As before, the system is composed of point nuclei with coordinates and momenta , and of electrons defined by spherical Gaussian wave packets with positions , translational momenta , sizes , and radial momenta :

(6.2) |

Then the overall energy is a sum of the Hartree product kinetic energy, Hartree product electrostatic energy, and exchange and correlation energies:

We define an exchange energy as a pairwise sum over same-spin electrons, and a correlation energy as a pairwise sum over opposite-spin electrons. For the uniform electron gas, we use exchange and correlation functions defined as:

where the parameters are , hartrees, ; and the kinetic energy sum and average electron size are defined as

For systems with nuclei, we use a modified exchange function: