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The Bond Localization Energies in the Aromatic Bismethano[14]annulenes.

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the D F calculations were compared with those of the more traditional MP2
[29,301technique. It was found that all DF and MP2 methods behaved essentially equivalently in this study, and that the accuracy of the results is more
dependent on quality of basis set. Based on assessments of the results of 1, it
was then considered most economical to optimize the geometry of 2 at only the
BPW9l!dz(d) level of theory. Frequency calculations were performed where
appropriate to establish the character of minima found. The quantitative measure of the delocalization stabilization was estimated by using one of a variety
of possible reaction schemes for bond separation [31,32]. We have previously
found that a similar qualitative picture results over all treatments [33,34].
Additionally. NMR shielding tensors were calculated from fully optimized
structures at select levels of theory, by using the Gauge-Independent Atomic
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basis sets were used for NMR calculations on [18]annulene (1) and we found
these levels to be self-consistent. Such basis sets [38,39]are necessary to describe
properly the NMR properties of structures with such complex interactions
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[47] Energy value in brackets includes the thermal and scaled zero-point vibrational
energy corrections for 1
Verlogspsellschofl mhH. 0-69451 Weinheim, 1997
The Bond Localization Energies in the
Aromatic Bismethano[ 14]annulenes**
Maja Nendel, Kendall N. Houk,* L. M. Tolbert,
Emanuel Vogel, Haijun Jiao, and
Paul von Rague Schleyer*
New experimental and theoretical developments have returned the concept of aromaticity to center stage.“] Substituents
that distort benzene towards “cyclohexatriene” structures have
been found.[’] Arguments over the fundamental origin of bondlength equalization in aromatic compounds continue.[31Electron-correlated ab initio methods are often employed to predict
the structures and energies of delocalized aromatic systems,[4.
but examples have been found for which both MP2 and DFT
methods give errors.[6.1’
Two key questions are addressed in this study: How much
energy is required to distort aromatic systems having equalized
bond lengths to structures with alternating double and single
bonds? Does bond-length localization alter the magnetic properties‘’] when good overlap of the cyclic array of TC orbitals is
maintained? Besides answering these questions, we also report
that high-level computations, usually considered to give reliable
predictions, can give unbalanced descriptions of localized polyolefins and delocalized aromatic structures. When this is not
recognized, erroneous interpretations and predictions can result.
Vogel’s[’* 91 isomeric syn- (1) and anti-bismethano[l4]annulenes (2) have strikingly different structures and magnetic properties; the nature of
bonding can be summarized by the representations shown. In
syn-1 the C-C double
bonds are nearly equal
in length (X-ray data: r = 1.37-1.42 8, or 1.39k0.03 A),[’’’
whereas the 2-methoxycarbonyl derivative of anti-2 has alternating single and double C-C bonds ( r =1.34-1.508, or
1.42 IfI 0.08 8,) around the perimeter.“ syn-1 has a strong diamagnetic ring current (the ‘HNMR signals of the perimeter
protons have downfield chemical shifts (6 = 7.4-7.9), while the
signals of the methano bridge protons are shifted upfield to
6 = 0.9 and - l.2).‘’] No ring current is apparent from the
‘ H N M R shifts of anti-2 (perimeter protons at 6 = 6.2 and
methano bridge protons at 6 = 2.5 and 1.9).[’] The energy of the
“aromatic” (delocalized) form of 2 can be estimated from the
[*I Prof. Dr. K. N Houk, M. Nendel
Department of Chemistry and Biochemistry
University of California, Los Angeles
Los Angeles, CA 90095-1569 (USA)
Fax: Int. code +(310)206-1843
e-mail: houk(n
Prof. Dr. P. von R. Schleyer. Dr. H. Jiao
Institut fur Organische Cheniie der Universitit Erlangen-Nurnberg
Henkestrasse 42. D-91054 Erlangen (Germany)
Fax: Int. code +(9131)85-9132
Prof. Dr. L. M Tolbert
School of Chemistry and Biochemistry, Georgia Institute of Technology
Atianta, GA 30332-0400 (USA)
Prof. Dr. E. Vogel
Institut fur Organische Chemie der Universitit Koln (Germany)
[‘*I This work was supported by the U. S. National Science Foundation and the
San Diego Supercomputer Center at UCLA, and by the Fonds der Chemischen
Industrie. the Deutsche Forschungsgemeinschaft. the Stiftung Volkswagenwerk, and the Convex Computer Corporation in Erlangen. Support from the
Alexander-von-Humboldt Foundation made this collaboration possible.
