The electrostatic free energy can also be expressed by taking the process of the charging system. The following expression utilizes chemical potential of solute molecules and implements the Poisson-Boltzmann Equation with the Euler-Lagrange functional: Δ Δ G el = ∫ ∫ V ( k T ∑ ∑ i c i ∞ ∞ [ 1 − − exp ⁡ ⁡ ( − − z i q U k T ) ] + p f U − − − − ε ε ( ∇ ∇ U ) 2 8 π π ) d V