Theoretical and structural analysis of long C-C bonds in the adducts of polycyanoethylene and anthracene derivatives and their connection to the reversibility of diels-alder reactions

Article abstract of DOI:10.1002/chem.201303276

X-ray structure determinations on four Diels-Alder adducts derived from the reactions of cyano- and ester-substituted alkenes with anthracene and 9,10-dimethylanthracene have shown the bonds formed in the adduction to be particularly long. Their lengths range from 1.58 to 1.62 A, some of the longest known for Diels-Alder adducts. Formation of the four adducts is detectably reversible at ambient temperature and is associated with free energies of reaction ranging from -2.5 to -40.6 kJ mol^-1. The solution equilibria have been experimentally characterised by NMR spectroscopy. Density-functional-theory calculations at the MPW1K/6-31+G(d,p) level with PCM solvation agree with experiment with average errors of 6 kJ mol^-1 in free energies of reaction and structural agreement in adduct bond lengths of 0.013 A. To understand more fully the cause of the reversibility and its relationship to the long adduct bond lengths, natural-bond-orbital (NBO) analysis was applied to quantify donor-acceptor interactions within the molecules. Both electron donation into the σ-anti-bonding orbital of the adduct bond and electron withdrawal from the σ-bonding orbital are found to be responsible for this bond elongation. Copyright

Full text of DOI:10.1002/chem.201303276

DOI: 10.1002/chem.201303276
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&
Cycloaddition Reactions
Theoretical and Structural Analysis of Long CÀC Bonds in the
Adducts of Polycyanoethylene and Anthracene Derivatives and
Their Connection to the Reversibility of Diels–Alder Reactions
Anna K. H. Hirsch,[a, c] Philippe Reutenauer,[a] Marc Le Moignan,[b] Sꢀbastien Ulrich,[a, d]
Peter J. Boul,[a] Jack M. Harrowfield,[a] Peter D. Jarowski,*[b] and Jean-Marie Lehn*[a]
Abstract: X-ray structure determinations on four Diels–Alder
adducts derived from the reactions of cyano- and ester-sub-
stituted alkenes with anthracene and 9,10-dimethylanthra-
cene have shown the bonds formed in the adduction to be
particularly long. Their lengths range from 1.58 to 1.62 ꢁ,
some of the longest known for Diels–Alder adducts. Forma-
tion of the four adducts is detectably reversible at ambient
temperature and is associated with free energies of reaction
ranging from À2.5 to À40.6 kJmolÀ1. The solution equilibria
have been experimentally characterised by NMR spectrosco-
py. Density-functional-theory calculations at the MPW1K/6-
31+G(d,p) level with PCM solvation agree with experiment
with average errors of 6 kJmolÀ1 in free energies of reaction
and structural agreement in adduct bond lengths of 0.013 ꢁ.
To understand more fully the cause of the reversibility and
its relationship to the long adduct bond lengths, natural-
bond-orbital (NBO) analysis was applied to quantify donor–
acceptor interactions within the molecules. Both electron
donation into the s*-anti-bonding orbital of the adduct
bond and electron withdrawal from the s-bonding orbital
are found to be responsible for this bond elongation.
Introduction
since its discovery, but whereas the (forward) cycloaddition re-
action finds wide synthetic application, the retro-Diels–Alder
(rDA) reaction has attracted considerably less attention. This is
presumably because it often requires elevated temperatures,
a factor that reduces its synthetic utility substantially. The fac-
tors determining both the equilibrium position and the kinetics
of the forward and back reactions are not completely under-
stood and few examples of systems displaying readily moni-
tored rDA properties have been described. The DA reaction be-
tween isodicyclopentadiene and tetracyanoethylene, for exam-
ple, has been shown to reach an equilibrium involving
appreciable quantities of the reactants at 08C,[4] and other ex-
amples are provided in the equilibria involving certain furans
and 1,1,1-trichloro-3-nitro-2-propene.[5] There is much room for
further work to elucidate the factors controlling the reversibili-
ty of DA reactions. Progress has certainly been made through
computational studies largely focused on estimation of activa-
tion energies and thus upon calculation of both ground- and
transition-state structures and energies.[6–9] Recent work using
the highly accurate compound method CBS-QB3 on DA reac-
tions of maleimide[7] has shown that the reaction thermody-
namics are functionally tunable and can cover a wide range of
reaction free energies based on a relatively simple chemical
substitution strategy. For DA adducts formed from substituted
cyclopentadienes and benzoquinone in particular,[6c] it has also
been shown that electron-density transfer from the substitu-
ents on the bridge of the adduct to the s* molecular orbital of
the adduct bonds is an important factor in increasing the
bond length, an aspect of the adduct ground-state, which can
Since the discovery by Diels and Alder of the pericylic reaction
between maleimides and furans,[1] which now bears their
names, the scope of the Diels–Alder (DA) reaction has widened
to the point that it was described in the 1970s as the most
useful and powerful synthetic tool of all.[2] The product, or DA
adduct, results from the cycloaddition of a conjugated diene
to an alkene in which two bonds are formed in a single opera-
tion, affording an unsaturated six-membered ring; the mecha-
nism of this reaction has been the subject of intense scrutiny.[3]
The DA reaction has been known to be detectibly reversible
[a] Dr. A. K. H. Hirsch, Dr. P. Reutenauer, Dr. S. Ulrich, Dr. P. J. Boul,
Prof. J. M. Harrowfield, Prof. Dr. J.-M. Lehn
Institut de Sciences et d’Ingꢀnierie Supramolꢀculaires (ISIS)
Universitꢀ de Strasbourg, 8 allꢀe Gaspard Monge
67000 Strasbourg (France)
E-mail: Lehn@unistra.fr
[b] M. Le Moignan, Dr. P. D. Jarowski
Department of Physics, Advanced Technology Institute
University of Surrey, Guildford, GU2 7XH (UK)
E-mail: p.d.jarowski@surrey.ac.uk
[c] Dr. A. K. H. Hirsch
Current address: Stratingh Institute for Chemistry
University of Groningen, Nijenborgh 7, 9747 AG (The Netherlands)
[d] Dr. S. Ulrich
Current address: Institut des Biomolꢀcules Max Mousseron (IBMM)
UMR 5247, Ecole Nationale Supꢀrieure de Chimie de Montpellier
8 rue de l’Ecole Normale, 34296 Montpellier Cedex 5 (France)
Supporting information for this article is available on the WWW under
http://dx.doi.org/10.1002/chem.201303276.
