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 :

(5.1) |

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

There are two major changes from the old eFF. First, we divide electrons into core and valence electrons, and assume they do not switch categories over the course of the simulation. We assume an electron is a core electron if and , where

Second, we make the kinetic and Pauli energies depend on the hybridization of an electron, which can vary during the course of the simulation, and depends on the proximity of the electron to the nuclei present in the system. We have

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

and the factors , , and are defined as follows:

which depend on the hybridization variables and , which equal one for an electron with character only, and zero for an electron with character only. Hybridization is a function of an electron's position relative to the protons and cores (nuclei with core electrons on top of them) in the system. We assume that all nuclei with have core electrons on top of them. The expression for is

while the expression for is

The parameters , , , , , are shown in Table 5.1.

The functions and determine how an electron's versus character varies with their distance from the protons and cores in the system. They are defined as piecewise quintic splines specified so that the function's value, first, and second derivatives match at the points given:

Explicit polynomial expressions for and are given in Table 5.2.