CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

quantum mechanics based approaches bypass this problem, investigations based on this
approach are limited only to clusters of small size 82-83 . More importantly, simulation or
quantum mechanics based study does not provide any explicit analytical expression for
the dependence on the number of solvent molecules. Work in this direction was earlier
initiated by Jortner and coworkers 33 . Theoretical considerations of the ion solvation in
clusters of finite size predict that the detachment energies of a solvated anion should scale
as 1/R linearly, where R is the radius of the solvated clusters and is proportional to the
solvent number, n. In this model, the solvent number dependent detachment energy (both
ΔE VDE (n) and ΔE ADE (n) ) of the cluster expressed as 9 ,
∆E =∆E ∞ +A ‐1/3
1
Where, refers to ADE or VDE, ∆E ∞ is the bulk detachment energy and A is the
proportionality constant. Here δ is an equivalent solvent number corresponding to the
solute and accounts for the contribution of the solute to the cluster volume. However, the
extrapolation results obtained from this simple model are found to be in poor agreement
with the experimental results 9, 35 .
Dixon and coworkers raised an important question concerning whether the
exponent (1/3) is constant for all anionic clusters of different charges or not and argued
that the exponent should be dependent on the nature of the ion. 35 Accordingly, another
empirical law was proposed, written as
∆E = ∆E ∞ + A (n+ ‐p
2
The calculated results based on this model were better than the earlier models but
the error was still quite significant, particularly for the di-anion hydrated clusters. Most
importantly, the variation of p from system to system is not properly defined. The
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