Subject: Re: CCL:Electrostatic solvation model

From: Hans Martin Senn <[email-masked]>
Date: Wed, 13 Mar 2002 21:31:41 -0700

At 17:22 Uhr +0000 13.3.2002, Andrew Horsfield wrote:

>Can anyone point me to a proof of the following equation for the
>electrostatic contribution to the solvation energy:
>
>   U = 1/2 \sum_{ij} Q_i q_j / r_{ij}
>
>where Q_i is a charge on the solute, and q_j is an induced charge on the
>solute/solvent interface.

At 21:33 Uhr +0100 13.3.2002, Andreas Bender wrote:
>d) But - now you counted each interaction twice! Divide by 2, and you have
>the equation you mentioned.

This is not about double-counting; the Q and the q are different entities.

The factor 1/2 comes from the polarization of the dielectric (or the 
destabilizing interaction between the induced charges q, if you wish) 
that consumes exactly 1/2 of the stabilizing interaction between the 
solute charges and the induced charges. So the net gain in energy, U, 
is only half the interaction energy.
The underlying assumption here is that the dielectric is homogeneous, 
isotropic, and linear. That is, the polarization of the dielectric 
depends linearly on the electric field.

This goes all under the label "electrostatics of polarizable media". 
The ultimate reference is
	C. J. F. Böttcher, Theory of Electric Polarization, 2nd ed.,
	Elsevier, Amsterdam, 1973, Vol. 1.
But Jackson (i.e., J. D. Jackson, Classical Electrodynamics, 3rd ed., 
Wiley, New York, 1999) should also give a derivation. I think a clear 
and simple explanation in terms of a charging process is given in
	http://gilsonlab.umbi.umd.edu/ce_www1a.pdf.

Cheers,

Hans

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