from benzene reveals striking correlations. The eigenvalues of the LDMs taken as
absolute predictors of aromaticity (not compared with benzene) are also highly
correlated with these aromaticity measures as well.
The correlations of common aromaticity indices with the Frobenius distance of a
ring in a PBH from benzene are generally non-linear except possibly in the case of
PDI. Some of these correlations are depicted in Fig. 3.5 and listed in Table 3.2 and
discussed in greater detail elsewhere [72, 73]. Cyclohexane is excluded from
Fig. 3.5 despite of falling on the general trend lines to improve the resolution of the
plot in the region of aromatic rings in PBHs.
3.4.3 LDM-Eigenvalues as Predictors in QSAR
One of the more useful manipulations of a matrix are the linear transformations
giving rise to eigenvectors and eigenvalues. One of us (IS) has recently observed
that there is a strong correlation between the number of electrons (N(Ω)) in the
atomic basins and the eigenvalues of the LDM matrices. The largest eigenvalues are
Fig. 3.5 Correlations between the Frobenius distance of various rings listed in Table 3.2 from
benzene and four common aromaticity indices: HOMA, PDI, FLU, and NICS(0)
74
C.F. Matta et al.