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be considered to decrease the activation energy for the rDA
step.
fins that reach an equilibrium under ambient conditions.[12,13]
To shed light on the factors operating at the molecular level,
we report here X-ray structure determinations of four of these
adducts, which we use in association with computational stud-
ies to analyse the thermodynamic parameters obtained from
variable-temperature studies (using NMR spectroscopy) of the
solution equilibria. The lengths of the bonds formed in the ad-
duction reactions are among the longest that have been re-
ported for DA systems. We provide compelling theoretical evi-
dence that the bond elongation observed results from both
the presence of electron-withdrawing substituents in the
dienophile and the electron-donating effect of the diene sub-
stituents at the bridgehead of the aromatic group.
So as to rationally expand the range of rDA reactions,
a deeper understanding of the electronic factors that influence
the overall free energy change is needed. This change reflects
the difference between ground-state energies of the adduct,
the diene and the dienophile. In simple thermodynamic terms,
given that the forward reaction takes place with a decrease in
entropy, the lower the reaction enthalpy, the more favourable
should be the retroreaction. Given the common observation of
marked bond-length distortions within DA adducts, it is as-
sumed that the ground-state enthalpy of the adduct is the
most significant variable determining the overall enthalpy
change, and hence considerable effort has been devoted both
to characterisation of bond deformations in the adduct by
crystallographic studies and to computation of the ground-
state properties.[6–9] These calculations necessitate the use of
detailed electronic-structure theory, which we have applied in
the present work to the analysis of equilibrium-constant mea-
surements as well as to the interpretation of bond distortions
apparent in several structure determinations.
Results and Discussion
Synthesis of the dienes, dienophiles and their DA adducts
We based the present study on DA reactions of the commer-
cially available dienes 9,10-dimethylanthracene (1) and anthra-
cene (2) with three cyano-olefins 3–5 acting as dienophiles
(Scheme 1). The synthesis of dienophile 3 has been reported in
the literature.[13] Dienophiles 4 and 5 were obtained in one
step from commercially available starting materials (Scheme S1
in the Supporting Information). Formation of the four DA ad-
ducts [1,3], [1,4], [2,4] and [2,5] was monitored by recording
Our motivation for investigating the factors controlling re-
versibility in the DA reaction stems from its great potential for
applications in dynamic combinatorial chemistry (DCC)[10] or
controlled release.[11] The DA reaction is synthetically versatile,
thus providing access to structural and functional diversity,
and, as noted elsewhere,[12] it is a self-contained process. In
seeking to broaden the scope of reactions that can be exploit-
ed in DCC, we have previously described systems based on the
DA reaction of anthracenes or fulvenes with certain cyano-ole-
1
the H NMR spectra of equimolar amounts of the reactants in
CDCl3 solution (100 mm) at room temperature.
The reversibility of the initial DA reaction was confirmed by
adding 10 equivalents of the competing dienophile tetracyano-
ethylene (6) to each reaction mixture (Scheme 2).[14] This led to
the appearance of new DA adducts [1,6] or [2,6] with a con-
comitant increase in the intensity of the peaks of the dieno-
Abstract in French: La dꢀtermination des structures cristallog-
raphiques par diffraction des rayons X de quatre adduits de
Diels–Alder issus des rꢀactions d’alcꢁnes substituꢀs par des
groupements nitriles et esters avec l’anthracꢁne et le 9,10-dimꢀ-
thylanthracꢁne montre que les liaisons formant les adduits sont
particuliꢁrement longues. Leurs longueurs vont de 1.58 ꢂ 1.62 ꢃ,
les classant parmi les plus longues connues pour des adduits de
Diels–Alder. La formation des quatre adduits est rꢀversible ꢂ tem-
pꢀrature ambiante et est associꢀe ꢂ des ꢀnergies libres de rꢀac-
tion comprises entre À2.5 et À40.6 kJmolÀ1. Les ꢀquilibres en so-
lution sont caractꢀrisꢀs expꢀrimentalement par spectroscopie de
RMN. Des calculs de la fonctionnelle de densitꢀ au niveau
mPWPW91/6-31+g(d,p) utilisant le modꢁle de solvatation PCM
sont en accord avec les valeurs expꢀrimentales avec des erreurs
moyennes de 6 kJmolÀ1 en ꢀnergie libre de rꢀaction et de 0.013 ꢃ
pour les longueurs des liaisons . Pour comprendre plus en profon-
deur l’origine de la rꢀversibilitꢀ et sa relation avec la longueur im-
portante des liaisons de l’adduit, l’analyse des orbitales naturelles
de liaison (de type NBO) est utilisꢀe pour quantifier les interac-
tions de type donneur-accepteur au sein des molꢀcules. Les den-
sitꢀs ꢀlectroniques augmentꢀes dans l’orbitale anti-liante s* et rꢀ-
duites dans l’orbitale liante s de la liaison de l’adduit ont ꢀtꢀ
identifiꢀes responsables de cet allongement des liaisons.
