A R T I C L E S
Ferna´ndez et al.
Our calculations (uBP86/def2-TZVPP) indicate that the
lowest energy form of the parent 1,2-cyclopentadiene is a
biradical singlet state which lies ca. 2.1 kcal/mol below the
triplet structure. To see whether a biradical singlet state may
also play a role for allenes 1a-c, we first checked the stability
of the BP86 wave functions. The calculations clearly indicate
that the BP86 wave function is stable with regard to its spin
state. Moreover, we obtained the same optimized structures
using the unrestricted uBP86 method with no measurable spin
contamination (〈S2〉 ) 0.000). Therefore, it is not surprising that
the MP2/def2-TZVPP level of theory also leads to quite similar
optimized structures (see Figure 1) and to stable wave functions.
Furthermore, we also performed a multireferential CASSCF/
def2-TZVPP calculation including the π-framework (5 orbitals)
and the lone pair orbital at the central carbon atom in the active
space for 1a. The one electron symbolic density matrix which
is calculated at the CASSCF level clearly indicates that there
is negligible mixing of the configurations which provides further
support to the stability of the wave function. Therefore, a
multireferential character for compounds 1a-c similar to the
parent 1,2-cyclopentadiene can be safely ruled out. Additionally,
we also computed the triplet-singlet gaps for the latter com-
pounds at the BP86/def2-TZVPP level. The computed energy
differences (∆E ) 38.9, 64.0, and 54.2 kcal/mol for 1a, 1b,
and 1c, respectively) show that the situation in the allenes 1a-c
is very different from the parent 1,2-cyclopentadiene.
The theoretical data for 1d-g suggest that the same conclu-
sion can be drawn as for 1a-c (Figure 2, Table 1). It is worth
noting that the optimized geometry for 1f agrees quite well with
the structure which was determined by X-ray structure analysis.
To gain further insight into the degree of aromaticity in
derivatives 1a-g, we calculated the magnetic (NICS)9 and
geometric (HOMA)10 aromaticity indices (Table 2). 3,5-
Unsubstituted derivatives 1a and 1d are predicted to have a high
degree of aromaticity by both magnetic and structural criteria,
whereas 3,5-bis(π-donor) substituted derivatives 1b-c and 1e-g
demonstrate a significant reduction in aromatic character.
Figure 1. Optimized structures (top, BP86/def2-TZVPP and MP2/def2-
TZVPP, in parentheses) for 1a, 1b, and 1c (white, gray, red, and blue colors
denote hydrogen, carbon, oxygen, and nitrogen atoms, respectively), and
their HOMO, HOMO-1, and lowest energy occupied π-type orbitals
(HOMO-5, HOMO-7, and HOMO-6, respectively, bottom) computed at
the BP86/def2-TZVPP. Bond distances are given in Å.
systems 1a-c, and experimentally relevant molecules 1d-g. The
optimized (BP86/def2-TZVPP and MP2/def2-TZVPP) structures
for 1a-c are shown in Figure 1 (top), and selected geometric
parameters for all allenes 1 are summarized in Table 1, along
with crystallographically determined values for compound 1f.
Apparent trends for model compounds 1a-c are the lengthening
of the endocyclic NN and NC bonds, and the increasing bond
order of the exocyclic CY bonds, as the donor strength of the
substituent increases. Concurrently, the endocyclic nitrogen
atoms increasingly pyramidalize, the sum of bond angles going
from 360.0° to 336.8° and 331.1° for the parent 1a, the hydroxyl
substituted 1b and amino substituted 1c, respectively. It is worth
noting that the exocyclic amino groups in 1c are less pyrami-
dalized (sum of angles ) 344.1°) than the endocyclic ones
(computed hybridization: sp1.75 for the exocyclic N atoms and
sp2.01 for the endocyclic ones in their respective CN bonds).
Moreover, the exocyclic N atoms are engaged in shorter bonds
with C3 and C5 than the endocyclic ones, which is also reflected
in higher bond orders.
Thus, from a purely structural perspective, it seems that while
cyclic electron delocalization, as in Lewis structure 1′, is
prevalent for the parent compound 1a, the placement of donor
substituents in the 3 and 5 positions of the ring favors noncyclic
conjugative interactions as in 1′′; not surprisingly, the weight
of form 1′′ increases with the donor strength of the substituent.
The analysis of the occupied π-type orbitals for 1a-c further
supports the conclusion that delocalization involving the exo-
cyclic substituents occurs at the expense of aromaticity. In
particular, the lowest lying occupied π-type orbital resembles
that of the isoelectronic and aromatic cyclopentadienide in the
case of 1a, but shows significant discontinuity around the ring
for 1b, and even more for 1c (Figure 1, bottom).
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