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.