar, J.; Spellmeyer, D.; Jorgensen, W. J. Am. Chem. Soc. 1984,106, 903–910. [36] Gaiduk, A. P.; Zhang, C.; Gygi, F.; Galli, G. Chem. Phys. Lett. 2014, 604, 89–96. [37] Bankura, A.; Carnevale, V.; Klein, M. L. Molecular Physics 2014,112, 1448–1456. 1.1. BIBLIOGRAPHY 13 [38] Faginas-Lago, N.; Lombardi, A.; Albert´ı, M.; Grossi, G. J. Mol. Liq. 2015,204, 192–197. [39] Spangberg, D.; Hermansson, K. J. Phys. Chem. 2004,120, 4829–4842. [40] Azam, S. S.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Phys. Chem. 2009,113, 1827–1833. [41] Pham, V.; Fulton, J. L. J Chem. Phys. 2013,138, 044201. [42] D’Angelo, P.; Persson, I. Inorg. Chem 2004,43, 3543–3519. [43] Fan, Q.; Tanaka, M.; Tanaka, K.; Sakaguchi,; Takahashi, Y. Geochim. Cosmochim. Acta 2014,135, 49–65. [44] M¨ahler, J.; Persson, I. Inorg. Chem 2011,51, 425–438. [45] Ikeda, T.; Boero, M. J. Chem. Phys. 2012,137, 041101(1)–041101(4). [46] Lee, S. H.; Rasaiah, J. C. J. Chem. Phys. 1994,101, 6964–6974. [47] San-Rom´an, M. L.; Hern´andez-Cobos, J.; Saint-Martin, H.; OrtegaBlake, I. Theor. Chem. Acc. 2010,126, 197–211. [48] Pfund, D. M.; Darab, J. G.; Fulton, J. L.; M, Y. J. Phys. Chem. 1994, 98, 13102–13107. [49] Deublein, S.; Reisser, S.; Vrabec, J.; Hasse, H. J. Phys. Chem. B 2012, 116, 5448–5457. [50] Harris, D. J.; Brodholt, J. P.; Sherman, D. M. J. Chem. Phys. B 2003, 107, 9056–9058. [51] Seward, T.; Henderson, C.; Charnock, J.; Driesner, T. Geochim. Cosmochim. Acta 1999,63, 2409–2418. [52] Persson, I.; Sandstrom, M.; Yokoyama, H.; Chaudhry, M. Z. Naturforsch 1995,50a, 21–37. 14 CHAPTER 1. INTRODUCTION [53] Caminiti, R.; Misinu, A.; Paschina, G.; Pinna, G. J. Appl. Cryst. 1982, 15, 482–487. [54] Parkman, R. H.; Charnock, J. M.; Livens, F.; Vaughan, D. J. Geochim. Cosmochim. Acta 1998,62, 1481–1492. [55] Ramos, S.; Neilson, G.; Barnes, A.; Capit´an, M. J. Chem. Phys. 2003, 118, 5542–5546. [56] Hofer, T.; Randolf, B.; Rode, B. J. Phys. Chem. B 2006,110, 20409– 20417. [57] Raieri, P.; Demichelis, R.; Gale, J. D. J. Phys. Chem. C 2015,119, 24447–24458. [58] Larentzos, J. P.; Crescenti, L. J. J. Phys. Chem. 2008,112, 14243– 14250. [59] Tofteberg, T.; ¨ Ohrn, A.; Karlstr¨om, G. Chem Phys. Lett. 2006,429, 436–439. [60] Boda, A.; De, S.; Musharaf, S.; Tulishetti, S.; Khan, S.; Singh, J. J. Mol. Liq. 2012,172, 110–118. [61] Hofer, T. S.; Rode, B. M.; Randolf, B. R. Chem. Phys. 2004,312, 81–88. [62] Matsuda, A.; Mori, H. J. Solution Chem. 2014,43, 1669–1675. [63] Lindqvist-Reis, P.; Persson, I.; Sandstr¨om, M. Dalton Trans. 2006,28, 3868–3878. [64] Migliorati, V.; D’Angel, P. Inorg. Chem. 2016,55, 6703–6711. [65] Smirnov, P.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998,102, 4802–4808. [66] Rudolph, W. W.; Pye, C. C. J. Phys. Chem. 2000,104, 1627–1639. 1.1. BIBLIOGRAPHY 15 [67] Vchirawongkwin, V.; Kritayakornupong, C.; Tongraar, A.; Rode, B. Dalton Trans. 2012,41, 11889–11897. [68] Chillemi, G.; Barone, V.; D’Angelo, P.; Mancini, G.; Persson, I.; Sanna, N. J. Phys.Chem. B 2005,109, 9186–9193. [69] Akesson, R.; Pettersson, L. G. M.; Sandstr¨om, M.; Wahlgreen, U. J. Am. Chem. Soc 1994,116, 8691–8704. [70] Inada, Y.; Hayashi, H.; Sugimoto, K.; Funahashi, S. J. Phys. Chem. A1999,103, 1401–1406. [71] Spezia, R.; Duvail, M.; Vitorge, P.; Cartailler,; Tortajada, J.; Chillemi, G.; D’Angelo, P.; Gaigeot., M. J. Phys. Chem. A 2006,110, 13081–13088. [72] Angelo, P. D.; Spezia, R. Chem. Eur. J 2012,18, 11162–11178. [73] Duvail, M.; Spezia, R.; Vitorge, P. ChemPhysChem 2008,9, 693–696. [74] Villa, A.; Hess, B.; Saint-Martin, H. J. Phys. Chem. B 2009,113, 7270–7281. [75] Torapava, N.; Persson, I.; Eriksson, L.; Lundberg, D. Inorg. Chem. 2009,48, 11712–11723. [76] Rothe, J.; Denecke, M.; Neck, V.; Muller, R.; Kim, J. Inorg. Chem. 2002,41, 249–258. [77] Marjolin, A.; Gourlaouen, C.; Clavagu´era, C.; Ren, P.; Wu, J.; Gresh, N.; Dognon, J.; Piquemal, J. Theor. Che, Acc. 2012,131, 1198. [78] Carnaval, L.; Weiss, A.; Rode, B. Comput. Chem. 2013,1022, 94–102. [79] Spezia, R.; Beuchat, C.; Vuileumier, R.; D’Angelo, P.; Gagliardi, L. J. Phys. Chem. B 2012,116, 6465–6475. [80] R´eal, F.; Trumm, M.; Vallet, V.; Schimmelpfenning, B.; Masella, M.; Flament., J. J. Phys. Chem. B 2010,114, 15913–15924. 16 CHAPTER 1. INTRODUCTION [81] Yang, T.; Tsushima, S.; Suzuki, A. J. Phys. Chem. A 2001,105, 10439–10445. Chapter 2 Methods Several theoretical tools as quantum mechanical calculations, ab-initio intermolecular potentials, molecular dynamic simulations and x-ray absorption spectroscopy have been used in this work to study the ion hydration. In this section the main concepts of these techniques are briefly explained. 2.1 Quantum mechanics Quantum mechanics (QM) is a theory applicable to interpret and predict the electronic structure and reactivity of chemical systems. This implies the resolution of the Schr¨odinger equation, ˆ Hψ = Eψ. The resolution of the equation for polyelectronic systems implies the use of approximations. The most used methods are the wavefunction based ab-initio methods and the density functional methods. The simplest ab-initio method is the Hartree-Fock (HF) approach, which does not include any electron correlation except the Pauli exclusion principle, since it constructs a one–determinant electron wavefunction moving in the average field of the remaining electrons. In order to overcome this limitation the post–HF methods are used. These include different amounts of electron correlation. Among them, the MP2 method is used in this work. 17 18 CHAPTER 2. METHODS Another way to include electron correlation is based on the DFT methods which, in general are less demanding computationally. DFT computes the electron correlation energy as an estimated functional of the electron density. Its main drawbacks are due to the fact that it is a single configuration methodology, and there is not a systematic way to improve its performance. 2.1.1 Moller-Plesset second order theory The Moller Plesset perturbation theory is a post-HF method where correlation energy is included by means of the Rayleigh–Schr¨odinger perturbation theory. Møller-Plesset theory adds higher excitations to Hartree-Fock as non-iterative corrections. Moller-Plesset theory is based upon dividing the Hamiltonian into two parts, ˆ H=ˆ Ho+λV, being ˆ Hothe independent electron Hamiltonian or unperturbed Hamiltonian, V is a small perturbation and λa dimensionless parameter. The one electron Hamiltonian is defined as the sum of one electron operator, ˆ f: ˆ Ho=Xˆ f(2.1) and the perturbation is defined as the energy difference between the true molecular electronic Hamiltonian and the unperturbed Hamiltonian: V=ˆ H−ˆ Ho=X iX j>i 1 rij −X iX jˆ J−ˆ K(2.2) where ˆ J, is the exchange operator and ˆ Kis the exchange operator. When this approximation is included into the Schr¨odinger equation it implies the expansion of the energy and wavefunction of the perturbed system in powers of λ: (ˆ Ho+λV)ψ=Eλψ(2.3) 2.1. QUANTUM MECHANICS 19 E=E0+λE1+λ2E2+λ3E3+.. (2.4) Being E2the correlation energy calculated for a second order perturbation. The correlation energy is obtained from the second order expansion term: Ecorr =E2+E3+E4+.. (2.5) There are ways to minimize the cost of a Moller-Plesset calculation as the Frozen Core approximation (FC). On the FC approximation part of the occupied orbitals are constrained to remain double occupied while others are not, being included in the perturbative process.1,2 2.1.2 Density functional theory DFT3is based on two theorems of Hohenberg-Kohn. The first theorem states that the electron density, ρ, is defined for a given external potential, Vext, and hence the total energy, E, is a functional of the electron density: E(ρ) = F[ρ] + ZρVext(ˆr)dˆr(2.6) And the second theorem states that the exact electron density of a non–degenerate ground state can be calculated by determining the density that minimizes the energy of the ground state. δE(ρ) δρ = 0 (2.7) As a practical consideration the electrons are considered as non interacting particles moving under the same external potential. Being the ground state energy defined by the minimum of the Kohn-Sham equations: ˆ E(ρ) = ˆ T+ˆ Vne +ˆ Vee +Exc (2.8) 26 CHAPTER 2. METHODS statistical dynamical disorder. There are also other relevant parameters specific for the pair of atoms involved in the process, as the mean free path, λ, the amplitude reduction factor, S0, the amplitude function of the backscattered path i,Fi, and the phase shift function, δi. χ(k) = ΣNS2 0Fi(k) kR2 i sin(2kRi+δi)e−2σ2 ik2e −2Ri λ(k) (2.21) The XANES interpretation is complicated as there is not a simple analytic description. But it is known to be sensitive to the valence state of the absorber, the ligand type and the coordination geometry around the absorber atom.26,27 EXAFS and XANES spectra can be simulated using ab-initio codes, in this work the FEFF code28 has being used. FEFF uses an ab-initio self-consistent real space multiple scattering (RSMS) approach, where corehole effects are included, local field corrections and self-consistent spherical muffin-tin scattering potentials are also taken into account. EXAFS simulations in this work were carried out using the Hedin-Lundquist exchangecorrelation potential for the fine structure and for the atomic background. To remove phase differences between simulated and experimental spectra Fermi level has been slightly shifted when generating the theoretical EXAFS function in order to get of phase between the simulated and experimental spectra. XANES simulations were run using the ground state potential model considering the full multiple scattering terms. In the XANES simulation the optical absorption and the edge position has been shifted a feweV to accommodate the simulated spectra to the experimental one. It must be pointed out that FEFF carries out ab-initio computations of the ionization potential of core levels, which are in the order of thousands of eV. All the XAS simulations were performed in two steps. In the first step the backscattering potential was calculated, considering all the atoms inside an 8˚ A sphere centered on the absorber cation. For the rest of the calculation the hydrogen atoms were removed, because the backscattering capabilities of the