Structures, Stability, Vibration Entropy and IR Spectra of Hydrated Calcium Ion Clusters [Ca(H₂O)_n]²⁺ (n = 1−20, 27): A Systematic Investigation by Density Functional Theory

Abstract

The low-lying candidates of hydrated calcium ion clusters, [Ca(H(2)O)(n)](2+) with n = 1-20 and 27, have been extensively sought by using density functional theory (DFT) at BLYP/6-311+G(d,p) level. The results showed 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. Furthermore, we revealed that the vibration entropy contributed to the free energy of an isomer 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 realistic products of [Ca(H(2)O)(n)](2+) should be a mixture of the best candidate and some of metastable isomers for a given cluster size. For a cluster having second and/or third shell of water molecules, we found structural transitions between a low-lying structure and the lowest-energy structure undergoing much lower energy barriers. In addition, the IR spectra of the best candidates were predicted, in which the evolution of hydrogen-bond configurations with the cluster size was revealed.

The Structural Features of the Hydrated Ferrous Ion Clusters: [Fe(H2O) n ]2+ (n = 1–19)

“…3 Figure 3 clearly indicates that the coordination number of the second shell is seven, which is lower than the values for the other hydrated divalent metal ion clusters such as the [Ca(H 2 O) n ] 2? (n = 1-20, 27) clusters [18]. Furthermore, it is also lower than the coordination number of the second shell obtained by means of molecular dynamics from the previous theoretical results [5,6,11], in which the average coordination number of the second shell is 12.4, 12, and 13, respectively.…”

“…That is to say, the third hydration shell just appears in the case of [Fe(H 2 O) 14 ] 2? complex, which differs from the hydrated calcium ion clusters [18]. 6, respectively, show the other two kinds of growing patterns for n = 14-19.…”

“…Usually, the number of selected initial geometries lies on the cluster size. For a smaller sized cluster, e.g., in the case [18]. (2) Considering the structural properties of the hydrated iron ion clusters available from the previous studies [11], we design the initial geometries of [Fe(H 2 O) n ] 2?…”

“…7, the free energy curve of the ground state is always below those of the metastable states in the temperature range of 0-400 K. This suggests that the ground state always keeps its relative stability with up to the 400 K. The similar situation was also found in other sized hydrated ferrous ion clusters. This is a disparate result compared with hydrated calcium ion clusters, in which the ground state can transform to be the metastable state at finite low temperature [18]. clusters is computed according to…”

“…These electronic characteristics are in agreement with those of previous studies on [Ca(H 2 O) n ] 2? (n = 1-20, 27) clusters [18].…”