Previously we introduced an electron force field which we used to simulate matter at extreme conditions -- the dissociation and ionization of hydrogen at intermediate densities, and the Auger dissociation of hydrocarbons. We would like to simulate excited electron dynamics at lower temperatures, investigating processes such as electrolysis, electrochemistry, combustion, unimolecular decomposition, and organic reactions with solvated electrons. For this to be possible, we need to improve the scope and accuracy of the electron force field.
We assumed previously that we could treat the electrons as if they were all the same shape and could be well-represented by spherical Gaussian functions. For hydrogen and saturated hydrocarbons with excess energy, this approximation was a reasonable one. For molecules with lone pairs or multiple bonds, however, the approximation breaks down and in the old eFF (1) atoms with lone pairs were too easily ionized, (2) radical electrons in alkyl radicals were too diffuse, and (3) multiple bond electrons were too diffuse, all indications that we were not properly describing p electrons.
In this chapter, we describe a way to include the effects of different electron shapes. This results in an improved description of first-row atoms, atom hydrides, and hydrocarbons and, to a lesser extent, hydrogen bonds and molecules containing heteroatoms.
How can we incorporate electrons with different shapes into an electron force field? One approach is to make the electron's shape explicit, by writing each orbital as a sum of higher angular momentum functions. This is the tack taken by most ab initio methods today. With the floating spherical gaussian orbital (FSGO) method, water has a too-small bond angle of versus exact , but making the lone pairs variationally optimized sums of floating and functions makes it possible  to raise the bond angle to .
It is difficult however to make this approach general. Adding floating higher angular momentum basis functions to FSGO causes the method to become as complex and expensive as traditional ab initio methods, with the added complication that there are additional parameters to optimize, and problems if basis functions move on top of each other and become linearly dependent.
We take a different approach. First, we make electron shape an implicit scalar variable that depends solely on the electron's proximity to the nuclei in the system. This approximation arises from the observation that it is the nuclei and their associated core electrons that most greatly perturb and determine electron shape. Second, we make energy terms such as Pauli repulsion and wavefunction kinetic energy depend on electron shape. Using such an approach, we maintain the simplicity of the spherical Gaussian description while still accounting for the diversity of electron shapes present in excited electron systems.
The chapter is organized as follows. First we discuss the new energy expressions, and give a physical motivation for the terms we have changed and added. Then we study the energies and structures of first row atoms, atom hydrides, carbon-carbon single and multiple bonds, heteroatom single and multiple bonds, and van der Waals dimers. Along the way we point out both how eFF has improved, and what systems it can describe better, and then demonstrate systems that we can newly describe that the old eFF could not describe. We also discuss limitations that remain, and suggest what the causes of those limitations might be.