Electronic effects versus distortion energies during strain-promoted alkyne-azide cycloadditions: A theoretical tool to predict reaction kinetics

Article abstract of DOI:10.1002/ejoc.201201627

Second-order reaction kinetics of known strain-promoted azide-alkyne cycloaddition (SPAAC) reactions were compared with theoretical data from a range of ab initio methods. This produced both detailed insights into the factors determining the reaction rates and two straightforward theoretical tools that can be used to predict a priori the reaction kinetics of novel cyclooctynes for strain-promoted cycloaddition reactions. Multiple structural and electronic effects contribute to the reactivity of various cyclooctynes. It is therefore hard to relate a physical or electronic property directly and independently to the reactivity of the cyclooctyne. However, we show that Hartree-Fock LUMO energies, which were acquired while calculating activation energies at the MP2 level of theory, correlate with second-order kinetic rate data and are therefore usable for reactivity predictions of cyclooctynes towards azides. Using this correlation, we developed a simple theoretical tool that can be used to predict the reaction kinetics of (novel) cyclooctynes for SPAAC reactions. Activation energies, distortion energies, and TS conformational data were compared in a set of strained cyclooctynes in strain-promoted azide-alkyne cycloaddition (SPAAC) reactions. Only electronic effects could be accurately related to experimental rate data. Copyright

Full text of DOI:10.1002/ejoc.201201627

Job/Unit: O21627
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FULL PAPER
Strained Molecules in Cycloaddition
J. Garcia-Hartjes, J. Dommerholt,
T. Wennekes, F. L. van Delft,
H. Zuilhof* ..................................... 1–10
Electronic Effects versus Distortion Ener-
gies During Strain-Promoted Alkyne-Azide
Cycloadditions: A Theoretical Tool to Pre-
dict Reaction Kinetics
Activation energies, distortion energies,
and TS conformational data were com-
pared in a set of strained cyclooctynes in
strain-promoted azide–alkyne cycload-
dition (SPAAC) reactions. Only electronic
effects could be accurately related to exper-
imental rate data.
Keywords: Reaction mechanisms / Ab initio
calculations / Cycloaddition / Click chemis-
try / Strained molecules / Alkynes
0000, 0–0
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H. Zuilhof et al.
FULL PAPER
DOI: 10.1002/ejoc.201201627
Electronic Effects versus Distortion Energies During Strain-Promoted Alkyne-
Azide Cycloadditions: A Theoretical Tool to Predict Reaction Kinetics
Jaime Garcia-Hartjes,[a] Jan Dommerholt,[b] Tom Wennekes,[a] Floris L. van Delft,[b] and
Han Zuilhof*[a,c]
Keywords: Reaction mechanisms / Ab initio calculations / Cycloaddition / Click chemistry / Strained molecules / Alkynes
Second-order reaction kinetics of known strain-promoted az-
ide–alkyne cycloaddition (SPAAC) reactions were compared
with theoretical data from a range of ab initio methods. This
produced both detailed insights into the factors determining
the reaction rates and two straightforward theoretical tools
that can be used to predict a priori the reaction kinetics of
novel cyclooctynes for strain-promoted cycloaddition reac-
tions. Multiple structural and electronic effects contribute to
the reactivity of various cyclooctynes. It is therefore hard to
relate a physical or electronic property directly and indepen-
dently to the reactivity of the cyclooctyne. However, we show
that Hartree–Fock LUMO energies, which were acquired
while calculating activation energies at the MP2 level of
theory, correlate with second-order kinetic rate data and are
therefore usable for reactivity predictions of cyclooctynes
towards azides. Using this correlation, we developed a sim-
ple theoretical tool that can be used to predict the reaction
kinetics of (novel) cyclooctynes for SPAAC reactions.
