Descriptors for Organometallic Complexes - Fundamental QSARs for Metal Ions - page 109

An electron that receives energy equal to the energy of the HOMO orbital leaves
the molecule via ionization. An electron that receives energy equal to the difference
in energy between two molecular orbitals can occupy a molecular orbital that was
unoccupied initially (molecular excitation).
The number of occupied orbitals, the orbitals' energies, and the differences
between the energy of orbitals are descriptors. For example, expression of the ion-
ization potential and the electron affinity through the energies of the HOMO and
LUMO orbitals (Delchev et al. 2006) allows definition of the chemical hardness as
(E LUMO - E HOMO )/2. The value of these descriptors often correlates with certain mac-
roscopic properties such as reactivity, magnetic, electrical, and optical properties.
For the guanine A isomer in Figure 4.4 , E LUMO = −0.59 and E HOMO = −9.04 are
calculated, and for the guanine B isomer, E LUMO = −0.67 and E HOMO = −8.88 are cal-
culated. The value of the chemical hardness for isomer B is smaller than that of
isomer A.

4.3.6 s tatic i indices oF r eactiVity
Some authors (Fukui et al. 1954; Klopman 1974; Fukui 1975) believe that the HOMO
and LUMO orbitals have a particular importance for the reactivity of the molecules.
In the case of a donor-acceptor type of interaction, an electron transfer takes
place between molecule A and B. In the case of a change type of interaction, an elec-
tron transfer takes place between molecule A and B. As a rule, when two molecules
A and B interact, the electron transfer that requires the smallest energy is the transfer
from the HOMO orbital of a molecule to a LUMO orbital of the other molecule.
Which molecule participates in the interaction with the HOMO orbital and which
participates with the LUMO orbital depends on the relative value of the differences
Δ 1 and Δ 2 between the energies of those particular orbitals.

Δ 1 = E LUMO A − E HOMO B Δ 2 = E LUMO B − E HOMO A (4.15)

The literature in the field does not specify the value for which the differences
Δ 1 and Δ 2 should be considered large or small. When the differences Δ 1 and Δ 2 are
large, the donor-acceptor interactions are charge-controlled reactions. In this case,
the interaction between the molecules A and B is made through the atoms that pos-
sess the largest net charges (of opposite sign). When the differences Δ 1 and Δ 2 are
small, the donor-acceptor interactions are orbital-controlled reactions. In this case,
the interaction between the molecules A and B is made through the atoms that pos-
sess the highest absolute values of the orbitals' coefficients.
For each heavy atom in the analyzed molecule, one can calculate (Fukui 1975) the
reactivity indices I N (nucleophilic), I E (electrophilic), and I R (one-electron).

I N = Σ c 2 HOMO /(1 − E HOMO ) (4.16)

I E = Σ c 2 LUMO /(10 + E LUMO ) (4.17)

I R = ΣΣ c HOMO c LUMO /(E LUMO − E HOMO ) (4.18)