Linear Relationship between 13C NMR Chemical Shifts and the Bending of sp-Carbon Chains

Article abstract of DOI:10.1002/chem.201902617

Polyynes show a strictly linear relationship between the energy impact and the bending of the polyyne chain. The energy, which is necessary to bend the acetylenic chain, decreases with the increasing number of acetylene units. A deviation from linearity i

Full text of DOI:10.1002/chem.201902617

A Journal of
Accepted Article
Title: Linear Relationship between 13C NMR Chemical Shifts and the
Bending of sp-Carbon Chains
Authors: Mathis Kreuzahler, Abdulselam Adam, and Gebhard
Haberhauer
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10.1002/chem.201902617
Chemistry - A European Journal
Linear Relationship between 13C NMR Chemical Shifts and the Bending of sp-
Carbon Chains
Mathis Kreuzahler†, Abdulselam Adam† and Gebhard Haberhauer*†
† Institut für Organische Chemie, Universität Duisburg-Essen, Universitätsstr. 7, D-45117
Essen, Germany
Email address: gebhard.haberhauer@uni-due.de
ABSTRACT:
Polyynes show a strictly linear relationship between the energy impact and the bending of
the polyyne chain. The energy, which is necessary to bend the acetylenic chain, decreases
with increasing number of acetylene units. A deviation from linearity in polyynes can be
realized in solution by violation of the mutual-exclusion principle between IR and Raman
spectra. However, there is still no possibility to measure the extent of the non-linearity in
solution. Here, we show that the 13C NMR spectroscopy represents an appropriate tool for
this as we found an almost perfect linear relationship between the bending of the alkyne
chain and the change of the chemical shift of the outer acetylenic carbon atoms. By using
molecular bows in which the alkyne chain can be bent by switching the azobenzene unit, this
correlation can be proved experimentally. In the future, this correlation should enable the
determination of the extent of the bending and the strain energy in polyynes. Consequently,
polyynes could be employed as probes for measuring further molecular forces.
Table of Contents graphic:
1
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Polyynes consisting of alternate single and triple bonds can be found in interstellar space, in
plants, mushrooms and in marine organisms.[1] They are also used intensively as building
blocks for materials and in supramolecular chemistry.[2] Investigations of the stability of
polyynes reveal that the reactivity regarding their dimerization[3] and decomposition increases
with growing chain length.[4] Therefore, it is necessary for the synthesis of higher polyynes to
attach large, sterically demanding end-capping groups in order to prevent dimerization of the
polyyne.[5] Using this strategy the synthesis and isolation of a polyyne with 22 conjugated
triple bonds was achieved.[6]
With increasing number of acetylene units, the energy of the bending vibration along the
molecular axis decreases and therefore a deviation from the linearity of the molecular
structure can be expected.[7] Indeed, in the solid state the alkyne chains are found to be bent
which can primarily be explained by solid state interactions.[8] However, Tykwinski et al. were
able to show that the bending of the alkyne chain also occurs in solution.[9] The possibility of
bending in solution resulted in the speculation of a potential carbon double helix.[10] However,
the experimental proof of the bending in solution is difficult. One approach is the use of the
principle of mutual exclusion: The vibrational bands for centrosymmetric compounds are
either IR or Raman active. The violation of this principle is a proof for the non-linearity of the
polyynes in solution.[11,9] This bending can be explained by a static, a dynamic or a
combination of both processes.
We were looking for a method that allows a valuation of the extent of the bending of polyynes
resulting in a bow-shaped conformation. We found the 13C NMR spectroscopy to be the
method of choice. The 13C NMR spectroscopy delivers separate values for each carbon
atom, that are extremely sensitive to changes of the electron environment. Another
advantage is the possibility of calculating the expected values with DFT approximations. The
calculated values are in general in good agreement with the experimentally found values for
linear polyynes.[12] An initial benchmark study confirms the agreement also for bow-shaped[13]
polyynes (see Supporting Information). First, we chose the model compounds 1-8 for the
quantum chemical calculations (Scheme 1). The compounds 1-6 are the terminal polyynes
H(C≡C)nH, whereby n includes 4 to 10. The molecules 7 and 8 are internal polyynes in which
methyl groups (7) and triaryl groups (8), respectively, are attached to the outer sp-hybridized
carbon atoms. The distance between the outer sp-hybridized carbon atoms (C1 and C1’) in
the linear state is defined as d whereas the distance in the bent state is d’. The bending β of
the whole sp carbon chain is defined as:
ꢃ
ꢀ = ꢁ1 − ꢂꢂ ꢄ ∗ 100%
(1)
2
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Scheme 1. a) The polyynes 1-6 were used as model compounds. b) Definition of the
ꢃ
bending, β, of the sp carbon chain: ꢀ = ꢁ1 − ꢂꢂ ꢄ ∗ 100%. c) Model compounds 7 and 8.
