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18O/16O and D/H Isotopic Preference in Hydration Spheres of Alkali Metal

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18O/16O and D/H Isotopic Preference in Hydration Spheres of Alkali Metal 18O=16O and D=H Isotopic Preference in Hydration Spheres of Alkali Metal Ions Takao Oi Faculty of Science and Technology, Sophia University, 7-1 Kioicho, Chiyodaku, Tokyo 102-8554, Japan Reprint requests to T. O.; Fax: +81-3-3238-3361, E-mail: [email protected] Z. Naturforsch. 66a, 569 – 575 (2011) / DOI: 10.5560/ZNA.2011-0019 Received January 27, 2011 / revised May 7, 2011 With the final goal set at theoretical elucidation of experimentally observed isotope salt effects, molecular orbital calculations were performed to estimate the 18 O=16 O and D=H isotopic reduced partition function ratios (RPFRs) of water molecules around lithium, sodium, and potassium ions. As model water molecules in the ith hydration sphere of the cation in aqueous solutions containing that cation, we considered water molecules in the ith hydration sphere that were surrounded by wa- + ter molecules in the (i + 1)th hydration sphere in clusters, M (H2O)n (M = Li, Na or K; n up to 100). The calculations indicated that the decreasing order of the 18 O preference over 16 O in the pri- mary hydration sphere is: Li+ > (bulk water) ≥ Na+ > K+. That is, water molecules in the primary hydration spheres of the Li+, Na+, and K+ ions are, respectively, enriched, slightly depleted, and depleted in the heavier isotope of oxygen relative to water molecules in bulk. No such preference was observed for hydrogen isotopes in any hydration sphere or for oxygen isotopes in the secondary and outer hydration spheres. Key words: Reduced Partition Function Ratio; Isotope Salt Effects; Hydrogen and Oxygen Isotopes; Alkali Metal Ions; Hydration Spheres. 1. Introduction ferent from that in bulk water. In relation with isotope effects, this difference will be reflected in the values of The distribution of isotopic water molecules in the 18 O=16 O and D=H reduced partition function ra- vapour and liquid phases has been and still is of tios (RPFRs) of water [7], which will cause changes in great concern in such areas as geochemical studies the degree of isotope fractionation. on the natural isotope fractionation processes of wa- Estimation of isotopic reduced partition function ra- ter and isotope separation by distillation techniques. tios (RPFRs) based on molecular orbital (MO) calcu- Between pure liquid water and its vapour in equilib- lations is a useful tool for the elucidation of equilib- rium, the heavier isotopes of oxygen, 18 O, and hydro- rium isotope effects that solely depend on the molecu- gen, D, are both preferentially fractionated into the liq- lar vibration of isotopic species, since the equilibrium uid phase and the lighter ones, 16 O and H, into the constant of the isotope exchange reaction between two vapour (vapour pressure isotope effects of water) [1,2]. chemical species or between two phases of the same Even if salt is added to the liquid phase, the direc- substance is given as the ratio of the RPFRs of the two. tion of the 18 O=16 O and D=H isotope fractionations In our previous paper [8], we reported the estimation does not change, but the degrees of the fractionation of the 18 O=16 O and D=H RPFRs of water molecules change depending on the kind of salt added and its con- in hydration spheres around a sodium ion based on the centration (isotope salt effects) [3–6]. To understand molecular orbital (MO) calculations as a step towards and elucidate these experimental results, knowledge the satisfactory elucidation of isotope salt effects ex- on 18 O=16 O and D=H isotope effects in hydration perimentally observed. Similar calculations were ex- spheres around solute ions is certainly required. The tended to lithium and potassium ions. In this paper, we sum of forces acting on an oxygen atom or a hydrogen report the results of such calculations and compare the atom of a water molecule forming hydration spheres 18 O=16 O and D=H RPFRs of water molecules around around a solute ion in aqueous solution may be dif- lithium, sodium, and potassium ions. c 2011 Verlag der Zeitschrift fur¨ Naturforschung, Tubingen¨ · http://znaturforsch.com 570 T. Oi · O and H Isotopic Preference in Hydration Spheres 2. Theory and Calculational Method used for the MO calculations [10], and Gauss View (Gaussian Inc.) and Free Wheel (Butch Software Stu- When two chemical species or two phases of a sub- dio) were used for the graphics. The value of the scale stance are in equilibrium with each other, the heav- factor for the wave number correction was 0.8985, ier isotope tends to