We begin with point nuclei with coordinates and momenta , and electrons defined by spherical Gaussian wave packets with positions , translational momenta , sizes , and radial momenta :

(4.1) |

Then the overall energy is a sum of the Hartree product kinetic energy, Hartree product electrostatic energy, and antisymmetrization (Pauli) energy:

where and are the Pauli potential functions:

where is a measure of the kinetic energy change upon antisymmetrization, and is the overlap between two wave packets:

where , , and . We will explain the motivation for the Pauli expression, and the consequences of the combined energy terms in more detail below.