University of Groningen
Autonomy and Chirality in Molecular Motors
Kistemaker, Jozef Cornelis Maria
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Kistemaker, J. C. M. (2017). Autonomy and Chirality in Molecular Motors. Rijksuniversiteit Groningen.
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23 Parts have been published as:
J. Chen, J. C. M. Kistemaker, J. Robertus, B. L. Feringa, J. Am. Chem. Soc. 2014,
136, 14924–14932, doi:10.1021/ja507711h.
Chapter 2: First Generation Molecular Motors
Herein is reported: An introduction into first generation molecular motors and the use of molecular modelling in the study thereof. The potential energy surface of the smallest first generation molecular motor known to date is investigated, followed by the design of a molecular motor as a photoswitchable DNA hairpin linker, and lastly a study on the dynamic behaviour of molecular motors of increasing size in viscous media is reported.
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Introduction
Stilbene is well known example of an alkene that is able to interconvert between its trans and cis isomers.[1] The thermal barrier for rotation around the carbon–
carbon double bond is high (>150 kJ·mol−1) and therefore ensures the stability of
the two stereoisomers at room temperature. However, stilbene (1) and its analogues such as dinaphthylethene 3 are able to undergo photochemical cis-trans isomerization.[2,3] Irradiation of the trans-alkenes with UV-light leads to their
excited state in which relaxation brings the switches through conical intersections to their cis isomer. Photoexcitation of the alkenes allows for the reversed
cis-trans isomerization, though it suffers from a significant side-reaction in which the cis-alkenes undergo photocyclization. Oxidation of these intermediates leads to the
aromatic products 2 and 4. Besides stringent oxygen or otherwise oxidant free conditions, there is a structural ways to prevent undesirable photocyclization. A straightforward method involves the obstruction of the oxidation sites on the aromatic positions ortho to the ethylene. This has been achieved for example in dimesitylethene[4] and dianthracenylethene[5] which remain disubstituted alkenes.
An interesting family of alkenes is comprised of tetrasubstituted alkenes in which the regions between the substituents with a cis vicinal relationship are crowded to such an extent that the double bond is forced away from planarity. These compounds are dubbed overcrowded alkenes and the first examples, such as bifluorenylidene and bixanthylidene, date from the nineteenth century.[6,7] A
striking example of an overcrowded alkene is the fixation of the naphthyl moieties in 3 by the addition of a six membered ring (4) connecting the geminal positions on both sides of the double bond (Figure 2.1).[8] The overcrowded nature of the
double bond in 4 forces the substituents from planarity in both stereoisomers (E–Z nomenclature applies to double bonds with more than 2 substituents) and therefore allows alkene 4 to be optically active. Compound 4 allowed for the first instance of an isolation of the enantiomers of both the E and Z isomers of an overcrowded alkene.
Twenty years later Feringa and co-workers studied the properties and behaviour of the unique olefin 4 in greater detail.[9–12] They identified the pathways for thermal
helix inversion (THI) between the P,P and M,M enantiomers of E-4 and Z-4. In an effort to assign the absolute stereochemistry theoretical CD spectra were calculated which even today is not always a simple task (see Chapter 6). Even though an appreciable correlation was observed between the experimental and theoretical results, a chiral derivative 5 was synthesized to unequivocally determine the absolute stereochemistry (Figure 2.2). This chiral overcrowded alkene confirmed the earlier findings and its photochemical switching behaviour was used to obtain
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FIRST GENERATION MOLECULAR MOTORS
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stable (R,R,Z)-(P,P)-5, however, the presence of metastable states was not reported. Two years later Koumura et al. reported an extended study which shows that this overcrowded alkene undergoes unidirectional rotation (Figure 2.2).[13]
Figure 2.1. Photoisomerization behaviour of stilbenes 1, 3 and 4 and the oxidative cyclization of
cis-1 and cis-3.
Overcrowded alkene 5 was obtained by a McMurry dimerization[14] of its ketone
precursor and found only as a single diastereoisomer (R*,P*,R*,P*,E)-5, which will be designated as ‘stable’, and its enantiomers were resolved by chiral HPLC. Stable-(R,P,R,P,E)-5 is found to be C2-symmetrical with the methyl groups at the
stereogenic centres in a pseudo-axial orientation and the six membered rings in a boat conformation anti-folded with respect to each other. Irradiation with UV-light at low temperature allows it to undergo a photochemical E–Z isomerization to form a metastable (MS) species which was identified as MS-(R,M,R,M,Z)-5 in which the six membered rings are again anti-folded with respect to each other. Prolonged irradiation leads to a perceived equilibrium between the forward and backward photo-isomerization dubbed the photostationary state (PSS). It should be noted that the principle of microscopic reversibility does not hold for these photochemical reactions. Therefore, the two photochemical E–Z isomerizations are unidirectional when investigated individually. The methyl groups in MS-(R,M,R,M,Z)-5 have adopted a pseudo-equatorial orientation which introduces steric strain due their proximity to the hydrogens on their neighbouring stereocentres. The molecule retains a C2-symmetry axis though the axis changed to a perpendicular orientation
with respect to the plane through the π orbitals of the central alkene while for E-5 the axis lies in this plane.
