Accuracy of calculations of heats of reduction/hydrogenation: Application to some small ring systems

Article abstract of DOI:10.1021/jo302118b

The enthalpies of reduction of carbonyl compounds and hydrogenation of alkenes have been calculated at the HF, B3LYP, M06, MP2, G3, G4, CBS-QB3, CBS-APNO, and W1BD levels and, in the case of the first four methods, using a variety of basis sets up to aug-cc-pVTZ. The results are compared with the available experimental data, and it is found that the compound methods are generally more satisfactory than the others. Large basis sets are usually needed in order to reproduce experiments. Some C-C bond hydrogenolysis reactions also have been examined including those of bicycloalkanes and propellanes. In addition, the dimerization of the remarkably strained bicyclo[2.2.0]hex(1,4)ene was studied. The reaction forming a pentacyclic propellane was calculated to have ΔH = -57 kcal/mol, and the cleavage of the propellane to give a diene had ΔH = -71 kcal/mol. The strain energies of these compounds were estimated.

Full text of DOI:10.1021/jo302118b

Article
pubs.acs.org/joc
Accuracy of Calculations of Heats of Reduction/Hydrogenation:
Application to Some Small Ring Systems
Kenneth B. Wiberg*
Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, United States
S
* Supporting Information
ABSTRACT: The enthalpies of reduction of carbonyl compounds and
hydrogenation of alkenes have been calculated at the HF, B3LYP, M06,
MP2, G3, G4, CBS-QB3, CBS-APNO, and W1BD levels and, in the
case of the first four methods, using a variety of basis sets up to aug-cc-
pVTZ. The results are compared with the available experimental data,
and it is found that the compound methods are generally more
satisfactory than the others. Large basis sets are usually needed in order
to reproduce experiments. Some C−C bond hydrogenolysis reactions also have been examined including those of bicycloalkanes
and propellanes. In addition, the dimerization of the remarkably strained bicyclo[2.2.0]hex(1,4)ene was studied. The reaction
forming a pentacyclic propellane was calculated to have ΔH = −57 kcal/mol, and the cleavage of the propellane to give a diene
had ΔH = −71 kcal/mol. The strain energies of these compounds were estimated.
quite similar in structure. These enthalpies of reduction are
particularly useful in this context since there is a considerable
body of experimental result and the enthalpies may be obtained
in several ways.
1. INTRODUCTION
The heats of formation are one of the principle quantities
required for completely characterizing compounds. These data
are useful in studying a variety of reactions and in making
estimates of whether or not a reaction may occur. Currently,
there are few precise thermochemical measurements being
carried out, and computational methods have been developed
to fill the breach. Compound methods have become popular for
this purpose, and examples include Pople’s G series,1
Petersson’s CBS methods,2 Martin’s W1 method,3 and others.4
They will generally give heats of formation with an average
error of ∼1−2 kcal/mol or better and also provide estimates of
the free energy of reaction.
The quality of these methods is generally assessed by a
comparison of calculated and observed heats of formation for a
test set of molecules. Another method would make use of the
calculated total enthalpies. Since all are variationally bound
(except for some small semiempirical corrections), the best
method should usually yield the lowest total enthalpy. Such a
comparison for acetone is given in Table 1. The differences are
substantial since 1 H = 627.51 kcal/mol.
2. RESULTS AND DISCUSSION
2a. Reduction of Carbonyl Compounds. We have first
examined the reduction of carbonyl compounds,5 and Table 2
gives the experimental results for a group of small aldehydes
and ketones. Here, column A gives the enthalpies derived from
gas-phase hydrogenations,6 column B gives values obtained via
heats of reduction of the carbonyl compounds using
triethylaluminum hydride in diglyme,7 columns C and D give
enthalpy changes derived from the equilibrium constant for the
hydrogenation reaction in the gas phase,8 and column E gives
the independently determined difference in enthalpy between
the carbonyl compound and the hydroxyl product as obtained
via combustion calorimetry.9
The enthalpy of hydrogenation of acetone has been
measured in four different ways, giving remarkable agreement.
