J.-F. Gal, O. Mó et al.
fairly good agreement with the experimental values.[42,43] Although DFT
methods do not properly describe dispersion interactions, these are a
rather small component of LCB values and the good performance of
these methods, as far as Li+ complexes are concerned, has been assessed
in several combined theoretical and experimental studies.[18–20,44]
All calculations have been carried out by the Gaussian 03 series of pro-
grams.[47] The bonding characteristics of the complexes formed were ana-
lyzed by means of the atoms-in-molecules (AIM) theory.[48] For this pur-
pose, the electron density was evaluated at the different bond critical
points (bcps), and the corresponding molecular graph was obtained.
Li+ binding enthalpies, LBE values, were evaluated by subtracting the
energy of the neutral ligand and that of Li+ from the energy of the com-
plex, after including the zero point energy (ZPE) corrections and the
aforementioned thermal corrections at 373 K, which is the temperature
of the reference scale used to anchor our data. The corresponding lithium
cation basicities (LCB values, Gibbs free energy of binding) were ob-
tained by using the entropy values evaluated at the B3LYP/6-31G(d)
level. The use of a harmonic approximation induces errors in the low-fre-
quency torsions of the systems under investigation, which are significant-
ly anharmonic, and therefore in our estimates of the Gibbs free energies.
Unfortunately, we have not found experimental information on the en-
tropy for large saturated hydrocarbons, such as n-heptane, but this infor-
mation is available for n-butane[45] and for tetramethylsilane,[46] which has
four free-rotating methyl groups. Our calculated entropies at the B3LYP
level differ from the experimental one by 7.5 and 7 kJmolꢀ1 Kꢀ1, respec-
tively, which implies an error in the Gibbs free energy at 373 K of 2.6–
2.8 kJmolꢀ1. Hence, we can estimate that our error of the Gibbs free en-
ergies for the compounds under investigation should not be larger than
4 kJmolꢀ1. Given that, as discussed above, both neutral and cationized
species are a mixture of several conformers in the gas phase, we have
also included the corresponding entropy of mixing, evaluated as follows
[Eq. (3)]:
Acknowledgements
Dr. Michꢂle Decouzon and Dr. Christine Dubin-Poliart are gratefully ac-
knowledged for their highly skilled technical assistance in performing
FTICR experiments. This work has been partially supported by the DGI
Project No. BQU2003-0894, by the Project MADRISOLAR. Ref.: S-
0505/PPQ/0225 of the Comunidad Autónoma de Madrid, and by the
COST Action D26/0014/03. A generous allocation of computational time
at the CCC of the Universidad Autónoma de Madrid is also gratefully ac-
knowledged. We also thank Dieter Barth for his help in recent synthesis
work.
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ly
(Scheme 3).
The different conformers were gener-
stretched
aliphatic
chain
n
n+1
ꢀ
Scheme 3.
ated by torsions around the C C
bonds (n=1–9, numbering given in
Scheme 1). Each of the conformers
generated in this way can now be
ꢀ
taken as a precursor of new conformers by successive C C torsions. It is
obvious that, in particular for PhACTHERNG(U CH2)4Ph, but mainly for PhACHTRE(UGN CH2)7Ph,
the number of conformers is so high that it would be an impossible task
to calculate all of them. Nevertheless, from the exploration of the smaller
compounds with two and three methylene groups in the aliphatic chain,
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very high in energy. Even though, more than one hundred structures
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that of the global minimum by less than 7 kJmolꢀ1, assuming that in
terms of a Boltzmann distribution the population in the gas phase of the
less-stable conformers would be negligibly small. To make our discussion
more systematic, the different conformers were numbered following the
stability order.
The situation is quite different for the [Li+···Ph
(CH2)nPh] complexes.
Here again, the number of conformers is very high and increases dramat-
ically as the number of carbon atoms in the aliphatic chain increases.
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with only one of the benzene rings (which are the great majority of the
local minima on the PES) are much less stable than those in which the
metal interacts with both of the benzene rings. Hence, only the latter
(which are very few) matter as far as the calculation of the Li+ binding
energies is concerned.
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7682
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