hydrogen atoms are overestimated as found in previous works.29–31 2.4. AB-INITIO INTERMOLECULAR POTENTIALS 27 2.4 Ab-initio intermolecular potentials The ab-initio intermolecular potentials are parameterized equations that, using information from QM calculations, define the interactions among atoms and molecules. In this work the ion-water interactions have been modelled by effective pairwise site-site potentials. The first requirement to build a site-site intermolecular potential is to define the equations that rule the interactions among the different particles, these equations together with the appropiate parameters, define the called force fields. In order to model an ab-initio potential an initial set of values for the force field parameters are nedeed together a minimization algorithm and a PES to drive the parametrization process. This process ends when the difference between the ab-initio interaction energies and the calculated by the interaction potential ones is below an user defined energy threshold, standard deviation. There is not a ”magic” recipe for the configurations to be included in a PES to build an intermolecular potential. However, but the inclusion of representative structures that may adopt the system we want to study is highly required. There is not a minimum or maximum number of structures to be included in the fitting procedure but it is safe to include a representative number of them. The intermolecular potential can be refined by including situations extracted from preliminary simulations in order to include relevant information previously not taken into account. Some flexibility can be introduced in the fitting procedure by including weights on the different structures. An increase of the weight for a given structure means to priorize it in the fitting. This process implies the location of a minimum in a multidimensional space that does not guarantee the absolute minima location. Then, the assessment of the energetic properties must be analyzed, together with the structural properties of the minimum energy structures. The underestimation or overestimation of these properties on the fitting will be reflected in the computer simulation results. 28 CHAPTER 2. METHODS 2.4.1 Hydrated ion model The original implementation of the Hydrated Ion model32–34 consists of the parametrization of two interaction potentials: the interaction between the ion with its first-shell water molecules (Ion-Water 1st shell) and the interaction of the aqua ion with the bulk water molecules (Hydrated Ion Water interaction): Figure 2.1: Scheme of the HIW model where the first-shell water molecules are defined differently to the bulk ones (left) and of the exchangeable HIW model where all the water molecules are defined by the same force field (right). The HIW model allows the simulation of an aqua ion with a fixed number of first-shell water molecules that are structurally and electronically different from those bulk. In previous works33,34 the first hydration shell water molecules have been defined with the water ab-initio geometry and incorporating the charge transfer state defined by the quantum mechanical minimum structure of the aqua ion. This Hydrated Ion approach generates a realistic model to be used in the determination of several properties of the first and second hydration shells. But it is no longer valid when the residence time of the first-shell water molecules are smaller than the simulation time, i.e when first-shell water molecule release appears. 2.4. AB-INITIO INTERMOLECULAR POTENTIALS 29 In order to overcome this limitation the exchangeable HIW version of the model was proposed.35,36 iithin this new model, first-shell water molecule exchange is permitted together with a flexible and polarizable water model that allows the solvent molecule properties to be modified by the environment. Additionally, in this model the polarizability of the ion is taken into account explicitly because its no consideration leads to an overestimation of the first hydration shell rigidity. 2.4.2 Water model The MCDHO237 water model have been used throughout this work. The MCDHO2 water molecules are described as flexible and polarizable and the potential has been built parametrizing the single molecule dipole, quadrupole, polarizability, the monomer deformation energy and the theoretical limit of dimerization energy at the MP2/aug-cc-pVQZ’ level. The MCDHO2 water model is a reparametrization of the MCDHO38 water model where the water mobility has been improved. As can bee seen in the Table 2.1 both models give a good picture of the water molecule in gas phase and in solution. Table 2.1: Water model properties Phase Properties Experimental38 MCDHO38 MCDHO2 ROH (˚ A) 0.9572 0.9590 0.9585* Gas θHOH (◦) 105.44 104.52 103.99* ~µ (D) 1.870 1.8494 1.8671* ROH (˚ A) 0.970 0.982 0.98337 Liquid θHOH (◦) 106.1 102.7 103.337 ~µ (D) 2.9 2.94 2.8937 D (10−5cm2/s) 2.4 1.16 1.837 * this work 30 CHAPTER 2. METHODS The water molecule is defined by its three positive charged nuclei (ZO and ZH) and a negative mobile charge density (q): Figure 2.2: Schematic representation of a MCDHO/MCDHO2 water molecule The polarizability of the water molecule is modeled by a harmonic function connecting the mobile charge density and the oxygen nucleus: Uk=1 2k·r2(2.22) The mobile charge is defined as a Gaussian charge distribution having a decaying constant λ: ρ(r) = q πλ3e−2r λ(2.23) The oxygen-hydrogen bond flexibility is defined by a Morse potential: UdOH =DOH e−2γ(Rβ−re)−2e−γ(Rβ−re)(2.24) The water internal angle is defined by a quartic function: UΘHOH = a1(Θ −Θe)+a2(Θ −Θe)2+ a3(Θ −Θe)3+ a4(Θ −Θe)4(2.25) 2.4. AB-INITIO INTERMOLECULAR POTENTIALS 31 The internal energy of a water molecule is then given by the addition of all the previous contributions: Uinternal =1 2kr2 O+Z2 H R1,2 +qZH rβh1−rβ λ+ 1e−2rβ/λi+Uk+UdOH1+UdOH2+UΘHOH (2.26) The energy of a cluster of Nwater molecules is defined by a LennardJones potential for the interactions among oxygen and hydrogen atoms and mobile charges of the different solvent molecules. Utotal = N X n=1 n−1 X m=1 A rnm 12 −B rnm 6 +q2 rnm +qZβ rnβ h1−rnβ λ+ 1e−2rnβ/λi + q X β∈mAαβ rαβ 12 −Bαβ rβα 6 +Zαβ rαβ (2.27) MCDHO2 force field parameters are given in section 3.12. In a previous Thesis12 of the group an energetic gap between the MCDHO and the M062x/def2-TZVPP was found in scans of water dimers with particular orientations and distances (see Figure 2.3). A maximum energy discepancy of 2 kcal/mol was established. Aggregates with distances below this limit are excluded. The study for the MCDHO2 carried out in this work reveals minimum distances collected in Table 2.2. It can be seen that the MCDHO2 is less restrictive with respect the hydrogen-hydrogen distances. An energy gap between the M062x/def2-TZVPP level and the MCDHO2 for first-shell ion-dipole configurations has been found. This gap depends on the QM level and on the distance between the water molecules. The energy error becomes higher for shorter water-water distances what introduces a bias in the coordination number. As a normal rule, for a given cation higher coordination numbers have slightly longer metal-ligand distances but the inter-ligand distance shortens, i.e. steric repulsion between 32 CHAPTER 2. METHODS Figure 2.3: Water dimer scans employed in the filter criteria. 2.4. AB-INITIO INTERMOLECULAR POTENTIALS 33 Table 2.2: MCDHO and MCDHO2 filter criteria Properties MCDHO criteria12 MCDHO2 criteria ROO (˚ A) 2.22 2.34 ROH (˚ A) 1.64 1.42 RHH (˚ A) 2.30 2.00 ligands increases with the coordination number. As shown in Figure 2.4, when the cation is removed from an optimized hydrated ion cluster and a symmetric scan for all the water molecules approaching the centroid is carried out, i.e. the former position of the cation, the water model gives more repulsive energies, and this energy difference increases when water molecules approach each other. This problem has been found to mainly affect trivalent and tetravalent hydrates. This energy difference is clearly detected when an aqua ion of a given coordination is fitted and the derived potential is used to check another coordination. Obviously it is possible to reduce the standard deviation of the fitting involving more than one coordination, but this leads to unnappropiate effects in the structural properties. As shown in the original MCDHO2 water model work37 up to a 6 % larger metal-oxygen distance can be expected. This energy error was very similar for all the QM levels used and the water model. Also it was found that when using the MP2 level the error decreases when increasing basis set size, being the gap smaller when is used the same quantum level employed in the water model parametrization (MP2/aug-cc-pVQZ’). Due to the high quantum-mechanical level used in the water model building, it was not possible to compute the hydrated ion clusters at the same level in order to reduce the energy gap. 34 CHAPTER 2. METHODS Figure 2.4: Interaction energy difference (∆E = EQM-EPot) between the quantum-mechanical energy at the M062x/def2-TZVVP level and MCDHO2 potential energy function for water clusters in ion-dipole configuration corresponding to thullium optimized hydrates as a function of distance to the centroid position. 2.4.3 Ion-water model The modelization of the ion-water interactions is based on the MCDHO2 scheme, which is composed by a water molecule formed by three sites (O, H and q) and the ion defined as a ”core ion” (ZM) and a mobile charge density (qM). The charge values of ZMand qMguarantee the desired net charge. The constant associated to the harmonic function of the mobile charge of H2O or the Mn+defines either their molecular solvent or cation polarizability (Equation 2.22). In the case of the ion the value was chosen to reproduce its experimental molar refractivity.39 In Table 2.3 are shown the experimental values used of molar refractivity and the calculated ”spring” constant. 