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Figure 2.2. Photochemical and thermal isomerizations of the first unidirectional repetitive molecular
rotary motor.
The strain in MS-(R,M,R,M,Z)-5 is released through a thermally activated helix inversion of the aryl moieties. During the thermal helix inversion (THI) an intermediate is identified in which a single ring-flip of the six membered ring has taken place and the aryl moieties have adopted a syn-folded geometry ((R,M,R,P,Z)-5). This intermediate quickly goes on to flip the other ring, by slipping the other aryl moiety past the first to give rise to stable-(R,P,R,P,Z)-5 with the six membered rings again in boat conformations and the methyl groups in a pseudo-axial orientation facing away from the molecule. The energy of activation for this process was not determined, however, for an analogue methylated in the 7 positions (Figure 2.2)[15–17] the Gibbs free energy of activation was determined to
be 91±3 kJ·mol−1. The conversion of MS-Z-5 to stable-Z-5 is quantitative,
indicative of the large energy difference between the two states (>8 kJ·mol−1), and
therefore locks the unidirectional rotation made in the photochemical and subsequent thermal isomerization steps. The orbital overlap over the double bond has increased in Z-5 with respect to E-5 which is characterized by a bathochromic shift of the lowest energy band in the absorption spectrum. This allows for the use of UV-light of a higher wavelength to facilitate an E–Z isomerization of stable-(R,P,R,P,Z)-5 to MS-(R,M,R,M,E)-5. This photochemical E–Z isomerization (PEZ) is performed at room temperature on account of the higher stability of MS-E-5 with respect to MS-Z-5 and prolonged irradiation gives rise to a PSS. In the metastable
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FIRST GENERATION MOLECULAR MOTORS
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(R,M,R,M,E)-5 the six membered rings adopt an anti-folded conformation though in a twist boat conformation and with the methyl groups in a pseudo-equatorial orientation. The major source of strain does not stem from steric hindrance directly related to the methyl groups but the proximity of the individual aryl moieties to the hydrogens at the opposite stereocentres. A THI is observed at elevated temperatures with an energy of activation of 110 kJ·mol−1 or a Gibbs free energy of activation
for the methylated analogue 107±4 kJ·mol−1. During the THI of
MS-(R,M,R,M,E)-5 to stable-(R,P,R,P,E)-MS-(R,M,R,M,E)-5, both possessing C2-symmetry, the motor passes through the C1-symmetrical MS-(R,M,R,P,E)-5, which was most clearly identified in an
analogue with isopropyl instead of methyl moieties at the stereogenic centre.[17,18]
This second PEZ–THI sequence completes the 360° rotation with the last THI again locking the unidirectional rotations.
This behaviour constitutes full autonomous rotation which means the molecules are able to rotate when presented a fuel (ultraviolet light) without the need for an operator. Furthermore, this molecular motor rotates in an autonomous unidirectional fashion. Here autonomous unidirectionality means that the molecule rotates in a single direction which is determined by the motor itself, and not by a chiral fuel (e.g. circularly polarized light) or by a chiral auxiliary. The inherent difference between the E/Z isomers imparts one metastable state with a much higher thermal barrier compared with the other. While this adds complexity to the system, it also allows for a high degree of selectivity. Overcrowded alkenes with the capacity to rotate autonomously based on the structure of molecule 5 are dubbed first generation molecular motors.
For photochemical molecular switches, the yield for the switching process expressed by the PSS ratio is of great importance in comparing the efficiency of the systems. For molecular motors, however, the PSS ratio is of no importance, but theoretically the rotational efficiency depends solely on the quantum yield of the photochemical step while the rotational rate depends mainly on light intensity.[19,20]
A hypothetical sample of a concentrated solution of motor 5 would ensure full absorption of UV-light used to bring about PEZ. At elevated temperatures, the quantum yield of 5 would then determine the yield of the rotation which will be directly locked by a subsequent THI. Under such conditions the rate would be fully dependent on the light intensity. Increasing the light intensity shifts the dependence to the THI rate, which would be evident from the observation of the presence of the metastable state, which can again be solved by increasing the temperature. Maximum efficiency with respect to yield might be obtained by an optimization of the quantum yield for the PEZ by structural modification. This efficiency of rotation can also be managed by an increase in light intensity; however, maximum
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rate at lower temperatures can only be realized by lowering the barrier for THI. This was accomplished by a ring contraction of the six membered ring to a five membered ring (Figure 2.3).
