ABSTRACT
The Fukui function, denoted by f(r), is defined as the differential change in electron density due to an infinitesimal change in the number of electrons [1]. That is,
f (r) ¼ @r(r) @N
, (18:1)
where r(r) is the electron density and
N ¼ ð r(r)dr (18:2)
is the total number of electrons in the system. For isolated molecules at zero temperature, the Fukui function is ill-defined because of the derivative discontinuity [2-4]. To resolve this difficulty, Fukui functions from above and below are defined using the one-sided derivatives,
fþ(r) ¼ @r(r) @N
¼ |{z}lim «!0þ
rNþ«(r) rN(r) «
(18:3)
f(r) ¼ @r(r) @N
¼ |{z}lim «!0þ
rN(r) rN«(r) «
: (18:4)
When a molecule accepts electrons, the electrons tend to go to places where fþ(r) is large because it is at these locations that the molecule is most able to stabilize additional electrons. Therefore a molecule is susceptible to nucleophilic attack at sites where fþ(r) is large. Similarly, a molecule is susceptible to electrophilic attack at sites where f(r) is large, because these are the regions where electron removal destabilizes the molecule the least. In chemical density functional theory (DFT), the Fukui functions are the key regioselectivity indicators for electron-transfer controlled reactions.