Turner et al.[8] on the ΔH of hydrogenation of unsaturated
aliphatic compounds (including cyclooctyne), Bertozzi later
assigned significant rate enhancements to the ring strain of
18 kcal/mol[9] for 1 compared with unstrained alkynes. Sub-
sequently, the use of electron-poor cyclooctynes was shown
to speed up the reaction significantly, specifically in 3,3-
difluorocyclooct-1-yne (DIFO, 2).[5d,10] Some of us devel-
oped bicyclo[6.1.0]non-4-yne (BCN, 3)[11] with the ad-
ditional advantage over earlier cyclooctynes that it is readily
prepared and symmetrical, thus avoiding the formation of
regioisomeric adducts upon cycloaddition with an organic
azide (Figure 2). Apart from electron-withdrawing groups,
such as the fluorine groups in compound 2, the addition of
extra ring strain was also shown to be advantageous, as for
example implied from the observed high rates for the reac-
tion with 3,7-dibenzocyclooctyne (DIBO) 4.[13] In 2010, di-
fluorobenzocylooctyne (DIFBO) was described,[14] which
combines the electron-withdrawing effect of the fluorine
atoms of 2 with the ring strain of 4. This compound was
shown to be the most rapidly reacting cyclooctyne towards
azides reported to date, but was not taken up in the current
study because of its lack of stability outside a protective
cyclodextrin shell. Based on the framework of 4, two endo-
cyclic nitrogen-containing dibenzocyclooctyne derivatives
have been published that contain either a CH2 group and a
nitrogen atom in the ring (DIBAC, 5),[15,16] or an endocyclic
amide (lactam) functionality and no saturated carbon
atoms in the cyclooctyne ring (BARAC, 6).[17] Kinetic data
are available for 2–6 (Table 1), and for an analogue of 1 that
contains an alkoxy moiety at the 3-position.[9] Compound
7 was described in the literature,[12] but not in reaction with
azides. Compounds 8–10 are strained models that, to the
Introduction
The strain-promoted azide–alkyne cycloaddition
(SPAAC) reaction is increasingly applied for bio-orthogonal
purposes. Cyclooctynes have proven valuable because of
their relative biological inertness and their strain-induced
high efficiency, and selectivity towards azides in cycload-
dition reactions.[1] Unlike in the copper-catalyzed variant
of Huisgen’s 1,3-dipolar cycloaddition,[2] i.e., the copper-
catalyzed azide–alkyne cycloaddition (CuAAC), which
emerged over the years as the prototypical “click reac-
tion”,[3] there is no need for toxic additives such as CuI.
This is advantageous because copper ions can induce unde-
sirable side-reactions such as non-specific binding to thiol-
groups and oxidative damage that both CuI and CuII ions
are able to inflict on biomolecules.[4] Furthermore, because
cyclooctynes are generally not reactive towards other cellu-
lar components in aqueous media, they can be used in stud-
ies on the cellular level.[5]
In 1953, Blomquist,[6] and later Wittig and Krebs,[7] de-
scribed the reaction of cyclooctyne (OCT, 1; Figure 1) with
phenyl azide as an “explosive reaction”. Based on work by
[a] Laboratory of Organic Chemistry, Wageningen University,
Dreijenplein 8, 6703 HB, Wageningen, The Netherlands
E-mail: Han.Zuilhof@wur.nl
Homepage: www.wageningenur.nl/orc
[b] Institute of Molecules and Materials, Radboud University
Nijmegen,
Heijendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands
[c] Department of Chemical and Materials Engineering, King
Abdulaziz University,
Jeddah, Saudi Arabia
Supporting information for this article is available on the
WWW under http://dx.doi.org/10.1002/ejoc.201201627.
2
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Strain-Promoted Alkyne-Azide Cycloadditions
best of our knowledge, have not been described in literature Table 1. Experimental data of SPAAC second-order reaction kinet-
ics of cyclooctynes with benzyl azide.
at the time of writing.
k [·10–3 –1 s–1]
m
Solvent
Ref.
[a]
Relatively little theoretical work has been published that
correlates experimental and calculated data of these strain-
promoted cycloadditions. Various properties are known to
influence the reaction kinetics of these cyclooctynes in
SPAAC reactions (Figure 3). For example, Houk and co-
workers performed B3LYP/6-31G(d) optimizations to com-
pare the reactivity of 1 and 2,[19] which were more recently
Compd.