Figure 2.3. Changes in structures of first generation molecular motors.
Motor 6 was investigated by ter Wiel et al.[21] and a substitution of the naphthalene
moiety for a xylene moiety by Pollard et al.[22] provided motor 7 which simplified
functionalization. Various methods have been developed to introduce bromines and alcohols in the 5 and 6 positions in enantiopure 7 (2,2',4,4',7,7'-hexamethyl-2,2',3,3'-tetrahydro-1,1'-biindenylidene)[23,24] while similar methods also allows for
the introduction of other functional groups instead of the methyl groups in the 7 position[25,26]. The 1st generation motors appended by five membered rings show an
interesting change in behaviour with respect to their six membered analogues. Where the THI barrier is highest for the E configuration in 5, the THI barrier is highest for the Z configuration in 6 and 7. The folding of the six membered rings allows for the aromatic moieties to pass each other in the Z configuration in which they go through a local minimum with the moieties in a syn-folded configuration. The five membered rings do not allow for such folding in the Z configuration which significantly increases the barrier for the helix inversion. The opposite is observed in the E configuration where there is more room in 6 and 7 with respect to 5 for the aryl moieties to pass the opposite stereocentres in their THI’s. The photochemical and thermal behaviour of compounds 5 and 7 has been studied computationally.[27– 30]
Calculated Behaviour of 1
stGeneration Molecular Motors
The experimental behaviour of 7 was studied by Pollard et al. and is summarized in Figure 2.4.[22] It exhibits the same responses as 5 did to irradiation and heat.
Irradiation with UV-light of E-7 led to a PEZ yielding a PSS between
stable-E-7 and MS-Z-7 of varying ratios, strongly depending on substitution pattern and
solvent.[23,31,32] The metastable state required heating to allow it to undergo THI to
stable-Z-7, characterized by a Gibbs free energy of activation of 101 kJ·mol−1,
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FIRST GENERATION MOLECULAR MOTORS
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analogues though slightly lower than their E isomers. At low temperatures
stable-Z-7 is able to form a PSS upon irradiation of which the ratio can be modified by
solvent selection. The photogenerated MS-E-7 readily undergoes THI to complete the unidirectional rotary cycle. The barrier for this step is significantly lower than the previously described thermal isomerizations (Δ‡G° 71 kJ·mol−1).
Throughout this thesis there will be made use of quantum chemistry to study the behaviour of molecular motors. The main method used for these computational investigations is density functional theory (DFT). Next we would like to give a practical introduction into the use of theoretical quantum chemistry on the thermal behaviour of molecular motors. For this purpose we use the first generation molecular motor 7 as an example.
Figure 2.4. Photo-chemical and thermal isomerizations of 7
The goal is to describe the potential energy surface (PES) of the molecular motor, by identifying the global and local minima and their connectivity through transitions states. The procedure used most starts by a molecular mechanics optimization of the overcrowded alkene, which interestingly most often provides the metastable configuration when Chem3D is used on a structure created in ChemDraw. Manual manipulation and some structural insight are required to transform the geometry to the stable configuration. This can also be obtained by molecular dynamics, which especially for flexible compounds, such as 5, provides
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additional insight into the possible minima conformations. These geometries are then submitted to optimization with a semi-empirical method using the Gaussian 09 program.[33] The geometries obtained by the semi-empirical PM3 method agreed
slightly better than the PM6 method with the geometries optimized at the DFT level, though the PM6 method performed the computations faster. Therefore PM6 was used for PES scans while PM3 was used for single geometry optimizations. Investigation of the PES is performed by modifying molecular coordinates such as bond lengths, angles or dihedral angles in small steps in which the particular coordinate is frozen after each increment while all other coordinates are optimized. Performing such a relaxed PES scan by modifying the dihedral of four consecutive atoms, also called torsion angle (such as θ in Figure 2.5), has been successfully used to describe the PES of biaryls, azobenzenes and bifluorenylidenes.[34–38]
However, for overcrowded alkenes with a degree of flexibility, such as molecular motors, this approach is problematic and leads to a poor description of the PES.[39]
This situation is illustrated by the PES depicted in Figure 2.5 for a scan over the θ-dihedral of motor 7. There is a steep drop in energy past a certain point (indicated by the circle) at which the molecule strongly changes its conformation and attempts to find a transition point from this geometry are mostly fruitless. An elegant though laborious solution to this is the inclusion of an additional restrained dihedral angle in the PES scan which allows for the construction of a three dimensional surface.[30]
This is, however, not a practical solution when regarding computation costs.
