Chemistry Reference
In-Depth Information
r
C
is a constant (the radius of the carbon atom in the sp
3
hybridization state)
r
i
are constants (tabulated values for atomic radii in different hybridization states)
Using the shape indices K
1
and K
2
, the Kier algorithm calculates the flexibility
index, Φ.
Φ = K
1
· K
2
/ N
(4.39)
According to the value of the flex1
1
index, propane is very rigid; however, accord-
ing to the Φ index, this hydrocarbon has an average flexibility. The flex1
1
descriptor
estimates the order of flexibility 2,2,3,3 - tetramethyl-butane <
trans
- decaline <
cycloheptane <
n
-butane, yet, for the same four hydrocarbons, the flexibility order
according to the index Φ is exactly the reverse. The inverse of the descriptors of flex-
ibility flex2,
1
, flex2,
2
, and Φ can be considered rigidity descriptors.
4.3.15 a
roMaticity
d
escriptors
The application of quantitative methods for the evaluation of the molecular aroma-
ticity is common (Bird 1992; Schleyer et al. 1996; Fores et al. 1999; Cyranski et al.
2002; Bultinck et al. 2005; Espinosa et al. 2005; Mitchell et al. 2005; Zborowski
et al. 2005; Shishkin et al. 2006; Tarko 2008a; Tarko 2010); however, the listing of
aromaticity descriptors has emerged recently (Tarko 2008a; Tarko 2010).
The aromaticity A for (just) one chemical bond can be computed using the empir-
ical formula based on the B
PM6
bond order of analyzed bond,
A = 1000 - 6250 ∙ (1.4406 - B
PM6
)
2
.
(4.40)
The range of A values for aromatic bonds is [0, 1000]. The range of A values for
anti-aromatic bonds is [−1000, −350]. For groups of adjacent chemical bonds, that
is, various topological routes on the kenograph, the formula for the calculation of
aromaticity is much more complicated because it measures the alternating character
of chemical bonds (Tarko 2008a).
The number of aromatic bonds; minimum, average, and maximum value of the
aromaticity of the aromatic bonds; percentage of aromatic bonds; number of aro-
matic molecular zones; or aromaticity of the peripheral topological path can be cal-
culated as descriptors. Some descriptors simultaneously reflect the aromaticity and
size of the molecule. Other descriptors reflect the concentration of aromaticity in
small areas of the molecule.
When the values of aromaticity descriptors have been obtained, the application
of QSPR/QSAR methodology makes possible the verification of the dependence of
some macroscopic properties (magnetic, electrical, optical, biochemical) on aroma-
ticity (Tarko 2010).
Figure 4.8
shows the aromaticity map for Black
Indanthrone
(Tarko 2010), a
molecule having semiconductor properties (Inokuchi 1952). The presence of single
bonds that are invisible on the map induces the existence of some nonaromatic cycles
and the fragmentation of the molecule in five aromatic areas having low, medium,