2.4. AB-INITIO INTERMOLECULAR POTENTIALS 35 Figure 2.5: Schematic representation of the ion Table 2.3: Spring constants based on experimental polarizability Properties qIon qmobile R∞(10−6m2/mol)39 krexp (h/bohr) Li+2 -1 0.08 4.67282 Na+2 -1 0.65 0.575250 K+3 -2 2.71 0.551890 Rb+3 -2 4.10 0.364708 Cs+3 -2 6.89 0.217025 Sr2+ 5 -3 2.65 1.269662 Ba2+ 5 -3 5.17 0.650790 Co2+ 5 -3 2.05 1.641271 The ion polarizability, α, can be defined by the experimental value of the molar refractivity, R∞39 : α=3 π4NA R∞(2.28) The spring constant kris defined by the ion polarizability and the charge value q: α=q2 kr (2.29) 42 CHAPTER 2. METHODS [14] Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005,7, 3297– 3305. [15] Rappoport, D.; Furche, F. J. Chem. Phys. 2010,133, 134105(1)– 134105(11). [16] Fujiwara, T.; Mori, H.; Mochizuki, Y.; Osanai, Y.; Miyoshi, E. Chem. Phys. Lett. 2011,510, 261–266. [17] Fujiwara, T.; Mori, H.; Mochizuki, Y.; Takewaki, H.; Miyoshi, E. J. Mol. Struct. 2010,949, 28–35. [18] Yang, J.; Dolg, M. Theor. Chem. Acc. 2005,113, 212–224. [19] Tomasi, J.; Mennucci, B.; Camini, R. 2005,5, 2999–3094. [20] Alder, B.; Wainwright, T. J Chem. Phys. 1959,31, 459. [21] Swope, W.; Andersen, H.; Berens, P.; Wilson, K. J. Chem. Phys. 1982, 76, 637–649. [22] Nos´e, S. J. Chem. Phys. 1984,81, 511–519. [23] Hoover, W. G. Phys. Rev. A 1985,31, 1695–1697. [24] Mu˜noz-P´aez, A.; S´anchez Marcos, E. En Comprehensive Inorganic Chemistry {II}(Second Edition), second edition ed.; Poeppelmeier, J. R., Ed.; Elsevier: Amsterdam, 2013; p´ags. 133 – 159. [25] Rehr, J.; Albers, R. Rev. Mod. Phys. 2000,72. [26] Koningsberg, D. C.; Prins, R. X-ray absorption, principles, aapplication, techniques of EXAFS, SEXAFS and XANES.; Wiley: New York, 1988. [27] Bianconi, A.; Dell’Aricia, M.; Durham, P. J.; Pendry, J. B. Phys. Rev. B1982,26, 6502–6508. 2.5. BIBLIOGRAPHY 43 [28] Rehr, J. J.; Kas, J. J.; Vila, F. D.; Prange, M. P.; Jorissen, K. Phys. Chem. Chem. Phys. 2010,12, 5503–5513. [29] Palmer, B.; Pfund, D.; Fulton, J. J. Phys. Chem. 1996,100, 13393– 13398. [30] Campbell, L.; Rehr, J.; Schenter, G.; McCarthy, M.; Dixon, D. J. Synchrotron Radiat. 1999,6. [31] Merkling, P. J.; Mu˜noz-P´aez, A.; S´anchez Marcos, E. J. Am. Chem. Soc. 2002,124, 10911–10920. [32] Pappalardo, R.; S´anchez-Marcos, E. J. Phys. Chem. 1993,97, 4500– 4504. [33] Mart´ınez, J. M.; Pappalardo, R. R.; S´anchez Marcos, E. J. Chem. Phys. 1998,109, 1445–1455. [34] Mart´ınez, J.; Pappalardo, R.; S´anchez Marcos, E. J. Am. Chem. Soc. 1999,121, 3175–3184. [35] Galbis, E.; Hern´andez-Cobos, J.; den Auwer, C.; Naour, C. L.; Guillaumont, D.; Simoni, E.; Pappalardo, R. R.; S´anchez Marcos, E. Angew. Chem. Int. Ed. 2010,22, 3811–3815. [36] Galbis, E.; Hern´andez-Cobos, J.; Pappalardo, R. R.; S´anchez Marcos, E. J. Chem. Phys. 2014,140, 214104. [37] Villa, A.; Hess, B.; Saint-Martin, H. J. Phys. Chem. B 2009,113, 7270–7281. [38] Saint-Martin, H.; Hern´andez-Cobos, J.; Bernal-Uruchurtu, M. I.; Ortega-Blake, I.; Berendsen, H. J. C. J. Chem. Phys. 2000,113, 10899–10912. [39] Marcus, Y. Ion properties; Markel Dekker, Inc, 1997. [40] Zhao, Y.; Truhlar, D. Chem. Phys. Lett. 2011,502, 1–13. Chapter 3 Intermolecular potentials In this section the results of the potential fitting are shown. In order to assess the fitting quality, the interaction energy and the metal-oxygen average distance of the quantum mechanical structures and those given by the potential are compared. The interaction energy has been calculated as the energy difference between the hydrated cluster energy and the energy of its isolated components at its minimum energy geometry. Eint = E[M(H2O)n]m+−(EMm++ nEH2O) (3.1) The notation origin of the geometry used//quantum level employed in the calculation is used: if the structure is optimized at a quantum mechanical level the label is QM//QM, Pot//QM denotes single point calculations using the classical potentials over the QM structure, and Pot//Pot denotes optimized structures with the potential. Structures with water molecules in the first (i) and second shell (j) are defined as [i+j] structures. To describe the calculation level the notation Level/Basis set is used, that is refered to the quantum mechanical method and the basis set used for the ion, oxygen and hydrogen, respectively. If a pseudopotential is used for the metal it will be detailed in the corresponding section. 45 46 CHAPTER 3. INTERMOLECULAR POTENTIALS 3.1 Alkaline group The alkaline group from lithium to caesium has been studied. The intermolecular potential has been built at the M062x/def2-TZVPPD level using an already generated1Potential Energy Surface (PES) together with new sets of structures for K+, Rb+and Cs+. For Rb+and Cs+the ECP28MBW2and the ECP46MBW2effective core pseudopotentials (ECP) have been employed, respectively, together with the def2-TZVPPD basis set to describe the valence electrons (8 electrons that are filling the s and p orbitals of higher energy). 3.1.1 Light alkalines Lithium-water and sodium-water intermolecular potentials were built using inner cluster structures with 3-5 water molecules in the first hydration shell and up to 5 water molecules in the second shell for lithium. For sodium, clusters including 4-6 water molecules in the first hydration shell and up to 4 water molecules in the second shell were used. In the case of lithium the ion was not considered polarizable. The hard character of this small cation justifies this option. Moreover, a polarizable Li+ion would force the use of a spring constant extremely high that would need an extremely short timestep for MD simulations. The optimized lithium tetrahydrate has been calculated at the MP2/augcc-pVTZ level. An interaction energy of -102.4 kcal/mol and an average intermolecular ion-distance of 1.96 ˚ A were obtained. Similar interaction energies were found in previous theoretical works, at the MP2/6311++G(3d,3p)3level counterpoisse corrected -100.4 kcal/mol, at a MP2/6311++G(2d,2p)//MP2/6-31+G(d,p)4calculation -99.9 kcal/mol and at the MP2/6-31G*//RHF/6-31+G*5a binding energy at 298 K of -98.6 kcal/mol. These values are similar to those obtained at the M062x/def2TZVPPD, where the interaction energy is -107.4 kcal/mol and the interatomic distance is 1.92 ˚ A. 3.1. ALKALINE GROUP 47 Sodium hexahydrate at the MP2/aug-cc-pVTZ level has an interaction energy of -95.4 kcal/mol and an intermolecular distance of 2.50 ˚ A. A larger interaction energy was found for the hydrate at the M062x/def2-TZVPPD level, -107.7 kcal/mol with a metal-oxygen distance equals to 2.38 ˚ A. Gledening et al.5found a binding energy at 298 K of -91.2 kcal/mol for the sodium hexahydrate at the MP2/6-31+G*//HF/6-31+G* level. As can be seen in Table 3.1, there is a good energetic and structural agreement of the most usual coordinations in solution, being the Lithium 4+1 structure more stable than the pentahydrate in the case of the potential. Also there is a good reproduction of the entire set of structures included in the fitting (see Figures 3.6 and 3.7) obtaining a mean error of 1.9 kcal/mol and 2.7 kcal/mol for lithium and sodium, respectively, with the obtained force field parameters (see Table 3.13). Table 3.1: Energies (kcal/mol) and distances (˚ A) of Li+and Na+hydrates. Structure QM//QM QM//Pot Pot//Pot RQM RPot Li(H2O)3+-89.4 -91.7 -92.6 1.88 1.86 Li(H2O)4+-107.4 -107.6 -108.6 1.92 1.93 Li(H2O)5+-118.1 -114.0 -122.6* 2.02 4x1.93/1x3.63 Na(H2O)4+-80.1 -81.7 -82.3 2.28 2.28 Na(H2O)5+-93.5 -93.0 -94.5 2.36 2.35 Na(H2O)6+-107.5 -102.6 -105.4 2.38 2.38 *4+1 structure 3.1.2 Heavy alkalines An initial intermolecular potential with inner cluster structures was built for the heavy alkalines potassium, rubidium and caesium. These potentials systematically overestimated the cation-oxygen distance in solution. When surface clusters were included in the set of structures to fit the new potentials represented much better the experimental properties of these ions in 48 CHAPTER 3. INTERMOLECULAR POTENTIALS water. The surface clusters were generated running a gas phase MD simulation at 100 K of hydrates containing from 7 to 10 water molecules. From these simulations 50 equidistant structures were extracted, and optimized classically. The 5 structures having lower energies were optimized at the quantum mechanical level and added to the set of structures to be used in the fitting. In addition, the 10 lowest energy structures optimized classically are included in the training set. Figure 3.1 and 3.2 show the Rb+clusters belonging to inner and surface clusters for coordination numbers 8 and 9. Figure 3.1: Rb+octahydrate minimum structures, inner (left) and surface cluster (right). In Table 3.2 the interaction energy values of the minimum energy structures of potassium, rubidium and caesium hydrates are displayed. In Figures 3.3, 3.4 and 3.5 shown a normalized histogram (normalized by the maximum amount of structures in a given range) of the interaction energy values of the structures included in the fitting. It can be seen that the interaction energy for potassium surface cluster structures with coordination 7 and 8 have similar energies to the lower energy of inner aggregates. However, this is not the case for Rb+and particularly for Cs+. For these 3.1. ALKALINE GROUP 49 Figure 3.2: Rb+enneahydrate minimum structures, inner (left) and surface cluster (right). two cations surface clusters are more stable. Table 3.2: QM interaction energy for surface and inner minimum energy structures (kcal/mol) of heavy alkalines. Structure inner structure surface structure K(H2O)7+-103.4 -102.9 K(H2O)8+-115.1 -116.9 Rb(H2O)8+-108.9 -113.3 Rb(H2O)9+-114.0 -126.1 Cs(H2O)8+-105.8 -107.1 Cs(H2O)9+-109.2 -118.3 The lowest energy structures for K+, Rb+and Cs+with 7, 8 and 9 water molecules, respectively, have been optimized at the MP2/aug-cc-pVTZ level obtaining interaction energies of -93.2 kcal/mol, -99.3 kcal/mol and -127.7 kcal/mol (at MP2(full)/aug-cc-pVTZ), respectively are similar values to those obtained at the M062x/def2-TZVPPD level, -102.9 kcal/mol, -113.3 kcal/mol and -118.3 kcal/mol for the same type of structures. 50 CHAPTER 3. INTERMOLECULAR POTENTIALS Figure 3.3: Energy distribution of K+heptahydrate (left) and octahydrate (right). Figure 3.4: Energy distribution of Rb+octahydrate (left) and enneahydrate (right). 