Kruk et al.
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them involve different number of steps, the data obtained
seem to be unexpected.
modes, those whose main contribution is made by the
Ca—N bond are of special attention, since they remain
almost invariant in both the free bases of porphyrins and
their metal complexes and are barely sensitive to the peri-
pheral substitution of the macrocycle. It should be em-
phasized that we are far from intention to assign the
measured energy value to any certain vibrational mode,
but the role of vibrational modes involving the Ca—N bond
should be distinguished. If this mode (or modes) is pro-
moting, the coordination of metal ions can be considered
as the isoenergetic (adiabatic) motion along the reaction
coordinate. From the thermodynamic point of view, this
promoting mode will be the most efficient regardless of
the symmetry of this mode (there are modes of various
symmetry involving the Ca—N bond).13 It is important
that the same character of compensation for both the free
base and doubly deprotonated porphyrins excludes all
modes involving the N—H bond, because the latter has
no hydrogen atoms bound to the pyrrole rings in the
macrocycle core.
The dependence of ΔH≠ on ΔS≠ made it possible to
determine the compensation temperature (Tc) equal to
342 16 K. The pair correlation coefficient for the linear
regression was found to be 0.966. We found that the cal-
culation of the compensation temperature separately for
the free bases and doubly deprotonated porphyrins showed
the value in the same range but with higher root-mean-
square deviations. This indicates that the common analy-
sis of two sets of data improves the correlation parameters.
There were attempts to ascribe some physical meaning
to the Tc value.10—12 We used the simple statistical Sharp
model for processing the data on Tc.10 The model describes
a conservative polyatomic system with a complex potential
function including various types of interactions between
the atoms. This choice of the potential funciton results in
the quasi-continuous distribution of energy levels. An
important feature of this model is that the model requires
no knowledge of the explicit shape of the energy level
distribution when the number of disturbed states is not too
high and the perturbation is significant. The developed
model makes it possible to obtain the estimation of the
compensation temperature
It has been assumed previously14 that the linear char-
acter of the enthalpy—entropy compensation can be
considered as the manifestation of the additivity source in
the studied systems; i.e., in the considered case, all por-
phyrins in the series should have the same source of ad-
ditivity. This source can be the effect of electronic substi-
tution, which was recently discussed in detail.9 The
electron energy redistribution between the macrocycle and
periphery by both resonance and inductive effects should be
considered as the main reason for the observed tendencies
in changing the complex formation rate with metal ions.
It can be mentioned that the solvent or, more exactly,
vibrational modes of the solvate shell should also be con-
sidered as a source of promoting modes, since the changes
in the solvate shell upon the coordination of the metal ion
in the macrocycle core can also be proposed as a source
of compensatory processes for chemical reactions in solu-
tion.15 However, these effects should be omitted for the
discussed set of data, because the plot reflects the additive
effects in the system and they are due to the differences in
the porphyrin structure rather than in the solvate shell.
This specific feature (structural distinctions) should be
considered as the main one, since in the same solvent with
the same coordinating metal ion in the studied series of
porphyrins the structural diversity of the latter seems to
be the only possible source of the observed effect. By
contrast, only one porphyrin and one metal salt can be
taken but a series of solvents will be used, which would
result in the dependence appeared only as a result of
changing the structure of the solvate shell. Thus, when the
choice of the data set is valid, the single contribution
can be remained and all other possible contributions can
be excluded (or at least suppressed). Such an analysis of
possible contributions will be the subject of our further
research.
Tc = T/(1 – kT/δE),
(1)
where k is the Boltzmann constant, and δE is some char-
acteristic energy for the disturbed transition state (differ-
ence in energies between the disturbed and initial states).
According to the description presented above, δE should
be considered as some average or most probable value
related to the group of disturbed energy levels rather than
the single value. After substitution of the Tc values, tem-
perature T = 298 K (at which the experiments were carried
out), and the Boltzmann constant into Eq. (1), we have
that δE = 19.2 kJ mol–1 (about 1600 cm–1). We believe
that Tc correlates with the energy of promoting vibrational
modes of the reaction, which provide/facilitate the coor-
dination of the metal ion. Thus, the δE value about
1600 cm–1 can be interpreted as the energy of the corre-
sponding vibrational modes of the tetrapyrrole macrocycle.
It is known that the vibrational modes of the porphyrin
macrocycle are not localized12 and all atoms of the macro-
cycle are involved more or less in all vibrational modes.
The role of the molecular fragment (atom, bond, group
of atoms) is described by its contribution to the potential
energy distribution of this vibrational mode, and the same
fragment can contribute substantially to several vibrational
modes. The Ca—Cb, Ca—N, Cb—Cb, and Ca—Cm bonds
contribute predominantly to the potential energy distri-
bution of vibrational modes in a frequency range of
1300—1600 cm–1. The modes with the contribution of the
Ca—Cb, Ca—N, and Ca—Cm bonds, which are necessary
for the arrangement of the metal ion, directly affect the
size (and shape) of the macrocycle core. Among these
Ivanova, Yu. B.
