CHEM01200604005 A. K. Pathak - Homi Bhabha National Institute

vertical detachment energy (VDE) and adiabatic detachment energy (ADE), defined
respectively as
∆E , (r, ω) ] , ,
∆E , , , (, , ,
(5a)
5b
Where, A is the electron affinity of the ion A q- in gas phase. In order to have an explicit
expression for VDE and ADE of the system containing finite number of solvent particles,
what is needed is a relation between the pair distribution function g i (r, ω) of the infinite
system and its finite system counterpart g i (r, ω, n). Such a relation may be derived by
following the approach of Salacuse et.al. by means of Taylor-series expansion in powers
of 1/n. 84 Here, the derivation is extended from the nonpolar system to the case of ionpolar
system. Semi-grand canonical ensemble is considered where only the number of
solvent molecules is allowed to fluctuate but the single negative ion is kept fixed in each
member of the ensemble. 85
In this semi grand canonical ensemble, the two-particle
distribution function may be expressed as
, , P P , ,, 6
Where, P is the probability that in equilibrium the system contains n solvent
molecules and a single ion and P
, ,, is the pair distribution function for a
system containing a single anion and n solvent molecules. Here, , and represent
the position vector of the ion, and the position vector and orientation of the solvent
molecule, respectively. Now expanding , ,, in the number of particles around
the average number of particles, one get
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