Therefore, we have used it as the test compound for a series of
different calculations that are summarized in Table 3. It
includes B3LYP10 that is one of the oldest, but still widely used,
hybrid DFT methods, and M0611 that is one of the more recent
methods. MP2 was included because it is one of the most
frequently used ab initio methods that include correction for
electron correlation. Basis sets include 6-311+G*, 6-311++G**,
and aug-cc-pVTZ.12 The first is fairly flexible with diffuse (+)
functions and polarization functions (*) at the non-hydrogen
atoms and the second includes them on all af the atoms. The
One might expect that heats of reaction could be calculated
with a smaller error than heats of formation as a result of some
cancellation of errors. This might especially be the case for
enthalpies of hydrogenation where the reactant and product are
Table 1. Calculated Total Enthalpies for Acetone
method
H
CBS-QB3
G3B3
−192.81411
−192.99480
−193.02176
−193.06123
−193.14254
G4
CBS-APNO
W1BD
Received: September 26, 2012
Published: October 18, 2012
© 2012 American Chemical Society
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Table 2. Experimental Enthalpies of Hydrogenation of Carbonyl Compounds, 298 K
compd
A
B
C
D
E
formaldehyde
acetaldehyde
propanal
−22.1 0.1
−16.5 0.1
−15.4 0.3
−15.9 0.1
−15.1 0.1
−16.3 0.3
−13.0 0.1
−12.7 0.3
−10.9 0.2
−14.1 0.2
−10.9 0.3
−9.3 0.3
−6.0 0.2
−15.7 0.2
−16.9 0.3
−16.6 0.2
−16.8 0.3
−16.2 0.3
−13.3 0.2
butanal
2-methylpropanal
acetone
−16.3 0.2
−13.2 0.1
−13.2 0.1
cyclobutanone
cyclopentanone
cyclohexanone
cycloheptanone
cyclooctanone
ethyl acetate
−12.3 0.2
−15.2 0.2
−11.6 0.6
−14.4 0.7
−6.4 0.2
Table 3. Effect of Computational Level on the Calculated
Enthalpy of Reduction of Acetone
Results are also given for the compound methods. Table 3
includes approximate relative CPU times for these methods
including the calculation of the vibrational frequencies. Small
differences are insignificant since the time will depend on that
required to optimize the initial structure. But it is clear that
going from 6 to 311+G* to aug-cc-pVTZ increases the total
time for acetone by about 50−100. With the compound
methods, CBS-QB3 required little more time than MP2 using
the smaller basis set. CBS-APNO increased the execution time
relative to CBS-QB3 by about 10, and W1BD increased it by
about 500. The relative times will depend on the molecule
studied since different methods respond differently to the size
of the molecule.
With all of the methods used, there were significant changes
in calculated reduction enthalpies on going from the fairly
flexible 6-311+G* basis set to the larger 6-311++G** and the
much more flexible aug-cc-pVTZ. The energy changes
calculated using the former basis set were in poor agreement
with the observed value, indicating the importance of the choice
of basis set. The DFT values, even with the larger basis set, had
a 2−3 kcal/mol error.
a
level
ΔH(298 K) (kcal/mol)
rel CPU time
HF/6-311+G*
HF/aug-cc-pVTZ
B3LYP/6-311+G*
B3LYP/6-311++G**
B3LYP/aug-cc-pVTZ
M06/6-311+G*
MM06/6-311++G**
M06/aug-cc-pVTZ
MP2/6-311+G*
MP2/6-311++G**
MP2/aug-cc-pVTZ
CBS-QB3
−8.3
−10.1
−7.1
−10.0
−10.1
−9.4
−12.7
−11.5
−6.6
−12.8
−14.5
−12.6
−13.1
−13.5
−14.1
−13.2 0.2
1
106
2
4
90
4
6
250
3
7
500
5
G4
60
55
2700
CBS-APNO
W1BD
expt
a
These times are for acetone and are only approximate since they
depend on the time required to optimize the starting structures. They
had first been optimized at a lower level. The relative times for
isopropyl alcohol are about the same. The long execution times for
DFT and MP2 using the largest basis set are largely due to the time
needed to calculate the vibrational frequencies.