Figure 2.5. Relaxed PES scan of 7. Scans using semi-empirical PM6 with a single dihedral angle
constrained. θ = dihedral 7a-1-1’-7a’; φ = dihedral 10-7-7’-10’; ξ = dihedral 10-4-4’-10’. IRC’s indicated by dotted line.
The restrained coordinate under investigation is not required to be a sequence of connected atoms, and a careful study of such ‘disconnected’ dihedrals revealed several combinations which are able to describe the thermal helix inversions in a continuous fashion (Figure 2.5, φ- and ξ-dihedrals). Transition state optimizations from the maxima of these scans (indicated by a circle) readily provide optimized transition state geometries each identified by a single imaginary frequency.
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Figure 2.6. Optimized geometries, IRC’s and HOMO-LUMO gaps of 7 [DFT B3LYP/6-31G(d,p)].
The minima and transition states obtained from the scans at the semi-empirical level are submitted to optimizations using DFT. The functional used here is B3LYP which has been proven to be very suitable for the description of the behaviour and properties of overcrowded alkenes.[40–43] As basis set 6-31G(d,p) is used, for which
the obtained geometries agree well with those obtained at higher levels. It is noteworthy that the geometries obtained by semi-empirical PM3 or PM6 often agree equally well or even better with those obtained by DFT B3LYP/6-31G(d,p) than those optimized with the use of smaller basis sets such as STO-3G and 3-21G.
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Transition states and minima are confirmed by the absence or presence of a single imaginary frequency in the vibrational analysis, respectively. To ensure the connectivity of two minima by an identified transition state, intrinsic reaction coordinates (IRC) are calculated (performed using the Firefly QC package,[44]
which is partially based on the GAMESS (US)[45] source code, using the
Gonzalez-Schlegel second order method). In an IRC, the steepest descent in mass-weighted coordinates is followed from a TS in both a ‘forward’ and ‘backward’ direction to the first minimum encountered on its path (Figure 2.6).
Table 2.1. Thermochemistry of motor 7 [DFT B3LYP/6-31G(d,p)].
MS-(E)-7 TS-(E)-7‡ S-(E)-7 MS-(Z)-7 TS-(Z)-7‡ S-(Z)-7
ΔG° (kJ·mol−1) 22.3 97.0 13.8 20.6 125.6 0.0
ΔH° (kJ·mol−1) 20.3 89.4 14.2 21.3 121.3 0.0
ΔS° (J·mol−1·K−1) −6.9 −26.0 1.3 2.4 −14.5 0.0
The calculated behaviour agrees well with the experimental observations. Going from S-(Z)-7 to MS-(E)-7 the HOMO-LUMO gap drops corresponding to the experimentally observed bathochromic shift (schematic excited state depicted in Figure 2.6) and the helicity of the overcrowded alkene is inverted. MS-(E)-7 is calculated to be 8.5 kJ·mol−1 higher in energy than its diastereoisomer S-(E)-7 to
which it isomerizes by a THI (TS-(E)-7‡) with a calculated barrier of 73.1 kJ·mol−1
agreeing well with the experimentally determined barrier of 71 kJ·mol−1. It is
important to note that in 1st generation molecular motors, the THI exists out of two
redundant transition states with identical activation energies. This is explained by the C2-symmetry of the local minima, which does not express a preference for
which half of the molecule rotates first in a THI. Therefore, there are two vibrational modes that lead to two transition states with identical barriers. Such an occurrence would allow twice the amount of isomerizations over an amount of time and thus double the rate (k). A doubling of rates results in a lowering of the theoretical Gibbs free energy barrier by 1.69 kJ·mol−1 (individual Δ‡G° of
TS-(E)-7‡ is 74.8, and corrected for the double rate equals to 73.1 kJ·mol−1). The
HOMO-LUMO gap of S-(E)-7 was found to be the largest of all isomers, and of the maximum absorption bands in the experimental UV-vis spectra of all isomers, that of S-(E)-7 was found to be the most hypsochromic. In contrast, the HOMO-LUMO gap of MS-(Z)-7 was calculated to be the smallest of all isomers corresponding to the strongest bathochromically shifted experimental absorption spectrum. The optimized transition state (TS-(Z)-7‡) was confirmed by IRC to connect the metastable species to the stable configuration S-(Z)-7. Evident from the mass-weighted displacement in the IRC, the THI of Z-7 requires a structurally much more
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significant reorganization than that of E-7 does. Additionally, the barrier of
TS-(Z)-7‡ is substantially higher, calculated to have a corrected Gibbs free energy of 103 kJ·mol−1 which agrees very well with the experimentally determined barrier of
101 kJ·mol−1. The IRC’s have been projected on the scans in Figure 2.5 to highlight
the functionality of the disconnected dihedral scan and the failure of the torsion angle to describe the motor’s behaviour during the THI.