3.1. ALKALINE GROUP 51 Figure 3.5: Energy distribution of Cs+octahydrate (left) and enneahydrate (right). The rubidium and caesium fittings were performed using hydrated clusters from 6 to 10 water molecules in the first-shell, and up to 2 water molecules in the second shell for inner cluster structures. In the case of potassium structures with coordination number from 4 to 10 were employed, with up to 2 water molecules in the second shell for the inner cluster structures. The new potentials were performed including the surface cluster structures and reparametrizing the previous potential without any constraint. The inclusion of surface cluster structures in the fitting provoqued a shortening of the intermolecular distances, as can be see in Table 3.3 and 3.4. On the fittings a good energetic reproduction has been found, having a fitting sigma error of 2.2 kcal/mol, 1.9 kcal/mol and 1.6 kcal/mol (see Figures 3.8, 3.9 and 3.10) for K+, Rb+and Cs+, respectively (see 3.13). 58 CHAPTER 3. INTERMOLECULAR POTENTIALS kcal/mol, whereas the QM/QM energy is -539.3 kcal/mol). Pot4 and Pot8 are just two more extreme situations, in Pot4 the EP ot I−Wcompensation is the smallest one whereas in the Pot8 is the biggest. Thus, Table 3.9 collects for the Sc(H2O)63+ an interaction energy of -527.5 kcal/mol given Pot4//QM and -5606.5 kcal/mol given by Pot8//QM. MCDHO2 model was built at the MP2/aug-cc-pVQZ’ level with a correction of the 50% of the BSSE. When the calculation of the (H2O)6is performed at the MP2/aug-cc-pVQZ’ level the interaction energy turns to be 17.2 kcal/mol, and when is added a 50% correction of the BSSE the interaction energy is 17.7 kcal/mol. Thus, one factor responsible of the energy difference is related to the different calculation condition and other factor could be the parametrization of the ion-dipole configurations existing in the hydration shells of highly polarizing cations, as the Sc3+ case is. The potential was performed for each coordination number because when the fitting of two coordinations was tried, simultaneously simultaneously forcing to reproduce the Eint of both coordinations the ion-water distance increases a 15%. In the way the scandium potentials have been built the fitted coordination has been well reproduced (see Figure 3.14, 3.15, 3.16 and 3.17) having a sigma error of 0.8 kcal/mol, 1.3 kcal/mol, 1.1 kcal/mol and 0.8 kcal/mol, for Pot6, Pot7, Pot4 and Pot8, repectively (see Table 3.15). In spite of this water model limitation we were able to build a potential that describes quite well the coordination fitted. Being the main problem the energy understimation of higher coordinations. An illustrative way to quantify this problem, can be seen in the Pot6 section of Table 3.9. The interaction energy for Sc(H2O)63+(H2O) using the MP2/aug-cc-PVTZ level is 4 kcal/mol more stable than Sc(H2O)73+, but in Pot//Pot6 gives a difference of 16 kcal/mol. Although the energy difference increases, this does not modify that the Sc(H2O)63+(H2O) is more stable than the Sc(H2O)73+. Although this comparison should not be taken as the way to evaluate the most probable coordination, because in Sc(H2O)63+(H2O) the second shell water molecule 3.4. LANTHANIDES 59 Table 3.9: Energies (kcal/mol) and distances (˚ A) of Sc3+ hydrates. Structure QM//QM Pot4//QM Pot4//Pot4 RPotQM RPot4 Sc(H2O)63+ -539.3 -527.5 -531.4 2.18 2.18 Sc(H2O)63+(H2O) -574.2 -555.7 -564.7 6x2.24/1x4.181 6x2.18/1x4.32 Sc(H2O)73+ -570.5 -542.1 -547.4 2.23 2.26 Sc(H2O)73+(H2O) -606.2 -572.3 -594.6* 7x2.21/1x4.043 6x2.14/2x4.08 Sc(H2O)83+ -601.0 -560.4 -595.3* 2.28 6x2.17/2x3.91 Structure QM//QM Pot6//QM Pot6//Pot6 RPotQM RPot6 Sc(H2O)63+ -539.3 -539.4 -543.1 2.18 2.18 Sc(H2O)63+(H2O) -574.2 -566.8 -576.5 6x2.24/1x4.18 6x2.18/1x4.32 Sc(H2O)73+ -570.5 -554.7 -559.7 2.23 2.25 Sc(H2O)73+(H2O) -606.2 -585.4 -606.5* 7x2.21/1x4.043 6x2.17/2x4.12 Sc(H2O)83+ -601.0 -573.9 -607.3* 2.28 6x2.17/2x3.90 Structure QM//QM Pot7//QM Pot7//Pot7 RPotQM RPot7 Sc(H2O)63+ -539.3 -554.1 -557.8 2.18 2.17 Sc(H2O)63+(H2O) -574.2 -580.6 -591.3 6x2.24/1x4.18 6x2.17/1x4.31 Sc(H2O)73+ -570.5 -570.5 -607.2 2.23 2.25 Sc(H2O)73+(H2O) -606.2 -601.6 -621.5* 7x2.21/1x4.04 6x2.17/1x4.31 Sc(H2O)83+ -601.0 -590.6 -622.5* 2.28 6x2.16/2x3.90 Structure QM//QM Pot8//QM Pot8//Pot8 RPotQM RPot8 Sc(H2O)63+ -539.3 -566.5 -570.8 2.18 2.15 Sc(H2O)63+(H2O) -574.2 -591.0 -604.6 6x2.24/1x4.18 6x2.15/1x4.30 Sc(H2O)73+ -570.5 -581.9 -586.4 2.23 2.23 Sc(H2O)73+(H2O) -606.2 -613.8 -634.9 7x2.21/1x4.04 6x2.15/1x4.10 Sc(H2O)83+ -601.0 -601.3 -635.8* 2.28 6x2.14/2x3.88 *[6+2] structure forms two hydrogen bonds with first-shell water molecules, something that does not and this not happen in solution, then overestimating its interaction. 3.4 Lanthanides The Lanthanide potentials has been built using M06 family functionals together with the def2-TZVPP basis set for oxygen and hydrogen. The Lanthanum PES was calculated during a previous work1at the M06/def2TZVPP level using the ECP46MBW16,17 pseudopotential and ECP46MBW- 60 CHAPTER 3. INTERMOLECULAR POTENTIALS I basis set for the ion. The neodymium and thullium PES were built at the M062x/def2-TZVPP level using the pseudopotentials ECP49MWB16,17 and ECP58MWB,16,17 respectively. In these pseudopotentials the f electrons are included in the core, with 8 valence electrons occuping the higher energy s and p orbitals, that are described by the ECP49MWB-I and ECP58MWB-I basis sets. In a published work at the the MP2 level,18 where the spMCP-dzp basis for Oxygen and the cc-pVDZ for hydrogen were used an interaction energy of -509.2 kcal/mol and an interatomic distance of 2.63 ˚ A for the lanthanum enneahydrate were found. Similar values were provided by the M06/def2-TZVPP1description: interaction energy of -493.2 kcal/mol and interatomic distance of 2.631 ˚ A. Dolg and collegues19 computed the binding energy taking into account the water cluster energy as monomer, and considering the ZPE correction and including the COSMO solvation model in the calculation, given a value of -406.6 kcal/mol, -426.7 kcal/mol and -461.8 kcal/mol and an average MO distance of 2.591, 2.534 and 2.378 ˚ A for the lanthanum and neodymium enneahydrates and thullium octahydrate. For the thullium octahydrate at the MP2/aug-cc-pVTZ level, an interaction energy of -532.0 kcal/mol and an intermolecular distance 2.39 ˚ A is found, which are similar values to those obtained at the M062x level: interaction energy of -556.6 kcal/mol and interatomic distance of 2.38 ˚ A. For the Neodymium enneahydrate at the MP2/aug-cc-pVTZ level, the interaction energy is -509.8 kcal/mol and the interatomic distance 2.54 ˚ A, similar to the interaction energy of -529.0 kcal/mol with interatomic distance of 2.55 ˚ A found at the M062x/def2-TZVVP. The fittings were performed using the minimum energy structure, a water extraction from the cluster, rotated scans, structures from normal modes of vibrations and structures with a first-shell and a partial second shell with first-shell coordinations between 7 and 8 for thullium and struc- 3.4. LANTHANIDES 61 tures with coordination numbers of 8 and 9 for lanthanum and neodymium, and up to 2 water molecules in the second shell for all the cations. As in the scandium case there is a water model effect that limits the quality of the fittings when the first-shell water molecules have shorter distances among them and when there is more than one coordination to fit. Differently from the scandium case, for the lanthanoids there are more than one coordination number included in the fitting as this pathology has less impact on the fit. In this case the fitting has been performed in two steps. In the first step the most probable coordination, 8 for thulium and 9 for neodymium and lanthanum, have been fitted. At that point the force field exponentials terms Uinter(qO, qM) and Uinter(Zi, ZM) were fixed, and the rest of the structures with other coordination numbers being added to get the final reparametrization. As can be seen in Figures 3.20, 3.21 and 3.22 all the structures are not well reproduced. The main coordination fitted 8 in thullium and 9 in neodymium and lanthanum are well fitted. Meanwhile the lower coordinations 7 in thullium and 8 in neodymium and thullium are overestimated. The general sigma errors for the fitting are 4.3 kcal/mol, 2.8 kcal/mol and 4.4 kcal/mol for thullium, neodymium and thullium, respectively. As can be seen in Table 3.10 there is a good agreement in the energy and structural properties for the main coordination numbers fitted, and the energetic bias explained in the previous section is observed. For higher coordinations is obtained an energy underestimation and for lower coordinations an overestimation. Anyway the structural properties are well reproduced for all coordinations. 62 CHAPTER 3. INTERMOLECULAR POTENTIALS Table 3.10: Energies (kcal/mol) and distances (˚ A) of La3+, Nd3+ and Tm3+ hydrates. Structure QM//QM Pot//QM Pot//Pot dQM dPot La(H2O)83+ -464.4 -467.8 -472.1 2.59 2.59 La(H2O)82+(H2O) -494.3 -494.6 -499.2 8x2.59/1x4.41 8x2.59/1x4.40 La(H2O)93+ -493.2 -491.3 -495.5 2.62 2.63 Nd(H2O)83+ -498.7 -506.4 -509.7 2.52 2.52 Nd(H2O)82+(H2O) -529.8 -533.3 -537.3 8x2.51/1x4.35 8x2.51/1x4.34 Nd(H2O)93+ -529.0 -528.3 -532.0 2.55 2.56 Tm(H2O)73+ -518.2 -527.8 -532.0 2.35 2.34 Tm(H2O)73+(H2O) -553.8 -558.8 -563.5 7x2.35/1x4.14 7x2.34/1x4.15 Tm(H2O)83+ -556.3 -555.3 -559.0 2.38 2.38 Tm(H2O)83+(H2O) -588.1 -583.1 -583.1 8x2.38/1x4.24 8x2.38/1x4.23 Tm(H2O)93+ -583.2 -569.2 -585.9* 2.43 8x2.38/1x4.16 *[8+1] structure 3.5 Actinide 3.5.1 Thorium The thorium potential was built at the M062x/def2-TZVPP level employing the ECP78MWB20 and the basis set ECP78MWB-AVTZ on the cation. In this ECP 78 electrons are included in the core and the valence electrons are filling the higher energy s and p orbitals. In previous study at the B3LYP/6-31G*21 level an interaction energy of -785.0 kcal/mol was found and in other at the MP2/cc-pVTZ22 was found an interaction energy of -786.6 kcal/mol. This work found an interaction energy of -832.1 kcal/mol and an interatomic distance of 2.51 ˚ A. In the building of the thorium-water potential, as in the case of scandium and lanthanoids, limitations were experimented. The potential was built following the same process performed in the lanthanoid case, i.e. including coordination numbers from 9 to 10 in a