Shouldn't the form be \nabla \cdot \textbf{D} = \rho_{free} which would have me missing a part of the total charge?
Going through the steps using \textbf{D}=-\epsilon(r)\nabla V(r) gives me the following result:
-\int \frac{1}{2} V(r) \rho_{free}(r) d^{3}r + \int \rho_{total}(r) V(r) d^{3}r...
This is actually a question pertaining to a paper I'm trying to understand (PRB 73, 115407 (2006)), but I decided to put it here just to be safe.
Homework Statement
The paper I'm reading involves starting with an electrostatic energy contribution, and rewriting it with a green's function...