Theoretical Investigation Of Structures And Properties Of The Hydrated Metal Ion Clusters[M（H₂O）_N]²⁺（M=Ca, Fe, Pb）

In this thesis, we investigated the structures and properties of three kinds of hydrated metal ion clusters,[Ca(H2O)n]2+,[Fe(H2O)n]2+and [Pb(H2O)n]2+, by using density functional theory. The lowest energy structure of each sized cluster had been determined. For the hydrated calcium ion clusters and the hydrated ferrous ion clusters, we proposed different growth patterns, respectively. We found that the coordination number in the first hydration shell was6for both Ca2+and Fe2+ions. The second hydration shell contained9and7water molecules for Ca2+and Fe2+ions, respectively. Our calculations indicated that the structures of [Ca(H2O)n]2+and [Fe(H2O)n]2+clusters were all holo-directed in our considered size range, whereas the structures of [Pb(H2O)n]2+clusters were hemi-directed at the smaller cluster size and holo-directed at the larger cluster size (n≥14). Furthermore, we revealed that the vibration entropy contributed to the free energy of an isomer for [Ca(H2O)n]2+and [Fe(H2O)n]2+clusters. We also predicted the IR spectra of the best candidates of the [Ca(H2O)n]2+clusters and the [Fe(H2O)n]2+clusters, in which the evolution of hydrogen-bond configurations with the cluster size was revealed. By examining the percentage occupied by Pb2+lone pair (LP) on the p orbital and the natural charges on Pb2+ion, the origin of hemi-directed and holo-directed geometries of hydrated Pb2+ion clusters was proposed. Finally, we studied the proton transfer reaction of [Pb(H2O)2,4,8]2+clusters. Obviously, the hemi-directed structures of small sized [Pb(H2O)n]2+clusters provided the convenience for the proton transfer reaction.This thesis is composed of six chapters. In the first chapter, we introduced the importance of water, the harm of water pollution, the microstructure and properties of water, and the main progress in the research of three kinds of hydrated metal ion systems. All life is inseparable from the water, but the water pollution is becoming more and more serious. The contaminative water contains all kinds of metal ions. We mainly concern the hydration of alkali earth metal ion Ca2+, transition metal ion Fe2+and heavy metal ion Pb2+. For the hydrated calcium ion system, intensive studies had been carried out both theoretically and experimentally, but a variety of experimental techniques and the different theoretical level produced the different results. For the hydrated ferrous ion system, a few works focused on the structures and the dynamics. For the hydrated lead ion system, in the gas phase experiments, there was no evidence of [Pb(H2O)n]2+ions, instead the proton transfer reaction products [PbOH(H2O)x]+and [H(H2O)y]+ions were observed.In the second chapter, we briefly introduced the density functional theory and the Gaussian package used in this thesis.In the third chapter, the structures, stability, vibration entropy and IR spectra of the hydrated calcium ion clusters [Ca(H2O)n]2+(n=1-20,27) were presented. We found that the first hydration shell around the calcium ion was fully occupied by six water molecules, whereas the second hydration shell might be fully occupied with different numbers of water molecules. This just corresponds to different growth patterns of the hydrated calcium ion clusters. The pattern having the nine water molecules in the second shell was found to be more favored than the others. Furthermore, we revealed that the vibration entropy contributed to the free energy of an isomer of hydrated calcium ion clusters significantly. As a result, the stability of some low-lying candidates at zero-temperature was not maintained at finite temperatures. Therefore, we suggested that, at finite temperatures, the experimental observations of [Ca(H2O)n]2+should be a mixture of the best candidate and some of metastable isomers for a given cluster size. In addition, the calculated IR spectra of the best candidates reflected the structural features of the hydrated ion clusters, in which the evolution of hydrogen-bond configurations with the cluster size was revealed.In the fourth chapter, we calculated the structures and energies, the vibration entropy, IR spectra, the successive water binding energy and the natural charges population on ferrous ion at each possible spin multiplicity, discussed the structural features and growth patterns of the hydrated ferrous ion clusters,[Fe(H2O)n]2+(n=1-19). We extensively searched a large number of low-lying isomers of the hydrated ferrous ion clusters,[Fe(H2O)n]2+(n=1-19), and the lowest-energy structures were determined. We found that all the lowest-energy states of [Fe(H2O)n]2+(w=1-19) clusters were spin quintet states. The first and the second hydration shells showed six coordinate and seven coordinate, respectively. These lowest-energy states kept well even at finite temperatures. The analyses of the successive water binding energy and the natural charges population on ferrous ion clearly showed that the influence of ferrous ion on the surrounding water molecules was very weak beyond the second hydration shell.In the fifth chapter, we investigated the geometries and proton transfer of the hydrated divalent lead ion clusters [Pb(H2O)n]2+(n=1-17). We found that the hydrated lead ion clusters [Pb(H2O)n]2+were hemi-directed structures at smaller cluster size and holo-directed structures at larger cluster size (n≥14). We revealed that the hemi-directed and holo-directed geometries of the hydrated Pb2+ion clusters are mainly due to the status of the lone pair of Pb2+ion. That is, when the lone pair occupied the directional p orbital, the cluster forms the hemi-directed geometry; contrarily, when the lone pair occupied the s orbital with sphere symmetry, it favours the holo-directed geometry. The hemi-directed structures of hydrated lead ion clusters favor their proton transfer reaction. Our calculated proton transfer reaction products were in good agreement with the experimental observation.In the sixth charpter, we summarized the similarities and differences of the structural features, growth patterns, the relative stabilities and so on, for the hydrated metal ions clusters [Ca(H2O)n]2+,[Fe(H2O)n]2+and [Pb(H2O)n]2+. By analyzing the electron configurations of Ca2+, Fe2+and Pb2+ions, and the frontier orbital of [Ca(H2O)n]2+,[Fe(H2O)n]2+and [Pb(H2O)n]2+clusters, we explained the similarities and differences of three kinds of hydrated metal ions clusters. Finally, we proposed the issues remained and the works to be performed in the future.