fitting step-by-step process. First of all, the most probable coordination, 9, is included in the fitting, in a second step the coordination 10 is included keeping the exponencial param- 3.5. ACTINIDE 63 eters of the force field fixed. Structures with 9 and 10 water molecules in the first hydration shell, including the minimum structure, water extractions, structures from normal modes of vibration, rotated scans and structures with a first hydration shell and a partial second shell were employed. As can be seen in Figure 3.23 there is not a well reproduction of the whole set of points, as we have a sigma error of 7.7 kcal/mol. In Figure 3.23 shows how decacoordinated and ennea-coordinated structures lie on either side of the perfect fitting line (red line), meaning a systematic underestimation on the decacoordinated structures and a systematic overestimation of the ennea-coordinated structures. Even though this uncertainty in the fitting can be seen in Table 3.11 that the interaction energy values obtained with the potential are similar to the quantum values and there is a good structural agreement with the obtained force field parameters (see Table 3.17). Table 3.11: Energies (kcal/mol) and distances (˚ A) of Th4+ hydrates. Structure QM//QM Pot//QM Pot//Pot dQM dPot Th(H2O)84+ -786.7 -806.5 -811.7 2.47 2.47 Th(H2O)94+ -832.1 -840.6 -846.1 2.51 2.51 Th(H2O)94+(H2O) -874.9 -878.8 -884.9 9x2.51/1x4.29 9x2.51/1x4.31 Th(H2O)104+ -864.5 -857.6 -884.1* 2.55 9x2.51/1x4.29 *9+1 structure 64 CHAPTER 3. INTERMOLECULAR POTENTIALS 3.6 Suplementary information 3.6.1 Water model force field coefficients Harmonic constant, kM, is in H/Bohr2, electrostatic decaiment, λO, is in Bohr, distances are in Bohr and angles are in radians. Table 3.12: MCDHO2 coefficients. MCDHO2 ZH0.62 ZO2.00 qO-3.24 kO1.00 λO1.90 DOH 0.42954802 rOH 1.3440633 αOH 1.1131102 θHOH 1.927 aHOH 0.031621 bHOH 0.043914 cHOH -0.012721 dHOH -0.00866 3.6. SUPLEMENTARY INFORMATION 65 3.6.2 Ion-water force field coefficients Harmonic constant, kM, is in H/Bohr2, ion electrostatic decaiment, λ0 M, is in Bohr, pre-exponential terms are in H and exponential terms are in Bohr−1. Table 3.13: Fitted parameters of the alkaline potentials. Li+Na+K+Rb+Cs+ kM4.672820 0.575250 0.551890 0.217025 0.364708 λ0 M0.368792 0.261673 0.515188 0.621742 0.995166 AMO 44.103664 134.158515 388.755193 539.102465 449.494649 αMO 2.659083 2.198363 1.636593 1.357374 1.413723 BMO -0.048328 -1.147140 -249.062663 -383.448443 -362.094604 βMO 0.485383 1.169133 1.548374 1.293485 1.371814 CMH 0.032213 0.027106 1072.600533 1857.808870 1776.523448 γMH 0.635698 1.750888 1.547942 0.857618 0.834310 DMH -0.000702 -0.000009 -1076.366645 -1859.064561 -1776.616635 δMH 5.745071 0.045655 1.549057 0.857790 0.834339 Table 3.14: Fitted parameters of the alkaline-earth potentials. Sr2+ Ba2+ Ra2+ kM1.269662 0.650790 1.000000 λ0 M0.414399 0.435619 0.554093 AMO 277.432810 205.594587 248.886579 αMO 1.560342 1.445294 1.474152 BMO -162.291509 -88.434493 -88.710280 βMO 1.454231 1.289500 1.294386 CMH 53.495873 79.272175 105.444582 γMH 2.603508 3.226664 2.628450 DMH 0.000038 0.000048 0.000045 δMH 1.415779 1.574448 1.256433 66 CHAPTER 3. INTERMOLECULAR POTENTIALS Table 3.15: Fitted parameters of the scandium potentials. Sc3+ Pot 6 Sc3+ Pot 7 Sc3+ Pot 4 Sc3+ Pot 8 kM1.600000 1.600000 1.600000 1.600000 λ0 M0.490671 0.531754 0.517506 0.500254 AMO 100.036705 94.717791 101.098026 100.036705 αMO 1.916500 1.880000 1.933011 1.916500 BMO -1.357411 -1.942813 -1.038266 -1.865932 βMO 1.060138 1.060138 1.079167 1.060138 CMH 66.066941 69.396867 65.840777 67.391159 γMH 5.714136 6.005367 5.694794 5.885833 DMH 0.001121 0.001132 0.001118 0.001143 δMH 2.777914 2.919571 2.795934 2.833474 Table 3.16: Fitted parameters of the transition metal potentials. Co2+ Cd2+ kM1.000000 1.000000 λ0 M0.501619 0.591948 AMO 100.027184 110.325440 αMO 1.407187 2.044628 BMO -75.696036 -0.097990 βMO 1.335787 0.434356 CMH 6.380953 69.896007 γMH 7.111711 8.171032 DMH 0.001844 0.001516 δMH 3.720043 3.766755 3.6. SUPLEMENTARY INFORMATION 67 Table 3.17: Fitted parameters of the Lanthanide and Actinide potentials. La3+ Nd3+ Tm3+ Th4+ kM1.011070 1.050000 1.120000 1.050000 λ0 M0.506308 0.353208 0.362722 0.423617 AMO 165.681078 322.805834 132.738900 354.010287 αMO 1.422303 1.451632 1.800000 1.960000 BMO -76.695518 -219.290154 -6.782221 -0.938932 βMO 1.280927 1.376586 1.196806 0.816922 CMH 46.872467 49.845695 2.793025 40.492113 γMH 4.463182 2.804860 4.324097 3.680997 DMH 0.001724 0.000034 0.001460 0.000036 δMH 3.362880 1.228342 2.849904 1.545206 3.6.3 Global energetic fitting comparison Figure 3.6: Li+fitting. 74 CHAPTER 3. INTERMOLECULAR POTENTIALS Figure 3.19: Cd2+ fitting. Figure 3.20: La3+ fitting. 3.6. SUPLEMENTARY INFORMATION 75 Figure 3.21: Nd3+ fitting. Figure 3.22: Tm3+ fitting. 76 CHAPTER 3. INTERMOLECULAR POTENTIALS Table 3.18: Fitting error Ion σerror Li+1.9 Na+2.7 K+2.2 Rb+1.9 Cs+1.6 Sr2+ 3.5 Ba2+ 2.7 Ra2+ 3.7 Sc3+ /Pot 6/ 0.8 Sc3+ /Pot 7/ 1.3 Sc3+ /Pot 4/ 1.1 Sc3+ /Pot 8/ 0.8 Co2+ 3.2 Cd2+ 1.7 La3+ 4.4 Nd3+ 2.8 Tm3+ 4.2 Th3+ 7.7 3.7 Bibliography [1] Morales, N. Estudio te´orico de propiedades fisicoqu´ımicas de cationes met´alicos en disoluci´on: Evoluci´on en el grupo de los alcalinos y en la serie de los lant´anidos. bilio, Universidad de Sevilla, 2015. [2] Leininger, T.; Nicklass, A.; Kuchle, W.; Stoll, H.; Dolg, M.; Bergner, A. Chem. Phys. Lett. 1996,255, 274–280. [3] San-Rom´an, M. L.; Carrillo-Tripp, M.; Saint-Martin, H.; Cobos, J. H.; Ortega-Blake, I. Theor. Chem. Acc. 2006,115, 177–189. [4] Li, X.; Yang, Z. J. Phys. Chem. A 2005,109, 4102–4111. 3.7. BIBLIOGRAPHY 77 Figure 3.23: Th4+ fitting. [5] Glendening, E.; Feller, D. J. Phys. Chem. 1995,99, 3060–3067. [6] Lim, I.; Stoll, H.; Schwerdtfeger, P. J. Chem. Phys. 2006,124, 034107. [7] Kerridge, A.; Kaltsoyannis, N. Chem. Eur. J 2011, [8] Boda, A.; De, S.; Musharaf, S.; Tulishetti, S.; Khan, S.; Singh, J. J. Mol. Liq. 2012,172, 110–118. [9] Matsuda, A.; Mori, H. J. Comput. Chem. Jpn. 2014,13, 105–113. [10] Dolg, M.; Weding, U.; Stoll, H.; H.Preuss, J.Chem. Phys. 1987,86, 866–872. [11] Furukawa, K.; Ohashi, K.; Koga, N.; Imamura, T.; Judai, K.; Nishi, N.; Sekiya, H. Chem. Phys. Lett. 2011,508, 202–206. [12] Akesson, R.; Pettersson, L. G. M.; Sandstr¨om, M.; Wahlgreen, U. J. Am. Chem. Soc 1994,116, 8691–8704. [13] Huzinaga, S. 1965,42, 1293. 78 CHAPTER 3. INTERMOLECULAR POTENTIALS [14] Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990,77, 123–141. [15] Rudolph, W. W.; Pye, C. C. J. Phys. Chem. 2000,104, 1627–1639. [16] Dolg, M.; Stoll, H.; Savin, A.; Preuss, H. Theor. Chim. Acta 1989,75, 173–194. [17] Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1993,6, 441–450. [18] Fujiwara, T.; Mori, H.; Mochizuki, Y.; Takewaki, H.; Miyoshi, E. J. Mol. Struct. 2010,949, 28–35. [19] Ciupka, J.; Cao-Dolg, X.; Wiebke, J.; Dolg, M. Phys. Chem. Chem. Phys. 2010,12, 13215–13223. [20] Moritz, A.; Cao, X.; Dolg, M. Theor. Chem. Acc. 2007,118, 845–854. [21] Yang, T.; Tsushima, S.; Suzuki, A. J. Phys. Chem. A 2001,105, 10439–10445. [22] Marjolin, A.; Gourlaouen, C.; Clavagu´era, C.; Ren, P.; Wu, J.; Gresh, N.; Dognon, J.; Piquemal, J. Theor. Che, Acc. 2012,131, 1198. Chapter 4 System definition and analyzed properties In the following chapters the main results from the Molecular Dynamics simulations are shown. Simulated systems are defined by one cation and 1000 water molecules. Simulations were run using the DLPOLY1code in the NVT ensemble and with a boxlength which reproduces the water experimental density at 300K, 0.997 g/cm3. The dynamical shell model to account for the polarization,2the Ewald summation to calculate the electrostatic interactions3and periodic boundary conditions (PBC)4to approximate to bulk conditions were employed. The results are obtained from 1 ns simulation production period wich was previously equilibrated during 200-300 ps. Initial configurations come from a previous simulation of the same cation or from a similar one. The results are shown for each cation individually. At the end of the sections the evolution of some properties along the group or series are discussed. First-shell coordination number is calculated as the running integral of the first M-O peak in the RDF up to the first minimum. The coordination number of the second shell is calculated as the integration of the M-O RDF between the first and the second minima of the distribution. 1st and 2nd 79 80 CHAPTER 4. SYSTEM DEFINITION AND ANALYZED PROPERTIES shell distances are taken from M-O RDF maxima. The Debye-Waller factor (DW), an index employed in EXAFS analysis that reflects geometrical fluctuations, is considered as the second cumulant of the first-shell distances. The tilt angle, φ, is calculated as the angle between the ion-oxygen vector and the vector of the bisector of the water molecule plane. The molecular eccentricity, , was calculated by means of the equation 4.1, i.e. the distance between the metal cation position and the center of mass of the first hydration shell. This structural parameter accounts for the assymetry of the hydrated ion, i.e. the displacement of the metal ion from the mass center of the hydrate. =|~rMn+−~rCM |(4.1) The hydrogen bonds are calculated using the geometrical Chandra criteria:5R(O···H) ≤2.45 ˚ A, R(O···O) ≤3.5 ˚ A and ∠O···H-O ≤30◦. The hydration enthalpy, ∆Hhyd, is calculated as the energy difference between a box with the ion plus a given number of water molecules, Udis, and a box with the same number of water molecules under the same simulation conditions, Uwater, plus the ion energy in gas phase. ∆Hhyd =Hdis −Hwater −Hion ≃Udis −Uwater −0.6kcal/mol (4.2) The interaction energy per hydrogen bond, EHB, has been computed by the formula: EHB =EAB −(EA+EB) (4.3) This calculation has been performed extracting all the dimers forming hydrogen bonds and computing a single point calculation of the dimer and monomers keeping the polarization formed in the simulation. Then, EHB is averaged for each type of hydrogen bond analyzed. 