What Does It Mean for an Ion to Be Hydrated
Introduction
Hydration of ions plays a significant role in the chemical (1) and biological sciences, (ii) etc. In most of the previous studies, only hydrated individual ions were identified. The hydration number of ions and the gratis energy of ion hydration were adamant experimentally by proton nuclear magnetic resonance (proton NMR), (3) Ten-ray Compton scattering, (4) neutron scattering, (5) and theoretically by density functional theory, (6, 7) perturbation theory, (viii) as well equally molecular simulations. (nine-11) For additional data, ane can see refs 12−14 and the references therein. In addition to hydrated private ions, the presence of hydrated ion pairs were also noted. Most studies on hydrated ion pairs involve their free energies of hydration (-15-17) and their structure. (eighteen, 19) For more information regarding ion pairing, i can see refs xx and 21 and the references therein.
In previous papers, (3-10, 12-21) the focus was on hydrated individual ions and hydrated ion pairs. Notwithstanding, how many hydrated private ions and ion pairs are present in solutions was not determined. Furthermore, ion clusters and how many there are have not been identified and calculated. In our previous paper, ion clusters were identified for a nanomembrane in an electrolyte solution. (11) 2 issues are considered in this paper. The start one is concerned with the dependence of the mole fractions and the hydration numbers of hydrated individual ions, ion pairs, and larger ion clusters on electrolyte concentration. The second one is the dependence of the hydrogen bonding number of all H2O molecules of the first hydration layer on the electrolyte concentration and nature of ions. In addition, we emphasize that in the current paper, we apply the TIP3P model (22, 23) for the water molecules. Still, different force fields may provide different results. In our ongoing work, we calculate the hydration number of ions, ion pairs, and ion clusters using molecular simulation with different force fields, including the AMOEBA force field, (24-26) and quantum density functional theory.
Simulation Details
Molecular dynamics simulations were carried out using the nanoscale molecular dynamics (NAMD) program (version two.nine). (27) Snapshots were obtained using the Visual Molecular Dynamics (VMD) plan. (28) The CHARMM 27 force field (29, 30) and the TIP3P model (22, 23) were employed for ions and h2o, respectively. The long-range Coulomb interactions were calculated using the particle-mesh Ewald (PME) method. (31) After minimization at 0 K, the temperature was raised to 300 K, and 4 ns isothermal–isobaric ensemble (NPT ensemble) simulations were carried out. Finally, 120 ns canonical ensemble (NVT ensemble) simulations were performed with a time step of 2.0 fs. In this paper, the electrolyte concentration in aqueous solutions was varied from 0.1 to 1.0 One thousand. Each system possessed more than 30 000 atoms.
Results and Discussion
Every bit examples, iv electrolyte solutions, NaCl, KCl, CaCl2, and MgClii, were examined. An ion pair or ion cluster was formed when an ion(s) was(were) trapped in the first hydration beat out of another ion. A h2o molecule belongs to the hydration vanquish of an individual ion or an ion pair or a larger ion cluster when the distance between its oxygen atom and the nearest ion is smaller than the distance of the offset hydration trounce of the corresponding individual ion. We calculated the hydration numbers of individual ion both past the above process and the radial distribution function, and found that they provide the same results. For example, the hydration number of Na+ under 0.1 mol/L is v.4 ± 0.1 for both the present process and the radial distribution function. For the hydration numbers of ion pairs and ion clusters, we utilize only the present procedure because the radial distribution functions cannot provide the hydration numbers for ion pairs and ion clusters.
The conformations of hydrated ion pairs and larger ion clusters are presented in Figure ane. An ion pair has a linear construction (Figure 1a). In our simulations, contact ion-pairs were identified, and no solvent separating ion-pairs was establish; just cation–anion pairs were present. A hydrated cluster with three ions (i cation and two anions, or two cations and one anion) possesses a "5"-shape structure (Figure 1b,c). A hydrated cluster with four ions tin can take the structure of a planar triangle (Figure 1d–f), of a triangular pyramid (Figure 1g), and of an alternative cation–anion arrangement (Figure 1h). The structure of culling cation–anion structure can take several conformations, amidst which one is linear (i.due east., four ions in line) and another has a planar "N"-shape of cation–anion. Both the ion pairs and the ion clusters are composed of cation(s) and anion(southward). We did not find that ion pairs or larger ion clusters are composed of just cations or anions. When an individual ion is introduced into the bulk h2o, some hydrogen bonds (H-bonds) betwixt the water molecules are broken, resulting in the reorientation of h2o molecules around the ions. When hydrated ion pairs or larger ion clusters are formed, they volition further intermission H-bonds. The h2o molecules around the ion pairs and particularly ion clusters are disordered. It should exist mentioned that the ion pairs and larger ion clusters can be negatively charged, positively charged, or neutral.