0570-083319713407-07483 17 S0+.50/0
Angeu. Chem.
Ed. EngI. 1997. 36. N o . 7
barrier to double bond isomerization, 7.1 kcalmol- '
from dynamic ' H NMR experiments.[']
We have investigated the delocalized and localized
structures of syn- (1) and anti-bimethano[l4]annulene
(2) with common computational methods.'' The
four RHF,%-31G*-optimized geometries are shown in
Figure 1, and the relative energies at various theoretical levels are summarized in Figure 2. To compare the
different methods, the dashed line represents the average energy of the localized syn (1L) and anti (2L)
structures. The geometric and magnetic parameters
are given in Table 1.
Table 1 Geometricel parameters (Arm[a] and A [b]), and total magnetic susceptibility exaltations ( A . in ppmcgs) of s p - (1L and ID) and
unri-bismethano[l4]annulenes (ZL and ZD) by various computational
methods [c]
(0 03)
RHF.6-31G* 0 07
(0 03)
BLYP/6-31G* (0.02)
B3LYP.6-ilC' [d]
(0 02)
( 1 D)
(2 D)
(0 01)
(0 99) (-98.3)
(0.99) ( - 105.8)
(0.99) (-103.0)
[a] Arm (maximum deviation of the mean C-C bond) in A. [b] A (Julg
parameter) is unitless. [c] The values for the delocalized structures. 1D
and ZD, are given in parentheses. [d] No localized structures at this
Figure I . RHF/6-31G*-optimized geometries for localized (1L and ZL)and delocalized (1D and
ZD) .sy-and anti-bismethano[l4]annulenes.
At the RHF/6-31G* level both localized structures
(1L and 2L) have nearly planar dimethylenecycloheptadiene moieties (right half of each structure in Fig26.5-2D
ure l ) , which are doubly linked to a cycloheptatriene
(left half of each structure). The carbon skeletons are
similar in the localized (1L) and delocalized (1D) syn
structures. In contrast, the localized anti structure
(2L) has little K orbital overlap between the central
15.0- 1D
and bridgehead carbons, and the angle between the n
orbitals at these carbons is 79" in 2L, compared to
only 34' in 1L. Effective n orbital overlap in the delocalized anti structure (2D) can only be achieved when
the central ring is almost planar, but this introduces
considerable strain.
Both the semiempirical PM3 and the a b initio
RHF/6-3 l G * methods favor bond-localized structures for the syn and anti isomers (Figure 2 ) . Errors in
the computed energies can be estimated based on the
experimental barrier to double bond isomerization
between 2L and 2D (7.1 kcalmol-'). Due to the neglect of correlation energy (Figure 2),[131 PM3 overPM3
estimated this barrier by 25.9 and RHF/6-31G*
Figure 2. Summary of relalive energies [kcalmol"] of localized and delocalized . s y - (1L and
by 19.4 kcal mol- When these errors are subtracted
1D) and onti-bismethano[l4]annuIenes (ZL and 2D) from calculations at the PM3. RHF/6-31G*
( R H F ) . MP2/6-31G*//6-31G* (MP2), BLYP/6-31G* (BLYP). Becke3LYP531G' (BSLYP-I),
from the energy of lD, 1D becomes more stable than
and Becke3LYP/6-311 + G**//Becke3LYP/6-31G* (B3LYP-11) levels. il Single-point calculalL, as is found experimentally.
tion on the RHF/6-31G* geometries.
MP2i6-3 1G*//RHF/6-3 1G* single-point calculations favor the delocalized structures to such an extent
that both ID and 2D are more stable than IL and 2L. MP2
BLYP/6-31G* optimizations also strongly overestimate the
underestimates the energy difference between 2L and 2D by
extent of delocalization and provide two minima with delocal13.4 kcalmol-' (Figure 2). This considerable error indicates
ized structures. The syn structure (1D) is more stable than the
that MP2 overestimates the correlation energies of aromatic
anti structure (2D), primarily due to the distortion of the carbon
framework to accommodate x overlap in the latter. BLYP/6systems'' 41 and "aromatic" transition states."
