Chemistry Reference
In-Depth Information
surface, and total negative surface are calculated, as are the numerous differences,
ratios, and products of these types of surfaces. Moreover, some CPSA descriptors are
calculated using only the donor-acceptor hydrogen atoms, while other descriptors
use only the surface that is accessible or inaccessible to the solvent. There are almost
40 CPSA descriptors.
4.3.11 M
olecular
s
hape
and
s
ize
d
escriptors
The value of these descriptors depends on the spatial distribution of atoms; therefore,
they are a measure of the shape and size of a molecule. The descriptors that do not
consider the connectivity of the atoms could be considered geometrical descriptors.
The descriptors that do consider the connectivity of the atoms are called
topological
descriptors
.
One of the simplest descriptors of molecular shape is the radius of gyration (R
G
).
R
2
G
= 1/M · Σ m
i
r
2
i
.
(4.23)
In Formula (4.23), M is the molecular mass,
m
is the mass of the atom
i
, and
r
is
the distance between the atom
i
and the center of mass. Using the tabulated values of
the atomic mass
m
and interatomic distances
r
(distances that are a result of geom-
etry optimization), a gravitational index I
grav
is calculated.
I
grav
= Σ (m
1
· m
2
/r
12
2
).
(4.24)
The summation in Formula (4.24) can be calculated for all atom pairs or only for
all pairs of bonded atoms. The gravitational index is a measure of the spatial distri-
bution of masses in the molecule and is similar to the geometrical principal moments
of the inertia descriptor. An
electronic index
I
elec
is calculated with a similar formula
I
elec
= ∑ (| q
1
- q
2
|/r
12
2
).
(4.25)
where q are net atomic charges and r is the distance between the atoms with the
charges q
1
and q
2
.
The I
elec
index is a measure of the spatial distribution of the electrical charges in
the molecule. Similar to the I
grav
index, the electronic index I
elec
can be calculated for
all pairs of atoms or only for all pairs of bonded atoms.
A wide range of topological indices are calculated for molecular graphs. In these
calculations, kenographs are usually used, that is, the graphs in which the vertices
are the heavy atoms (any type) and the edges are chemical bonds (any type also).
The
g
degree of the vertex is the number of vertices linked directly to the considered
vertex, and the vertices having
g
= 1 are the peripheral atoms.
The values in the adjacency matrix and the values in the distances matrix are
used for calculations. In the adjacency matrix, there is the value 1 if vertices on
the line
i
and column
j
are connected, and the value 0 if the vertices are not con-
nected. The distances matrix contains the topological distances between vertices,
that is, the least number of steps in the graph of the molecule to reach the vertex