The large basis set MP2 calculation and the G4, CBS, and
W1BD calculations gave satisfactory agreement with the
experimental value. However, it would not be appropriate to
choose between them based on only one compound.
Therefore, we have examined a variety of small aldehydes
and ketones along with ethyl acetate (Table 4). These
compounds do present conformational problems that need to
be addressed. The product alcohol generally can adopt one of
aug-cc-pVTZ basis set is considerably larger and is of triple-ζ
quality.
Table 4. Calculated Enthalpies of Reduction of the Lowest Energy Carbonyl Conformers (kcal/mol)
a
a
a
compd
B3LYP
M06
MP2
QB3
G3B3
G4
APNO
W1BD
obsd9
H2CO
−20.6
−14.0
−13.4
−13.6
−14.0
−10.1
−25.0
−9.1
−21.6
−15.5
−15.1
−15.1
−16.4
−11.5
−26.7
−12.0
−9.5
−22.4
−17.2
−16.9
−17.1
−17.7
−14.5
−29.8
−14.2
−11.8
−17.2
−6.1
−20.4
−15.1
−15.0
−15.2
−15.7
−12.6
−27.7
−12.1
−9.7
−20.6
−15.5
−15.2
−15.4
−15.9
−13.2
−27.8
−12.4
−9.9
−21.0
−15.9
−15.6
−15.8
−16.3
−13.1
−28.5
−12.9
−10.4
−14.5
−5.1
−21.9
−16.2
−16.1
−15.7
−16.9
−13.5
−28.9
−13.1
−10.4
−14.8
−5.1
−22.6
−17.2
−16.8
−22.1 0.1
−16.5 0.1
−16.6 0.2
−16.3 0.3
−16.3 0.3
−13.2 0.1
NA
MeCHO
EtCHO
nPrCHO
iPrCHO
Me2CO
−14.1
−29.6
cyclopropanone
cyclobutanone
cyclopentanone
cyclohexanone
ethyl acetate
rms error
−12.7 0.3
−11.6 0.6
−14.4 0.7
−6.4 0.2
−7.0
−11.0
−6.4
−14.2
−4.1
1.4
−14.0
−2.7
1.7
−14.3
−3.9
1.3
−7.4
0.7
3.0
1.2
0.8
0.7
a
aug-cc-pVTZ calculations for both geometry optimizations and vibrational frequencies.
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Table 5. Enthalpies of Hydrogenation of Alkenes, 298 K (kcal/mol), Using aug-cc-pVTZ for DFT and MP2
reaction
ethene + H2 = ethane
B3LYP
M06
MP2
CBS
G4
APNO
W1BD
expt
−31.4
−74.6
−27.8
−24.7
−53.3
−30.3
−65.4
−24.0
−45.2
−25.3
−49.0
−38.2
−57.2
4.4
−34.8
−77.5
−31.8
−28.6
−54.1
−34.1
−68.5
−27.7
−52.5
−29.8
−58.2
−51.7
−60.6
2.4
−34.1
−74.5
−31.4
−27.0
−55.6
−33.2
−67.2
−27.6
−51.0
−29.7
−56.8
−47.0
−60.8
1.7
−31.8
−73.4
−29.1
−26.8
−54.0
−31.3
−63.6
−25.6
−48.3
−27.5
−53.5
−45.3
−59.1
1.5
−32.0
−73.9
−29.3
−27.1
−54.6
−31.7
−63.4
−25.9
−49.0
−27.9
−53.3
−47.1
−59.7
1.1
−33.5
−76.4
−30.6
−28.1
−55.7
−32.9
−65.2
−27.9
−51.7
−29.1
−56.1
−49.0
−60.9
1.3
−33.1
−75.7
−30.3
−28.0
−55.3
−32.4
−64.9
−26.6
−50.6
−32.5 0.1
−74.5 0.2
−29.8 0.2
−27.3 0.3
−53.5 0.6
−30.8 0.5
−64.8 3.8
−26.4 0.4
−50.4 0.4
−28.3 0.3
−55.0 0.3
−49.2 03
na
ethyne +2H2 = ethane
propene + H2 = propane
2-butene + H2 = butane
cyclopropene + H2 = cyclopropane
cyclobutene + H2 = cyclobutane
cyclobutadiene+H2 = cyclobutene
cyclopentene + H2 = cyclopentane
cyclopentadiene+2H2 = cyclopentane
cyc1ohexene + H2 = cyclohexane
1,3-cyclohexadiene + 2H2 = cyclohexane
benzene +3 H2 = cyclohexane
bc[220]hex(1,4)ene + H2 = bc[220]ane
rms error
−49.8
1.0
two conformations. With ethanol, for example, the hydroxyl
hydrogen may be trans to the adjacent methyl group or it may
adopt one of the energetically equivalent gauche conformations.