1
2
3
4
5.8
76
140
170
120
310
960
CD3CN/D2O
CH3CN
CD3CN/D2O
CD3OD
CD3CN
CD3OD
[5d]
[11]
[13]
[18]
[15]
[17]
5
6
CH3CN
[a] Current work; see the Supporting Information for details.
complimented with a more extensive series of SCS-MP2/
6-311G(d) single-point computations on B3LYP-optimized
geometries.[20] These studies concluded that the difference
in the reactivity of various cyclooctynes is based on the dif-
ference in distortion energies of the alkynes, which is re-
quired to deform it from the reactant geometry to the ge-
ometry it has in the transition state (TS). In addition, the
ring strain in cyclooctynes has been investigated systemati-
cally by Bach with B3LYP/6-311+G(3df,2p) calculations.[21]
He calculated that the barrier for cycloaddition of the
benzyl azide and DIFO (2) is 2.3 kcal/mol lower than ad-
dition to 1 (Figure 4). This method was also used to investi-
gate the trends in activation barriers for the 1,3-dipolar cy-
cloadditions of azides with various cyclooctynes, dibenzo-
cyclooctynes, and azacyclooctynes. Subsequently, Goddard
and co-workers concluded that suitable placement (e.g., on
the position next to the sp-hybridized alkyne carbons) of
electron-withdrawing substituents leads to LUMO-lowering
effects on the alkyne, and that this is accompanied by
higher reactivity of cyclooctynes towards cycloaddition
with azides.[22] Houk et al. showed an approximately 2 kcal/
mol increase in reactivity of 2 with respect to the parent
compound 1. Gold et al. confirmed this finding and elabo-
rated with Natural Bond Order (NBO) analysis that hyper-
conjugative donation of the alkyne π-system to the σ*C–
F orbital directly leads to the TS stabilization through the
assistance in alkyne bending,[23] which, together with the
LUMO-lowering effect described by Goddard earlier, is the
apparent driving force for the 50-fold increase of reactivity
Figure 1. Cyclooctynes under study.
Figure 2. SPAAC of strained cyclooctyne BCN (3) and allyl azide,
yielding triazole 11.
Figure 3. TS conformation of DIFO (2) (left) and trans-cyclobutyl-substituted 10 (right) with allyl azide, with focus on the various
properties of the cycloocytnes that influence their SPAAC reaction kinetics.
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Figure 4. TS conformations of 1 and allyl azide, calculated with MP2, B3LYP, and M06-2X, respectively.
of 2. Both Gold and Goddard supported the strategy of to undergo – in addition to SPAAC reactions – for example,
lowering the energy of the TS to increase reactivity towards a thiol-yne reaction with cysteines, which would complicate
azides rather than reactant destabilization. In case of 2, in- the application of these cyclooctynes in biosciences. The
creased reactivity is a direct result of Ea lowering. Gold ability to tune the reactivity of cyclooctynes by combining
hinted at a theoretical tool that could be developed to pre- an increase in reactant stability with a high efficiency dur-
dict reactivity in the form of a combination of the calculable ing SPAAC, is therefore of paramount importance in both
molecule properties described above. Recently, the reaction biological and material sciences.[25] Hence, it would be ad-
kinetics of BARAC (6) derivatives were shown to vary de- vantageous if the design of novel cyclooctynes with, for ex-
pending on the addition of several substituents.[24] The reac- ample, extra groups that increase the water solubility, could
tion kinetics of the derivatives were subsequently compared be guided by predicting their reactivity before embarking
with the results of B3LYP/6-31G(d) calculations. It was on a resource-consuming synthetic undertaking.
found that addition of fluorine groups on the aryl groups
We here present precisely this: a theoretical tool that can
of BARAC (6), resulted in an increase in reactivity of ca. be used to accurately predict SPAAC reaction kinetics.
75% compared with its parent compound 6. On the basis Furthermore, we describe an even simpler, albeit less accu-
of B3LYP calculations, this was attributed to increased sta- rate, tool that can be used by non-theoreticians that only
bilizing interaction energy in the TS. In the same study, a requires a ChemDraw-like chemical structure as input to
decrease in the alkyne bond angle was correlated to an in- quickly give an indication of the reactivity of new cyclooc-
crease in reactivity. The authors suggested that the calcu- tynes before they are actually developed. In the study pre-
lated TS distortion and interaction energies could be used sented here, we further elucidate the relationship between
in the design of novel cyclooctynes. To date, however, a gen- SPAAC kinetics and cyclooctyne electronic properties, by
erally applicable computational tool that can be used to investigating the SPAAC transition state structures and en-
correlate the structures of these cyclooctynes to their reac- ergies for a structurally diverse set of ten cyclooctynes (1–
tion kinetics, has not yet been described.