First Generation Motor as a Hairpin Switch
Nucleic acids and analogues control key biological processes such as replication, transcription and translation and are therefore attractive targets for the incorporation of photoswitches. Letsinger and Wu were the first to incorporate a photoswitchable linker in the phosphate backbone.[46] Irradiation of the A
6
-stilbene-T6 hairpin led to a 10 °C decrease of the melting temperature (Tm). The authors
propose that this change derives from an unusual stability of the trans hairpin due to π-stacking effects, which is lost upon photoswitching to the cis isomer. Unfortunately, π-stacking also leads to quenching and low isomerization rates. The method was further improved by the work of Sugimoto and co-workers[47], who
also considered the conformational effect of photoisomerization. Using molecular dynamics simulations they calculated the backbone-backbone distance in a hairpin to be 13.30 Å and subsequently synthesized an azobenzene linker that is 13.36 Å long in its trans configuration but contracts to 10.50 Å in the cis isomer. Switching forces the hairpin to become much more conformationally strained, resulting in a
Tm difference of 20 °C for AAAAG-azobenzene-CTTTT. The shift in Tm for a
similar, but slightly longer and more flexible linker was less than 2 °C. With these results in mind, we sought to design a new type of photoswitchable backbone linker. Upon photoisomerization and subsequent thermal helix inversion, the distance between the two halves of a molecular motor changes much more than in an azobenzene or stilbene. Therefore, we hope to induce much larger conformational effects while at the same time reduce π-stacking effects.
Figure 2.7. Proposed first generation molecular motors 8 and 9 for hairpin switching
Two first generation molecular motors were proposed as suitable hairpin switches which were, contrary to the azobenzene example, expected to pull the strands apart in the unfavourable configuration (Figure 2.7). The unfavourable configuration
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being E here in which the phosphates connected to the motor will be pulled away from each other with respect to the desired ‘optimal’ orientation in the Z isomer. Before synthetic effort was to be put towards obtaining these compounds, they were investigated computationally in order to identify the most effective design. After initial optimizations at the semi-empirical level, the stable E and Z isomers of 8 were optimized using DFT B3LYP/6-31G(d,p). Subsequently, PES scans were performed with the oxygen-oxygen bond constrained using DFT B3LYP/6-31G(d,p) which eventually afforded the PES depicted in Figure 2.9.
Figure 2.8. Structures and global minimum geometries of stable E and Z isomers of 8.
Figure 2.9. PES of the oxygen-oxygen distance in 8.
During the initial scan maxima were observed along the PES due to the large range of possible conformations around the single bonds shown in red in Z-8 in Figure 2.8. Beyond each maximum, a steep drop was observed, similar to those described
0 10 20 30 40 5 10 15 20 SCF Energy / kJ·mol −1 O–O distance / Å (Z)-8 (E)-8 13.3
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for Figure 2.5. Therefore, after each drop an additional scan was performed in the opposite direction and for each O–O distance the lowest energy conformer is shown in the PES in Figure 2.9. The resulting PES is clearly very shallow for both the E and Z isomers of 8. And although the global minimum is slightly off from the 13.3 Å, which is considered the optimal distance between the two oxygen atoms, the energy cost to bring either isomer to this distance is minimal. With that said, actually none of the conformations with a distance ranging 7–19 Å for (Z)-8 and 12–20 Å for (E)-8 requires additional energy with respect to the global minimum. This is caused by the previously discussed conformational freedom around the single bonds shown in red in Z-8 in Figure 2.8. From Figure 2.9 can be concluded that molecular motor 8 only functions as a geometry altering switch when O–O distances less than 11 Å are paramount. For such cases, (Z)-8 would be accommodated in the overall geometry without a significant cost in energy with respect to the molecules global minimum down to 7 Å, while (Z)-8 would require additional energy and therefore destabilize the overall structure.
Figure 2.10. Structures and global minimum geometries of stable E and Z isomers of 9.
A replacement of the appending benzene moieties in 8 for acetylene moieties provides molecular motor 9 in which the rotating single bonds are reduced to only 2, indicated in red in (Z)-9 (Figure 2.10). The reduction in degrees of freedom results in a much deeper PES compared to 8 (Figure 2.11). Global minima are found at O–O distances of 15.0 Å for (Z)-9 and 17.4 Å for (E)-9, which clearly are not the desired distance of 13.3 Å, though it only costs 1.4 kJ·mol−1 for (Z)-9 while it costs
22.9 kJ·mol−1 for (Z)-9 to reorganize to this distance. From the difference between
the two scans (delta shown in purple in Figure 2.11) it is evident that below 15.0 Å and above 17. 6 Å O–O distance, the difference in energy is larger than 10 kJ·mol−1.