The differences in energy are generally small, and for this part
of the study we give the results for the lowest energy carbonyl
compound going to the lowest energy product. The corrections
that result from including the higher energy conformations may
be found in the Supporting Information.
When the aug-cc-pVTZ basis set was used, most of the
methods gave fairly satisfactory calculated enthalpies of
reduction. B3LYP gave the largest deviations, followed by
M06, with MP2 giving the more satisfactory results. The
compound methods were generally more satisfactory, with
CBS-APNO and W1BD giving the best results. Unfortunately,
they also have the largest computational requirement. If making
comparisons between calculations and experiments it should be
remembered that the stated experimental uncertainties do not
include the unknown systematic errors associated with most
experiments
the gas-phase enthalpies of catalytic hydrogenation of volatile
alkenes with considerable accuracy.15 In other cases they were
obtained from the heats of formation of the alkene and the
alkane, and in the very interesting case of cyclobutadiene, it was
measured via a set of gas-phase studies.16 One might expect
that these enthalpies might be more easily calculated than those
for carbonyl compounds because there are negligible electro-
negativity differences and no lone pairs. The enthalpies have
been calculated at a variety of theoretical levels giving the data
summarized in Table 5. The DFT and MP2 calculations made
use of the aug-cc-pVTZ basis set.
The conformers of the hydrocarbons are well-known,17 and
usually there is a large enough difference in energy so that only
the lowest energy conformer need be considered. In the case of
n-butane, the energies of both the trans and gauche forms were
calculated (W1BD ΔH = 0.60 kcal/mol, ΔG = 0.60 kcal/mol),
and the correction to the tabulated hydrogenation enthalpies is
0.2 kcal/mol.
Although the observed values are well-known, there some are
some aspects that deserve comment. Except for formaldehyde,
all of the aldehydes have essentially the same enthalpies of
reduction. The change in reaction enthalpies on going from
formaldehyde to the other aldehydes, and then acetone parallel
the changes in ease of hydration.13 Formaldehyde is essentially
completely hydrated in aqueous solution, acetaldehyde is
partially hydrated, and acetone gives very little hydrate in
aqueous solution. The stabilization of the carbonyl group by
alkyl substitution is a reflection of the polar character of the
CO bond giving the carbon considerable carbocation
character. Cyclobutanone, cyclopentanone, and cyclohexanone
have enthalpies of reduction that are similar to that of acetone,
but cyclopropanone14 is more like formaldehyde and is
completely hydrated in aqueous solution. Cyclopropane and
cyclobutane have almost the same strain energies, but whereas
the hydrogenolysis of cyclopropanone giving acetone has a
calculated (CBS-APNO) ΔH = −56.6 kcal/mol, the conversion
of cyclobutanone to 2-butanone is much smaller with ΔH =
−36.7 kcal/mol. Clearly, a CO group has more difficulty in
accommodating a small ring angle than does a CH2 group, but
other factors may also be involved.14
Using aug-cc-pVTZ, there is relatively little difference in the
values calculated using several methods. B3LYP gives too high
enthalpies, whereas M06 gives values that are too negative.
