Chemistry Reference
In-Depth Information
methods are quite different. It seems that the accuracy of the PM6 method in the
calculation of this descriptor is higher than the accuracy of some
ab-initio
quantum
mechanics methods (Stewart 2007).
isomer B of guanine ΔHf
f
= + 120.9 KJ. The value of this descriptor suggests that the
isomer A of guanine is much more stable and is present in a much larger quantity in
the mixture of the two isomers. A considerable heat of formation is also calculated
for other isomers of guanine when the hydrogen atoms are bound to the nitrogen
atoms in a different manner.
The value of this descriptor depends on the number and type of atoms, and on the
number and type of chemical bonds in the analyzed species. Accordingly, the heat of
formation weighted by the number of atoms and the heat of formation weighted by
the number of chemical bonds are also used as descriptors.
4.3.8 g
eoMetrical
d
escriptors
The values of the diverse geometrical descriptors depend only on the type of atoms
and on the Cartesian coordinates of these atoms in the minimum energy conformer.
The type of a particular atom can be identified by the tabulated values of the atomic
number, mass, or van der Waals radius. Often included in this category are descrip-
tors whose value depends on other characteristics of atoms. For instance, topologi-
cal indices are sometimes considered geometrical descriptors. However, topological
indices can only be calculated after the identification of the way in which atoms are
connected.
The principal moments of inertia are simple geometrical descriptors defined as
the sum of products of the atomic masses with the distance to the main rotation
axis
x
.
I
x
= Σ m
i
[r
2
i
]
x
(4.19)
The three principal moments of inertia characterize the mass distribution in the
analyzed molecule. The maximum and minimum values of the inertia moments,
I
M
and I
m
, allow the calculation of eccentricity (Arteca 1991), which is a measure of
the deviation from the spherical shape.
ε = [(I
M
)
2
- (I
m
)
2
]
1/2
/I
M
(4.20)
Other very simple geometrical descriptors are the average distance to geometric
center, the maximum distance to geometric center, the standard deviation (SD) of
distances to geometric center, and the variance coefficient of distances to geomet-
ric center. The variance coefficient of distances is SD/average ratio. If the variance
coefficient is calculated considering only the peripheral atoms, this descriptor can be
considered a measure of the unevenness of the molecular surface, a measure of the
deviation of the form of the molecule from the spherical shape, or even a symmetry
index.