Figure 1
Figure 1. Snapshots of hydrated ion pairs and ion clusters: (a) hydrated cation–anion pair; (b) hydrated anion–cation–anion cluster; (c) hydrated cation–anion–cation cluster; (d and d1) hydrated anion–anion–cation–anion cluster; (e, e1,g, and g1) hydrated cation–cation-anion–cation cluster; (f, f1, h and h1) cation–anion–cation–anion cluster. Red: oxygen atoms of h2o; white: hydrogen atoms of h2o; light-green: chlorine ions; blue: cations (K+, Na+, Ca2+, Mgii+).
Figure two plots the mole fractions (10 i) of hydrated individual ions, of ions involved in hydrated ion pairs and in hydrated ion clusters as functions of electrolyte concentration C. For KCl or NaCl solutions, as the electrolyte concentration increases, the mole fractions of hydrated individual cations and hydrated individual anions decrease, but the mole fractions of hydrated ion clusters with 3 ions and four ions increase. This occurs because, equally the electrolyte concentration increases, the probability of private ions to form ion pairs or larger ion clusters increases. For C = 0.1 mol/L, well-nigh ions are nowadays in water as individual ions (with mole fractions larger than 0.95). Withal, for C = 1.0 mol/L, the mole fractions of individual ions decrease to 0.84 and 0.seventy for NaCl and KCl, respectively.
Effigy 2
Figure 2. Mole fraction (x i) of hydrated individual cation (triangle up), hydrated private anion (dashed line), hydrated individual ions (both cation and anion, circle), hydrated ion pairs (square), and hydrated ion clusters with three ions (triangle downwardly) and 4 ions (solid line) as functions of electrolyte concentration C.
For CaCltwo solutions, as the electrolyte concentration increases, the mole fractions of hydrated private ions decrease, and the mole fraction of hydrated clusters with three ions increases. The mole fraction of individual ions is approximately 0.71 at C = 0.i mol/Fifty, much smaller than the mole fractions of hydrated individual ions in aqueous KCl and NaCl solutions at the same concentration. The mole fraction of hydrated individual ions decreases to 0.24 for an electrolyte concentration of 1.0 mol/L.
For a MgCl2 solution, every bit the electrolyte concentration increases, the mole fractions of hydrated individual Mg and Cl ions decrease, and the mole fractions of hydrated ion pairs and larger ion clusters with three ions increase. Information technology should be mentioned that in MgCl2 solutions, ane can ignore the ion clusters with 4 or more ions because their mole fractions are extremely low.
Figure 2 shows that, for a selected electrolyte concentration, the mole fractions of hydrated individual cation ions follows the society Na+ > Yard+ > Mgtwo+ > Ca2+.
The hydration numbers (considered equally the number of water molecules in the first hydration shell) of individual ions, ion pairs, and larger ion clusters were calculated and listed in Tabular array i. In a KCl solution, as the electrolyte concentration C increases, the hydration number of K+ decreases from half dozen.viii (at C = 0.1 mol/50) to half dozen.iii (at C = one.0 mol/L). A like behavior of the hydration numbers of individual ions was found experimentally by Mancinelli et al. (32) As the electrolyte concentration C increases, the hydration number of Cl– remains constant and approximately 7.3. The hydration numbers of ion pairs, ion clusters with three ions, and ion clusters with four ions are 10.9–11.five, 14.5–15.3, and 18.0–18.6, respectively. (The range of values is a issue of the dependence of the hydration number on electrolyte concentration.)
Table i. Boilerplate Hydration Number of Individual Ions, Ion Pairs, and Larger Ion Clusters for KCl, NaCl, CaCl2, and MgCl2 Solutions with Various Concentration C
For a NaCl solution, every bit the electrolyte concentration increases, the hydration numbers are 5.4–v.5, 7.one–7.3, 9.9–10.three, 12.viii–thirteen.two, and 15.4–16.0 for individual Na+, individual Cl–, ion pairs, ion clusters with three ions, and ion cluster with 4 ions, respectively. The hydration number of individual Na+ agrees with the issue (5.3) experimentally provided by Mancinelli et al. (32) and the upshot (five.v) theoretically provided by Straatsma and Berendsen. (ix) Our results show that the hydration numbers of private Na+ is well-nigh insensitive to electrolyte concentration.