Scheme 1. Diels–Alder equilibria between 3 and 1, 4 and 1 or 2 as well as 5
and 2 and their corresponding DA adducts [1,3], [1,4], [2,4] and [2,5].
a) CDCl3, 258C.
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electron-accepting power of the dienophile, with the excep-
tion of the about 10 kJmolÀ1 shift towards the DA adduct com-
paring the dicyano fumarates [2,4] to [1,4]. In this case, this
difference is related to the increased donating power of the
diene caused by the donating methyl groups or possibly by
steric interactions. Stronger donor–acceptor character would
likely favour more loosely associated adducts that can benefit
from strong charge-transfer stabilisation while avoiding the in-
creased steric strain that comes with tighter associations. This
basic concept is well demonstrated in the analysis of the
single crystal X-ray data below.
Scheme 2. Dynamic equilibria between adducts [1,3], [1,4], [2,4] and [2,5]
with tetracyanoethylene (TCNE, 6). a) addition of 10 equiv 6 in CDCl3 at
258C.
philes 3, 4 and 5, respectively. The extent to which the diene
was abstracted by the competing dienophile 6 provided an-
other index of the position of the dynamic equilibrium in each
system studied (Table S1 in the Supporting Information).
X-ray crystallography
Our studies of reversible DA reactions have dealt with a variety
of DA adducts.[12,13] The dynamic nature of the adducts, leading
to the presence of the starting materials in the media in which
the crystallisations take place, complicates the preparation of
crystals suitable for X-ray diffraction. Thus, only the four ad-
ducts described in this study ([1,3], [1,4], [2,4] and [2,5]) afford-
ed crystals of sufficient quality for structural analysis by X-ray
diffraction (Figure 1 and Figures S3–S14 in the Supporting In-
formation). Use of CrystalExplorer[15] to analyse interactions
within the lattices shows that, unsurprisingly, supramolecular
contacts involve largely just the polar substituents (cyano,
ester and nitro groups), with p–p stacking seemingly playing
a minor role, if any, with the shortest centroid···centroid separa-
tion of parallel rings being more than 3.8 ꢁ in the most likely
instance. Significantly, there are
Equilibrium thermodynamics of the DA reactions
In the systems presently described, the rDA reaction was readi-
ly detectable at room temperature, meaning that both the
starting materials and the DA adducts were present and their
concentrations readily measured by 1H NMR spectroscopy.
Using such data to determine the equilibrium constants over
a range of temperature (Figure S1 in the Supporting Informa-
tion, the thermodynamic parameters DGr0, DHr0 and DSr0 for
CDCl3 solution were extracted (Figure S2 in the Supporting In-
formation) for each adduct system and are given in Table 1.
no indications of contacts to the
Table 1. Experimental thermodynamic parameters of DA reactions affording DA adducts [1,3], [1,4], [2,4] and
[2,5].[a]
atoms linked by the adduct
bonds, implying that there are
no direct solid-state influences
upon the length of these bonds.
For the four present struc-
tures, the lengths of the two
bonds formed between the
diene and dienophile are given
in Table 1 as B1 and B2 and de-
fined in the caption of Figure 1.
Where the molecules contain
a C2 symmetry element the two
bonds are unequal due to asym-
Compound
DHr
[kJmolÀ1
DSr
[JmolÀ1 KÀ1
DGr
[kJmolÀ1
Keq
Adduct bond lengths [ꢁ]
]
]
]
B1
B2
average
[1,3]
[1,4]
[2,4]
[2,5]
À66.3Æ7.3
À214.2Æ2.6
À2.50Æ0.3 (2.4Æ0.2)ꢃ100 1.622
1.614
1.588
1.584
1.590
1.618
1.590
1.583
1.582
À164.4Æ18.1 À449.3Æ49.4 À30.5Æ3.4
À197.9Æ21.8 À527.5Æ58.0 À40.7Æ4.5
(2.9Æ0.9)ꢃ104 1.591
(3.3Æ1.7)ꢃ106 1.579
(3.7Æ0.7)ꢃ103 1.575
À49.8Æ5.5
À101.5Æ11.2
À19.6Æ2.2
[a] The enthalpies (DHr) and free energies (DGr) of reaction are given at 298 K. Adducting bond lengths for B1
and B2 (defined in Figure 1) determined from single crystal X-ray crystallography and their averaged values [ꢁ]
are also presented.
