Why is RCM favoured over dimerisation? Predicting and estimating thermodynamic effective molarities by solution experiments and electronic structure calculations

Article abstract of DOI:10.1002/chem.201101662

The thermodynamic effective molarities of a series of simple cycloalkenes, synthesised from α,ω-dienes by reaction with Grubbs' second generation precatalyst, have been evaluated. Effective molarities were measured from a series of small scale metathesis reactions and agreed well with empirical predictions derived from the number of rotors and the product ring strain. The use of electronic structure calculations (at the M06-L/6-311G* level of theory) was explored for predicting thermodynamic effective molarities in ring-closing metathesis. However, it was found that it was necessary to apply a correction to DFT-derived free energies to account for the entropic effects of solvation. Complete control: Can classical theory, developed for ring-closing metathesis (RCM) reactions that involve σ-bond formation, describe the thermodynamics of RCM reactions forming π bonds? Empirical theory and modern electronic structure calculations have been employed to predict the outcome of RCM reactions of simple α,ω-dienes with Grubbs' second generation pre-catalysts, resulting in mixtures of cycloalkenes and oligomers (see scheme). Copyright

Full text of DOI:10.1002/chem.201101662

FULL PAPER
DOI: 10.1002/chem.201101662
Why is RCM Favoured Over Dimerisation? Predicting and Estimating
Thermodynamic Effective Molarities by Solution Experiments and Electronic
Structure Calculations
David J. Nelson,[a] Ian W. Ashworth,[b] Ian H. Hillier,*[c] Sara H. Kyne,[a]
Shanthi Pandian,[c, d] John A. Parkinson,[a] Jonathan M. Percy,*[a]
Giuseppe Rinaudo,[a] and Mark A. Vincent[c]
Abstract: The thermodynamic effective
molarities of a series of simple cycloal-
kenes, synthesised from a,w-dienes by
reaction with Grubbsꢀ second genera-
tion precatalyst, have been evaluated.
Effective molarities were measured
from a series of small scale metathesis
reactions and agreed well with empiri-
cal predictions derived from the
number of rotors and the product ring
strain. The use of electronic structure
calculations (at the M06-L/6-311G**
level of theory) was explored for pre-
dicting thermodynamic effective molar-
ities in ring-closing metathesis. Howev-
er, it was found that it was necessary to
apply a correction to DFT-derived free
energies to account for the entropic ef-
fects of solvation.
Keywords: cycloalkenes · homoge-
neous catalysis · metathesis · ring
closure · thermodynamics
Introduction
eration pre-catalyst 2,[2] forms the product rings 3 with a p-
bond and proceeds via a sequence of organoruthenium in-
termediates (Scheme 1). The RCM reaction has become one
of the most powerfully transformative reactions in synthetic
organic chemistry and is widely used for the synthesis of
structurally complex molecules in the laboratory,[3] and in
some cases, for industrial syntheses.[4] The strategic impor-
tance of the pre-catalysts which enable this and related reac-
tions was awarded with the Nobel Prize for chemistry in
2005.[5]
The concept of effective molarity (EM) is valuable for as-
sessing and comparing the efficiencies of cyclisation reac-
tions.[1] Much of our empirical knowledge derives from stud-
ies of reactions that form ethers, lactones and anhydrides, in
which the formation of a new s-bond closes the ring, often
irreversibly and via transition states that resemble the prod-
uct geometry closely. However, we know relatively little
about reaction classes in which a different type of union is
made. For example, the ring-closing metathesis (RCM) reac-
tion of a,w-dienes 1, using commercial Grubbsꢀ second-gen-
[a] D. J. Nelson, Dr. S. H. Kyne, Dr. J. A. Parkinson,
Prof. Dr. J. M. Percy, Dr. G. Rinaudo
WestCHEM/Department of Pure and Applied Chemistry,
University of Strathclyde
Thomas Graham Building, 295 Cathedral Street
Glasgow, G1 1XL (UK)
Fax : (+44)0141-548-4822
E-mail: jonathan.percy@strath.ac.uk
[b] Dr. I. W. Ashworth
Global Research and Development, AstraZeneca
Silk Road Business Park, Charter Way
Macclesfield, SK10 2NA (UK)
Scheme 1. RCM reaction of a,w-dienes 1, using Grubbsꢀ second-genera-
tion pre-catalyst 2, forms the product rings 3 and proceeds via a sequence
of organoruthenium intermediates. Cy=cyclohexyl.
