A common question in organic chemistry is that of regioselectivity: "where will my molecule react?" This is an important question, but it can be difficult to predict (automated transition state finding is unreliable, and even if it were reliable, it would quickly become quite expensive).
One of the more interesting 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.
Fukui indices are generated using CM5 charges computed at the GFN1-xTB level of theory, which serve as a low-cost surrogate for DFT-level charge information. The input molecule is first optimized with GFN2-xTB, and then charges for the neutral, reduced, and oxidized molecules are computed. From these values, the three Fukui indices can be calculated. Let Qn represent the atom-centered charges of the reduced molecule, Q0 represent the atom-centered charges of the neutral molecule, and Qp represent the atom-centered charges of the oxidized molecule. Then:
f(-) := Qp - Q0
f(+) := Q0 - Qn
f(0) := (Qp - Qn) / 2
Global electrophilicity is computed at the GFN2-xTB level of theory. The global electrophilicity index ω is computed in terms of the electronic chemical potential μ and the chemical hardness η, which in turn can be computed in terms of the electron affinity (EA) and ionization potential (IP):
μ = -(EA + IP) / 2
η = IP - EA
ω := η**2 / 2*μ
For DFT methods, Janak's theorem can be used to replace EA and IP with the HOMO and LUMO energy, respectively, which simplifies the calculation of the global electrophilicity index. For semiempirical methods, EA and IP are computed directly using vertical excitation energies.