2.3 Derivation of quantum chemical reactivity descriptors:
The global reactivity descriptors51,52 like highest
occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital
(LUMO) gap53, ionization potential (I), electron
affinity (A), global hardness (η), global softness (S), chemical
potential (μ), electronegativity (χ), electrophilicity index (ω) were
calculated and compared for the optimized geometries of most stable
conformations of all modifications54-58. The local
descriptors like local softness, local electrophilicity, and local
electrophilic attack were also derived for all these geometries.
Ionization potential (I) = -EHOMO (1)
Electron affinity (A) = -ELUMO (2)
Global hardness (η) = (I-A)/2 (3)
Global softness (S) = 1/2η (4)
Chemical potential (μ) = - (I+A)/2 (5)
Electronegativity (χ) = (I+A)/2 (6)
Electrophilicity (ω) = μ2/2η (7)
Local reactivity descriptors
Fukui function (FF)59-61 provides information about
the local reactivity site within the molecule and it provides a way for
understanding of chemical reactions. These values represent the
qualitative descriptors of reactivity of various atoms in the molecule.
Fukui functions have been done with the basis of B3LYP/6-311G(d,p) level
of theory for electrophilic and nucleophilic attacks. With the help of
Mulliken atomic charges of cationic and anionic states, local Fukui
functions (f k+,f k-)59-61,
local softness values (sk+,
sk-)62,63, and local
electrophilicity indices (ωk+,
ωk-)56-58 have been
calculated using the following equation:
f k+ = [q (N+1) – q (N)]
for nucleophilic attack (8)
f k- = [q (N) – q (N-1)]
for electrophilic attack (9)
f k0 = 1/2 [q (N+1) + q
(N-1)] for radical attack (10)
Local softness values and electrophilicity indices were calculated using
sk+ =
Sf k+,
sk-- =
Sf k-
ωk+ =
ωf k+,
ωk- =
ωf k-,
The + and – signs show nucleophilic and electrophilic attack,
respectively. Where q(N) is the charge on the kth atom for neutral
molecules while q(N+1) and q(N-1) are the same for its anionic and
cationic species, respectively.