For CaCl2 solutions, as the electrolyte concentration increases, the hydration numbers of individual Ca2+, individual Cl–, ion pair, cluster with three ions, and cluster with four ions, are in the ranges 6.4–6.7, half-dozen.eight–seven.four, 8.8–ix.5, 12.i–xiii.4, and 13.1–15.8, respectively.
For MgCl2 solutions, when the electrolyte concentration varies from 0.1 to 1.0 mol/L, the hydration numbers of Mg2+, Cl–, ion pair, and clusters with iii ions, are in the ranges 5.6–five.vii, seven.0–vii.three, viii.5–ix.0, and xi.8–12.0, respectively. The hydration number of private Mgii+ ion is in agreement with the first-principles molecular dynamics result (5.8) provided by Tommaso and de Leeuw. (33) Yet, in Tommaso and de Leeuw'south work, no ion pairs or larger ion clusters were investigated.
To provide information regarding the construction of water beyond the get-go hydration crush of any private ion, ion pair, or larger ion cluster, the hydrogen bonding numbers were calculated. A hydrogen bond is generated when the altitude between the donor O atom in one water molecule and acceptor O atom in the other water molecule is less than 3.5 Å and the angle O–H···O is less than 30°. (28) When the H2O molecules of the first hydration beat out of any individual ion, ion pair, or larger ion cluster are present as donors, for whatsoever KCl solution, the hydrogen bonding numbers of H2O of the offset hydration shell of individual M+, individual Cl–, ion pairs, and ion clusters with three ions are in the ranges 6.46–7.35, 4.02–4.28, viii.29–9.06, and 10.65–12.50, respectively (Figure 3a). From Tabular array ane, one tin can see that the hydration numbers of Thou+ and Cl– are around vii. However, the hydrogen bonding numbers of H2O of the kickoff hydration trounce of individual K+ is much larger than those from Cl–. This is caused by the orientation of water molecules around the ions. The O atoms in H2O prefer K+ and the H atoms prefer Cl–. Hence, the H2O molecules around K+ prefer to exist donors, while the H2O molecules effectually Cl– adopt to be acceptors (this decision is confirmed by both Figures iii and 4). The hydrogen bonding number for all H2O molecules in the kickoff trounce of ion clusters with three ions possess larger fluctuations than those from individual ions and ion pairs. This occurs because the ion clusters with three ions can acquire various conformations, which provide different hydrogen bonding networks. The hydrogen bonding numbers in NaCl solutions take a similar behavior (Figure 3b).
Figure 3
Effigy iii. Hydrogen bonding numbers of H2O of the first hydration beat of individual Q (Q = K+, Na+, Ca2+, Mg2+, circle), private Cl– (square), ion pair (triangle upwards), and ion cluster with iii ions (triangle down) as functions of electrolyte concentration when the HtwoO of the first hydration shell of private ion, ion pair, or ion cluster present as donors.
Figure four
Figure 4. Hydrogen bonding numbers of H2O of the showtime hydration vanquish of individual Q (Q = Chiliad+, Na+, Ca2+, Mg2+, circumvolve), private Cl– (square), ion pair (triangle up), and ion cluster with three ions (triangle down) every bit functions of electrolyte concentration when the HiiO of the beginning hydration crush of private ion, ion pair or larger ion cluster are present equally acceptors.
For CaCl2 solutions at a selected concentration, the hydrogen bonding numbers of HiiO of the first shell of Ca2+ is close to those of ion pairs (Figure 3c). The hydrogen bonding number of all H2O molecules of the first shell of Ca2+, Cl–, ion pairs, and ion clusters with three ions follows the order Cl– < Ca2+ ∼ ion pairs < ion clusters. For MgCl2 solutions, the hydrogen bonding number of H2O of the first shell of Mg2+, Cl–, and ion pairs follows Cl– < Mgii+ < ion pair (Figure 3d).
Based on Tabular array one and Effigy iii, the hydrogen bonding number per H2O molecule of the first hydration shell was obtained when all H2O molecules of the offset hydration shell of ions, ion pairs, and larger ion clusters are present as donors. In KCl solutions, the hydrogen bonding numbers per H2O molecule were one.02–one.09, 0.55–0.59, 0.74–0.79, and 0.72–0.82 for H2O molecules of the first hydration trounce of individual Chiliad+, individual Cl–, ion pairs, and ion clusters with three ions, respectively. In NaCl solutions, the hydrogen bonding numbers per HtwoO molecule were 1.x–ane.15, 0.56–0.59, 0.75–0.lxxx, and 0.73–0.92 for the H2O molecules of the starting time hydration beat of individual Na+, private Cl–, ion pair and ion clusters with three ions, respectively. In CaClii solutions, the hydrogen bonding numbers per HiiO molecule are 1.17–1.24, 0.56–0.59, 0.82–0.98, and 0.73–0.79 for HtwoO of the offset hydration crush of individual Ca2+, individual Cl–, ion pair and ion clusters with 3 ions, respectively. In MgCltwo solutions, the hydrogen bonding numbers per H2O molecule are i.21–1.30, 0.55–0.59, and 0.88–i.00 for H2O of the kickoff hydration trounce of individual Ca2+, individual Cl–, and ion pair, respectively.