30
a)
C1 C2 C3
C4 H1
y = 2.168 β
R² = 0.997
25
20
15
10
5
0
0
2
4
6
8
10
12
-5
Bending β [%]
30
25
20
15
10
5
b)
C1 C2 C3
C4 H1
y = 2.106 β
R² = 0.997
0
0
2
4
6
8
10
12
-5
Bending β [%]
Figure 1. Plot of the change of the 13C NMR signals (∆δ in ppm) as a function of the bending
(β in %) of the tetrayne 1. The 13C NMR data were calculated using B3LYP/aug-cc-pVQZ (a)
and B3LYP/TZVP (b). The results of the linear regression for the 13C NMR shift of C1 are
also given.
The structures of these model systems were optimized by using the DFT potential B3LYP[14]
with the additional empirical dispersion correction D3[15] and the basis set TZVP[16]. All
calculations were performed by using the program package Gaussian 16[17] and no symmetry
3
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restriction was applied. The optimized geometries of all structures were characterized as
minima by subsequent frequency calculations. To obtain the geometries of the bent
polyynes, the distance d between the outer sp-hybridized carbon atoms of the acetylenes 1-6
was fixed while all other parameters were optimized. An analogous procedure was chosen
for polyynes 7 and 8. However, here the distance e was fixed to certain values (Scheme 1c).
The 13C NMR shifts for all structures were calculated using GIAO-B3LYP and GIAO-PBE0.
As basis sets 6-311+G(2d,p)[18], TZVP and aug-cc-pVQZ[19] were employed. The thus
obtained results are summarized in Tables 1 and S1-S7 as well as in Figures 1 and S1-S15.
A glance at the data shows that with increasing bending of the acetylene chain, the energy of
the structures increases (Table 1); at the same time a shift of the 13C NMR signals can be
observed. The change of the chemical shift, ∆δ, is strongly depending on the respective
carbon atom. The largest change affects the carbon atoms with odd numbers (C1, C3, C5),
whereas the change for the carbon atoms with even numbers (C2, C4, C6) are small. For
example, bending of tetrayne 1 by 10% leads to a downfield shift for carbon atoms C1 and
C3 of over 20 ppm (Table 1 and Figure 1). On the contrary, carbon atoms C2 and C4 only
show a small change of about 3 ppm to once higher values (C4) and once lower values (C2).
The change of the chemical shift is hardly depending on the employed method or basis set:
B3LYP/TZVP, B3LYP/aug-cc-pVQZ, B3LYP/6-311+G(2d,p) and PBE0/TZVP deliver similar
data for the chemical shifts of 1 (Table 1).
Table 1. Energies (∆Ebending in kcal/mol), distances between the carbon atoms C1 and C1’ (d
in Å), bending (β in %) and 13C NMR shifts of different carbon atoms (∆δ in ppm) of the
tetrayne 1 calculated by different methods.
Distancea Bendinga
a
∆Ebending
13C NMR shifts ∆δ [ppm]
d [Å]
[kcal/mol]
C1b
C1c
C1d
C1e
C2b
C3b
C4b
β [%]
8.904
8.80
8.70
8.60
8.50
8.40
8.30
8.20
8.10
8.00
0.0
1.2
2.3
3.4
4.5
5.7
6.8
7.9
9.0
10.2
0.00
0.81
1.76
2.71
3.67
4.63
5.60
6.58
7.55
8.54
0.0
1.5
0.0
1.6
0.0
1.6
0.0
1.5
0.0
-0.6
-0.9
-1.1
-1.4
-1.6
-1.8
-2.1
-2.3
-2.5
0.0
1.4
0.0
-0.1
0.2
0.6
1.0
1.4
1.8
2.2
2.7
3.2
4.2
4.3
4.3
4.2
4.3
6.8
7.1
7.0
6.9
7.1
9.4
9.7
9.6
9.4
10.0
12.8
15.5
18.3
21.0
23.7
12.0
14.4
16.8
19.2
21.5
12.3
14.8
17.3
19.7
22.1
12.2
14.6
17.2
19.6
21.9
12.0
14.4
16.8
19.2
21.5
a
b
c
B3LYP-D3/TZVP.
