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.

The reduced partition function ratios (RPFRs) of Li + (Solv) n (in which Solv ) H 2 O, H 2 S, and CH 3 OH) clusters with different values were calculated, to investigate the solvent effect of the isotopic effect of the lithium. Structures of three solvated clusterssLi + (H 2 O) n , Li + (H 2 S) n , and Li + (CH 3 OH) n swere optimized by an ab initio molecular orbital method, and their RPFRs were calculated by frequency analysis. The RPFR of the solution was estimated by the extrapolation of the cluster values. The most-stable isomers of all three clusters for n g 4 have four solvent molecules in their first shell. The RPFR is dependent mainly on the number of solvent molecules in the first shell, and the size dependence of the RPFR plateaus at n ) 4. The extrapolation of these values can be regarded as the RPFR in the solutions. The RPFRs are ∼1.07 for Li + (H 2 O) n and Li + (CH 3 OH) n and are ∼1.03 for Li + (H 2 S) n . The smaller RPFR of Li + (H 2 S) n is attributed to the smaller binding energy of the Li-S bond, which is weaker than that of the Li-O bond. The present results suggest the possibility of ionophores with S atoms (such as thioether, etc.) for lithium isotopic separation.