10; Figure 1). This was performed with a combination of
In the current paper, we will focus in more detail on the DFT (B3LYP,[27] M06-2X[28]) and SCS-MP2[29] calcula-
transition states of SPAAC reactions, and describe tools tions. Among the ten selected cyclooctynes, six (1–6) have
that predict a priori the reaction kinetics of novel cyclooct- been previously used in SPAAC reactions and four (7–10)
ynes for application in these cycloaddition reactions. Given have not yet been used. Finally, to improve the benchmark-
the still growing interest in SPAAC reactions, it is highly ing of our calculations, additional competition experiments
desirable to have a simple theoretical tool that can predict and kinetic constant determinations were performed on cy-
the reactivity of novel, hypothetical cyclooctynes. Until clooctynes 1–3.
now, researchers have mainly focused on the development
of faster reacting cyclooctynes. However, the cost of in-
creased reactivitis often paid by decreased stability. This is,
Computational and Experimental Methods
for example, seen in DIBO (4),[13] which needs to be stored
while deprived of light and oxygen. The decreased stability
Calculations were performed using the Gaussian 09 set
of highly reactive cyclooctynes hampers the further devel- of programs.[30] Structures (reactants and transition states)
opment of SPAAC reactions in material sciences such as, were optimized, and the resulting geometries were shown
in our own experience, the development of biosensors.[26] to be real minima or transition states on the potential en-
Furthermore, these compounds with a high intrinsic energy ergy surface by vibrational frequency computations. The
are prone to lose their selective reactivity by also being able standard IEFPCM dielectric continuum solvent model for
4
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Strain-Promoted Alkyne-Azide Cycloadditions
MeOH with UA0 radii was used. Optimization was consist- Table 2. Calculated activation energies (kcalmol–1) in the gas phase
and in MeOH (IEFPCM solvent model), of the SPAAC reaction
ently performed using the 6-311G(d,p) basis set, at the
for the studied cyclooctynes with allyl azide (A) or benzyl azide (B)
B3LYP, M06-2X, and MP2 levels of theory. Following the
optimization, single-point energies were obtained by using
obtained by SCS-MP2, B3LYP, and M06-2X calculations.
Compd. SCS-MP2
Gas MeOH
B3LYP
Gas
M06-2X
MeOH Gas
the 6-311+G(2d,2p) basis set for all these three methods,
while for the MP2-optimized geometries SCS-MP2 energies
were obtained.[29b] Zero-point energies were included in all
values. Geometries and vibrations were visualized using
Gaussview 4. The syntheses of 1 and allyl azide were per-
formed as described in the Supporting Information. Deter-
mination of the reaction kinetics of unsubstituted cyclooct-
yne (1) with benzyl azide was performed according to the
literature,[11] as described in detail in the Supporting Infor-
mation. Competition experiments of 1, benzyl azide and
MeOH
1 + A
1 + B
10.5 11.3
9.6 10.5
6.4
12.1
11.9
11.5
11.6
13.0
n.d.[b]
16.5
15.0
13.7
12.9
12.0
12.1
13.8
13.3
15.2
13.2
9 8.2
11.6
11.9
14.1
11.8
11.1
9.4
13.0
12.7
9.7
9.9
12.9
2 + A[a] 6.7
2 + B[a] 6.3
6.0
7.4
7.1
7.7
7.7
5.2
3.5
6.3
5.9
9.5
8.7
10.7
9.6
3 + A
3 + B
4 + A
4 + B
5 + A
6 + A
6.5
6.2
6.3
5.7
3.5
2.1
5.7
5.4
8.6
7.5
11.7
n.d.[b]
12.3
11.5
9.4
17.9
11.6
15.4
14.5
12.9
7.9
15.1
14.6
16.5
13.9
13.4
11.2
9.5
11.6
11.8
14.1
13.8
14.1
7.7
allyl azide were performed as described in the Supporting 7 + A
10.8
10.8
12.6
12.2
12.6
7 + B
8 + A
9 + A
Information.
