ABSTRACT
To account for the stability of a molecule, Pearson [19] has introduced an important parameter, viz., chemical hardness. For an N-electron system, the second derivative of energy with respect to N, keeping external potential v r( ) xed, is considered to be a measure of the chemical hardness [20]:
η = ∂ ∂
1 2
2 E
(13.2)
The hardness can be expressed in terms of ЄHOMO and ЄLUMO as follows [17]:
(13.3)
Electronegativity (χ) [21] (negative chemical potential [μ] [22]) for an N-electron system is de ned as the rst-order number derivatives of total energy (E) as follows:
χ −µ= = ∂ ∂
(13.4)
where v r( ) is the external potential. Using a nite difference approximation, χ may be expressed as [17]
χ = +I A
2 (13.5)
The nucleus-independent chemical shift (NICS) has been de ned as [23] “absolute magnetic shieldings computed at ring centers (nonweighted mean of the heavy atom coordinates).” The NICS is considered as the negative value of the magnetic shielding at a chosen point in a molecule. In general, a small value (negative or positive) of NICS identi es a system as nonaromatic, whereas a signi cant negative NICS value indicates the system as aromatic and a signi cant positive NICS value classi es a system as antiaromatic.
