First, thanks for the quick response!
However, I guess it has a different reason:
Typically the Coulomb energy is calculated by determining the potential due to a charge distribution q(r), let's say phi(r). Then, the Coulomb energy of the charge distribution is given by 1/2 integral dr phi(r) * q(r). Here, the factor of 1/2 comes in due to double counting. If, however, a potential phi_ext(r) due to some external charge distribution is given the Coulomb energy should be integral dr phi_ext(r) q(r) without the factor of 1/2.
Now comes the part I'm only guessing:
Probably espresso determines one potential due to the internal charge distribution and the boundary condition set with "pot_diff" and hence has this prefactor of 1/2 for both terms.
Why is this such a problem for me? Well, I try to simulate a simple model of a super capacitor (ions between electrodes). Here, I'm interested in calculating the heat flow or the change in entropy. The only way to do this at the moment is calculating the electric work dW needed to charge the capacitor and then calculating the heat dQ from the change in internal energy dU via dQ = dU - dW. Using the energy observable (which includes the Coulomb term that yields the strange energies) I get utterly ridiculous results (dQ >> dW). Unfortunately, I cannot calculate the missing Coulomb term from the quantities offered by the energy variable ("coulomb", ("coulomb", 0)...). Maybe you have some thoughts?
Thanks for bearing with me and I'm looking forward to hearing from you.