eFF, a method to simulate large scale excited electron dynamics

Basic concept

We have developed a modified version of eFF, called eFF2, that better describes p electrons. It does so by modifying the interactions between valence electrons that are in the vicinity of a core electron (Figure 24).

For example, it causes the Pauli interaction between valence electrons in a nitrogen atom to be attractive, reflecting the exchange stabilization present between same-spin electrons in the high-spin multiplet ground state (Hund's rule). There is another term that increases the kinetic energy of valence electrons surrounding the core slightly, in accordance with the additional node present in a p versus an s orbital. These terms are analogous to angle and bond terms in classical force fields.

Figure 24: Pauli interaction between electrons with varying degrees of p character. (a) Electrons near the core become more p-like, while the presence of nearby protons causes electrons to become more s-like. (b) The core makes electrons in an annular region around it p-like. (c) p-like electrons attract each other, in accordance with Hund's rule. (d) p-like electrons have an angular dependence in their repulsion which encourages them to be $ 90^{o}$ away from each other.

Improved atoms

With eFF2, ionization potentials of atoms match experimental values (Figure 25), and valence electrons close-pack into symmetric shells (Figure 26).

Figure 25: The new eFF reproduces the correct periodic trend of ionization potentials for hydrogen through neon, while the old eFF is only suitable for describing hydrogen through carbon.

Figure 26: Valence electrons of boron through neon arrange themselves into symmetric shells.

We also compute polarizabilities, which have units of volume, and can be taken as a measure of the size of electrons in a system. Values for atoms are reasonable, and for helium-like ions [49] agree with high-level theory over six orders of magnitude (Figure 27).

Figure 27: The new eFF computes reasonable polarizabilities for first-row atoms. Oxygen and fluorine are exceptional cases, as eFF gives those two atoms a permanent dipole moment which they should not have.

eFF may prove to be a fast and useful way to obtain molecular polarizabilities, since dipole-dipole, atomic polarizabilities, and Pauli effects are taken into account in a self-consistent way.

Improved multiple bonds in hydrocarbons

Double and triple bonds with eFF2 are well described (Figure 28) with excellent geometries and reasonable bond dissociation energies (Figure 29).

Figure 28: Electrons in single, double, and triple bonds.

Figure 29: Bond dissociation energies and geometry parameters for ethane, ethylene, and acetylene.

Geometries of complex hydrocarbons with multiple bonds match closely to DFT geometries (Figure 30).

Figure 30: Optimized eFF and B3LYP/6-311g** alkenes superimposed, with root-mean-squared deviations (RMSD) given in parenthesis (angstroms).

This includes hydrocarbons whose bonds with the original eFF were too long (Figure 31).

Figure 31: Improved geometries for old eFF ``problem hydrocarbons''.

Good description of atom hydrides, both open and closed shell

The dissociation energies and geometries of atom hydrides and simple hydrocarbons, including ones with multiple bonds, are well reproduced (Figures 323334).

Figure 32: eFF describes both open-shell and closed-shell atom hydrides properly. Red and blue spheres denote electrons with up and down spins while gray sphere represent electron pairs.

Figure 33: Atom hydride bond angles and lengths.

Figure 34: Atom hydride bond dissociation energies.

Work still remains

Lone pairs do not repel each other strongly enough, causing bonds between heteroatoms to be too strong. For example, the bond dissociation energy of $ \mathrm{F_{2}}$ using eFF2 is 275 kcal/mol versus 38 kcal/mol experimental.

The electrons in intramolecular complexes do not repel each other strongly enough either. For example, water dimer is bound too strongly and at too short of a separation distance. And the repulsion between two $ \mathrm {H_{2}}$ molecules is too weak, causing the hydrogen shock Hugoniot to be incorrect.

For these reasons, we continue to use the original version of eFF for atoms with Z=1-6, and development efforts continue to turn eFF2 into a replacement for eFF.