Relative to the measurements obtained using fulvenes as
dienes, the equilibria here are shifted more towards the DA ad-
ducts.[11] This may be due to the energetic stabilisation arising
from the formation of two aromatic systems in the DA adducts
derived from anthracene or derivatives thereof. The equilibra-
tion kinetics varied greatly, although the dimethylanthracene
1 gave in all cases the more rapid reaction, those with tricya-
noacrylates and dicyanofumarates requiring 1 and 3 h, respec-
tively, to reach effective equilibrium. Reactions of diene 2,
however, took several days to reach equilibrium although they
were more complete. The formation of DA adduct [1,3] is an
extreme case and was by far the least complete reaction, as in-
dicated by its small equilibrium constant. The series follows
a pattern of decreasing reaction free energy with increasing
metries induced by crystallisation, but the differences in their
lengths are very small. There is an apparent correlation be-
tween the mean bond lengths and the equilibrium constants
and free energies, where, in general, the shorter the adduct
bonds, the greater is the equilibrium constant and more nega-
tive the free energy.
The formally single bonds between saturated carbon atoms
show relatively large values, which would be slightly larger
after librational corrections, and a search of the Cambridge
Structural Database (CSD), using the software ConQuest,[16] for
bond lengths in similar DA adducts (Figure S15 in the Support-
ing Information) shows that they are amongst the highest
values known. The longest bond found in this compilation was
one of 1.62 ꢁ for a fullerene adduct with 9,10-dimethylanthra-
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tached. Thus, bond elongation
would seem to follow the same
pattern as the free energies, for
which increasing electron-ac-
cepting power of the directly at-
tached groups increases the ad-
ducting bond length.
We have also looked in detail
at the pyramidalisation of the
carbon atoms involved in adduct
bond formation measured as the
improper dihedral angle, for ex-
ample C14-C17-C16-C15 and C8-
C6-C14-C7 in [2,5]. The increase
of this geometric feature is asso-
ciated with increased p-atomic
orbital character of the formed
bonds, and thus, bond elonga-
tion. However, all adducting
carbon atoms express improper
dihedral angles of between 278
and 368 without any obvious
correlation to bond length. This
compares to the fully tetrahedral
improper dihedral angle in
methane, for example, of rough-
ly 358. It can be said that the ad-
ducts are “fully” formed through
unsaturated CÀC bonds. Addi-
tionally, the long bond lengths
should be associated with rela-
tively “late” transition-state struc-
tures in the adducting reaction
and “early” transition states for
the rDA reaction leading to pu-
tative low transition-state ener-
gies for the latter using the ter-
Figure 1. X-ray crystal structures of DA adducts [1,3] (B1: C7ÀC20, B2: C15ÀC17), [1,4] (B1: C15ÀC17, B2: C7ÀC22),
[2,4] (B1: C14ÀC15, B2: C7ÀC20) and [2,5] (B1: C14ÀC16, B2: C7ÀC15).
cene, in which special consequences may arise from the fuller-
ene structure.[17] The extreme effects in the present cases thus
make these adducts especially useful for investigation of the
origins of the bond extensions. The small increase in mean
bond length for [1,4] compared to [2,4] (0.007 ꢁ) has no appar-
ent effect on the conformational situation of the fumarate sub-
stituents in the crystal structure other than distal changes to
the orientation of bromine that presumably arise from crystal-
packing effects. Thus, 9,10-dimethyl substitution of anthracene
likely acts to increase the bond length by through-bond hyper-
conjugative donation. Adduct [2,5] contains the shortest ad-
ducting bond presented here for B1 (see caption of Figure 1)
at 1.575 ꢁ, which is nearly the same as B1 for [2,4]. At the
same time, the adducting bond formed with the dicyano-
methylene group in [2,5] (B2) is 1.590 ꢁ, one of the longer ad-
ducting bonds, but considerably shorter than the analogous
bond (B2) in [1,3] (1.614 ꢁ) where, again, 9,10-dimethyl substi-
tution may play a role in this extra elongation. The other ad-
ducting bond here (B1) is the longest bond presented in this
study (1.622 ꢁ) with the nitrophenyl substituents directly at-
minology of Hammond. Without further kinetic studies little
more can be said at this time.
Computational study
In order to identify the origin of the especially long adduct
bonds in molecules [1,3], [1,4], [2,4] and [2,5], we have opti-
mised the molecular structures and analysed the reaction ther-
mochemical parameters using density functional theory (DFT).
