QUANTUM COMPUTATIONAL STUDIES ON PORPHYCENE - Theoretical and Computational Research in the 21st Century - page 169

the so-called zero differential overlap (ZDO) approximation in which δ μv
is set equal to zero unless μ and v are equal. Actually orbitals, which are
centered on the same or even on two directly bonded atoms, have a rather
larger differential overlap. Setting such differential overlap equal zero is
far from being a correct approximation. As mentioned earlier, the essential
advantage of applying the ZDO approximation is the considerable simpli-
fication, it introduces in the computation. The capability of the ZDO meth-
ods to describe the different molecular properties is an important measure
of the appropriateness of the ZDO approximation. Practical experience
with different ZDO methods has proved that they can be brought about
to reasonably represent chemical properties [37-41]. However, it is not
expected that ZDO methods may provide calculated values, which are in
good agreement with rigorous ab initio calculations.

9.3 METHOD OF COMPUTATION

The hardness, softness, electronegativity, electrophilicity index, local soft-
nesses, and Fukui functions, and so on were calculated on the basis of a
new panorama in chemistry called “conceptual density functional theory
(CDFT)” [42], which has ramified research in theoretical chemistry in the
present time.
The AcuraHuckel Version 1.2 software [43] was used to generate the
Hückel determinant for the molecules pyrrol and porphycene. Solving this
determinant, eigenvalues are obtained for the molecular orbitals in terms
of α and β.
The eigen values for the HOMO and the LUMO are taken as the orbital
energy of HOMO and LUMO. The global reactivity descriptors for the
molecules were evaluated considering I = −ε HOMO and A = −ε LUMO (Koop-
mans' theorem) and using the density functional defi nitions [22, 23] [Eqs.
(1), (7), (8), (4), and (13)] of the corresponding reactivity descriptors.
In addition, we have used the eigen functions for the HOMO and the
LUMO to compute the local reactivity parameters, the Fukui functions,
and the local softnesses for the corresponding molecule. The Fukui func-
tions and local softnesses for each site of the molecules are computed us-
ing the Eqs. (23-25) and (27-29).
In order to evaluate the value of α and β for the molecule studied in this
work, we have compared the HOMO and LUMO orbital energies obtained