be enriched in the species or the having been determined by the least-squares method phase with a larger RPFR. The general expression for using the observed and calculated wave numbers of the RPFR is, under Born–Oppenheimer and harmonic monomeric H2O species in the gas phase [11]. oscillator approximations, given as, + We first optimized the structures of the M (H2O)n f clusters (n = 1 – 10, 12, 16, 20, 24, 28, 32, 36, 40, 0 ui exp(−ui=2)=f1 − exp(−ui)g (s=s ) f = ∏ 0 0 0 ; (1) 44, 50, 56, 62, 70, 80, 90, and 100; M = Li and i=1 ui exp(−ui=2)=f1 − exp(−ui)g + K) in a sequential way. For example, Li (H2O)100 0 0 where ui = hcwi=(kT) and ui = hcwi=(kT); f is the de- was optimized starting from the optimized structure of + gree of freedom of molecular vibration, h the Planck’s Li (H2O)90 and ten water molecules set up around it. 0 + constant, c the velocity of light; wi and wi are the wave For larger n values, two series of M (H2O)n clusters + numbers of the ith molecular vibration of the heav- were considered; two series of Li (H2O)n (n = 12 or + ier and the lighter isotopic species, respectively; k is larger) clusters starting from the optimized Li (H2O)8 + the Boltzmann constant and T the absolute tempera- and two series of K (H2O)n (n = 62 or larger) start- + ture [7]. ing from the optimized K (H2O)56 were optimized. As models of lithium ion- or potassium ion-bearing No symmetry consideration was made in the geom- + aqueous solutions, we considered M (H2O)n (M = etry optimization calculations: For each of the struc- Li, K) clusters with n up to 100. We tried to locate the tures considered, bond lengths, bond angles, and di- metal ion at the center of the cluster as much as pos- hedral angles were varied independently to achieve sible. In the clusters, a water molecule in the primary the geometry optimization. At the optimized struc- hydration sphere was defined as the one that directly ture, the vibrational analysis was carried out. The interacted with the metal ion through its oxygen atom. RPFR of a specific hydrogen or oxygen atom was A water molecule in the secondary hydration sphere then calculated by using scaled wave numbers of was defined as the one hydrogen-bonded to a water the isotopic species. Only the mono isotope substi- molecule in the primary hydration sphere, and so forth. tutions were considered for all the possible combi- As models of a water molecule in the primary hydra- nations of isotopic species with the H and 16 O ba- tion sphere in lithium ion- or potassium ion-bearing sis. That is, for each of the optimized structures, the + 16 16 + 16 aqueous solutions, we considered water molecules in RPFRs of the M [HD O(H2 O)n−1]=M (H2 O)n + + 18 16 + 16 M (H2O)n (M = Li, K) that directly interacted with and M [H2 O(H2 O)n−1]=M (H2 O)n (M = Li, K) the metal ion and were surrounded by (hydrogen- isotopic pairs were estimated. bonded to) water molecules in the secondary hydra- tion sphere. Similarly, as models of the water molecule 3. Results and Discussion in the secondary hydration sphere in lithium ion- or 3.1. Optimized Structures potassium ion-bearing aqueous solutions, we consid- + ered water molecules in M (H2O)n (M = Li, K) As an example of the optimized structures of the + that were hydrogen-bonded to water molecule(s) in M (H2O)n (M = Li, K) clusters considered, that of + the primary hydration sphere and surrounded by wa- the Li (H2O)100 cluster is shown in Figure1. No ter molecules in the third hydration sphere, and so imaginary wave number was obtained in the vibra- forth. tional analyses of those clusters that were used for the All MO calculations were made at the HF/6-31G(d) RPFR estimation. Every optimized structure was thus level of theory for the consistency with our previous at the global or local minimum of the potential energy calculations on RPFRs of water clusters, (H2O)n with surface. n up to 100, modelling bulk water [9] and on RPFRs Except for small n values, the hydration number in + of Na (H2O)n clusters with n up to 100, modelling the primary hydration sphere of the lithium ion was sodium ion-bearing aqueous solutions [8]. The Gaus- four, which was within the range of four to six gener- sian 98 and 03 program packages (Gaussian Inc.) were ally accepted for the aqueous lithium ion [12, 13]. As T. Oi · O and H Isotopic Preference in Hydration Spheres 571 Fig. 2. Water molecules with an oxygen atom with a hydro- gen bond (G1) and without a hydrogen bond (G2) in the primary hydration sphere of the lithium ion in the optimized + Li (H2O)100 cluster. The black sphere denotes the lithium ion and the darker and lighter gray spheres denote oxygen and hydrogen atoms, respectively.
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