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Therefore, the switching between the two stable states of this molecular motor is very suitable to bring about significant geometrical changes. This molecular motor is currently being synthesized and will be connected to a DNA hairpin.[48,49]
Switching experiments will then investigate the influence of the geometrical change in the molecular motor on the melting temperature of the hairpin.
Figure 2.11. PES of the oxygen-oxygen distance in 9.
Molecular Stirrers
A series of first-generation light-driven molecular motors with rigid substituents of varying length was synthesized (6 and 10–13, Figure 2.12), envisioned to act as
molecular stirrers.[50,51]
Figure 2.12. First generation light-driven molecular motors 6 and 10–13 with different substituents
at the 6- and 6’-positions.
The rotary motion of 6 & 10–13 from stable-(E) to stable-(Z) was studied by 1H
NMR and UV–vis absorption spectroscopy in a variety of solvents with different
0 10 20 30 40 50 60 70 80 5 10 15 20 SCF Energy / kJ·mol −1 O–O distance / Å (Z)-9 (E)-9 13.3 Delta
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FIRST GENERATION MOLECULAR MOTORS
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polarity and viscosity. Their behaviour agreed with that of previously studied first generation molecular motors where a fast photo-equilibrium is reached between stable-(E) and metastable-(Z) by irradiation with UV-light at lower temperatures after which the metastable state isomerizes through a thermal helix inversion to stable-(Z) at higher temperatures (Figure 2.13).
Figure 2.13. Photochemical isomerization and thermal helix inversion steps of 6 and 10–13.
Quantitative analyses of the kinetic and thermodynamic parameters show that the rotary speed is affected by the rigidity of the substituents and the length of the rigid substituents and that the differences in speed are governed mainly by entropy effects (Table 2.2). Most pronounced is the effect of solvent viscosity on the rotary motion when long, rigid substituents are present.
Table 2.2. Kinetic parameters and the viscosity dependent factor α of the helix inversion step of 6
& 10–13 in THF at rt Motor t½ (min) Δ ‡G° (kJ·mol−1) Δ ‡S° (J·mol−1·K−1) Δ ‡H° (kJ·mol−1) α 6 74.0 93.2 −31.7 84.0 0.16 10 78.5 93.3 −31.6 84.0 0.20 11 97.8 93.8 −33.1 84.1 0.19 12 124 94.4 −35.1 84.2 0.28 13 215 95.7 −39.3 84.2 0.40
To understand how solvent viscosity and the shape and size of the substituents affect the rotary speed of motors, Doolittle’s free-volume model,[52] derived from
Kramers’ theory,[53] is applied.[54] According to the model, molecular motion in a
liquid medium is only possible when the molecules available free volume (Vf) is at
least as large as its critical volume (V0). The fluidity (η–1) is proportional to the
probability factor [exp(−V0/Vf)] for the translation motion. Therefore, the
free-volume dependence of the viscosity can be expressed as follows
/ 1
where A is a proportionality factor. Gegiou et al. noted that in contrast to translational diffusion, molecular rearrangements (in their case a photochemical
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cis-trans isomerization of stilbene) require only a fraction (α) of the critical
volume.[55] In the study of photochemical and thermal isomerizations, α can be
viewed as a measure of the magnitude of the impact that increasing viscosity has on the process. The rate constant k of the molecular rearrangement is given by eq 2, and substitution of eq 1 into eq 2 affords eq 3, which can be rewritten to eq 4 predicting a linear relationship between ln k and ln η.
2
3
ln ln 4
This approach has been used successfully to rationalize the viscosity dependence of processes that involve large-amplitude rotation of molecules,[55–63] α values
higher than 0.3 have been observed before[1,64–66] but are rather exceptional. A more
extensive introduction and study regarding viscosity effects on the rotation of a second generation molecular motor will be presented in Chapter 4.
The double-logarithmic form of eq 3 predicts a linear dependence of ln k versus ln η (eq 4) from which the slope readily provides the α value. For this purpose, motors 6 and 10–13 were studied in mixed solvent systems of glycerol and THF in different ratios, providing a range of different viscosities. As is evident from the measured α values in Table 2.2, the rate constant k strongly depends on the viscosity for all motors under investigation, suggesting that the thermal helix inversion of these motors obeys the free-volume model. The obtained α values are comparable with or exceed the values reported previously for a number of viscosity-controlled isomerizations[55–61] and rearrangements[62,63].