[c] Prof. Dr. I. H. Hillier, Dr. S. Pandian, Dr. M. A. Vincent
School of Chemistry, University of Manchester
Oxford Road, Manchester, M13 9PL (UK)
Fax : (+44)0161-275-4734,
E-mail: ian.hillier@manchester.ac.uk
We have recently used electronic structure calculations to
probe the RCM of simple dienes to cycloalkenes (1a–f to
3a–f; n=1–6 in Scheme 1) in detail.[6]
It is generally agreed that the highest free energy barriers
are associated with the initial step which converts pre-cata-
lyst 2 into the active 14e catalyst through phosphane dissoci-
[d] Dr. S. Pandian
Current address: Universitꢁt Heidelberg
Anorganisch-Chemisches Institut, INF 270
69120 Heidelberg (Germany)
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/chem.201101662.
Chem. Eur. J. 2011, 17, 13087 – 13094
ꢂ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
13087

ation.[7] The view that RCM and cross metathesis (CM) re-
actions are reversible and thermodynamically controlled
processes, which occur after rate-limiting precatalyst activa-
tion (initiation), has become widely accepted.[8] If RCM is
fully reversible, it should be possible to predict reaction
equilibrium constants from the free energy differences be-
tween the substrate (diene) and the products (cycloalkene
plus ethene) alone without considering any of the organoru-
thenium intermediates which link the two states. Hence, we
should be able to use electronic structure calculations to
predict the efficiency of RCM reactions in a relatively un-
complicated and computationally inexpensive way. Quantifi-
cation of cyclisation efficiency in thermodynamically con-
trolled RCM reactions in this manner would allow the syn-
thetic chemist to select the appropriate conditions for RCM
with much less ’trial and error’. In particular, this would
allow informed selection of the maximum initial diene con-
centration, which is directly related to the cyclisation effi-
ciency to form the target ring.
chains of up to about 7 single bonds, from the number of ro-
tatable s bonds (rotors, r) ([Eq. (5)], DDS is in
calKꢀ1 molꢀ1).[9]
DDS ¼ ðDSintraꢀDSinterÞ ¼ 30 ꢀ 4r
ð5Þ
The thermodynamic advantage of cyclisation can there-
fore be anticipated from the number of rotors present in the
acyclic precursor and the strain energy of the cyclic product.
The experimental strain energies for the simple Z-cycloal-
kenes have been reported in the literature,[12] so predicting
EMT by this method is rather straightforward. Table 1 shows
the values calculated in this way.
Table 1. Thermodynamic effective molarities calculated using Mandoli-
niꢀs approach[9] and literature strain energies for cycloalkenes.
Ring size
Target cycloalkene
5
3a
6
3b
7
3c
8
3d
9
3e
10
3f
Log
Log
G
3.04
ꢀ0.64
5.0
2.18
1.52
0.9
1.3
0.43
ꢀ3.31
5.1
0
ꢀ0.17
ꢀ3.48
4.5
M
)
ꢀ2.51
ꢀ6.24
For systems under thermodynamic control, effective mo-
larity (EMT) derives from a ratio of equilibrium constants
[Eq. (1)],[1] which can be separated into enthalpic and en-
tropic contributions [Eq. (2)]. This parameter can be evalu-
ated from the reactant and product energies alone:[9]
5.2
8.5
[a] Strain energies of the Z-isomers from Ref. [11a] in kcalmolꢀ1
.
Figure 1 plots EMS versus ring size (EMH =1, representing
strain-free ring formation) and EMT calculated using the lit-
erature strain energies (referred to herein as EMTM).
EMT ¼ Kintra=Kinter ¼ exptl½ðDGinterꢀDGintraÞ=RTꢁ
ð1Þ
ð2Þ
EMT ¼ exptl½ꢀðDHintraꢀDHinterÞ=RTꢁ ꢂ exptl
½ðDSintraꢀDSinterÞ=Rꢁ ¼ EMH ꢂ EMS
This metric differs from the kinetic effective molarity,
which is based on the relative rates of ring formation and di-
merisation [Eqs. (3) and (4)] and considers energy barriers
associated with transition states on the potential energy sur-
face of the reaction rather than reactant/product energies.[1]
ꢀ
ꢀ
ð3Þ
ð4Þ
EM ¼ kintra=kinter ¼ exptl½ðDGinter ꢀDGintra Þ=RTꢁ
ꢀ
ꢀ
EM ¼ exptl½ꢀðDHintra ꢀDHinter Þ=RTꢁ ꢂ exptl
Figure 1. Plots of Log10ACTHNUTRGNEUNG
(EMTM) versus cycloalkene ring size a) setting
ꢀ
ꢀ
½ðDSintra ꢀDSinter Þ=Rꢁ
EMH =1 (representing strain-free ring formation) and thus EMT =EMS
M
*
(
) and b) EMT calculated using the literature strain energies for Z-cy-
*
cloalkenes ( ).