MP2 and CBS-QB3 are fairly satisfactory, but the best results
were obtained using G4, CBS-APNO, and W1BD.
How will smaller basis sets affect the DFT and MP2 results?
The enthalpies of reaction were calculated using 6-31G*, 6-
311+G*, and 6-311++G**, and the results are summarized in
Table 6.
The effect of basis set on the calculated enthalpies of
hydrogenation is much smaller than found in the carbonyl
reductions. The B3LYP values pass through the observed
values; those for M06 are always too negative but improve with
larger basis sets. The MP2 values are not as affected by the basis
set size and are close to the observed value.
The change in enthalpies of reaction on going from ethene to
propene and 2-butene is well-known and is presumably due to
stabilization of the CC group by methyl substitution.
Cyclobutene, cyclopentene, and cyclohexene have similar
enthalpies of reaction, but cyclopropene gives a much more
exothermic reaction in part because of the strong CH bonds in
the product.18 Bicyclo[2.2.0]hex(1,4)ene is one of the most
reactive of the alkenes that can be observed in solution,19 and it
gives a remarkably exothermic reaction. One of its reactions will
be discussed in a subsequent section.
3. HYDROGENATION OF ALKENES
The hydrogenation of CC bonds is also of considerable
interest. With the CC bonds it is often possible to measure
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of bicyclo[2.1.0]pentane would be ∼50 kcal/mol plus that of
cyclopentane (∼6 kcal/mol) or about 56 kcal/mol, and that of
bicyclo[2.2.0]hexane would be ∼53 kcal plus that of cyclo-
hexane (∼0) or about 53 kcal/mol. Thus, as noted previously,
their strain energies are about the sum of the strain energies of
the constituent rings.20
The hydrogenolysis enthalpy of hexamethylethane is more
negative than that of 2,3-dimethylbutane, whereas it might be
expected to be less negative on the basis of the effect of alkyl
substitution from ethane to dimethylbutane. The difference
probably reflects the strain introduced by the six opposing
methyl groups. However, the small change suggests that the
steric interaction is quite small.
The hydrogenolysis energy of [1.1.1]propellane (−39 kcal/
mol) is relatively small because the product bicyclo[1.1.1]-
pentane has a relatively high strain energy, and this is one factor
that allows this propellane to be isolated.21 On the other hand,
the hydrogenolysis energy of [2.2.2]propellane (−90 kcal/mol)
is quite large because bicyclo[2.2.2]octane is relatively un-
strained, and this must be one factor that leads to the relative
instability of the propellane.22
Table 6. Effect of Basis Set on the Calculated Enthalpies of
Hydrogenation of Propene
level
ΔH(298 K) (kcal/mol)
B3LYP/6-31G*
B3LYP/6-311+G*
B3LYP/6-311++G**
B3LYP/aug-cc-pVTZ
M06/6-31G*
M06/6-311+G*
M06/6-311++G**
M06/aug-cc-pVTZ
MP2/6-31G*
MP2/6-311+G*
MP2/6-311++G**
MP2/aug-cc-pVTZ
observed
−31.5
−29.3
−28.4
−27.8
−34.2
−32.7
−32.2
−31.8
−30.0
−30.2
−30.8
−31.4
−29.8 0.2
4. HYDROGENOLYSIS OF C−C BONDS
Unlike the above reactions, it is generally not possible to
experimentally measure the enthalpies of hydrogenolysis of C−
C single bonds. However, it is possible to obtain them from the
heats of formation of the reactant and the product, and it is
possible to calculate them. We have made use of CBS-QB3, G4,
CBS-APNO, and W1BD for the calculations, and the values
thus obtained are compared with the experimental data in
Table 7.
For this group of reactions, all levels from G4 to APNO and
W1BD give rather good agreement with the observed values.