Computed gas-phase structures are at the MPW1K/6-31+
G(d,p) density functional level of theory with solution-phase
thermochemical analysis performed at this same level, but
with optimisation using the PCM solvent model in CHCl3. Fur-
ther details can be found in the Experimental Section and opti-
mised coordinates are provided in the Supporting Information
(Table S2). MPW1K has been shown to give accurate structures
and energies for DA-type reactions involving cyano-olefins[18]
and is the best performer out of a number of DFT methods in
predicting heats of formation from atomisation energies of
cyano-rich organic molecules.[19] DA adducts of anthracene
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although the formation of [1,3] is experimentally found to be
Table 2. Theoretical thermodynamic parameters of DA reactions afford-
ing DA adducts [1,3], [1,4], [2,4], [2,5], [2,6], [2,7] and [2,8] at the
MPW1K/6-31+G(d,p) level of theory with PCM solvation in CHCl3.[a]
weakly exergonic. The agreement between experimental and
theoretical free energies is very good (M.A.D.=5.9 kJmolÀ1
,
S.D.=4.8 kJmolÀ1). However, the enthalpies perform less well
(M.A.D.=56.3 kJmolÀ1, S.D.=28.0 kJmolÀ1), but the experimen-
tal data for the enthalpy and entropy expresses uncertainties
in the same range. The free energies (R2 =0.87) correlate well
to the average adduct bond lengths over all adducts consid-
ered. Considering only anthracene-based adducts of 2 this cor-
relation is improved (R2 =0.91). When only [2,6], [2,7] and [2,8]
are considered the increasing cyano substitution and conse-
quent increasing electron-accepting power of the central
double bond of the dienophile is clearly directly related to the
decrease in reaction endergonicity and an increase in adduct-
ing bond length (R2 =0.94). It should be noted, however, that
[2,6] displays rather short bond lengths (1.581 ꢁ) despite the
expectation that TCNE is the most electron-accepting dieno-
phile present in this study. The reaction free energy affording
[2,6] is intermediate in value at À22.5 kJmolÀ1. The sterically
less demanding nitrile groups clearly allow for shorter bond
lengths while maintaining favourable charge-transfer interac-
tions (vide infra).
Compound DHr
[kJmolÀ1
DSr
DGr
Adduct bond lengths [ꢁ]
] B1 B2 average
]
[JmolÀ1 KÀ1
]
[kJmolÀ1
[1,3]
[1,4]
[2,4]
[2,5]
[2,6]
[2,7]
[2,8]
À68.0
À109.1
À105.8
À85.6
À267.4
À285.3
À231.3
À223.0
À218.8
À202.6
À209.1
11.6
À24.0
À36.8
À19.1
À22.5
À61.6
À40.6
1.604 1.596 1.600
1.589 1.589 1.589
1.567 1.567 1.567
1.565 1.584 1.575
1.581 1.581 1.581
1.549 1.549 1.549
1.559 1.559 1.559
À87.7
À122.0
À102.9
[a] The calculated enthalpies (DHr) and free energies (DGr) of reaction are
given at 298 K. Adducting bond lengths for B1 and B2 (Figure 1) and
their averaged value [ꢁ] are also presented.
with tetracyanoethylene (6), ethene (7) and 1,2-dicyanoethene
(8) ([2,6], [2,7] and [2,8], respectively) were also analysed and
used as base models to make comparisons (Table 2). Except for
[2,4], all molecules adopt their ground-state conformation in
the crystal lattices based on comparison to the minimum-
energy structures computed in the gas-phase. For [2,4], the
bromo-alkyl groups rotate away from the position above the
adduct bonds in the compact structure they present in the
solid-state to a more open structure with these chains more
proximal to the anthracene ring systems having a slightly re-
duced molecular energy according to the gas-phase computa-
tional results. Apart from this and other small deviations in
bond torsions, the gas-phase computed and X-ray structures
of [1,3], [1,4], [2,4] and [2,5] are in excellent agreement
(Table S3 in the Supporting Information). In particular, the
adduct bonds have a mean absolute deviation (M.A.D.) of
0.013 ꢁ (standard deviation, S.D.=0.004 ꢁ), confirming that the
long bonds are dictated by molecular forces and are not an ar-
tefact of crystal packing. The DFT calculations give slightly
shorter bond lengths in general. It should be noted that this is
a comparison between gaseous molecules (C2 symmetric in
some cases) to those in the solid-state with unit cell symmetry
distortions. The errors are most likely beyond improving and
are within reason for the present analysis. The theoretical solu-
tion-phase adduct bond lengths for compounds [1,3], [1,4],
[2,4] and [2,5] as well as [2,6], [2,7] and [2,8] are listed in
Table 2 along with their average bond lengths. The bond
lengths with and without PCM solvation in CHCl3 are nearly
identical in all cases, also indicating that the use of single crys-
tal X-ray data in interpreting solution-phase reaction thermo-
dynamics is reasonable.
It is expected that the electron distribution within the
adduct bonds and hence their length should be sensitive to
substituents such as aromatic rings and cyano groups. Patil
et al.[6c] investigated the rDA reaction of cycloadducts formed
from cyclopentadiene and p-benzoquinone. Using the natural-
bond-orbital (NBO) approach,[20] they found that the ground-
state adduct-bond elongation was predominantly caused by
the increase in electron population of the s*-anti-bonding or-
bital of the adduct bond. Herein, the NBO second-order pertur-
bation analysis of the interaction energy of the two-central
bonds using the gas-phase MPW1K wavefunctions show clear
correlations between bond lengths. The extent of interaction
between the adducting bonds with its neighbours can be seen
in Figure 2 and Figure 3. In Figure 2, the stabilisation energies
of all donating interactions from neighbouring groups, for ex-
ample, s(CH2ÀH), p(CꢀN) and p(C=C) to each of the adducting
The calculated reaction enthalpies and free energies at
298 K are given in Table 2. All four reactions were found to be
exothermic, with reaction enthalpies ranging over some
50 kJmolÀ1 (298 K) and decreasing in the order [2,4] to [1,4] to
[2,5] and [1,3]. The exothermicity of these reactions is offset by
unfavourable entropic factors as expected for a bimolecular re-
action, giving a range of reaction free energies of À36.8 to
11.6 kJmolÀ1 with only [1,3] on the endergonic side. The trend
in these values follows that of the experimental measurements,
Figure 2. The correlation between the bond length [ꢁ] of the adduct bonds
of DA adducts [1,3], [1,4], [2,4] and [2,5] and [2,7], [2,8] and [2,6] plotted
~
&
against their total s-bonding donor ( ) and s*-anti-bonding acceptor ( ) in-
teraction energies.
