in constrast to the observed crystal structure of Li(TPP)+.
Nevertheless, the calculated bond lengths agree quite well
with those observed in the crystal structure. The C-C and
C-N bond lengths clearly correspond to those expected from
the most reasonable valence-bond depiction of TPP, and
neutral TPP is simply acting as a donor ligand to the Li+
cation. The doubly oxidized porphyrin OETPP has similar
C-C and C-N bond lengths throughout its porphine core.10
The aromaticity of a normal-valent porphyrin is generally
understood to be a consequence of an 18 π-electron circuit
that is present in its ring system. The doubly oxidized
Li(TPP)+ would therefore be expected to have an antiaro-
matic 16 π-electron circuit, and exactly such a circuit is
evident in Li(TPP)+sit is highlighted in blue in Figure 2.
Evidence from 1H NMR and calculated nucleus-independent
chemical shifts (NICS)14 both agree with the picture of an
antiaromatic 16-membered C-N inner ring with four ap-
pended ethene groups. The 1H NMR spectrum of [Li(TPP)]-
[BF4] in CD2Cl2 contains a singlet due to the Câ protons
(see Figure 2 for atom-type labels) at 5.94 ppm (a chemical
shift typical of alkene protons), far upfield from the typical
resonance of about 9 ppm for the Câ protons of an aromatic
porphyrin. NICS values were calculated (Gaussian 03,
B3LYP/6-31G*) for Li(porphine)+ at the centroid of a
pyrrole ring (labeled “a” in Figure 2) and at the centroid of
two C-N bonds (labeled “b” in Figure 2). The NICS value
at “a” is -0.6 and that at “b” is +36.5, indicating a strong
paratropic ring current along the outlined 16-atom circuit
with the appended ethene groups excluded. Paratropic ring
currents are characteristic of antiaromatic systems,15 as
opposed to the diatropic ring currents of aromatic molecules.
An optimized structure of neutral “porphine” (TPP with the
phenyl groups replaced by hydrogen atoms) was calculated
(B3LYP/6-31G*), and in contrast to the planar structure of
Li(porphine)+ it is moderately saddled and slightly ruffled.
NICS values calculated at the center of the ring system of
porphine and at positions “a” and “b” (analogous to those
in Figure 2) were +13.5, -4.8, and +20.2 ppm, respectively.
The structure of porphine was minimized with an enforced
planar (C4h) geometry, and the calculated NICS values at
the center, “a”, and “b” were +20.0, -6.8, and +30.4,
respectively. All of those values are consistent with a
paratropic ring current in the central 16-atom C-N circuit
of porphine. The lower NICS value at “b” in the saddled
geometry of porphine (relative to either planar porphine or
Li(porphine)+) indicates that Li+ increases the paratropic ring
current, at least in part, by maintaining planarity in the ring
system. NICS calculations in the vicinity of a bare Li+ cation
show that it has negligible influence on NICS values.
Many porhyrin radical cations, in which the oxidation state
of the ring system is 1-, undergo a distortion that is often
described as a bond-length alternation along the 16-
membered C-N inner ring.4 The distortion is the same as
that observed in Li(TPP)+, except that the magnitude of the
distortions in the radical cations is smaller than that in
Li(TPP)+, and is at most half of that observed in Li(TPP)+.
A normal-valent porphyrin has nearly degenerate a1u and a2u
HOMOs, and the bond-length changes in the radical cations
are due to a pseudo-Jahn-Teller distortion caused by the
unequal occupancy of the (former) a1u and a2u molecular
orbitals.4 The bond-length alternation in Li(TPP)+ could be
considered to be a consequence of a similar pseudo-Jahn-
Teller distortion, but of a magnitude twice as large as that
in the porphyrin radical cations because two electrons have
been removed instead of one. The calculated HOMO of C4h
Li(porphine)+ (Figure 3) has the same au symmetry as the
Figure 3. The HOMO of Li(porphine)+ (left) and N-CR-Cmeso
CR and CR-Cmeso-CR-N dihedral angles (right).
-
SOMO of the porphyrin radical cations.4 The image of the
HOMO of Li(porphine)+ in Figure 3 is in the same
orientation as the valence-bond structure of Figure 2, and
the alternating bonding and antibonding π-interactions around
the 16-membered inner ring further clarify the cause of the
bond-length alternation. An alternative explanation of the
bond-length alternation in Li(TPP)+ is simply that it adopts
the valence-bond structure of Figure 2. The situation is quite
similar to that in the singly reduced Al(TPP)1 and the doubly
reduced Si(TPP),2 which both have alternating lengthened
and shortened C-C bonds along the 20-atom periphery of
their porphine core. The bond-length changes in Al(TPP)
are due to a Jahn-Teller distortion caused by the single
electron in one of its formerly degenerate eg LUMOs. The
distortion in Si(TPP) is approximately twice as large, and
can be viewed either as a larger Jahn-Teller distortion
(caused by two electrons instead of one) or simply as Si(TPP)
adopting a new valence-bond structure.
The deviations from planarity in the porphine core of
Li(TPP)+ can be understood in relation to its au HOMO, and
those deviations support the assertion that the 16-atom inner
ring is antiaromatic. For each pyrrole ring, the five atoms of
its ring and the two Cmeso to which it is attached are very
nearly coplanar. However, the combined ruffling and sad-
dling of Li(TPP)+ lead to the N-CR-Cmeso-CR and CR-
Cmeso-CR-N dihedral angles indicated in Figure 3. The
average dihedral angle across a C-C double bond (where
there is a π-bonding interaction in the au HOMO) is 1.5°
and that across a C-C single bond (where there is a
π-antibonding interaction in the au HOMO) is 24.4°. In a
normal conjugated system such as 1,3-butadiene, which is
neither aromatic nor antiaromatic, the lowest energy con-
formation is planar s-trans,16 which maximizes the interaction
(14) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer,
P. v. R. Chem. ReV. 2005, 105, 3842-3888.
(15) Pople, J. A.; Untch, K. G. J. Am. Chem. Soc. 1966, 88, 4811-
4815.
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