81 Mean residence times (MRT) are calculated by the Impey method,6 defined by equation 4.4. MRTs larger than 50 ps has been calculated from the entire simulation, and MRTs smaller than 50 ps has been calculated employing blocks of 200 ps from the full simulation time. τ=1 NtXNtn=1 XPj(tn, t;t∗) (4.4) In Equation 4.4 Ntis the number of configurations, Pjis a function that takes the value 1 when the water molecule jis inside a given region at time tnand t+tnwithout leaving the region for a time longer than t*, otherwise the function takes the value 0. Ion self-diffusion coefficient, Di, a measure of the ion mobility, is calculated by the mean square displacement (MSD) equation: Di=<|~ri(t)~ri(0)|> 6t.(4.5) Self-diffussion coefficients has been corrected of the effect of periodic boundary conditions using the Yeh and Hummer equation:7 Dcorr =Di+KBTζ 6πηL (4.6) where Diand Dcorr, are the self-diffusion coefficients before and after the correction,KBis the Boltzmann constant, T the temperature, ζis the self-term which for a cubic lattice at room temperature is 2.83773, ηis the viscosity and L is the boxlength. Reorientational times for the first and second order correlations functions associated to the reorientional motion of the dipole moment vector µ, the hydrogen-hydrogen vector HH, the normal vector to the molecular plane ⊥and the oxygen-hydrogen axis OH (see Figure 4.1) has been computed. Reorientational times (τ1and τ2) have been calculated from the correlation function defined in equations 4.7 and 4.8 (see the evaluated coordinates in Figure 4.1). Also, the time correlation of the eccentricity has 82 CHAPTER 4. SYSTEM DEFINITION AND ANALYZED PROPERTIES been evaluated. Figure 4.1: Reorientational time coordinates. C1,i(t) = (~ui(0)~ui(t))(4.7) C2,i(t) = 1 23(~ui(0)~ui(t))2−1(4.8) The reorientational correlation functions were calculated from a 1 ns simulation time with a distance between consecutive structures of 0.01 fs. The correlation dynamics of the eccentricity vector (Equation 4.9) has been calculated using Equation 4.10. ~ =~rMn+−~rCM (4.9) 4.1. BIBLIOGRAPHY 83 C(t) = <~ (t)~ (0) > < ~(0)2>(4.10) The EXAFS and XANES functions were simulated with FEFF 9.6 code8 using 500 snapshots evenly taken from the production period including first and second shells coordinates, except for the EXAFS simulations of the alkalines where the inclusion of the second shell added noise to the spectra. The models used in the XAS calculations are explained in section 2.3 and examples of inputs files are included in the Appendix (section 10.2). Experimental EXAFS spectra of K+,9Cs+,10 Co2+, Sc3+,11 Cd2+,12,13 Tm3+ and Nd3+ dilute aqueous solution have been extracted using the autobk code14 considering the maximum derivative of the edge as E0. Some spectra were digitalized as Ba2+ 15 and Th4+,16 and other spectra were provided by the authors of the original experiments as Na+ 17 and Rb+.18 4.1 Bibliography [1] Smith, W.; Forester, T.; Todorov, I. T. The DL POLY Classic. 2012; STFC Daresbury Laboratory, Daresbury (UK). [2] Mitchell, P.; Fincham, D. Condensed Matter Physics 1993,5, 1031– 1038. [3] Ewald, P. P. Ann. Phys. 1921,369, 253–287. [4] Allen, M.; Tildesley, D. Computer Simulation of Liquids; Clarendon Press, 1983; Cap´ıtulo 3. [5] Chandra, A. Phys. Rev. Lett. 2000,85. [6] Impey, R.; Madden, P.; McDonald, I. J. Phys. Chem. 1983,87, 5071– 5083. [7] Yeh, I.; Hummer, G. J. Phys. Chem. B 2004,108, 15873–15879. 90 CHAPTER 5. ALKALINES potassium, rubidium and caesium, 126◦, 125◦and 122◦. This is also reflected in the HB energy between first and second shell molecules, that is 0.3 kcal/mol less energetic than bulk in water (see Figure 5.25 and Table 5.9). Table 5.2: Properties of Na+aqueous solution. Standard deviation in parenthesis. Property this work Literature RM-OI(˚ A) 2.34 2.3,15 2.33,16 2.33-2.3613 2.34,52.35,12 2.37,14 2,432,43 2.372,46 2.41,17 2.41-2.4218 2.45,62.47,19 2.42-2.5238 CNI5.8 5.13,32 5.2,43 5.412,46 , 5.35,17,18 5.9,6,15 6.39,19 5.5-5.613 5.56,14 6.0,16 5.68-6.6238 DW 0.034 0.0061-0.0246 tilt angleI(◦) 131(22) 128-147,38 134,43 13214 RM-OII (˚ A) 4.40 4.35-4.60,38 4.506 CNII 16.9 13.9-15.5,38 17.56 tilt angleII (◦) 102(40) ∆µI(D) -0.1(0.3) -0.08,14 -0.0943 ∆µII (D) 0.0(0.3) MRT(t*=0) (ps) 15(2) ∼26.4,64.1-9.713 MRT(t*=2) (ps) 23(4) ∆Hhyd (kcal/mol) -94(12) -99.4,45 -98,14 -89–13538 D (10-5 cm2/s) 1.1(0.1) 0.3,43 0.73,32 1.3345 1.22,61.48-2.0338 Recently, XAS spectra of the sodium ion in aqueous solution has been recorded.46 The sodium XAS measurement is an experimental challenge due to the low absorption energy at its K-edge (∼1071 eV). Sodium atom 5.2. SODIUM 91 Figure 5.2: Enviromment of a Na+first-shell water molecule (orange). has a low X-ray absorption coefficient as this depends on the atomic number (µ∼Z4/E3, being Zthe absorber atomic number and Ethe radiation energy). Comparison between our result and the experimental EXAFS spectrum is shown in Figure 5.5. The experimental spectra contains two intense multi-electron excitations at 4 A−1and 5 A−1(KL2,3transitions,46 respectively). There is a good agreement in the frequency, meaning a good description of the first-shell distance, but there is a relevant difference in the signal intensity. It should be pointed out the high uncertainty in the intensity due to the importance of the self-absorption correction, which is important for low Z elements,46 together with the multi-electron excitation (MEE) effect, hinders the intensity comparison beyond 4 ˚ A−1. In the simulated spectrum, MEE effects have not been taken into account. Figure 5.6 shows the simulated XANES spectra using the FEFF code together with the experimental one.46 The agreement is acceptable except in the edge neighbourhood due to the multi-electron excitations which are not 92 CHAPTER 5. ALKALINES Figure 5.3: Time evolution of Na+coordination number in aqueous solution. Figure 5.4: Coordination number histogram of Na+in aqueous solution. 5.2. SODIUM 93 Figure 5.5: k2-weighted Na+K-edge EXAFS. Figure 5.6: Na+K-edge XANES. 94 CHAPTER 5. ALKALINES considered by the computations. 5.3 Potassium XAS spectroscopy studies of potassium aqueous solutions provide coordination numbers between 6.1 and 6.3 with interatomic distances between 2.73 and 2.69 ˚ A.3,4 Neutron diffraction studies on potassium halides solutions gave coordination numbers between 6 and 6.4 and a first coordination shell distance of 2.65 ˚ A.5Classical MD6,14,19 obtained coordination numbers between 6.9 and 8.0 with first-shell peak distances between 2.79 and 2.87 ˚ A. A series of QM/MM studies yielded a coordination number range between 6.2 and 8.3 and a peak distance between 2.70 and 2.81.13,15,47 A set of AIMD simulations18 using different theory levels obtained coordination numbers between 6.1 and 6.8 and peak distances between 2.74 and 2.9 ˚ A. Data are collected in Table 5.3. This work obtained a coordination number of 7.2 with peak distance at 2.72 ˚ A. There is a well defined second hydration shell formed by 18 water molecules at 4.80 ˚ A (see RDF’s in Figures 5.20 and 5.21). The first-shell is labile, allowing the coordination number to change between 5 and 10 along the simulation. The most common NC is 7, although there is an important percentage of 6 and 8 (see Figure 5.8). As already observed the case of sodium, the ion electric field is not enough to arrange the water molecules following an ion-dipole orientation. The simulated EXAFS function is compared with an experimental spectrum3in Figure 5.9. The experimental signal oscillations are observable up to 7 ˚ A−1. In the 2-7 ˚ A−1range there is a good frequency agreement, as well as discrepancy in the intensity. Figure 5.10 shows the comparison between the experimental3and the simulated XANES. Again the agreement is very satisfactory except for the fact that the intensity of the main ressonance is not as well reproduced. 5.3. POTASSIUM 95 Table 5.3: Properties of K+aqueous solution. Standard deviation in parenthesis. Property this work Literature RM-OI(˚ A) 2.72 2.73-2.77,32.69-2.73,42.655 2.7,15 2.8,32 2.82,48 2.8543 2.74-2.88,18 2.79,14 2.86,47 2.87,19 2.78-2.8113 CNI7.2 6.55,32 7.1,43 6.13 6.3-6.8,46-6.4,19 7.115 6-6.8,18 7.2,66.8619 7.8-8.3,13 6.2,47 7.9814 6.1-6.8,18 6.2-6.847 DW 0.049 0.0293,30.0294 tilt angleI(◦) 126(25) 124,43 12814 RM-OII (˚ A) 4.80 4.756 CNII 18.4 21.26 tilt angleII (◦) 101(39) ∆µI(D) -0.1(0.3) -0.1343 ∆µII (D) 0.0(0.3) MRT(t*=0) (ps) 6(1) ∼10044 MRT(t*=2) (ps) 10(1) ∆Hhyd (kcal/mol) -83(10) -79.8,45 -71,4-8814 D (10-5 cm2/s) 1.5(0.3) 1.96,45 2.026 96 CHAPTER 5. ALKALINES Figure 5.7: Time evolution of K+coordination number in aqueous solution. Figure 5.8: Coordination number histogram of K+in aqueous solution. 5.3. POTASSIUM 97 Figure 5.9: k2-weighted K+K-edge EXAFS. Figure 5.10: K+K-edge XANES. 98 CHAPTER 5. ALKALINES 5.4 Rubidium The hydration structure of the Rb+is an experimental challenge due to the weak ion-water interactions. In addition, its XAS spectra are affected by multi-electron excitations that makes much more difficult to extract the hydration structure from the EXAFS signal. There is a remarkable dispersion of coordination numbers in previous studies, values between 5.6 and 8 being found experimentally. Studies combining experimental techniques, such XAS-XRD and XAS-LAXS, obtained different results for the coordination numbers, 5.625 and 8.21 R(Rb+-O) has been found by means of EXAFS spectroscopy between 2.83 and 2.99 ˚ A.21–25 The computational methods didn‘t solve the coordination number dispersion, results between 6.8 and 8.9 and interatomic distances between 2.8 and 3.0 ˚ A6,20,26,27 being found. For the sake of comparison data are collected in Table 5.4. The structural analysis of our MD simulation shows a weak hydrate with an average coordination number of 8 with peak distance at 2.87 ˚ A (see RDF’s in Figure 5.20 and 5.21). During the simulation, the first-shell contains between 6 and 10 water molecules, but mainly between 7 and 9, as shown in Figure 5.11. The second shell is slightly defined between 3.66 and 5.77 ˚ A and contains over ∼19 water molecules (see Figure 5.20). The water molecules in the first-shell are not ion-dipole orientated towards the cation, tilt angle is 125◦. This arrangement between the water dipole and ion electric field produces a depolarization of the water molecules around 0.1 D, with respect to bulk water molecules. The rubidium EXAFS spectrum contains a multi-electron excitation at 6˚ A−1(KM4,5transition50) making not visible the EXAFS oscillations for higher k values. To increase the EXAFS range, a methodology to remove the MEE from the function has been used. This methodology was employed successfully in the analysis of lanthanoid aqua ions.51 The method is based on the parametrization of equation 5.1 with the k3-weighted EXAFS function. Because rubidium EXAFS spectrum doesn’t present clear oscillations above 6 ˚ A−1the method was adapted using only the previous 5.4. RUBIDIUM 99 Figure 5.11: Time evolution of Rb+coordination number in aqueous solution. Figure 5.12: Coordination number evolution of Rb+in aqueous solution. 