We also provide hydrogen bonding information when the HiiO of the first hydration shell of individual ions, ion pairs, or larger ion clusters are present as acceptors. Generally, for a selected electrolyte concentration, the hydrogen bonding number of a H2O molecule of the first hydration shell of ion, ion pairs, and larger ion clusters with three ions follows the lodge: ion clusters with three ions > ion pairs > Cl– > Q, where Q = K+, Na+, Ca2+, Mgtwo+ (Figure four). In KCl solutions, the hydrogen bonding numbers per H2O molecule of the first shell are in the ranges 0.70–0.75, 0.lxxx–0.87, 0.73–0.80, and 0.70–0.eighty for individual M+, individual Cl–, ion pair, and ion clusters with three ions, respectively. Based on Table 1 and Effigy 4, one can also obtain the hydrogen bonding number per HtwoO molecule of the get-go hydration trounce whose h2o molecules human activity every bit acceptors. For NaCl solutions, the hydrogen bonding numbers per H2O molecule are in the ranges 0.68–0.71, 0.81–0.86, 0.seventy–0.77, and 0.69–0.74 for individual Na+, individual Cl–, ion pair and ion clusters with iii ions, respectively. For CaCl2 solutions, the hydrogen bonding numbers per HtwoO molecule are 0.59–0.63, 0.70–0.85, 0.66–0.76, and 0.73–0.78 for individual Caii+, private Cl–, ion pairs, and ion clusters with three ions, respectively. For MgCl2 solutions, the hydrogen bonding numbers per HtwoO molecule are 0.61–0.68, 0.79–0.86, and 0.63–0.78 for private Ca2+, individual Cl–, and ion pairs, respectively.
The hydrogen bonding between the water molecules of the first hydration shell of individual ions, ion pairs, or larger ion clusters are small. For all the water molecules of the first hydration beat of private ions, the values are smaller than 0.four. The values of hydrogen bonds are smaller than 1.v and 2 for all water molecules of the first hydration shells of ion pairs and larger ion clusters with iii ions, respectively. From Figures 3 and 4, i tin conclude that the hydrogen bonding numbers of H2O of the commencement hydration shells of individual ions, ion pairs, and larger ion clusters are virtually insensitive to the electrolyte concentration; they are sensitive to the nature of ions, ion pairs, and ion clusters.
Determination
In conclusion, past employing molecular dynamics simulations, the ion structures and their hydration numbers in aqueous solution were adamant for private ions, ion pairs, and larger ion clusters. The hydration numbers of hydrated individual Na+ and Mg2+ ions are insensitive to the electrolyte concentration, whereas those of hydrated private K+ and Ca2+ ions are weakly sensitive. As the electrolyte concentration increases, the hydration numbers of ion pairs and larger ion clusters alter piddling. Nevertheless, the ion structures and their mole fractions are electrolyte concentration-dependent. For ion clusters of MgCl2, merely those with three ions could be identified. For NaCl, KCl, and CaClii solutions, ion clusters with three, four, 5 or even more than ions, were found, but for clusters with more than four ions, the mole fractions were extremely depression. Our results show that the nature and conformation of ions play a significant role in the hydrogen bonding numbers of H2O of the offset hydration shells of individual ions, ion pairs, and larger ion clusters. The hydrogen bonding numbers of H2O of the first hydration shells are insensitive to the electrolyte concentration. When H2O of the showtime hydration shell are donors, the hydrogen bonding number per HtwoO molecule follows the club Yard+ < Na+ < Ca2+ < Mgtwo+ for individual cations, the order 1000+ ∼ Na+ < Ca2+ ∼ Mg2+ for ion pairs, and the society Thou+ ∼ Na+ ∼ Ca2+ for ion clusters with three ions. When the H2Os of the start hydration shell are acceptors, the hydrogen bonding number per H2O molecule follows the social club K+ > Na+ > Mg2+ > Ca2+ for individual cations, the order K+ ∼ Na+ ∼ Ca2+ ∼ Mgtwo+ for ion pairs, and the lodge K+ ∼ Na+ ∼ Catwo+ for ion clusters with three ions.
Source: https://pubs.acs.org/doi/10.1021/acs.jpcb.5b06837
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