The outcomes of thermodynamically and kinetically con-
trolled reactions must be quantified in different ways. Our
preliminary study[10] treated the RCM of 1,7-octadiene 1b as
kinetically controlled, and evaluated a lower limit of EM ef-
fectively on the basis of the reaction yield. As only cyclo-
M
The EMT plot peaks for six-membered ring formation
(EMTM =33m) with the other cyclisations at least 100-fold
less efficient. The predictions are qualitatively consistent
with outcomes from the synthetic RCM literature in which
5- and 6-membered rings form easily and in high yield, 7-
membered rings begin to require higher dilution, 8- and 10-
membered rings (in non-annelative cases) are difficult to
form, while 9-membered rings are observed rarely.
1
hexene was detected in this reaction (using H NMR spec-
troscopy) and the reaction reached completion, the nature
of the control cannot be verified. However, systems that cy-
clise less cleanly can be interrogated more closely and
informatively.
Galli and Mandolini reviewed a large body of experimen-
tal work in solution dealing predominantly with lactone and
cyclic ether-forming reactions and analysed how EMT parti-
tions into enthalpic and entropic components,[9] drawing on
the fundamental contributions of Page and Jencks.[11] The
entropic component (EMS) can be calculated for short
We wished to test these predicted values, derived from a
classical treatment of EMT, against both experiment and the
results of electronic structure calculations using modern
density functional theory. Burt and co-workers have ex-
plored RCM reactions of butenoate esters to form lactones
by electronic structure calculation methods, and used reac-
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Chem. Eur. J. 2011, 17, 13087 – 13094

Thermodynamics of p-Bond-Forming Ring-Closing Metathesis Reactions
FULL PAPER
tion yields from the synthetic literature to test their predic-
tions.[13] However, to our knowledge, there has been no com-
bined electronic structure calculation and quantitative (or
even semi-quantitative) solution experimental approach to
date.
nene 3e was not observed by RCM, even at concentrations
as low as [1e]0 =0.5 mm. Instead, only a mixture of oligo-
mers and unreacted diene was obtained (confirmed by GC-
MS with chemical ionisation using methane).
Two very surprising results arose during this study. Firstly,
in the RCM of 1,8-nonadiene 1c, cycloheptene 3c was ac-
companied by a significant quantity of cyclohexene 3b (re-
1
Results and Discussion
vealed by the alkene H signal, dH (CDCl3)=5.69 ppm). At
higher [1c]0 (about 1m), more cyclohexene 3b was obtained
than cycloheptene 3c. Diene isomerisation in the presence
of ruthenium–alkylidene catalysts is well known and has
been exploited effectively in synthesis[19] but is uncommon
at room temperature.[20] Pre-catalyst 2 is known to favour
metathesis over isomerisation,[21] with isomerisation
common with “stressed” catalysts arising from high reaction
temperatures, high dilution or forced high turnover.[22] None
of these factors would appear to be relevant to the RCM re-
actions of 1c reported here. The 1H NMR spectrum of a
concentrated reaction ([1c]0 =2m in CDCl3) does contain a
peak consistent with the presence of diruthenium hydride 6
at ꢀ8.77 ppm (lit. dH (CD2Cl2)=ꢀ8.61 ppm)[23] but the
signal-to-noise ratio indicates that 6 is present in very low
concentration. There is significantly more 7 (the species
An experimental method that would minimise perturbation
of the reaction mixtures before analysis was essential to in-
terrogate the system shown in Scheme 1. Dienes 1a–f are all
commercially available and most cycloalkenes 3 are either
commercially available (3a–d and E- and Z-3 f) or known in
the literature (3e).[14] In addition, many of the dimers, prod-
ucts of cross-metathesis, are known (linear dimer 4a[15] and
cyclic dimers 5c–f).[16] The experimental approach was de-
scribed in our previous Communication, and utilises non-in-
vasive 1H NMR analysis to quickly quantify reaction out-
comes without processing the reaction mixture.[10] RCM of
each diene (1a–f) was carried out at a number of initial con-
centrations [1]0 in [D2]dichloromethane or [D]chloroform in
GC vials with an internal standard. Although the reactions
were not carried out under pressure, ethene did have the op-
portunity to accumulate in solution and was seen clearly in
a number of reaction product mixtures (dH =5.43 ppm in
CD2Cl2, 5.41 ppm in CDCl3) even after 18 h. Hence, the en-
ergetic consequences of ethene evolution were not included
in our subsequent calculations. The internal disubstituted
alkene resonances for dimers 4 and 5 all appear at d
ꢃ5.4 ppm and were observed by 1H NMR for all systems
except the RCM of 1b. End groups, arising from unreacted
diene and from dimers and higher oligomers, could be dis-
tinguished unambiguously using a range of 2D NMR tech-
from which 6 forms) and a reservoir of benzylidene 2, as
usual for these small scale experiments. If 6 is the sole cata-
lyst of the isomerisation reaction, it is a remarkably efficient
one. Further exploration of this chemistry forms the subject
of ongoing experiments in our laboratory. Ethylidene 8 was
identified at the end of these high [1c]0 reactions as a quar-
tet in the 1H NMR spectrum (dH (CDCl3)=18.6 ppm (J=
5.5 Hz)) with a single cross-peak in the 2D [1H,1H] CO-
SY NMR spectrum to a doublet signal at dH =1.6 ppm.[24] It
is likely that 8 is a product of the metathesis of isomerised
dienes (for example, 1,7-nonadiene RCM would yield cyclo-
hexene 3b and ethylidene 8).
