energies of the ground and excited states is equivalent to a mapping to the differences between these energies and, hence, to UV spectra.
The modeling based on the LDM is also shown capable of the empirical prediction of the substituents effects on the UV absorption surpassing the Hammett
constants model in this case. Smith et al. ascribe the inefficiency of modeling
spectra with Hammett constants to their calculations from ground state equilibrium
constants or bond dissociation energies when the energy gap between a ground and
an excited state is what governs UV absorption [37]. One can argue, however, that
the ground state equilibrium constants are rooted in the ground-state electron
density that fixes the Hamiltonian and the ground and excited eigenstates, as
stipulated by the first Hohenberg-Kohn theorem [35, 36]. It appears that it is by
virtue of this theorem that our modeling of UV spectra, based on the LDMs/DMs of
the ground states, can predict electronic excitation energies as described below.
Protonated para-benzoic acids exhibit a primary band *230 nm and a secondary weaker band *270 nm [37–39]. The primary band is red-shifted by substitutions in the aromatic ring whether electron donating or withdrawing [38].
Electron withdrawing substituents alter λ max of the secondary band only if they are
ππ*-chromophores e.g. −NO 2 and −NHCOCH 3 [38], two substituents which we
excluded from the correlation for that reason.
Non-chromophoric electron withdrawing groups can red-shift the primary band
so much as to overlap and merge with the secondary band sometimes. Electron
donors, in contrast, red-shift both the primary and secondary bands [38]. The first
band of a series of 8 para-substituted benzoic acids, modeled with the Frobenius
inter-matrix distances calculated for the −COOH sub-matrices taking unsubstituted
benzoic acid as reference is displayed in Fig. 3.4b and yields the following linear
regression equation:
k max ¼ 222:50 þ 3:4171 Â 10
3
 d
½COOH
LDM ðBA; BAS)
½r
2
¼ 0:973; q
2
¼ 0:944; St:Err: ¼ 5:74; n ¼ 8
;
ð3:27Þ
where the closeness of q
2 and r
2 is again indicative of strong predictivity of the
model that surpass the modeling with traditional descriptors such as the Hammett σconstants (see Ref. [21] for details).
3.4.2 LDM-Based Similarity of Rings-in-Molecules (RIMs)
to Benzene as a Measure of Local Aromaticity
Aromaticity remains one of the most elusive properties to define in chemistry. It is
an abstract term that implies a plethora of properties without being identified with
any of these properties. There are several measures of aromaticity that capture one
or another of these chemical or physical properties. These measures fall in at least
70
C.F. Matta et al.
The modeling based on the LDM is also shown capable of the empirical prediction of the substituents effects on the UV absorption surpassing the Hammett
constants model in this case. Smith et al. ascribe the inefficiency of modeling
spectra with Hammett constants to their calculations from ground state equilibrium
constants or bond dissociation energies when the energy gap between a ground and
an excited state is what governs UV absorption [37]. One can argue, however, that
the ground state equilibrium constants are rooted in the ground-state electron
density that fixes the Hamiltonian and the ground and excited eigenstates, as
stipulated by the first Hohenberg-Kohn theorem [35, 36]. It appears that it is by
virtue of this theorem that our modeling of UV spectra, based on the LDMs/DMs of
the ground states, can predict electronic excitation energies as described below.
Protonated para-benzoic acids exhibit a primary band *230 nm and a secondary weaker band *270 nm [37–39]. The primary band is red-shifted by substitutions in the aromatic ring whether electron donating or withdrawing [38].
Electron withdrawing substituents alter λ max of the secondary band only if they are
ππ*-chromophores e.g. −NO 2 and −NHCOCH 3 [38], two substituents which we
excluded from the correlation for that reason.
Non-chromophoric electron withdrawing groups can red-shift the primary band
so much as to overlap and merge with the secondary band sometimes. Electron
donors, in contrast, red-shift both the primary and secondary bands [38]. The first
band of a series of 8 para-substituted benzoic acids, modeled with the Frobenius
inter-matrix distances calculated for the −COOH sub-matrices taking unsubstituted
benzoic acid as reference is displayed in Fig. 3.4b and yields the following linear
regression equation:
k max ¼ 222:50 þ 3:4171 Â 10
3
 d
½COOH
LDM ðBA; BAS)
½r
2
¼ 0:973; q
2
¼ 0:944; St:Err: ¼ 5:74; n ¼ 8
;
ð3:27Þ
where the closeness of q
2 and r
2 is again indicative of strong predictivity of the
model that surpass the modeling with traditional descriptors such as the Hammett σconstants (see Ref. [21] for details).
3.4.2 LDM-Based Similarity of Rings-in-Molecules (RIMs)
to Benzene as a Measure of Local Aromaticity
Aromaticity remains one of the most elusive properties to define in chemistry. It is
an abstract term that implies a plethora of properties without being identified with
any of these properties. There are several measures of aromaticity that capture one
or another of these chemical or physical properties. These measures fall in at least
70
C.F. Matta et al.