Just as conventional force fields parameterize the ground state potential between nuclei, with electrons implicitly included, electron force fields parameterize the potential between nuclei and simplified electrons, with more detailed degrees of freedom implicitly included. The electrons in an electron force field are Gaussian wave packets whose only parameters are its position and its size.

Using a simple version of the electron force field, we compute the dissociation and ionization behavior of dense hydrogen, and obtain equations of state and shock Hugoniot curves that are in agreement with results obtained from vastly more expensive path integral Monte Carlo methods. We also compute the Auger dissociation of hydrocarbons, and observe core hole decays, valence electron ionizations, and nuclear fragmentation patterns consistent with experiment.

Despite the simplicity of the electron representation, with a judicious choice of potentials we are able to describe electrons of different shapes in different environments.

In one chapter, we show we can describe *p*-like valence electrons using spherical Gaussian functions, enabling us to compute accurate ionization potentials and polarizabilities for first row atoms, and accurate dissociation energies and geometries of atom hydrides and hydrocarbons.

In another chapter, we show that we can describe delocalized electrons in a uniform electron gas using localized eFF orbitals. We reproduce the energy of a uniform electron gas, including correlation effects; and following the historical development of density functional theory, we develop a preliminary eFF that can compute accurate exchange and correlation energies of atoms and simple molecules.

In the following pages, we have highlighted successes of eFF, but have not shied away from analyzing in depth areas where it could be improved. We hope that this combination of promising results and critical analysis stimulates and assists further research in this exciting field.