Secondly, Z-cyclooctene 3d was formed during the RCM
of 1,9-decadiene 1d and was seen clearly in the 1H NMR
spectrum (dH (CD2Cl2)=5.65 ppm), albeit in low conversion,
so accurate quantification of [3d] by 1H NMR integration
was not possible. However, observation of 3d in these reac-
tions is surprising as the literature suggests that Z-cyclooc-
tene cannot be formed from 1d by RCM. Non-annelative
closure of eight-membered rings is usually an unfavourable
reaction[25] and reactions that form Z-cyclooctenes usually
require either appropriate vicinal ring substitution, often re-
ferred to as “gearing”,[26] or fusion to other ring systems.[27]
We could also clearly see cyclohexene 3b (dH (CD2Cl2)=
1
niques including [1H,13C] HSQC-TOCSY,[17a] and ge-1D H
TOCSY[17b–d] (see the Supporting Information for illustrative
examples). The T1 relaxation times were measured for the
dienes and all commercially available cycloalkenes (typically
6–7 s for the olefinic resonances) to ensure reliable integra-
1
tion (sample H NMR spectra can be found in the Support-
ing Information).
There were marked differences in behaviour between dif-
ferent systems. 1,7-Octadiene 1b forms only cyclohexene 3b
when exposed to 2, even at [1b]0 =4m; we have previously
estimated a kinetic EM for cyclohexene 3b at about 80m
based on theoretical and experimental studies, which shows
that this is a remarkably efficient RCM reaction.[10] Mando-
lini calculated a value of 912m for the EMT of 3b based on
measured symmetry-corrected thermodynamic parameters
for 3b, hexane and hydrogen.[18] In stark contrast, cyclono-
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J. M. Percy, I. H. Hillier et al.
5.69 ppm) and cycloheptene 3c (dH (CD2Cl2)=2.15 ppm and
1.64 ppm) by 1H NMR in the metathesis of 1d. The presence
of products derived from one and two successive isomerisa-
tion steps followed by cyclisation demonstrates that the cyc-
lisation of the propagating carbene derived from 1d is par-
ticularly slow. Table 2 shows the highest [1]0 concentrations
subtracting [3b] from [1c]0 in the graphical treatment; the
curve now reaches a maximum [3c]=53 mm. This behaviour
represents good evidence that the systems really are under
thermodynamic control, and that overall changes in free
energy can be used to make quantitative predictions of effi-
ciency.
The concentrations tested were limited at the lower end
for 3d–f by reaction rate (dilute RCMs proceed slowly and
Table 2. Threshold concentrations and effective molarities for 3a–f.
may not have reached equilibrium). Dilute RCMs of 1d–f in
Ring
size
Target
cycloalkene
[1]
(max)
Log
G
Log10ACTHGNUTERNNUG
(EMT/m)[b]
1
CD2Cl2 required H
N
[mm][a]
see reaction products clearly, without interference from the
residual solvent peak (see the Supporting Information for
details and sample spectra). At the upper end of the concen-
tration regime, precipitation of insoluble polymeric material,
which perturbs the reaction equilibria, was observed at
about 3m 1c. At about 2m 1c the signal for 3c was no
longer sufficiently well resolved for accurate integration.
Owing to the low concentrations involved, quantification
5
6
7
8
9
10
3a
3b
3c
3d
3e
3 f
10
>4000
5
<0.5
<0.5
<0.5
ꢀ0.64
1.52
ꢀ2.51
ꢀ3.31
ꢀ6.24
ꢀ3.48
ꢀ0.27
@0.60
ꢀ1.28
ꢀ3.00 to ꢀ4.00
<ꢀ4.00
<ꢀ4.00
[a] The highest [1]0 at which only diene 1 and cycloalkene 3 are detected
by 1H NMR. [b] Experimentally determined or estimated (see Figure 2
and text).
