Fukui Index Calculation

A common question in organic chemistry is that of regioselectivity: "where will my molecule react?" This is an important question, but it is naïvely difficult to predict without complex transition-state studies, which requires scientists to have a detailed atomistic picture of the transition state.

One of the more interesting low-cost solutions to this problem is "Fukui indices," named after Kenichi Fukui (1981 Nobel Laureate in Chemistry), which quantify how a molecule's electron distribution changes upon adding or removing an electron.

How It Works

Fukui indices are generated using charges computed at a given level of theory. Rowan allows users to independently tune what level of theory is used for geometry optimization and what level of theory is used to compute the charges. For routine low-cost work, we recommend using GFN1-xTB or GFN2-xTB; for more complex cases, DFT charges are typically more accurate.

A typical Fukui calculation begins from a neutral molecule and computes charges for that molecule, the corresponding oxidized radical cation, and the corresponding reduced radical anion. From these values, the three Fukui indices can be calculated. Let $Q_n$ represent the atom-centered charges of the reduced molecule, $Q_0$ the atom-centered charges of the neutral molecule, and $Q_p$ the atom-centered charges of the oxidized molecule. Then:

Global electrophilicity can also be computed. The global electrophilicity index ω is computed in terms of the electronic chemical potential $\mu$ and the chemical hardness $\eta$, which in turn can be computed in terms of the electron affinity ($EA$) and ionization potential ($IP$):

For DFT methods, Janak's theorem can be used to replace the electron affinity and ionization potential with the HOMO and LUMO energy, respectively, which simplifies the calculation of the global electrophilicity index. For semiempirical methods, the electron affinity and ionization potential are computed directly using vertical excitation energies.