10 + A 9.6
Results and Discussion
[a] Only 1,4-addition (trans) transition states were calculated.
[b] n.d.: nNot determined.
Alkyne-Azide Cycloadditions
Table 2 depicts the activation energies obtained from cal-
culations with B3LYP, M06-2X, and SCS-MP2 methods for
the ten cyclooctynes under investigation. Because all com-
pounds clearly contain strain, triple-ζ [6-311G(d,p)] basis
sets were employed for the optimizations, whereas the sin-
gle-point energy calculations involved the flexible 6-
311+G(2d,2p) basis sets. From experimental studies on re-
action kinetics, it is well-known that 3 reacts appreciably
faster than 2 and at least an order of magnitude faster than
1 (Table 1). Originally, 1 was published including an alkoxy
substituent on the 3-position.[9] The second-order rate con-
stant was also published for this compound (k
=
2.4ϫ10–3 –1 s–1) but considering that the 3-substituent
m
may induce both steric and electronic effects on the reac-
tion, we decided not to use this data in the comparison with
the calculated activation energy. Therefore, 1 was synthe-
sized (see the Supporting Information for experimental de-
tails), and its second-order rate constant in the SPAAC re-
action with benzyl azide was determined to be k =
5.8ϫ10–3 –1 s–1 in CD3CN/D2O (3:1). All currently avail-
m
able kinetic data for the reaction of cyclooctynes 1–6 and
azides are presented in Table 1, and range over more than
two orders of magnitude. The approximate order of experi-
mental reactivity of these compounds in various media is 6
Ͼ 5 Ͼ 4 ≈ 3 Ͼ 2 Ͼ 1. This order was, however, not borne
out by B3LYP-based calculations, which yielded a relative
order of 2 Ͼ 1 Ͼ 6 Ͼ 3 Ͼ 5 Ͼ 4. To check whether this
discrepancy could be remedied by the use of another DFT
functional, while keeping the computational advantage of
the relatively fast density functional theory, Truhlar’s M06-
2X functional was employed. However, the M06-2X func-
tional was also unable to reproduce a qualitative trend that
was consistent with the experimental observation, and
yielded a rate order 6 Ͼ 5 ≈ 2 Ͼ 1 ≈ 3 Ͼ 4. In contrast,
MP2 calculations did follow the order of reactivity (see the
Supporting Information, Figure S6), but produced incor-
Figure 5. Plot of the logarithm of experimental second-order rate
constants (see Table 1 for references) versus calculated activation
energies obtained from (a) SCS-MP2/6-311+G(2d,2p)//MP2/6-
311G(d,p); (b) B3LYP/6-311+G(2d,2p)//B3LYP/6-311G(d,p), and
rect, negative, activation energies. When, however, scaled to (c) M06-2X/6-311+G(2d,2p)//M06-2X/6-311G(d,p) calculations.
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SCS-MP2 (Figure 5, a), the calculations could properly culated to be more reactive than 10 (see Table 2, and the
mimic the complete experimental trend in relative reactivi- Supporting Information, Figure S7 for TS geometries).
ties and also produced realistic activation energies (Table 2).
For example, it was clear from these calculations that 6 was
the fastest in reacting azides and 1 was the slowest.