1
of products in the RCM of 1d–f by H NMR was difficult,
allowing only estimation of EMT for 3d–f. Cyclooctene 3d is
detected at concentrations of about 10ꢀ1 mm in the RCM of
1d at concentrations of 0.5–5 mm, so EMT can be estimated
at about 0.1–1 mm. As no 3e could be detected even at low
at which clean RCM was achievable. This information is
useful to guide choice of synthetic conditions, but a more
quantitative approach was required. Cacciapaglia et al. de-
scribed a promising method based on reactions of bifunc-
tional monomers; for a given cyclic species Ci, increasing
the acyclic monomer concentration leads to an increase in
[Ci] up to a critical monomer concentration.[28] Above that
concentration, there is no further increase in [Ci], which is
then equal to the thermodynamic effective molarity (EMi)
for that species. The cyclisation of 1b to 3b is too efficient
to reach a maximum value under the attainable experimen-
tal conditions, and so EMT @ 4m.
However, the approach was much more successful with
the RCMs of 1,6-heptadiene 1a and 1,8-nonadiene 1c, yield-
ing curves of the expected shape (Figure 2).
Asymptotic fitting of the data afforded the maximum
values of [3]. For 1a, the curve reached a maximum [3a]=
538 mm following an initial linear portion (up to [3a]=
300 mm). For 1c, the isomerisation reaction represents a
complication; once formed, cyclohexene cannot re-enter the
equilibrium and thus depletes the reservoir of 1c. This dif-
ference between the two systems was thus represented by
1
(0.5 mm) concentrations by H NMR or GC-MS, EMT for 3e
1
can be estimated, at best, at the detection limit of H NMR
spectroscopy (about 10% of [1e]0 for such dilute reactions).
This leads to an estimated EMT of about 0.1 mm. Cyclode-
cene 3 f could be formed as either the E- or Z-isomer. Anal-
ysis of commercial samples of each isomer revealed differ-
ences in the chemical shift of the alkene protons (dH
(CDCl3)=5.49 ppm for E-3 f and 5.41 ppm for Z-3 f). The
presence of E-3 f in the small-scale reactions can be ruled
1
out by H NMR, but Z-3 f overlaps with signals correspond-
ing to dimers 4 and 5. However, when reaction mixtures
([1 f]0 =5 mm or 10 mm, without internal standard) were ana-
lysed by GC-MS, spiking with commercial samples of the E-
or Z-isomer), neither cyclodecene was present. The calculat-
ed and estimated EMT values from these experiments are
listed in Table 2.
These results reveal quite good agreement between ex-
periment and the predictions for 3a and 3b. However, it ap-
pears that the formation of cycloheptene is more efficient
than would be predicted from the alkene strain energy and
the number of rotatable bonds alone. We are unable to ex-
plain this discrepancy at this time, and are seeking to under-
stand this system more fully through more detailed kinetic
profiling of the RCM reaction.
The presence of diene at the end of the small scale reac-
tions is ambiguous: it could arise from the system reaching
equilibrium, or it could be due to the exhaustion of the pre-
catalyst/catalyst system. It was straightforward to test for
catalyst activity after 18 h at room temperature. Firstly, at
high pre-catalyst concentrations ([2]ꢃmm), we could ob-
1
serve the presence of pre-catalyst directly in the H NMR
Figure 2. a) Plot of [3a] after 18 h versus [1a]0 for the RCM of 1a in
spectra (dH (CDCl3)=19.2 ppm). Inoculation of one of these
reactions after 18 h with a fresh charge of 1b resulted in
turnover to cyclohexene. An alternative method to demon-
*
CDCl3
(
, the solid line represents the asymptotic fit). b) Plot of [3c]
*
after 18 h versus ([1]0ꢀ
[3b]) for the RCM of 1c in CDCl3
(
, dashed
line).
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Thermodynamics of p-Bond-Forming Ring-Closing Metathesis Reactions
FULL PAPER
DGRCM ¼ ðGcycloalkeneþGetheneÞꢀGdiene
DGDimer ¼ ðGdimerþGetheneÞꢀ2Gdiene
DDG ¼ DGRCMꢀDGDimer
ð6Þ
ð7Þ
ð8Þ
strate that a system has reached equilibrium is to show that
the same reaction mixture composition can be approached
from a number of different starting points. The RCM of 1,8-
nonadiene 1c is a good system for this test because it con-
tains unreacted diene after 18 h; 1c RCM (with 1 mol% or
3 mol% 2) leads to the same outcome as the ring-opening
metathesis polymerisation (ROMP) of cycloheptene 3c
(with 3 mol% 2 and about 100 mol% ethene) (Figure 3).