To elucidate the origin of the significant viscosity dependence of the THI of motors
6 and 10–13 the isomerization process was studied using quantum mechanical
modelling. The Gaussian 09 program was used for geometry optimizations and the calculation of energies.[33] Initial geometries were optimized using the
semi-empirical PM3 model. Subsequent geometry optimizations were performed on B3LYP/6-31G(d,p) using tight convergence criteria. To reduce the computational demands, ethoxy side groups were used instead of hexyloxy groups for motors 12 and 13. The resulting geometries possess nearly identical core structures in the metastable state, the transition state and the stable state, respectively, which is a desired feature in the design of the experiment. The reason for this desire is that it suggests that the substituents placed at the 6- and 6'-position of the naphthalene ring do not exert a direct effect on the steric crowding in the fjord region. In the
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FIRST GENERATION MOLECULAR MOTORS
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absence of such an effect it is expected that the rotational behaviour, which is governed by the core of the motor, will also be nearly identical (i.e. the changes in the internal coordinates of the motors will be very similar to one another during the thermal helix inversion).
To ensure minima and transition states were reached in the geometry optimizations, frequency analyses of the obtained structures were evaluated; all minima had no imaginary frequencies while all transition states were first-order. Additionally, the frequency analysis provides the thermochemistry of the three states of the motors from which the enthalpy of activation can be calculated for the THI (Table 2.3). All calculated enthalpies fall within a range of only 2 kJ·mol−1 with respect to each
other, but also with respect to the experimentally determined enthalpies, signifying a strong agreement between theory and experiment. The high similarity of the enthalpies reaffirms the hypothesis which suggests that the rotational behaviour is identical regardless of the substituent size, and effective differences in rate are caused by entropic effects on the barrier for THI.
Table 2.3. Enthalpies of the THI step, α values and calculated volumes, and a structural parameter
of motors 6 & 10–13. Motor 6 10 11 12 13 Calculated Δ‡H° (kJ·mol−1) 85.9 84.5 85.2 85.0 85.6 Experimental Δ‡H° (kJ·mol−1) 84.0 84.0 84.1 84.2 84.2 α 0.16 0.20 0.19 0.28 0.40 Mass (u) 360.2 808.7 560.3 1753 2954 Calculated mol. volume (Å3·mol−1) 441.2 1137 765.3 2837 4179
α × mol. volume (Å3·mol−1) 70.60 227.4 145.4 794.4 1671
Distance alkene to centre of mass (Å) 1.58 4.78 3.71 9.32 14.1
With the fraction of each motor which is involved in the rearrangement during the THI known – the α value, see Table 2.3 – it is interesting to be aware of the actual sizes of the rotating portions of the so called molecular stirrers. To gain some insight into the actual volumes of the molecular motors, volume calculations were performed for the metastable Z states (after reoptimizations of motors 12 and 13 in which the ethoxy groups were replaced by hexyloxy groups and all coordinates except for those of the replacements were frozen, and the volume defined as the volume inside a contour of 0.001 electrons/bohr3 density[67], Table 2.3). As
expected, parent motor 6, which has no substituents (R = H), exhibits the lowest α value: 0.16. The α value for motor 10 with hexadecyl chains was found to be slightly higher, at 0.20. This value is similar to that of motor 11 (α = 0.19), which
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has phenylacetylene functionalities but is significantly smaller in mass and calculated volume (∼2/3) (Table 2.3). This indicates that the rigidity of the substituents is an important factor affecting the rotary speed of motors. It is noteworthy that in pure THF motor 10 is almost as fast as its parent analogue 6 while motor 11 exhibits a significant deceleration, since the hexadecyl chains of motor 10 can re-orientate to minimize the disruption of the surrounding solvent molecules which is not possible for the stiff phenylacetylenes. However, it is evident from the larger α value of 10, that it loses this ability in more viscous solvents in which the van der Waals interactions of the long aliphatic chains with the solvent become increasingly substantial. Therefore, in the most viscous mixture, motor 10 slows down by such a large degree that its speed becomes comparable to that of motor 11.
Figure 2.14. Intrinsic reaction coordinates (IRC) of thermal helix inversion and 6, 6’-substituent
dihedral angle during thermal helix inversion of motors 6 and 11.