Transition State Activation Energies
Application of this method to compounds 7–10 con-
firmed the role of ring strain in determining the height of
Figure 5 shows plots of the logarithm of experimental
the SPAAC activation energy barrier. Increasing the cyclo- second-order rate constants against the calculated acti-
octyne ring strain in 7 and 8 by inclusion of sp2-hybridized vation energies as obtained by SCS-MP2, B3LYP, and M06-
carbon atoms was predicted to lead to a significantly in- 2X calculations. Clearly, the correlations of the experimen-
creased reactivity towards cycloaddition with azides com- tal rate constants with B3LYP data (R2 = 0.118) and M06-
pared with 1. Comparison of compound 7 with 4 revealed 2X data (R2 = 0.335) are insufficient to be used in predic-
that an increased size of the conjugated system also plays ting the reaction kinetics of novel cyclooctynes. Given the
an important role in lowering the activation energy barrier. significant differences in TS geometries (see Figure 5),
Both 7 and 4 have similar ring strain, but the latter has a doubts arise concerning the use of DFT-derived geometries
more extended π-electron system. In addition to the ring for single-point activation energy determinations. In con-
strain and size of the conjugated system, conformational trast, when the experimental rate constants were plotted
stabilities also affect the cyclooctyne reactivity. For exam- against SCS-MP2 calculated activation energies, using
ple, the trans-cyclobutyl moiety in 10 restricts the eight- MP2-derived geometries in the gas phase, a clear linear rela-
membered-ring conformation to a flattened structure (Fig- tion with good correlation was found (R2 = 0.937). The
ure 3). This impedes the formation of the chair-like confor- correlation was lower between the SCS-MP2 activation en-
mation that the eight-membered ring in cyclooctynes pref- ergies in MeOH and the experimental rate constants (see
erentially adopts in the TS of SPAAC reactions, as is shown the Supporting Information, Figure S8). The solvent model
for 2. The analogous cis-cyclobutyl-containing compound used, however, only provides a rough approximation of the
9 adopts a chair conformation and is correspondingly cal- complex interactions between MeOH and molecules in the
Figure 6. (left) TS geometries of 1–4 with allyl azide. (right) Structural data obtained from MP2/6-311G(d,p) optimization.
6
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Strain-Promoted Alkyne-Azide Cycloadditions
TS, which probably results in less accurate calculated acti- example, Figure 4 shows the relevant bond lengths for the
vation energies. The correlation between the experimental cycloaddition of 1 and allyl azide. With the B3LYP func-
and computational (gas phase) data might even improve tional, the calculations yielded asymmetric alkyne-azide
further if the experimental data were determined for one distances in the order of 2.17–2.31 Å. M06-2X calculations
solvent system, which is currently not the case (see Table 1). showed near-symmetric distances of approximately 2.20 Å,
For example, the experimental data for compounds 3, 4, whereas MP2 calculations showed “tighter” and also near-
and 5 were reported in protic solvents, which are known to identical distances of 2.10 Å. In all three cases, 1 adopted a
speed up the reaction with respect to acetonitrile.[18] Never- chair-like conformation. In Figure 6, the TS structures of
theless, the high linear correlation found showed that SCS- four cyclooctynes, 1–4, with allyl azide are described as op-
MP2 data was suitable for use in our envisaged predictive timized by MP2 calculations; all exhibit a chair-like confor-
tool. In the remainder of this study we therefore limited mation in the TS with allyl azide. On a first-level approxi-
ourselves to MP2-optimized geometries and the SCS-MP2 mation, given the exothermic nature of the reaction, lower
energies thereof.
activation energies could be expected for an earlier TS con-
SPAAC rate constants reported in the literature have formation, in which the C–N distance is larger. This is in-
mostly been experimentally determined with benzyl azide deed the case for the TS of 3 with allyl azide, in which
as the model compound (Table 1). The number of carbon the C–N distance is around 2.19 Å, and is more distant in
atoms makes the vibrational frequency calculations on the comparison with that in 1 (2.10 Å). Furthermore, in the
TS of benzyl azide and a cyclooctyne rather time-consum- case of allyl azide and 3, the azide angle is larger, which
ing to track computationally by using Møller–Plesset type means that less N–N–N bending is required to reach the
calculations. Therefore, we also studied the TS properties TS conformation. This latter feature is confirmed by the
with allyl azide, both theoretically and experimentally. Ki- distortion energy of allyl azide (energy difference between
netic data on benzyl azide and allyl azide reactivity with 1 the azide in the geometry of the optimized reactant and in
were obtained from second-order rate constant experi- the geometry it has in the TS), which is 7 kcal/mol lower
ments. A fivefold excess of a 1:1 mixture of allyl azide and than that of allyl azide in a TS with 1 (Table 3). However,
benzyl azide was reacted competitively with 1 in CD3CN/ for the also more rapidly reacting compound 4, the TS
D2O (3:1), and, in a separate experiment, with 3. Because seems to be later than for 1. For example, the C–N distances
the product ratios of the allyl and benzyl triazole products are around 2.05 Å, which implies a tighter TS than found
were 1:1.3 and 1:1.4, respectively (see the Supporting Infor- for 1. This corresponds to the larger distortion energy cal-
mation), it is clear that the reaction of allyl azide can be culated for the allyl azide and benzyl azide components re-
compared accurately to that of benzyl azide. This was con- acting with 4 in comparison with the reaction with 1 (26.1
firmed computationally: for compounds 1–4 the barriers and 27.2 kcal/mol for 4, and 24.8 and 24.4 kcal/mol for 1,
were computed for both allyl azide and benzyl azide, and respectively). In other words, although both 3 and 4 also
the difference between allyl azide and benzyl azide was less react appreciably faster than 1, the TS of 3 is characterized
than 0.9 kcalmol–1 for all four cases, with the barrier of by a lower distortion energy, whereas that of 4 is charac-
benzyl azide consistently lower than that of allyl azide terized by a higher distortion energy than observed for 1.