106 CHAPTER 5. ALKALINES Table 5.5: Properties of the Cs+aqueous solution. Standard deviation in parenthesis. Property this work Literature RM-OI(˚ A) 3.12 3.20-3.30,29 2.98,30 3.0731 3.25,63.01-3.0032 CNI9.9 7.0-8.2,32 7.8-9.129 8.0,30,31 106 DW (˚ A2) 0.075 tilt angleI(◦) 122(39) 119,32 135-15529 ∆µI(D) -0.1(0.3) ∆µII (D) 0.0(0.3) MRT(t*=0) (ps) 6(1) ∼100,44 1.5-2.229 MRT(t*=2) (ps) 12(1) ∆Hhyd (kcal/mol) −55(9) −67.645 D (10-5 cm2/s) 1.5(0.1) 2.1,45 1.77,57 1.1,32 0.836 5.6 Global properties in solution 5.6.1 Radial distribution function To analyze the evolution of the main structural properties along the group the metal-oxygen Radial Distribution Function (RDF) can be used. Lithium first hydration shell is well defined, showing a depletion between the first and the second shell. Also there is a well defined second shell. Sodium first-shell is located at longer distance, the first minimum does not decay to zero as in the lithium case, meaning more water exchanges in this case. The first peak of the Na-O RDF is wider than that of the Li-O RDF what indicates a less rigid aqua ion. For potassium, rubidium and caesium hydrates the g(r) between the first and second shell is higher, meaning more frequent water exchanges between shells. The second shell is slightly defined for these cations except for the caesium for which a second minimum is lacking and consequently it is not possible to properly assign a second 5.6. GLOBAL PROPERTIES IN SOLUTION 107 hydration shell. Figure 5.20: Metal-oxygen radial distribution function. The metal-hydrogen radial distribution function (see Figure 5.21) follows the same trend found M-O RDF, incorporating the effect of the tilt angle in the first maxima location as M-H RDF maxima position depends on the maximum of the M-O RDF and the tilt angle. The average tilt angle of the first-shell molecules decrease along the group, values of 137◦, 131◦, 126◦, 125◦, 122◦, for lithium, sodium, potassium, rubidium and caesium, were found respectively. The tilt angle runs parallel to the polarizing power, that decreases along the group at the same time that the ionic radii increases. In Figure 5.22 the RDFs between the first-shell oxygen and hydrogen atoms and the O-H RDF of the MCDHO2 water model are shown. There 108 CHAPTER 5. ALKALINES Table 5.6: Metal-oxygen radial distribution function data. Distances in ˚ A. Ion RM-OI(max) g(r)M-OI(max) RM-OI(min) g(r)M-OI(min) Li+1.91 9.5 2.70 0.0 Na+2.34 6.5 3.20 0.2 K+2.71 4.9 3.49 0.4 Rb+2.87 4.1 3.68 0.5 Cs+3.12 4.0 4.05 0.5 Ion RM-OII (max) g(r)M-OII (max) RM-OII (min) g(r)M-OII (min) Li+4.06 1.8 4.92 0.8 Na+4.02 1.5 5.35 0.8 K+4.74 1.2 5.66 0.9 Rb+4.9 1.1 5.77 0.9 Figure 5.21: Metal-hydrogen radial distribution function. 5.6. GLOBAL PROPERTIES IN SOLUTION 109 Table 5.7: Metal-hydrogen radial distribution function data. Distances in ˚ A. Ion RM-HI(max) g(r)M-HI(max) RM-HI(min) g(r)M-HI(min) Li+2.53 3.4 3.30 0.4 Na+2.90 2.9 3.79 0.6 K+3.24 2.5 4.14 0.6 Rb+3.39 2.3 4.38 0.7 Cs+3.60 2.0 4.62 0.6 Ion RM-HII (max) g(r)M-HII (max) RM-HII (min) g(r)M-HII (min) Li+4.67 1.4 5.60 0.9 Na+4.40 1.5 5.34 0.8 K+5.50 1.2 6.51 1.0 Rb+5.67 1.1 6.62 1.0 can be seen how the caesium function is similar to the water one but with a different intensity. Li+and Na+enviroments exhibit OH RDFs quite different from that of bulk water, while K+and Rb+are closer to that of Cs+. This comparison shows how the water bulk structure is recognized in the first shell water molecules of the heavy alkalines. 110 CHAPTER 5. ALKALINES Figure 5.22: RDF between oxygen and hydrogen atoms in the first hydration shell of alkaline cations and OH RDF of the water model. 5.6.2 Energetic properties The hydration enthalpy from the simulations follows the experimental45 trend (see Figure 5.23), with an average mean error of x. The average interaction energy between the ion and a first-shell water molecule have been computed together with the interaction among firstshell water molecules have been computed (see Table 5.8). The ion-water interaction decreases descending in the group as there is a relation between the interaction energy and the ionic radii, which determines how close the two particles can approach each other, as well as the relative water orientation with respect to the ion (tilt angle). For Li+the water molecules are oriented by the cation having a high repulsive interaction among them. 5.6. GLOBAL PROPERTIES IN SOLUTION 111 Figure 5.23: Hydration enthalpy (kcal/mol). Red dots experimental values.45 Black dots calculated values from the simulations with error bars defining its mean error. This water orientation evolves descending in the group loosing the iondipole orientation as the ion becomes larger and less polarizing. In the caesium case the first-shell water molecules are able to interact attractively among them. 5.6.3 Hydrogen bonding Descending in the alkaline group, the average number of hydrogen bonds formed by the first-shell water molecules increases, because the ion is lossing its ability to orient the water molecules (see Figure 5.24). Then, the water molecules can adopt part by the tetrahedral arrangement of liquid water, appearing hydrogen bonds among first-shell water molecules. 112 CHAPTER 5. ALKALINES Table 5.8: Average interaction energy between two first-shell particles (kcal/mol). I : Ion. W : water. Standard deviation in parenthesis. Ion EintI−W1st EintW1st−W1st Li+-40.6(2.2) 8.2(1.1) Na+-22.5(2.2) 4.5(1.2) K+-17.4(2.0) 2.5(1.6) Rb+-12.9(1.8) 0.7(1.7) Cs+-10.2(1.5) -1.0(1.8) Also, it is observed how the type of hydrogen bond changes when descending in the group (see Table 5.10). For the lithium the 77.4% of the hydrogen bonds among first-shell and second shell water molecules are formed by a first-shell water molecule donating the hydrogen to a water molecule of the second shell. For the caesium this percentage goes down to 66%. The relative number of accepted hydrogen bonds by first-shell molecules in the alkaline group is quite similar (23% for Li+and 34% for Cs+). It is interesting to point out that the lithium tetrahydrate adopts a structure where the four water molecules do not form hydrogen bonds among them. On the contrary, the caesium decahydrate adopts a structure where each of the first-shell water molecules is able to form on average one hydrogen bond among them, but less than two hydrogen bonds with second shell water molecules. The hydrogen bond network of the second shell is similar for all the cations, the main difference comes from to the relative number of water molecules in the second shell with respect to the amount of the first-shell solvent molecules. Table 5.9 and Figure 5.25 collects the hydrogen bond interaction energy (EHB) among first, second and third-shell (bulk) water molecules. As can be seen, EHB 1-1 and EHB 1-2 follow different trend along the group. EHB 1-2 decreases with the polarizing capabilities of the cation and the polarization of first-shell water molecules. Interestingly EHB 1-1 increases due 5.6. GLOBAL PROPERTIES IN SOLUTION 113 Figure 5.24: Average number of hydrogen bonds for first-shell water molecules. Black dots: average number of hydrogen bonds per molecule. Red dots: average number of hydrogen bonds between first-shell water molecules. to the same factors. As can be seen in Table 5.8 there is a smooth change between the ion-water and water-water repulsion along the group, whereas the ion-water interaction energy decreases the water-water interaction energy increases together with the hydrogen bond number between first-shell water molecules. Concerning first-second shell hydrogen bonds, only Li+, -7.1 kcal/mol, the interaction energy is greater than the pure water value, -6.6 kcal/mol, as it is the only cation that polarizes its first hydration shell strongly. The hydrogen bond interaction energy among water molecules of the first-shell increases along the group, but with values smaller than those corresponding 114 CHAPTER 5. ALKALINES to bulk, due to the first-shell geometrical constraints. It is observed that the hydrogen bonds among second-shell water molecules and second and third shell (or bulk) converges to the bulk value. Figure 5.25: Average hydrogen bond interaction energy (kcal/mol). Black dots: average interaction energy per hydrogen bond between a molecule of the first-shell and a molecule of the second shell. Red dots: average interaction energy per hydrogen bonds between first-shell molecules. Blue line: MCDHO2 bulk water value. 