The cleavage of the Me-Me bond is more exothermic than that
of the CH2−CH2 bond in butane, and the cleavage of the C−C
bond in propane is halfway between these values as might be
expected.
If one takes −10 kcal/mol as the “normal” value for the
cleavage of a CH2−CH2 bond and subtracts this from the
values found for the cycloalkanes, one obtains a result that
closely agrees with the commonly assumed strain energies.20
One might take the hydrogenolysis value for 2,3-dimethylbu-
tane (−8 kcal/mol) as that for CH−CH, and then the strain
energy of bicyclo[1.1.0]butane would be ∼39 kcal/mol plus
that of cyclobutane (∼27 kcal/mol) or about 66 kcal/mol, that
5. DIMERIZATION OF BICYCLO[2.2.0]HEX(1,4)ENE (A)
Although A can be prepared and its NMR spectrum can be
obtained,19,23 it undergoes fairly rapid dimerization even in
dilute solutions to give the cyclic diene (C). It is among the
most reactive alkenes that can be observed in solution. It is
difficult to imagine a process for this conversion that does not
involve the propellane B either as an intermediate or a
transition state. The formation of B probably involves a
diradical intermediate.24 We were interested in obtaining an
estimate of the energy changes that occur in the transformation.
DFT calculations for these compounds have been re-
ported,19,24,25 but in view of the results given above, it seem
desirable to reinvestigate them using CBS-QB3, G4, and CBS-
APNO (Table 8).
The enthalpy change on going from A to B is quite
remarkable considering that B is a propellane with five
cyclobutane rings. B is certainly highly strained, and its
conversion to C also is calculated to be very exothermic. The
values in Table 8 are significantly larger than those observed
Table 7. Calculated Enthalpies of Hydrogenolysis, kcal/mol
reaction
QB3
G4
APNO
W1BD
obsd
ethane + H2 → 2 methane
−12.7
−10.0
−7.2
−4.9
−6.3
−35.3
−33.9
−14.3
−7.9
−43.9
−52.2
−57.4
−35.9
−86.2
1.2
−15.4
−12.7
−9.7
−7.2
−8.5
−37.5
−36.4
−17.0
−10.7
−46.2
−54.3
−59.6
−37.6
−88.0
−1.4
−15.5
−12.8
−10.0
−7.9
−15.3
−12.8
−10.2
−15.6 0.2
−12.8 0.2
−10.0 0.2
−7.4 0.3
−10.2 0.4
−37.7 0.1
−36.6 0.3
−16.8 0.3
−10.4 0.3
−45.3 0.4
na
propane + H2 → ethane + methane
butane + H2 → 2 ethane
2,3-dimethylbutane + H2 → 2 propane
hexamethylethane + H2 → 2 isobutane
cyclopropane + H2 → propane
cyclobutane + H2 → butane
−9.4
−38.4
−37.0
−15.5
−11.1
−44.1
−57.5
−60.6
−37.9
−91.1
−38.3
−36.9
cyclopentane + H2 → n-pentane
cyclohexane + H2 → n-hexane
bicyclo[1.1.0]butane + H2 → cyclobutane
bicyclo[2.1.0]pentane + H2 → cyclopentane
bicyclo[2.2.0]hexane + H2 → cyclohexane
[1.1.1]propellane + H2 → bc[1.1.1]pentane
[2.2.2]propellane + H2 → bc[2.2.2]octane
biphenyl + H2 → 2 benzene
−47.6
−39.1
na
na
na
−4.0 0.6
−10.0 0.4
bibenzyl + H2 → 2 toluene
−5.8
−8.2
rms error
3.1
1.1
0.7
1.0
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double bonds would be about 2 × 26 or 52 kcal/mol. The
strain energy of D would then be 65−52 = 13 kcal/mol less
than that of C, or about 23 kcal/mol. This is in agreement with
the preceding estimate (26 kcal/mol) and seems to be a
reasonable value for a compound having two chair cyclohexane
rings. Although these are rough estimates and do not take into
account possible changes in CH bond energies,18 they do
provide a way to understand the large energy changes for the
set of reactions.