The difference between the predicted values using the
treatment of Mandolini (EMTM) (which follow the experi-
mental observations quite closely) and the results from elec-
tronic structure calculations (EMTESC) is roughly four orders
of magnitude for all the rings 3a–f examined, apart from the
7-membered ring. Taking the average over the other five
systems delivers a value of 4.4 log units. As the calculations
reproduced the literature strain energies closely, the origin
of the offset must be entropic. Reaction entropies for RCM
and dimerisation are recorded in Table 4.
Table 4. Reaction entropies for RCM to form cyclopropene to cyclode-
cene, and DDS calculated using Mandoliniꢀs expression [Eq. (5)]
(calKꢀ1 molꢀ1).
Figure 3. Profiles for the concentration of cycloheptene 3c in the ROMP
^
of 3c (about 40 mm 3c, about 100 mol% ethene, 1 mol% 2, ), the RCM
Rotors[a]
2
3
4
5
6
7
8
9
*
of 1,8-nonadiene 1c (about 40 mm 1c, 1 mol% 2, ) and the RCM of 1,8-
ESC
DSRCM
35.82 32.67 31.39 29.85 28.57 26.77 23.17 20.64
22 18 14 10
ꢀ0.8
*
nonadiene 1c (about 40 mm 1c, 3 mol% 2, ).
M[b]
DDSRCM
6
2
0
The product mixtures form well within the timescales of
the small scale reactions.
Figure 4 plots the calculated entropy changes for RCM
(DSRCM is plotted as the entropy changes upon dimerisation
are very small, that is, there is no change in the molecularity
associated with the reaction), and the values obtained from
Mandoliniꢀs expression against the number of rotatable s-
bonds, or rotors r [Eq. (5)].
We now wished to examine what reaction outcomes elec-
tronic structure calculations would predict. Diene-, product-
and dimer- free energies were calculated at the M06-L/6-
311G** level of theory and corrected for solvation effects
using a continuum model described previously.[6] Scheme 2
defines the reactions and equilibrium constants of interest,
and the calculated free-energy changes for RCM (DGRCM
)
and dimerisation (DGDimer) are recorded in Table 3.
The calculated free energies of the equilibria depicted in
Scheme 2 [Eqs. (6) and (7)] can be used to calculate DDG
and hence EMT (referred to herein as EMTESC) [Eq. (8)].
Figure 4. Entropy changes as a function of number of rotors, calculated
*
using Mandoliniꢀs equation ( /dashed line) and from electronic structure
Scheme 2. Reactions and equilibrium constants for the RCM and the di-
merisation of 1.
calculations of the RCM reaction (dienes 1 to cycloalkenes 3) at the
M06-L/6-311G* level of theory ( ).
*
Table 3. Free energies (M06-L/6-311G**, kcalmol-1) for RCM and dimer-
isation, and predicted thermodynamic effective molarities from electronic
structure calculations (EMTESC), an empirical treatment (EMTM) and ex-
periment.
Examining the individual components of DSRCM shows
that there is an increase in both Strans and Srot upon cyclisa-
tion due to an increase in the number of molecules during
the reaction. These increases in Strans and Srot are essentially
independent of system size, and have values of about 36 and
15 calKꢀ1 molꢀ1, respectively. There is a corresponding loss
of vibrational entropy upon cyclisation, due to the more re-
stricted motion of the cyclic product; this loss becomes
more important as the number of atoms in the system in-
Ring size
5
6
7
8
9
10
DGRCM
DGDimer
ꢀ3.98
0.98
3.62
ꢀ8.06
0.37
6.15
ꢀ3.55
0.77
3.15
ꢀ1.27
0.17
1.05
2.45
0.39
ꢀ0.27
0.46
0.53
ESC
Log
Log
Log
10A
10A(EMT
10A
)
ꢀ1.50
M
)
ꢀ0.63
1.52
ꢀ2.52
ꢀ3.31
ꢀ6.24
ꢀ3.48
[b]
[b]
[b]
[b]
ꢀ0.27
–
ꢀ1.28
–
–
–
[a] From experiment. [b] The EM could not be measured by this method.
Chem. Eur. J. 2011, 17, 13087 – 13094
ꢂ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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13091

J. M. Percy, I. H. Hillier et al.
creases, so that the change in DS shown in Figure 4 is due to
ꢀ
the freezing of an increasing number of C C s bonds. The
plot includes points for cyclopropene and cyclobutene for-
mation although these cycloalkenes do not form by RCM.