31G* single-point calculations on the RHF/6-31G* geometries
predict 2D to be too stable relative to 2L by 11.5 kcalmol-’.
This amounts to about half the error in the RHF calculations,
albeit in the opposite direction (Figure 2).
The hybrid density functional, Becke3LYP/6-31G*, is the
only method employed here that predicts the correct geometries
and gives a delocalized syn and a localized anti minimum. While
the barrier to double bond delocalization in 2 is underestimated
by 3.4-4.1 kcalmol-’, this method yields the smallest absolute
error of all the methods tested. Becke3LYP performs well because exchange is computed by a mixture of Hartree-Fock and
Kohn-Sham methods, each of which err in opposite directions.
Therefore, although the results may not represent quantum mechanics correctly, they do yield nearly the right energy difference
in this as in many other cases.c’6]
The computed magnetic susceptibility exaltations ( A ) of the
RHF/6-31G* geometries show that both 1D and 2D are strongly aroma ti^.^'^] In addition, 1L still is somewhat aromatic, possessing 40% of the magnetic susceptibility exaltation of the ID,
but the corresponding 2L is nonaromatic. Geometric criteria,
such as Arm (the maximum deviation of the mean C-C bond
length) and the Julg parameter A,[’*]give the same conclusion
(Table 1). The same results are achieved on the BLYP/6-31G*
and Becke3LYP/6-31G*delocalized geometries; in other words,
2D is more aromatic than ID, and 2L is not aromatic.
Due to the similar stability orders after energy correction, we
conclude that the syn delocalized structure (1D) is most likely
the global minimum. The strain due to repulsion of the two
inner methano bridge protons is compensated by the favorable
delocalization energy. Becke3LYP single-point calculations on
the RHF/6-31G* geometries of 1L and 1D predict ID to be
6.2-6.5 kcalmol-’ lower in energy.
Surprisingly, the aromatic stabilization energies of planar x
systems are not altered drastically either by bond localization or
by modest out-of-plane deformations, as long as TL overlap is
maintained.[’g] Similarly, the ring currents (as judged by the
magnetic criteria) decrease only modestly upon localization and
disappear only in twisted structures (such as the anti isomer, 2L)
in which 7c overlap is eliminated.
The consequences on future theoretical studies are clear: predictions of a specific delocalized or localized structure must be
made with caution; the magnitude and direction of errors expected from each type of calculation must be considered. MP2
and BLYP calculations may give significant errors. Predictions
of structures of large aromatic systems, such as the fullerenes,c2O1require highly correlated wavefunctions or appropriately parametrized semiempirical methodst2
The chemical consequences of this study are significant as
well. Systems such as benzene or 1, which can assume localized
structures by a simple “breathing” distortion, do so with little
energy loss (benzene: 4.3 kcaimol-’;r’9b1 1 : 6 kcalmol-I).
Such relatively small energy differences can be overcome by
other effects and bond alternating structures result. The partially localized cyclohexatriene structures[’] arise from the hyperconjugation interactions in the reference molecules analyzed
earlier by Jorgensen.Izzl While aromatic properties, including
stabilization, are maximized at the delocalized geometries, the
energies for such distortioiis in benzene or 1 are small compared
to the total stabilization of the system, and little loss of aromaticity results.[‘91
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Magnetic susceptibilities have been calculated using Kutzelnigg’s IGLO
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Received: June 10, 1996
Revised version: September 24. 1996 [Z 9219IEl
German version: Angeu. Chem. 1997. 109. 768-771
Keywords: ab initio calculations . annulenes * aromaticity
bond length alterations . density functional calculations
VCH Verlagsgesellschaft mhH, 0-69451 Weinheim, 1997
0570-0833/97/3607-0750$17.50+ ,5010
Angen.. Chem. Int. Ed. EngI. 1997. 36, No. 7
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bond, annulene, localization, bismethano, aromatic, energies
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