Table 8. Relative Enthalpies for Reaction of A, kcal/mol
6. CALCULATIONS
All calculations were carried out using Gaussian-09.27
7. CONCLUSIONS
Enthalpies of hydrogenation are relatively easy to calculate with
DFT and MP2 giving fairly good agreement with experiment,
especially when large basis sets are used. The compound
methods G4, CBS-APNO, and W1BD gave very good
agreement. On the other hand, it is considerably more difficult
to calculate the enthalpies of reduction of carbonyl compounds
using DFT or MP2, and very large basis sets are needed. Again,
G4, CBS-APNO, and W1BD gave quite satisfactory results.
The enthalpies of hydrogenolysis of C−C single bonds also
were calculated, and these results were used in examining some
small ring bicyclic hydrocarbons and propellanes. Calculations
for the reactions of the highly strained bicyclo[2.2.0]hex(1,4)-
ene and its derivatives provided information on the strain
release in each step.
reaction
CBS-QB3
G4
CBS-APNO
2 A → B
B → C
−56.0
−72.1
−128.1
−63.8
−36.9
−56.9
−71.4
−128.3
−64.5
−41.8
−57.2
2 A → C
C + 2H2 → D
D + 2H2→ 2-cyclohexane
using DFT. Even C has considerable strain associated with the
repulsion between the two CC bonds,26 and the eclipsed
methylene groups. This in turn leads to a large enthalpy of
hydrogenation giving D. The hydrogenolysis energy of D is
−42 kcal/mol as compared to two CH−CH bonds (−16 kcal/
mol) leading to a strain energy of about 26 kcal/mol.
The remarkably large energy changes shown in Table 8
require some further consideration. An estimate of the strain
energy of A might be obtained via consideration of the
sequential hydrogenolysis of the cyclobutane CH2−CH2 bonds:
ASSOCIATED CONTENT
* Supporting Information
Tables of calculated total energies for the several theoretical
models along with the calculated energy changes for the
reactions. This material is available free of charge via the
Internet at http://pubs.acs.org.
■
S
AUTHOR INFORMATION
Corresponding Author
*E-mail: kenneth.wiberg@yale.edu.
Notes
■
The CBS-APNO reaction enthalpies are −73.0 kcal/mol for
the first step and −33.6 kcal/mol for the second (see the
Supporting Information). The second step is calculated to be
similar to that for the hydrogenolysis of cyclobutane (−37.0),
whereas that for the first is 40 kcal/mol larger and might be
attributed to the extra strain in A that would be distributed over
the two rings. This must result in large measure from the
difficulty in bending the relatively stiff CC−Me bonds
(135°) to the small angle in A. The total strain energy of A
would then be about 40 plus that of the bicyclo[2.2.0]hexane
ring (53 kcal/mol) giving a total of about 93 kcal/mol. It can
also be estimated from the enthalpy of hydrogenation of A (61
kcal/mol, Table 5) and that of cyclobutene (33 kcal/mol) or 38
kcal/mol as the extra strain energy of A. Adding that of the
parent ring gives about 91 kcal/mol in agreement with the
above estimate.
The total strain energy for 2A is then about 184 kcal/mol.
Since the dimerization of ethylene to form cyclobutane is
exothermic by −19 kcal/mol, an estimate of the strain energy of
B is roughly 184 less 19 and the energy for the conversion of A
to B (57 kcal/mol) or about 108 kcal/mol. This is somewhat
less to five times the strain in cyclobutane or 130 kcal/mol. The
conversion of B to C is exothermic by −71 kcal/mol leading to
an approximate strain energy for C of 108 − 71 or 36 kcal/mol.
The hydrogenation of C to give D is exothermic by −65
kcal/mol, and the reduction of two tetrasubstituted unstrained
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Computational resources utilized in this work were supported
in part by the Yale University Faculty of Arts and Sciences High
Performance Computing Center and by the National Science
Foundation under Grant No. CNS-0821132, which partially
funded the acquisition of the requisite computer facilities.
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