B3LYP/TZVP//B3LYP-D3/TZVP.
B3LYP/aug-cc-pVQZ//B3LYP-
D3/TZVP. d B3LYP/6-311+G(2d,p)//B3LYP-D3/TZVP. e PBE0/TZVP//B3LYP-D3/TZVP.
4
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2.5
2.0
1.5
1.0
0.5
0.0
y = 4.387 e-0.18 n
R² = 0.999
2
4
6
8
10
12
Number of alkyne units n
Figure 2. Plot of the slope for the 13C NMR shift of carbon atom C1 as a function of the
number of alkyne units. The slopes stem from the plot of the change of the 13C NMR signals
(∆δ in ppm) as a function of the bending (β in %) of the terminal polyynes H(C≡C)nH (n = 4-
10) (see Figures 1 and S3-S9). The result of the non-linear regression is also given. All 13C
NMR data were calculated using B3LYP/TZVP.
To verify the existence of a linear relationship between the bending of the polyynes and the
change of the chemical shift (∆δ), we conducted a linear regression analysis for the 13C NMR
shifts of the carbon atoms C1 for all structures (Figures 1 and S1-S9). Fortunately, we found
an almost perfect linear relationship with coefficients of determination (R2) between 0.996
and 0.999. Then, we applied the slope determined by linear regression for each polyyne 1-6
against the number of alkyne units. This results in an exponential curve which is depicted in
Figure 2. Conducting a non-linear regression leads to the following equation for the change
of the chemical shift:
ꢆ
ꢈꢉ.ꢊꢋꢌꢍ
∆ꢅ = 4.387ꢇ
ꢀ
(2)
Here again, ∆δ describes the change of the 13C NMR shift, n is the number of alkyne units in
the polyynes and β [%] describes the extent of the bending. The coefficient of determination
(R2) amounts to 0.999. This equation allows the prediction of the change of the chemical shift
for the carbon atoms C1 of terminal polyynes at a certain degree of bending or the
calculation of the bending degree at a given shift, respectively.
At this point we would like to add that also an almost perfect relationship between the strain
energy (∆E) and the change of the chemical shift (∆δ) can be found (Figures S10-S15).
Accordingly, the size of ∆δ allows a conclusion on the extent of the bending and on the
magnitude of the strain energy.
Next, we wanted to verify if the change of the chemical shift for the 13C NMR signals by
bending can be substantiated experimentally. Therefore, we synthesized the model systems
9 and 10 (Scheme 2, see Supporting Information for a detailed description of the synthesis).
The systems resemble the early introduced model system 8 (see Scheme 1c). However,
both consist of an additional azobenzene unit which interconnects two phenyl units via CH2O
5
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groups (Scheme 2). The oxygen atoms are attached in meta- (9) and para-position (10),
respectively. The azobenzene unit can be used as a molecular switch. In the trans state the
distance e between the oxygen atoms is quite large and the alkyne chains of 9 and 10 show
a nearly linear arrangement. By using light as stimulus, the azobenzene unit can be switched
from the stretched trans state to the more compact cis isomer. This results in a decrease of
the distance between both oxygen atoms from e to e’ (see Scheme 2). The shortening of this
distance should also have an impact on the alkyne carbon chain leading to a bending. This
corresponds to the principle of a bow: An elastic object in which the actual bow (here the
acetylene chain) can be stretched by a bowstring (here the azobenzene unit). Therefore,
molecules 9 and 10 can also be considered as molecular bows. We expect that molecule 10
can be more strongly bent than molecule 9, due to the para connection of the azobenzene
unit.
Scheme 2. Structure of the molecular bows 9 (a) and 10 (b).
Figure 3. Molecular structures of the trans (left) and cis (right) isomer of the molecular bow
10 calculated by means of B3LYP-D3/TZVP. All hydrogen atoms are omitted for the sake of
clarity.
6
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In addition to the synthesis, the geometrical parameters of both trans and cis isomers of the
molecular bows 9 and 10 were optimized with the density functional B3LYP-D3 and the basis
set TZVP. The thus obtained structures are depicted in Figures 3 and S16. For both 9 and 10
the bending of the alkyne chain can be realized due to the trans→cis isomerization. As might
be expected this effect is more pronounced for 10 than 9. For 10 the distance d changes
from 8.91 Å to 8.79 Å, which corresponds to a bending of 1.3% for the cis isomer of 10. For
9, the distance only changes from 8.90 Å to 8.86 Å and hence cis-9 exhibits a bending of
0.4%.