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s*(CÀC) bonds have been summed and plotted against the as-
sociated bond length. The donating interaction from a given
s(CÀC) to the relevant neighbours, for example, s*(CÀN),
p*(CꢀN), s*(CÀC) and p*(C=C) are also summed and plotted
against the bond length. We assume that donation into the
s*(CÀC) adducting bond will increase the anti-bonding charac-
ter between these atomic centres leading to an elongation in
bond length. In addition, donation from the occupied adduct-
ing bonds s(CÀC) to its neighbours will lower their electron oc-
cupancy also leading to adducting-bond elongation. Together,
these effects should contribute to a weaker interaction be-
tween the two entities, as the interaction energy (bond enthal-
py) should decrease with increasing bond length according to
the Morse potential relationship. When the adducting s-bond
interacts more strongly with its neighbours, the bond length
increases as in Figure 2 concomitant with the greater interac-
tion energies for the accepting s*-orbital. When the two fac-
tors are working roughly together the result is the longest
bond lengths of the series presented herein, around 1.6 ꢁ. A
correlation is also observed when plotting the NBO electron-
occupancy values against the adduct bond length (Figure 3). It
Figure 4. A generic molecular-energy-level diagram for DA adducts high-
lighting the magnitude of the donating interactions to (solid) and accepting
interaction from (dashed) the adducting bonds to their neighbours.
More minor contributions from donating interactions from the
is found that a lower electron occupancy in the donating s(CÀ nitrile triple bonds (p(CꢀN)) and the s-bond donation from
C) orbital leads to a longer bond length. In contrast, a higher
electron occupancy of the accepting s*(CÀC) orbital of the
adduct bond results in shortened bond lengths.
the CÀO s-bond (s(CÀO)) of the ester functionalities in [1,4],
[2,4] and [2,5] to s*(CÀC) are also present and could result in
further elongation of the adducting bonds. The methyl CÀH
donation (s(CH2ÀH)–s*(CÀC)) of the dimethyl anthracene ad-
ducts are also particularly strong at about 20 kJmolÀ1 confirm-
ing the analysis above of the strong hyperconjugative effects
for these groups. Also, the Ph(p-NO2) group interaction (p(C=
C)–s*(CÀC)), which donates electrons through its p-bonds to-
wards the s*-anti-bonding orbital are present but of less im-
portance for [1,3].
Donation from the adducting CÀC s-bond (s(CÀC)) into the
anti-bonding orbitals s*(CÀN) and p*(CꢀN) of the nitrile
group, as well as to s*(CÀC) and p*(C=C) of the anthracene ar-
omatic rings will all serve to remove electron density from the
adduct bond thereby also leading to elongation of the adduct
bond length. The interaction energies with the s*(CÀN) and
p*(CꢀN) are the largest observed at 19 and 20 kJmolÀ1, re-
spectively. Thus considering the major contributors to the in-
teraction energies, the combined donation into the nitrile s*-
and p*-orbitals is the largest thermal driving force with the
greatest potential effect on bond-length elongation. This effect
is augmented considerably by strong donation into the s*(CÀ
C) orbital of the adduct bond by flanking aromatic double
bonds and in some cases hyperconjugative interactions from
the 9,10-dimethyl groups of anthracene. Thus, when both the
donating and accepting interactions are strong the bond
length will increase and the reaction free energy will decrease.
This can be considered as an increase in the ionic character of
the interaction between the diene and dienophile moving
away from formally covalent bonds (strong bonds) towards
ionic or charge-transfer associations as in a molecular complex
Figure 3. The correlation between the adduct bond lengths of DA adducts
[1,3], [1,4], [2,4], [2,5], [2,6], [2,7] and [2,8] plotted against their NBO occu-
~
&
pancy values in the s- ( ) and s*-orbitals ( ).
Looking at the specific interactions, Figure 4 shows a generic
energy-level diagram for all adducts, highlighting the key inter-
actions between orbitals with their relative magnitudes indicat-
ed by the arrow thickness. The relative arrow thicknesses are
averaged from the results of all eight molecules from the NBO
second-order perturbation analysis. Solid arrows indicate dona-
tion into the adduct s*-anti-bonding orbital from all others,
s*(CÀC), and dashed arrows indicates donation from the ad-
ducting s-bond, s(CÀC), into all others.
Flanking interactions from the p system of anthracene (p(C= (weak bonding). Again, [2,6] would appear to be a special case
C)) are strongly donating to the s*(CÀC) adducting bonds and
should lead to an increase in their anti-bonding character and
thus bond length. Their average value is at about 10 kJmolÀ1.
having shorter adducting bond lengths and strong acceptor in-
teractions due to the ability of the less voluminous nitrile to
accommodate shorter bonds.