(Table 2). Furthermore, the TS geometries for these two sys- A similar discrepancy is observed for 2, which also reacts
tems are highly similar. For example, in the MP2/6- faster than 1 but has a later TS (Figure 6). In general, plots
311G(d,p)-derived TS of 1 with benzyl azide, r(C–Nterm
)
of the activation energy versus alkyne or azide distortion
and r(C–Nint) are 2.100 and 2.099 Å, respectively, whereas energies show only a poor correlation for the studied cyclo-
for the allyl azide-derived TS these values are 2.102 and octynes (see the Supporting Information, Figure S9). From
2.108 Å, respectively (Figure 6). In addition, the imaginary these observations it can be concluded that the geometries
frequencies that track the potential energy curve for ap- of the TS structures and distortion energies of these cyclo-
proach of the reactants are almost identical (–272.2 and octynes cannot be generally correlated to activating energies
–273.8 cm–1, respectively). Therefore, all TS structures were of SPAAC reactions. Moreover, natural charges on the al-
optimized at the MP2 level of theory for the reaction with kyne carbon atoms and the azide nitrogen atoms could not
allyl azide, whereas for compounds 1–4 these TS structures be related to the reactivity of the cyclooctynes under study.
were also optimized with benzyl azide.
Table 3. Distortion energies per component (cyclooctyne or azide)
for the SPAAC reactions of cyclooctynes 1–4, allyl azide (A), and
benzyl azide (B) (in kcal/mol).
Transition State Geometries
Compound
Edistortion
Compound
Edistortion
To study the correlation of experimental and theoretical
data in more detail, an in-depth study was made of the TS
geometries. When comparing the geometrical features of
the TS as obtained by the various methods, the TS struc-
tures acquired from MP2 calculations were consistently
shown to be significantly “tighter” than those obtained
from either B3LYP or M06-2X calculations. As a typical
1 (+ A)
1 (+ B)
2 (+ A)
2 (+ B)
3 (+ A)
4 (+ A)
4 (+ B)
3.6
3.7
1.8
1.8
3.0
5.1
4.3
A (+ 1)
B (+ 1)
A (+ 2)
B (+ 2)
A (+ 3)
A (+ 4)
B (+ 4)
24.8
24.4
24.3
24.5
17.9
26.1
27.2
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H. Zuilhof et al.
FULL PAPER
Figure 7. Correlation of the activation energy (in kcal/mol) of the SPAAC transitions states with the LUMO energy (in eV) of cyclooctynes
1–10 (a) in the transition state geometry with allyl azide, or (b) in the geometry they have as a fully optimized reactant.
