Chemistry Reference
In-Depth Information
d
j
= Σ M
ij
(4.29)
μ = (d
i
· d
j
)
−1/2
(4.30)
J = L/(L − N + 2) Σ μ
k
(4.31)
The mean square distance (MSD) index is a weighted version of the W index,
where the weighting factor Z is the product N · (N - 1).
1/2
N
N
∑
∑
d
i
2
MSD1/Z·
=
(4.32)
i=1
j=1
The cyclomatic number (C) descriptor is simply defined to be L - N + 1, where
L is the number of chemical bonds and N is the number of atoms. In calculation of
the cyclomatic number, the molecular graph can be used with or without hydrogen
atoms.
In QSAR calculations, the number and size of circuits are descriptors. Circuits
are cyclic topological paths that, with the exception of the starting node, visit the ver-
tices only once. There are procedures that allow the identification, on the molecular
graph, of all topological paths, and therefore of all circuits (Balaban et al. 1985). The
minimum length of the circuits is 3 (cycle of 3 atoms). The identified circuits can
be ordered by length, starting with the shortest one. The first C circuits on the list
(C is the cyclomatic number) are the chemical cycles. For acenaphthene in Figure 4.7,
C = 14 - 12 + 1 = 3 is calculated and there are identified one circuit of length 5, two cir-
cuits of length 6, two circuits of length 9, one circuit of length 10, and one circuit of
length 11. Formula (4.33), where C is cyclomatic number (C > 1) and T is number of
circuits, calculates, according to PRECLAV documentation, a
crowding index
CIC
of circuits. This descriptor has values within the [0, 1] range.
CIC = (T - C)/(2
C
- C - 1)
(4.33)
The CIC = 1 for acenaphthene; therefore, the degree of condensation of the cycles
in this molecule is maximum.
A broad category of topological indices are calculated based on the values of
the Detour (
Maximal Topological Distance
) Matrix (Ivanciuc and Balaban 1994).
Recently, new descriptors have been proposed in this category, which are useful for
evaluating solubility in water (Talevi et al. 2006).
FIGURE 4.7
Acenaphthene.