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General experimental details
Conclusions
Reagents were used as received from commercial suppliers. All re-
actions were carried out under an atmosphere of dry N2. Yields
refer to homogeneous, analytically pure (1H NMR spectroscopy)
compounds and have not been optimised. Melting points were
measured on a Bꢄchi B-540 melting-point apparatus. 1H and
13C NMR spectra were recorded on a Bruker Avance spectrometer
at 400 or 100 MHz, respectively, and are reported as follows: chem-
ical shift (d) in ppm (multiplicity, coupling constant J in Hz, number
of protons). The residual deuterated solvent was used as the inter-
nal reference (CDCl3: dH =7.26 ppm, dC =77.0 ppm). The resonance
multiplicity is described as s=singlet, d=doublet, t=triplet, q=
quartet, br=broad, m=multiplet. High-resolution mass spectra
were recorded on a Bruker Micro TOF or a Bruker AutoFlex II mass
spectrometer at the Service de Spectromꢀtrie de Masse (Universitꢀ
de Strasbourg). X-ray crystallography was performed at the Service
de Radiocristallographie (Universitꢀ de Strasbourg).
NBO calculations on compounds [1,3], [1,4], [2,4] and [2,5] as
well as [2,7], [2,8] and [2,6] have provided calculated bond
lengths to compare with experimental data for compounds
[1,3], [1,4], [2,4] and [2,5], which are in excellent agreement.
Relative reaction free energies have been calculated and agree
with those collected from experimental work. The significant
energy values for interactions that occur between the donat-
ing s-bonding orbital of the adduct bond and other substitu-
ents as well as the interactions of these groups with the ac-
cepting s*-anti-bonding orbital of the adduct bond are shown.
Strong correlation between the bond length of the adduct
bond and the energy and electron-occupancy values calculat-
ed is also observed. Bond elongation results from the presence
of both highly electron-withdrawing substituents in addition
to the large electron-donating effect of the anthracene ring
system and the attachment of electron-donating substituents.
Finally, we have undertaken this study, in part, due to an in-
creasing interest in the limits of our conventional knowledge
of bonding.[21] Recent studies have shown that extremely long
CÀC bonds can exist both in the presence[22] and absence[23] of
supporting interactions. In this context, bond formation in the
present DA adducts is supported by strong ionic interaction
between the donor and acceptor reactants that allows for
a stable bond at increased distance, thereby minimising repul-
sive terms.
Synthesis of the Diels–Alder adducts
General procedure A: Dienophile (0.3 mmol) was added to a solu-
tion of diene in CHCl3 (100 mm, 3 mL). The reaction mixture was
left to stir at 258C, overnight, the solvent then evaporated and the
residue was purified by recrystallisation.
General procedure B: A solution of the diene in CHCl3 (200 mm,
3 mL) was added to a solution of the dienophile in CHCl3 (200 mm,
3 mL). The reaction mixture was left to stir at 258C, overnight, the
solvent then evaporated and the residue was purified by recrystalli-
sation.
Compounds and characterisation
15,16-Bis(2-bromoethyl) 15,16-dicyanotetracyclo[6.6.2.0.0]hexa-
deca-2,4,6,9,11,13-hexaene-15,16-dicarboxylate ([2,4]): Using
GPA [2,4] was obtained as a crystalline solid from CHCl3/iPr2O 1:1.
Experimental Section
1
Computational details
M.p. 133–1358C; H NMR (400 MHz, [D]CHCl3, 258C): d=7.55–7.57
(m, 2H), 7.43–7.44 (m, 2H), 7.31–7.21 (m, 4H), 4.93 (s, 2H), 4.54 (t,
J=6.4, 4H), 3.65–3.43 ppm (m, 4H); 13C NMR (100 MHz, [D]CHCl3,
258C): d=163.32 (2C), 138.58 (2C), 137.10 (2C), 127.99 (4C), 127.96
(2C), 127.74 (2C), 125.38 (2C), 115.19 (2C), 67.16 (2C), 56.39 (2C),
50.63 (2C), 27.12 ppm (2C); HRMS (ESI): m/z calcd for
C24H18Br2N2NaO4+: 580.951 ([M+Na]+); found: 580.948.
Post Hartree–Fock calculations were implemented with the Gauss-
ian 09 software package[24] to optimise final molecular structures.
Initial conformational analysis was performed in advance with Mac-
romodel.[25] The generalised gradient approximation (GGA) hybrid
exchange-correlation density functional MPW1K (mPWPW91) with
42.8% Hartree–Fock exact-exchange (X=42.8) and with the 6-31+
G(d,p) basis set was used to optimise the structures of all mole-
cules studied herein. For [1,3], [1,4], [2,4], [2,5], [2,6], [2,7] and
[2,8], conformational searches, using as initial coordinates those
from the crystal structures in the first four cases, were performed
with MacroModel to identify any significant alternative conformers.
