The electron force field traces its origins to two lines of inquiry that evolved over the past decades. The first was the development of fermion molecular dynamics methods [17] (FMD) in the late 70s and wave packet molecular dynamics (WPMD) methods [16] in the late 90s, which applied quasiclassical representations of elementary particles to the study of nucleon dynamics [14,15,18], hydrogen plasmas [11,38], ion collisions [19], and so on. In these studies, electrons and nucleons were often represented by Gaussian functions, and effective potentials between these functions were created to reproduce desired static and dynamic properties. The focus was less on describing the details of bonding and electronic structure, and more on obtaining qualitatively correct dynamics; the most advanced effective potentials due to Klakow were limited to describing the interactions of hydrogen, helium, and lithium atoms. Most of these methods employed pairwise potentials between particles, and scaled as , with being the number of particles.

The second was the development of the floating spherical Gaussian orbital (FSGO) method by Frost [8] in 1964, which combined a single Gaussian function per electron basis with an *ab initio* energy expression which scaled as . This method was able to describe bonding between atoms from hydrogen through argon, with good geometries for molecules containing at most one lone pair, and particularly good geometries for hydrocarbons. The energetics of bonding were described less well however.

The electron force field combines the scope of FSGO methods with the speed of WMPD methods, and improves on the accuracy of both methods. We discuss in the next chapter a first-generation eFF which contains kinetic energy, electrostatic energy, and pairwise Pauli repulsion terms, and gives a reasonable description of hydrogen atom reactions and hydrocarbons while scaling as . With this simple force field, we study matter at extreme conditions -- the dissociation and ionization of hydrogen at intermediate densities, and the Auger dissociation of hydrocarbons.

In subsequent chapters, we improve the accuracy of eFF by (1) considering the effects of different electron shapes and hybridizations, (2) considering the delocalized electrons in a uniform electron gas, and (3) parameterizing exchange and correlation as separate interactions. In our zeal to determine the optimal eFF for certain interactions, we emerged with with different force fields for different electron types, such as core-like electrons in lithium clusters, valence-like electrons in atom hydrides, and delocalized electrons in metals and the uniform electron gas. This collection of electron force fields constitutes the second generation eFFs.

In the future, we will attempt to reunify our many eFFs into a single third-generation eFF that can interpolate between extremes of reactivity and bonding, and act as a universal method for describing large-scale excited electron dynamics.