The slope of the plot is 2.01 calKꢀ1 molꢀ1 per rotor, which
represents the entropic cost to cyclisation efficiency of each
ꢀ
additional rotatable C C s-bond. There has been considera-
ble discussion in the literature concerning the loss of entro-
py which accompanies restrictions in the motion of flexible
chain molecules, particularly due to cyclisation as studied
here, but also in biological systems when, for example, flexi-
ble substrates bind to large protein molecules.[29] In the
latter case the entropy loss can be crucial to the binding free
energy and is thus central to the drug discovery problem. In
his analysis of the role of ring strain on the closure of bi-
functional chain molecules, Mandolini found a slope of
4 calKꢀ1 molꢀ1, which is significantly greater than the value
obtained in this study. Whitesides and co-workers prefer a
lower value, in the range 0–4 calKꢀ1 molꢀ1 for a single tor-
sion,[30] rather less than the value of about 4.5 calmolꢀ1 Kꢀ1
of Jencks.[11] The smaller value is more consistent with our
findings. The intercept of 39.7 calKꢀ1 molꢀ1 (DDSmax) com-
pares favourably with the estimate of the maximum advant-
age of intramolecularity for gas-phase reactions made by
Page and Jencks of 40–50 calKꢀ1 molꢀ1.[11]
Scheme 3. Examples of systems for which the substrate structure exerts a
dramatic effect on the reaction outcome.
for which the substrate structure exerts a dramatic effect on
the reaction outcome.
Forbesꢀ unsubstituted system 9a failed to return any cy-
cloheptenone 10a, whereas the tetramethyl analogue 9b
formed exclusively cyclic product 10b when neat diene was
exposed to Schrock catalyst 11. The EMT calculated for 9a
is lower than the experimental EMT for 3a (that is a produc-
tive RCM reaction) and close to the value for 3d, which is
The finding that a constant correction (independent of the
ꢀ
number of C C bonds in the reactant hydrocarbon) is
formed only in trace amounts by RCM. Hence, the calculat-
ESC
needed to bring the electronic structure predictions into
agreement with experimental solution phase data leads us to
suggest that it is a restriction of the rotational and transla-
tional motion in solution which is responsible for the overes-
timation of the entropy loss upon cyclisation. Such an effect
is not modelled by the continuum treatment of solvation
which we have employed. We therefore propose that DDG
values obtained from these electronic structure calculations
can be converted into more predictively useful quantities by
applying a 4.4 log unit correction to the calculated EM
values. This correction, which corresponds to an addition of
6 kcalmolꢀ1 to DGRCM at 298 K, makes the computed data
ed (corrected) EMT
for 9a is consistent with the experi-
mental observation that no 10a is formed under concentrat-
ed conditions. The contrast with 9b is clear; an EMT of 103 m
is entirely compatible with the clean RCM reaction ob-
served under solvent-free conditions. In the oxocene chemis-
try described by Linderman, unsubstituted and tert-butyl
substituted systems 12a and 12b failed to cyclise to respec-
tive products 13a and 13b when exposed to first generation
Grubbsꢀ catalyst 14. However, (tributylstannyl) derivative
12c afforded oxocene 13c in good yield (15 mm), along with
oligomer (10%) and recovered starting material (16%). The
calculations predict a progressive increase in EMT from 12a
to 12c; the EMT for latter diene is higher than the value es-
timated for the formation of cyclooctene 3d, and so is con-
sistent with a higher synthetic yield. These results are sum-
marised in Table 5.
more relevant to solution reactions. Once the correction is
applied, the EMT
perimental data for 5- and 7-membered ring formation. The
data predict that cyclodecene will not be observable from
these small scale RCM experiments, as it will be formed
ESC
values agree much better with the ex-
However, the RCMs of 12a–c are most likely irreversible
with 14, so the synthetic reactions are probably not strictly
representative of a thermodynamically controlled outcome.
1
below the detection limits of the H NMR method.
Our computed gain of translational and rotational entropy
of about 51 calKꢀ1 molꢀ1 must therefore be reduced to
31 calKꢀ1 molꢀ1, corresponding to the addition of 6 kcal
molꢀ1 to DGRCM at 298 K. This intercept (31 calKꢀ1 molꢀ1) is
now very close to the value proposed by Mandolini.
Table 5. Uncorrected and corrected DGRCM for systems in Scheme 3 de-
termined from DFT calculations at the M06-L/6-311G* level of theory
(energies in kcalmolꢀ1).