The trans→cis isomerization can experimentally be accomplished by irradiation with UV light
of the wavelength λ = 365 nm and monitored with UV spectroscopy (Figures S19 and S21).
The π-π* absorption bands at 330 nm and the n-π* absorption bands are characteristic for the
UV absorption of the azobenzene unit. The former is drastically reduced during the transition
from the trans to the cis isomer. The second absorption band slightly increases and underlies
a hypsochromic shift. The reverse isomerization of the trans to the cis state occurs via
irradiation with visible light of the wavelength λ = 405 nm (Figures S19 and S21).
Figure 4. Section from the 13C NMR spectra of the molecular bow 10: (a) after synthesis, (b)
after UV irradiation with λ = 365 nm in CDCl3. The signals of the carbon atoms of the isomers
trans-10 (blue) and cis-10 (red) are marked.
Fortunately, the activation energies for the isomerization processes of azobenzenes are
usually high enough to distinguish between the signals for the trans and cis isomers in both
1H and 13C NMR spectra. According to our calculations, the carbon atom C1 of compound 8
shows the most severely downfield shifted signal of the acetylene chain with 87.6 ppm; the
signal for the carbon atom C2 just appears at 71.9 ppm. This is typical for internal
polyynes.[20] Since the molecular bows 9 and 10 only differ from the model compound 8 by
7
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the additional azobenzene bridge, the signals for the carbon atoms C1 of 9 and 10 should
also exhibit the most downfield signals of the alkyne chain. Indeed, the most downfield
signals for the sp-hybridized carbon atoms are found at 84.2 ppm for trans-9 and at 84.9 ppm
for trans-10. The correlation in the HMBC spectrum of trans-10 clearly demonstrates that
these signals can be assigned to the corresponding carbon atoms C1 (Figure S22). Due to
the irradiation with UV light and the resulting formation of the cis isomers both signals
undergo downfield shift (Figures 4 and S18), which is in accordance to our calculations for
the bending of model compound 8 (Table S7). The measured ∆δ value is 0.6 ppm for 9
(Figure S18), whereas for 10 it amounts to 4.4 ppm (Figure 4). This is due to the stronger
bending of cis-10 compared to the bending of cis-9.
For the comparison of the experimental results and the calculations it is best to use the
model system 8 and comparing the ∆δ values of 8 at fixed distances with the ∆δ values of 9
and 10. Bending of 8 by 0.4% (∆Ebending = 0.53 kcal/mol) results in a change of the 13C NMR
shift of the carbon atoms C1 of about 1.4 ppm (Table S7). The experimental data gives a
chemical shift of 0.6 ppm (Figure S18). For the stronger molecular bow 10, which is bent by
1.4% (∆Ebending = 1.94 kcal/mol) in the cis isomer, the experimental shift (4.4 ppm) and the
calculated shift (4.9 ppm) are in good agreement (Figure 4 and Table S7). Considering that
the molecular bow 10 is only bent by 1.4% in the cis isomer, the change of the chemical shift
is remarkably high. Due to this observed high sensitivity the 13C NMR spectroscopy proves to
be a promising tool when it comes down to measuring molecular forces.
In conclusion, we were able to demonstrate the existence of an almost perfect linear
relationship between the extent of the bending of an alkyne chain and the chemical shift of
the outer sp-hybridized carbon atoms. For the terminal alkynes it is even possible to make a
simple equation that describes the downfield shift of the carbon atoms C1 as a function of the
bending of the alkyne chain and the number of alkyne units. By employing two different
molecular bows, which are each stretched by a photo switchable azobenzene unit, we were
able to demonstrate the 13C NMR spectroscopy to be – due to its high sensitivity – a valuable
tool for the experimental determination of the extent of the bending of alkyne chains. In the
future, it should be possible to easier determine the extent of the bending of an alkyne chain
in solution or in solid state with the knowledge of a reference system. Furthermore, this could
pave the way to use polyynes in combination with the 13C NMR spectroscopy as probes for
measuring such molecular forces that can cause the bending of an alkyne chain.
Supporting Information
Figures and tables, synthesis of new compounds, cartesian coordinates and absolute
energies for all calculated compounds, 1H NMR and 13C NMR spectra.
8
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Acknowledgments
This work was supported by the Deutsche Forschungsgemeinschaft (DFG; HA 2973/13-1). A
special thank goes to Professor Dr. Christian Mayer for numerous discussions and helpful
support.
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