The last remaining piece of the puzzle is the exchange correlation energy which remains unknown. No analytical form has yet been identified, therefore an approximation must be used.
In the Local Density Approximation (LDA) the contribution of each volume element to the total exchange correlation energy is taken to be that of an element of a homogeneous electron gas of the density at that point.
The values of 
used are based on Monté Carlo
calculations of the energy of homogeneous electron gases of varying
densities by Ceperley and Alder [5].
Generalised Gradient Approximations (GGA) estimate the contribution of
each volume element to 
based upon the magnitude and
gradient of the electron density within that element. The GGA used in
the calculations reported herein is that due to Perdew and Wang
[6].