**Self energy** The self-energy of a given charge distribution is the energy required to assemble the distribution by bringing in the constituent charges from infinity.

In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium's interactions with it.

The potential energy of two charges i and j is:

U

_{ij} = q

_{i}q

_{j}/r

_{ij} or U

_{ij} = ρ(r

_{i})dr

_{i}ρ

_{j}(r

_{j})dr

_{j}/r

_{ij} The total electrostatic energy U

^{ES} is:

U

^{ES} = ½∑

_{i,j}U

_{ij} = ½∑U

_{ij}= ½∫d

^{3}r

_{i}∫d

^{3}r

_{j}ρ(r

_{i})ρ(r

_{j})/r

_{ij} We can partition the charge density in arbitrary pieces, e.g. in A and B:

U

^{ES} = ½∫

_{A}d

^{3}r

_{i}∫

_{A}d

^{3}r

_{i}ρ(r

_{i})ρ(r

_{i})/r

_{ii} + ½∫

_{B}d

^{3}r

_{j}∫

_{B}d

^{3}r

_{j}ρ(r

_{j})ρ(r

_{j})/r

_{jj} +

2x½∫

_{A}d

^{3}r

_{i}∫

_{B}d

^{3}r

_{j}ρ(r

_{i})ρ(r

_{j})/r

_{ij} The first two terms are the self energies of A and B and the last term is the interaction energy between A and B.

Source:

http://en.wikipedia.org/wiki/Self-energy Intermoleculaire wisselwerkingen, Piet van Duijnen, 1993