Structures within approximately 10 kJmolÀ1 of the lowest structure
identified using the MMFF molecular mechanics force field were
further optimised at the MPW1K/6-31+G(d,p) level in the gas-
phase and also with PCM solvation in CHCl3 and their harmonic fre-
quencies determined at these same levels to establish that these
structures were indeed ground-state minima and for use in obtain-
ing thermochemical reaction parameters, which are reported with-
out scaling. All thermochemical analysis is on solvated structures.
The PCM model accounts for solvent effects using a polarisable
continuum of overlapping spheres to treat electrostatic forces
without explicit solvent molecules. Optimised structural coordi-
nates can be found in the Supporting Information along with the
computed energies and thermal corrections (Table S2 in the Sup-
porting Information). NBO calculations were performed on the gas-
phase optimised structures using the population analysis as imple-
mented in Gaussian 09.[24]
15,16-Bis(2-bromoethyl)
15,16-dicyano-1,8-dimethyltetracy-
clo[6.6.2.0.0]hexadeca-2,4,6,9,11,13-hexaene-15,16-dicarboxylate
([1,4]): Using GPB [1,4] was obtained as a crystalline solid from
1
CHCl3/n-heptane 1:1. M.p. 155–1578C; H NMR (400 MHz, [D]CHCl3,
258C): d=2.28 (s, 3H), 3.45–3.36 (dt, J=6.1, 12.2, 2H), 3.50 (dt, J=
12.2, 6.2, 2H), 4.42 (dt, J=12.2, 6.2, 2H), 4.56 (dt, J=12.2, 6.1, 2H),
7.40–7.29 (m, 4H), 7.50–7.40 (m, 2H), 7.53–7.55 ppm (m, 2H);
13C NMR (100 MHz, [D]CHCl3, 258C): d=163.34 (2C), 141.25 (2C),
139.94 (2C), 127.58 (2C), 124.81 (2C), 122.97 (2C), 115.36 (2C), 67.17
(2C), 63.04 (2C), 48.59 (2C), 27.27 (2C), 15.05 ppm (2C); HRMS (ESI):
+
m/z calcd for C26H22Br2N2NaO4
:
608.982 ([M+Na]+); found:
608.980.
Prop-2-yn-1-yl
15,16,16-tricyanotetracyclo[6.6.2.0.0]hexadeca-
2,4,6,9,11,13-hexaene-15-carboxylate ([2,5]): Using GPA [2,5] was
obtained as a crystalline solid from CHCl3/n-heptane 1:1. M.p. 148–
1498C; 1H NMR (400 MHz, [D]CHCl3, 258C): d=7.31–7.59 (m, 8H),
5.02 (s, 1H), 4.99 (s, 1H), 4.88 (dd, J=15.4, 2.4, 1H), 4.73 (dd, J=
15.4, 2.4, 1H), 2.60 ppm (t, J=2.4, 1H); 13C NMR (100 MHz,
[D]CHCl3, 258C): d=161.64, 137.72, 135.96, 135.64, 134.67, 129.34,
128.94 (2C), 128.53, 127.92, 126.65, 126.22, 125.94, 114.06, 112.26,
111.88, 77.60, 74.90, 57.50, 55.82, 53.68, 49.82, 45.05 ppm; HRMS
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(ESI): m/z calcd for C23H13N3NaO2+: 386.090 ([M+Na]+); found:
386.086.
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2469; b) S. Kotha, S. Banerjee, M. P. Patil, R. B. Sunoj, Org. Biomol. Chem.
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15-[4-Nitrophenyl]-1,8-dimethyltetracyclo[6.6.2.0.0]hexadeca-
2,4,6,9,11,13-hexaene-15,16,16-tricarbonitrile] ([1,3]): Using GPA
[1,3] was obtained as a crystalline solid from CHCl3/MeOH 1:1. M.p.
55–578C; 1H NMR (400 MHz, [D]CHCl3, 258C): d=7.36–7.67 (m,
12H), 2.48 (s, 3H), 1.90 ppm (s, 3H); 13C NMR (100 MHz, [D]CHCl3,
258C): d=148.87, 142.68, 139.68, 139.52, 138.38, 137.94, 130.84,
130.11, 129.17, 129.07, 128.74, 128.58, 125.55, 125.23, 124.94,
[11] K. C. Koehler, K. S. Anseth, C. N. Bowman, Biomacromolecules 2013, 14,
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[13] P. Reutenauer, P. J. Boul, J.-M. Lehn, Eur. J. Org. Chem. 2009, 1691–1697.
[14] O. Diels, W. E. Thiele, Chem. Ber. 1938, 71B, 1173–1178.
[15] M. A. Spackman, D. Jayatilaka, CrystEngComm 2009, 11, 19–32.
[16] a) F. H. Allen, Acta Crystallogr. Sect. B 2002, 58, 380–388; b) I. J. Bruno,
J. C. Cole, P. R. Edington, M. Kessler, C. F. Macrae, P. McCabe, J. Pearson,
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124.69, 124.42, 123.67, 117.20, 112.77, 112.32, 63.50, 50.90, 50.60,
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16.09, 15.44, 14.31 ppm; MS (ESI): m/z calcd for C27H18N4NaO2
453.4 ([M+Na]+); found: 453.2.
:
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Keywords: bond lengths · cycloaddition · density functional
calculations · natural bond orbitals · X-ray diffraction
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Received: August 20, 2013
Published online on December 11, 2013
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ꢂ 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim