Theoretical Estimation of Lithium Isotopic Reduced Partition Function Ratio for Lithium Ions in Aqueous Solution

Abstract

The reduced partition function ratio for lithium ions in an aqueous solution is derived from the extrapolation of the values of the reduced partition function ratio (r values can be calculated from the normal vibration frequencies according to Bigeleisen and Mayer's theory. To obtain the values of f n r , the normal vibration frequency calculations were carried out for optimized structures of [Li(H 2 O) n ] + (n ) 1-6) using the RHF/6-31+G(d), RHF/6-31++G(d,p), RHF/6-311+G(d) and MP2/6-31+G(d) methods by means of the ab initio molecular orbital method. All of those structures having high symmetry were confirmed to have real harmonic frequencies at the RHF/6-31+G(d) and RHF/6-31++G(d,p) levels. For the two RHF methods, the value of f n r increases to about 1.07 with an increase of the hydration number n, and reaches maximum at n ) 4. In the most stable isomers of [Li(H 2 O) n ] + clusters for n ) 5 and 6, respectively, the first hydration shell is saturated with the four water molecules, and the size dependence of the f n r values converges for n g 4. The converged value 1.07 can, therefore, be regarded as the reduced partition function ratio for lithium ions in aqueous solution, and gives the upper limit of the isotopic separation factor in an aqueous solution-exchanger system.

Lithium and boron isotopes in illite-smectite: The importance of crystal size

“…According to our results, the Li fractionation between illite and water at 300°C is ϳ6‰ larger than indicated by the empirical work (more negative ␦ 7 Li in the solid). An equation with the same slope as the empirically derived fractionation would nicely tie our datum with calculations of Li isotope fractionation between tetrahedral (aqueous) and octahedral (clay) coordinated lithium species based on reduced partition function ratios (Oi et al, Yamaji et al, 2001) supporting ␣ values of 0.976 at 25°C. The difference of Ϫ6‰ between our experimental results and the empirical data from marine sediments may be due to the crystal size effect and/or incomplete removal of interlayer Li, which would make bulk clay ␦ 7 Li analyses more positive.…”

Reduced partition function ratios for isotopes of hydrated alkali and alkaline earth ions calculated by a simple electrostatic model

“…It is seen that our values for lithium isotopes are close to the first set of results calculated by Yamaji et al (2001) or fall between their two sets. The same refers to β factors for magnesium and calcium isotopes, which are compared with results of Rustad et al (2010).…”

“…They also tried to calculate this equilibrium constant from statistical thermodynamics, but their value was evidently too large (1.29-1.33). Theoretical estimation of lithium isotopic reduced partition function ratio for lithium ions in aqueous solution were made by Yamaji et al (2001), who report their ab initio results for only one temperature (298 K): their maximum value of lithium isotope fractionation factor between hydrated ion and "Li + exchanger" is 1.07.…”

Lithium speciation in aqueous fluids at high P and T studied by ab initio molecular dynamics and consequences for Li-isotope fractionation between minerals and fluids

“…Aqueous fluids are usually thought to contain four-fold coordinated Li(H 2 O) 4 + -clusters (Yamaji et al, 2001;Ikeda et al, 2007). However, the assumption that Li(H 2 O) 4 + -clusters are the main lithium species in such fluids is based on theoretical calculations at ambient conditions (Yamaji et al, 2001;Ikeda et al, 2007).…”

“…However, the assumption that Li(H 2 O) 4 + -clusters are the main lithium species in such fluids is based on theoretical calculations at ambient conditions (Yamaji et al, 2001;Ikeda et al, 2007). It is unclear to what extent different cluster types with e.g.…”