5.6. GLOBAL PROPERTIES IN SOLUTION 115 Table 5.9: Energy of hydrogen bonds formed by water molecules of different shells (kcal/mol). Standard deviation in parenthesis Ion Li+Na+K+Rb+Cs+ EHB 1-1 -4.9(2.7) -5.0(2.6) -5.7(2.5) -6.0(2.5) EHB 1-2 -7.1(2.7) -6.3(2.4) -6.4(2.4) -6.2(2.3) -6.1(2.3) EHB 2-2 -6.6(2.5) -6.6(2.5) -6.6(2.4) -6.6(2.4) -6.6(2.4) EHB 2-3 -6.6(2.5) -6.6(2.4) -6.6(2.4) -6.5(2.4) -6.6(2.4) Table 5.10: Hydrogen bond statistics: average number of hydrogen bonds per water molecule in 1st and 2nd hydration shells. don/acc means the water molecule acting as donor/acceptor of the hydrogen bond. Ion Li+Na+K+Rb+Cs+ nHB 1st shell 2.4 2.5 2.7 2.7 2.8 nHB 1-1 0 0.1 0.4 0.6 0.9 nHB 1-2 2.4 2.3 2.2 2.2 1.9 nHB 1-2 don. 77% 71% 67% 66% 66% nHB 1-2 acc. 22% 29% 33% 34% 34% nHB 2nd shell 3.6 3.6 3.7 3.7 3.7 nHB 1-2 0.7 0.8 0.9 0.9 0.8 nHB 2-2 1.0 1.0 1.0 1.0 1.1 nHB 2-3 1.9 1.8 1.8 1.8 1.8 nHB 2-3 don. 59% 58% 57% 57% 56% nHB 2-3 acc. 41% 42% 43% 43% 44% 122 CHAPTER 5. ALKALINES 5.6.5 Molecular asymmetry Another interesting structural feature derived from the results is the degree of radial symmetry retained in the first hydration shell. The time correlation function of the eccentricity vector increases along the group. When the correlation times are examined it could be said that in the case of lithium the center of mass is defined by the same number of water molecules (that sometimes cross the cutoff of the first-shell) and for the case of the caesium there is also the effect of the continuous exchange of water molecules in the first-shell. This to say that the time for the caesium should be much larger if the water exchanges are reduced. Table 5.13: Comparison of the M-O peak distance and M-O average distance. Ion M-O peak (˚ A) <RM−O>(˚ A) ∆ R (˚ A) Li+1.91 1.95 0.04 Na+2.34 2.42 0.08 K+2.72 2.82 0.10 Rb+2.87 3.02 0.15 Cs+3.12 3.25 0.13 To illustrate how this eccentricity is reflected in the cation cluster structure, Figure 5.30 shows the closest hydration environment of Cs+in a representative snapshot taken from the MD simulation. The two views displayed show the presence of regions around the metal cation which are partially de-populated of water molecules (left side of Figure 5.30), whereas in a populated region the water molecules are interacting simultaneously with the cation and forming HBs with other water molecules of the same shell (right side of Figure 5.30). One might think that this snapshot could not be representative of the 5.6. GLOBAL PROPERTIES IN SOLUTION 123 Figure 5.29: Eccentricity, (˚ A), and eccentricity reorientational time, τ1, (ps). Standard deviation defined by error bars. 124 CHAPTER 5. ALKALINES Figure 5.30: Two views of a representative structure and its first hydration shell containing ten solvent molecules taken from the MD simulation. average hydration shell, but if the Li+hydration is considered the result would be very different. The Li+tetrahydrate exhibits a first-shell tetrahedral structure and the eccentricity of the first-shell water molecule mass center and the cation is only 0.2 ˚ A. Therefore, the tendency observed in the energetic analysis of the clusters [M(H2O)n]+concerning the preference of surface clusters is translated in some way to aqueous solutions where asymmetric coordination shells are defined for the two ions (see Figure 5.29). The eccentricity of the first hydration shell also contributes to an asymmetric M–O first peak, which is quantified by the difference between the peak maxima, and the first-shell RM–O average values. 5.7. GLOBAL PROPERTIES IN GAS PHASE 125 5.7 Global properties in gas phase In order to test the general character of the developed intermolecular potentials, we have checked the behaviour of them for gas phase clusters. 5.7.1 Average dipole moment The average dipole moment of the water molecules in alkaline hydrates was calculated in the gas phase, studying cluster with a number of water molecules varying from 1 to 25 at 100 K. In order to take into account the multiple minima problem an iterative procedure of heating was applied until convergence was achieved (50 iterations). In the heating step the cluster is equilibrated at 300 K to favor the rearrangement of the water molecules, inside a sphere that avoids the water evaporation. When increasing the size of the ion and the number of water molecules more configurations are needed to converge the property because the water structure beyond the first-shell becomes a delicate compromise between ion-water and waterwater interactions. When dealing with the monohydrate cation, its polarization depends on the capability of the ion. For the lithium the largest polarization is found and for the caesium the smallest one. When water molecules are added to the cluster the average polarization decreases as a consequence of the apparence of water-water interactions. However, when second hydration shell water molecules are incorporated the average dipole moment slighly increases as a consequence of the first-second hydrogen bonds (see Figure 5.31). When the first hydration shell does not accept more water molecules those molecules are located in a second shell. If the ion is not able to orient the water molecules following an ion-dipole orientation, the cluster looks like a water cluster with an ion attached to the surface instead of an ion that orders the water molecules in concentric shells (see Figure 5.32). Same tendence was obtained in previous theoretical works.63 126 CHAPTER 5. ALKALINES Figure 5.31: Average dipole moment of the water molecules. Figure 5.32: Lithium (left) and caesium hydrates (right) with 25 water molecules. 5.8. BIBLIOGRAPHY 127 5.8 Bibliography [1] Scrosati, B.; Garche, J. J. Power Sources 2010,195, 2419–2430. [2] Potassium and Sodium (In Biological Systems). Van Nostrand’s Encyclopedia of Chemistry.; 2005; Vol. g. [3] Glezaku, V.; Chen, Y.; Fulton, J.; Schenter, G.; Dang, L. Theor. Chem. Acc. 2006,115, 86–99. [4] Vao-Soongnern, V.; Pipatpanukul, C.; Horpibulsuk, S. J. Mater. Sci. 2015,50, 7126–7136. [5] Mancinelli, R.; Boti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. J. Phys. Chem. B 2007,11, 13570–13577. [6] Lee, S. H.; Rasaiah, J. Y. J. Phys. Chem. 1996,100, 1420–1425. [7] San-Rom´an, M. L.; Carrillo-Tripp, M.; Saint-Martin, H.; Cobos, J. H.; Ortega-Blake, I. Theor. Chem. Acc. 2006,115, 177–189. [8] Loeffler, H. H.; Rode, B. M. J. Chem. Phys. 2002,117, 110–116. [9] Lyubartsev, A. P.; Laasonen, K.; Laaksonen, A. J. Chem. Phys. 2001, 114, 3120–3126. [10] Tongraar, A.; Liedl, K. R.; Rode, B. M. Chem. Phys. Lett. 1998,286, 56–64. [11] Sripa, P.; Tongraar, A.; Kerdcharoen, T. J. Mol. Liq. 2015,208, 280– 285. [12] Sripa, P.; Tongraar, A.; Kerdcharoen, T. J. Phys. Chem. A 2013,117, 1826–1833. [13] Tongraar, A.; Liedl, K. R.; Rode, B. M. J. Phys. Chem. A 1998,102, 10340–10346. 128 CHAPTER 5. ALKALINES [14] Carrillo-Tripp, M.; Saint-Martin, H.; Ortega-Blake, I. The J. Chem. Phys. 2003,118, 7062–7073. [15] Ma, H. Int. J. Quantum Chem. 2014,114, 1006–1011. [16] Chandrasekhar, J.; Spellmeyer, D.; Jorgensen, W. J. Am. Chem. Soc. 1984,106, 903–910. [17] Gaiduk, A. P.; Zhang, C.; Gygi, F.; Galli, G. Chem. Phys. Lett. 2014, 604, 89–96. [18] Bankura, A.; Carnevale, V.; Klein, M. L. Molecular Physics 2014,112, 1448–1456. [19] Faginas-Lago, N.; Lombardi, A.; Albert´ı, M.; Grossi, G. J. Mol. Liq. 2015,204, 192–197. [20] Ikeda, T.; Boero, M. J. Chem. Phys. 2012,137, 041101(1)–041101(4). [21] D’Angelo, P.; Persson, I. Inorg. Chem 2004,43, 3543–3519. [22] Fulton, J.; Pfund, D.; Wallen, S.; Newville, M.; Stern, E.; Yanjun Ma, J. Chem. Phys. 1996,105, 2161–2166. [23] Kubozono, Y.; Hirano, A.; Kahino, S.; Emura, S.; Ishida, H. Z. Naturforsch. 1994,49a, 727–729. [24] Ohkubo, T.; Konishi, T.; Hattori, Y.; Kanoh, H.; Fujikawa, T.; Kaneko, K. J. Am. Chem. Soc. 2002,124, 11860–11861. [25] Pham, V.; Fulton, J. L. J Chem. Phys. 2013,138, 044201. [26] Lee, S. H.; Rasaiah, J. C. J. Chem. Phys. 1994,101, 6964–6974. [27] San-Rom´an, M. L.; Hern´andez-Cobos, J.; Saint-Martin, H.; OrtegaBlake, I. Theor. Chem. Acc. 2010,126, 197–211. [28] Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Comput. Chem. 2005, 26, 949–956. 5.8. BIBLIOGRAPHY 129 [29] Schwenk, C. F.; Hofer, T. S.; Rode, B. M. J Chem. Phys. A 2004, 108, 1509–1514. [30] Fan, Q.; Tanaka, M.; Tanaka, K.; Sakaguchi,; Takahashi, Y. Geochim. Cosmochim. Acta 2014,135, 49–65. [31] M¨ahler, J.; Persson, I. Inorg. Chem 2011,51, 425–438. [32] Ikeda, T.; Boero, M. J. Chem. Phys. 2015,143, 194510. [33] Bouazizi, S.; Nasr, S. J. Mol. Struct. 2007,837, 206–213. [34] Rudolph, W.; Brooker, M. H.; Pye, C. C. J. Phys. Chem. 1995,99, 3793–3797. [35] Mason, E.; Anell, S.; Neilson, G.; Rempe, S. B. J. Phys. Chem. B 2015,119, 2003–2009. [36] Licheri, G.; anf G. Pinna, G. P. Chem. Phys. Lett. 1975,35, 119–123. [37] Palinkas, G.; Radnai, T.; Hajdu, F. Z. Naturforsch 1979,35a, 107– 114. [38] Spangberg, D.; Hermansson, K. J. Phys. Chem. 2004,120, 4829–4842. [39] Szasz, G.; Heinzinger, K.; Palinkas, G. Chem. Phys. Lett. 1981,78, 194–196. [40] Larentzos, J. P.; Crescenti, L. J. J. Phys. Chem. 2008,112, 14243– 14250. [41] Impey, R.; Madden, P.; McDonald, I. J. Phys. Chem. 1983,87, 5071– 5083. [42] Bock, C.; Markham, G.; Katz, A.; Glusker, J. Theor. Chem. Acc. 2006,115, 100–112. [43] Ikeda, T.; Boero, M.; Terakura, K. J. Chem. Phys. 2006,126, 034501. 130 CHAPTER 5. ALKALINES [44] Ohtaki, H.; Radnai, T. Chem. rev. 1993,83, 1157–1204. [45] Marcus, Y. Ion properties; Markel Dekker, Inc, 1997. [46] Galib, M.; Baer, M.; Skinner, L.; Mundy, C.; Huthwelker, T.; Schenter, G.; Benmore, C.; Govind, N.; Fulton, J. J. Chem. Phys. 2017, 146, 084504. [47] Azam, S. S.; Hofer, T. S.; Randolf, B. R.; Rode, B. M. J. Phys. Chem. 2009,113, 1827–1833. [48] Liu, Y.; Haigang Lu, Y. W.; Li, Q. J. Chem. Phys. 2012,132, 124503. [49] Helm, L.; Merbach, A. Coord. Chem. Rev. 1999,187, 151–181. [50] Kodre, A.; Arcon, I.; Gomilsek, J. P.; Preseren, R.; Frahm, R. J. Phys. B2002,35, 3497–3513. [51] Ohta, A.; Kagi, H.; Tsuno, H.; Nomura, M.; Kawabe, I. Am. Mineralogist 2008,93, 1384–1392. [52] Bernieri, E.; Mobilio, S.; Filipponi, A. Phys. Rev. B 1988,38, 3298– 3304. [53] Qin, H.; Yokoyama, Y.; Fan, Q.; Iwatani, H.; Tanaka, K.; Sakaguchi, A.; Kanai, Y.; Zhu, J.; Onda, Y.; Takahashi, Y. Geochem. J. 2012,46, 297–302. [54] Ohta, A.; Kagi, H.; Tsuno, H.; Nomura, M.; Kawabe, I. Am. Mineral. 2008,93, 1384–1392. [55] Rossetti, I.; Sordelli, L.; Ghigna, P.; Pin, S.; Scavini, M.; Forni, L. Inorg. Chem 2011,50, 3757–3765. [56] Kodre, A.; Arcon, I.; Hribar, M.; Stuhec, M.; Villain, F.; Parent, P. J. Phys. IV 1994,4 (C9), C9–397–C9–400. [57] Sato, H.; Yui, M.; Yoshikawa, H. J. Nucl. Sci. Technol. 1996,33, 950. 5.8. BIBLIOGRAPHY 131 [58] Krynicki, K.; Green, C.; Sawyer, D. Faraday Discuss Chem. Soc. 1978, 66, 199–208. [59] Sripa, P.; Tongraar, A.; Kerdcharoen, T. Chem. Phys. 2016,479, 72– 80. [60] Dao, H.; Rasaiah, J.; Miller, D. J. Phys. Chem. B 2007,111, 209–217. [61] Waluyo, I.; Nordlund, D.; Bergmann, U.; Schlesinger, D.; Pettersson, L.; Nilsson, A. J. Chem. Phys. 2014,140, 244506. [62] Tielrooji, K.; van der Post, S.; Hunger, J.; Bonn, M.; Bakker, J. J. Phys. Chem. B 2011,115, 12638–12647. [63] Bucher, D.; Kuyucak, S. J. Phys. Chem. B 2008,112, 10786–10790.