The effectiveness of this approach can be tested by mod-
elling systems from the literature in the same way as the
RCM reactions of 1a–f have been treated (M06-L/6-311G*
level of theory) and comparing these data to the reported
experimental outcomes. The attempted syntheses of Forbes
and Wagener[31] and the oxocene forming RCMs described
by Linderman et al.[32] (Scheme 3) are examples of systems
ESC
Diene Uncorrected Corrected Corrected Log
N
)
Synthetic
outcome
DGRCM
DGRCM
DDG
9a
9b
12a
12b
12c
ꢀ1.83
ꢀ9.13
0.76
4.17
ꢀ3.13
6.76
5.55
4.09
3.62
ꢀ3.68
6.21
5.00
3.54
ꢀ2.65
2.70
ꢀ4.55
ꢀ3.67
ꢀ2.60
Oligomer
RCM
Oligomer
Oligomer
RCM
ꢀ0.45
ꢀ1.91
13092
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Chem. Eur. J. 2011, 17, 13087 – 13094

Thermodynamics of p-Bond-Forming Ring-Closing Metathesis Reactions
FULL PAPER
We would, however, expect an EMT of 10ꢀ3 m (that is be-
tween the EMT of 3c and 3d) to be a tipping point between
success and failure of RCM; cycloheptene formation by
RCM is competent at low concentrations, whereas cyclooc-
tene formation is sluggish. The corrected values from the
electronic structure calculations appear to identify that tip-
ping point quite well. This predictive ability may prove in-
valuable in the planning of synthetic campaigns, and even
more so in process optimisation, where calculated EMT
values could be used to allow a judicious choice of route or
dry GC vial fitted with PTFE-coated silicone septum, purged with dry
oxygen-free nitrogen and attached to a balloon of dry oxygen-free nitro-
gen through a syringe barrel and needle. Stock solutions were prepared:
one of diene and internal standard (1,3,5-trimethoxybenzene, 0.5 equiv)
and one of pre-catalyst 2. Each GC vial was first charged with the appro-
priate volume of solvent, then diene/standard solution, followed by pre-
catalyst solution. This order of addition avoids the artefact from tempo-
rarily increased diene concentration which may, especially for the larger
dienes, result in the formation of insoluble polymeric material. Reactions
were stirred for 18 h and carefully and quickly transferred to clean, oven-
dried NMR tubes. Samples were queued for analysis (8, 16 or 32 scans
depending on concentration; D1 =35 s) on either a Bruker AVANCE
400 MHz NMR spectrometer (with
a BBFO-z-ATMA probe) or a
reaction concentration.
Bruker AVANCE DRX 500 MHz NMR spectrometer (with a 13C/1H-
DUL probe). Where solvent-suppression techniques were employed,
samples were analysed at using a Bruker AVANCE II+ 600 MHz NMR
spectrometer (with triple-resonance TBI-z probe) (128 scans, D1 =2 s).
Reaction mixtures for GC-MS or detailed NMR spectroscopy analyses
were stirred over PhosphonicS STA3 silica-supported metal scavenger
overnight[35] and checked by 1H NMR spectroscopy before further analy-
ses. More detailed experimental information can be found in the Sup-
porting Information.
Conclusion
We have presented experimentally determined EMT values
for the formation of cyclopentene 3a and cycloheptene 3c
by RCM of dienes 1a and 1c respectively, using a straight-
forward series of small scale experiments that do not per-
turb the reaction mixtures. Estimations of EMT for 3d–f
have also been obtained through the course of this investiga-
tion. For most systems, EMT can be predicted using the
strain energy of the cyclic products, the number of rotatable
bonds and the treatment of Mandolini et al..[9]
The use of electronic structure calculations to predict
RCM outcomes based on free-energy differences has also
been explored. Due to entropic discrepancies, free energies
obtained from electronic structure calculations cannot be
used directly but a straightforward correction delivers pre-
dictively useful free energies. We believe that this approach
will aid the synthetic chemist in planning reaction conditions
for RCM.
Acknowledgements
We thank the EPSRC Initiative in Physical Organic Chemistry 2 (EP/
G013160/1 and EP/G013020/1, fellowship to S.K.), the University of
Strathclyde (fellowship to G.R.), AstraZeneca (Industrial CASE Award
to D.J.N.) and ORSAS (studentship for S.P.) for funding. We thank the
EPSRC National Mass Spectrometry Service at the University of Wales,
Swansea (particularly Service Manager Mrs Bridget Stein) for mass spec-
trometric measurements. We also thank Craig Irving for assistance with
NMR.
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Chem. Eur. J. 2011, 17, 13087 – 13094
ꢂ 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Received: May 31, 2011
Revised: August 11, 2011
Published online: October 4, 2011
13094
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Chem. Eur. J. 2011, 17, 13087 – 13094