LUMO Energy Levels as Predictive Tools
cloaddition reactions. To this end, we also plotted the
LUMO energy of the MP2-optimized cycloalkyne (i.e., full
optimization, without presence of azide) against the calcu-
lated activation energies (Figure 7, b). This again showed a
decent linear correlation (R2 = 0.829), albeit with clearly
more scatter than the linear correlation of the LUMO val-
ues that was obtained for the cyclooctynes in the transition
state. Even this simplified approach yielded the reactivity
order 6 Ͼ 5 Ͼ 4 ≈ 3 ≈ 2 Ͼ 1, which closely resembles the
experimentally observed order 6 Ͼ 5 Ͼ 4 ≈ 3 Ͼ 2 Ͼ 1. Even
quicker approaches, involving DFT, were less successful (R2
= 0.727 and 0.795, for B3LYP and M06-2X, respectively)
(see the Supporting Information, Figures S12 and S13,
respectively). Among the employed methods, only SCS-
MP2 is a uniformly robust method that can yield useful
SPAAC reactivity predictions. As LUMO energies can be
calculated in a straightforward manner in a variety of GUI-
assisted molecular simulation programs such as Gaussview
or ChemBio3D, this may simplify further experimental op-
timizations of strain-promoted cycloaddition reactions,
possibly also with other dipoles such as nitrones, nitrile ox-
ides,[18] and other alkynes. A step-by-step standard op-
erating procedure for performing these calculations, thereby
giving an indication of the reactivity of novel cyclooctynes
in SPAAC reactions, can be found in the Supporting Infor-
mation.
In addition to efforts to correlate activation energies to
geometrical features of the TS, interactions between the
most-involved molecular orbitals were also studied. This re-
vealed a linear correlation between the activation energy Ea
and the LUMO energy of the cycloalkyne as it is distorted
in the TS (Figure 7, a; R2 = 0.932), which is quite encourag-
ing given the spread of experimental conditions. A lower
LUMO energy of the cyclooctyne (in the MP2-calculated
TS geometry; please note: MP2 provides an energy correc-
tion on Hartree–Fock level-derived orbitals and, as such,
the LUMO energy is a Hartree–Fock energy) consistently
corresponded to a more rapidly reacting molecule. The
HOMO energy of the cyclooctynes could, however, not be
related to the activation energy in a convincingly linear
fashion (see the Supporting Information, Figure S10).
These findings confirm that the SPAAC reaction develops
predominantly through azide-HOMO and alkyne-LUMO
interactions.[12,20,31] However, the azide-HOMO energies
could also not be related to the SCS-MP2 activation energy
(R2 = 0.220; see the Supporting Information, Figure S11).
On the contrary, when cyclooctyne LUMO values are corre-
lated to the experimental rate constants, a very good re-
gression is observed (R2 = 0.960; Figure 8). This further
supports the idea that the reaction is cyclooctyne LUMO-
driven and that Hartree–Fock LUMO values are indeed a
good measure for the reactivity of the cyclooctynes in
SPAAC reactions with organic azides.
Conclusions
It is possible to predict the relative reactivity of strained
alkynes in SPAAC reactions from the LUMO energy of the
alkyne. The LUMO energy in the TS geometry correlates
accurately (R2 = 0.960) with the experimental rate order for
a diverse series of cyclooctynes. Even the alkyne LUMO
energy of the relaxed, fully optimized cyclooctyne yields a
good indication of relative reactivities. No good correlation
between the experimental rates and alkyne distortion ener-
gies was observed. By comparing experimental data with
theoretically derived activation energies, it was shown that
SCS-MP2 yielded accurate data, but that – although popu-
lar – the DFT methods B3LYP and M06-2X did not yield
Figure 8. Plot of logarithm of experimental second-order rate con-
stants for cyclooctynes 1–6 vs. the calculated MP2 LUMO energies
(in eV) of their geometry in the SPAAC transition state with allyl
azide.
Given this success, we wondered whether more simple theoretical predictions that correlated favorably with experi-
theoretical tools would be available to rapidly predict the ment. Given the efficiency and accessibility of basic compu-
order of reactivity of cyclooctynes in strain-promoted cy- tational chemistry on 21th century personal computers, the
8
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Strain-Promoted Alkyne-Azide Cycloadditions
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This work is co-financed via the program management Euregio
Rhein-Waal by the INTERREG IV, A Germany–Netherlands pro-
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ment Fund (ERDF), the Ministry for Economic 491 Affairs, En-
ergy, Building, Housing and Transport of the German Federate
State of North-Rhine Westphalia and the Dutch Ministry of Econ-
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