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 ( ) of hydrated lithium ion clusters [Li(H2O)n]+ up to n = 6. In [Li(H2O)n]+ clusters, the values can be calculated from the normal vibration frequencies according to Bigeleisen and Mayer's theory. To obtain the values of , the normal vibration frequency calculations were carried out for optimized structures of [Li(H2O)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 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(H2O)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 values converges for n ≥ 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.