Going from motor 11 to motors 12 and 13, the α value increases gradually from 0.19 to 0.28 and 0.40, respectively. It seems to correspond to the hypothesis that substitutions at the 6- and 6′-positions would directly contribute to the rearranging volume (α × molecular volume, Table 2.3), since they are on the periphery of the rotating moieties. If the relationship between molecular volume and rearranging
-150 -100 -50 0 50 100 150 -80 -60 -40 -20 0 20 40 60 80 100 120 IRC 6 IRC 11 6-6' 6 6-6' 11 En er gy ( kJ ·m ol -1 ) or d ih ed ra l an gl e (°)
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FIRST GENERATION MOLECULAR MOTORS
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volume is linear, an α value of 0.91 would be expected for motor 13 ( [volume 13 – volume 6 + rearranging volume 6] / volume 13 = [4179 – 441.2 + 70.60] / 4179 ). However, experimentally a considerably lower value of α = 0.40 is found for motor 13, which indicates that not all of the added periphery volume also adds to the rearranging volume.
To investigate this phenomenon, intrinsic reaction coordinates (IRCs) of motors 6 and 11 were performed using the Firefly QC package,[44] which is
partially based on the GAMESS (US)[45] source code, using the Gonzalez-Schlegel
second order method. A comparison of the IRCs of motors 6 and 11 showed very similar behaviours of the two motors (Figure 2.14). Motor 11 has to displace a larger amount of mass, which is equal to volume on account of a consistent degree of hybrization throughout the molecule. Comparing any internal coordinates during the rotation, for example, the 6- and 6′-substituent dihedral angles plotted in Figure 2.14, shows the same overall behaviour. This was expected based on the similarities in their core structure as well as enthalpy of activation. However, they clearly differ in their total energy of activation as well as their viscosity dependence. Therefore, since no distinct differences were observed when comparing internal relationships, absolute displacements were analysed.
Table 2.4. The summed atomic displacement of 6 and 11 Motor Alkene atoms (Å) Atoms 6+6’ (Å) Ratio
6 2.9 8.3 2.8
11 4.0 9.2 2.3
An increase in atomic displacement when substituents are added is evident from the IRCs (Figure 2.14, 179.3 vs. 295.6 amu1/2·bohr for 6 and 11, respectively), but
the change in ratio between the displacement of the central alkene carbons and the peripheral 6- and 6′-carbons is remarkable (Table 2.4). This indicates that, even though the internal behaviour remains the same (meaning internal coordinates show similar changes during the THI), its external behaviour (meaning that with respect to the surroundings) changes. The central displacement increases compared to the peripheral movement going from motor 6 to 11. To illustrate this effect, the rotation of the alkene was followed over the course of the IRC (specifically, the angle the double bond makes during the THI with respect to the double bond of the initial state, metastable-(Z), Figure 2.15).
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Figure 2.15 shows a clear distinction between the rotational behaviour of the overcrowded alkene of motors 6 and 11. The double bond of motor 11 shows not only a larger deviation from its starting point (the metastable Z state) but also a change in behaviour characterized by the difference in overall shape. This representation of change might, however, be quite abstract and is better visualized by an overlay of the animations of the IRCs of motors 6 and 11. From this animation snapshots were taken to provide a similar visualization of the change in behaviour of 6 (in red) and 11 (in blue) (Figure 2.16).
Figure 2.15. Rotational deviation of the double bond from the metastable Z isomer to stable Z
isomer during thermal helix inversion of 6 and 11 in degrees.
Motors 12 and 13 are expected to follow this behaviour, which predicts them to undergo the thermal helix inversion using the same pathway with comparable internal behaviour. It is expected that the change in external behaviour for motors 12 and 13 will be even larger to accommodate for a minimal mass displacement (IRCs of 12 and 13 are computationally too demanding), while still increasing the total amount of displacement of mass and, as a consequence, solvent displacement, with respect to motors 6 and 11 (Table 2.3). These results explain why the volume added in the 6- and 6′-positions does not add completely to the rearranging volume but only partially because of changes in spatial reorganization.
-150 -100 -50 0 50 100 150 0 20 40 6 11 D ouble bond d eviat ion (°)
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FIRST GENERATION MOLECULAR MOTORS
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Indeed, motors 12 and 13 possess an increasingly larger volume, which displaces solvent during rotation. The rigid substituents present in motor 13 increase the volume which displaces solvent during rotation from 70.60 Å3 for parent 6 to 1671
Å3, thereby using a 24 times larger volume to “stir its surroundings”. The effects
of viscosity on a molecular motor will be studied in further detail in Chapter 4, especially the influence of temperature on the viscosity dependence.
Figure 2.16. Snapshots from the overlaid animations of the IRCs of 6 (red) and 11 (blue).
Conclusion
Molecular modelling is able to illustrate the thermal behaviour of first generation molecular motors and reveals their three dimensional geometries. This allows for the intelligent design of novel and complex systems featuring molecular motors as
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has been shown for a potential hairpin switch. It also helps to gain a deeper understanding of the motor’s behaviour, for example it provided insight into the substituent effect on the thermal helix inversion of a first generation molecular motor in viscous media. The ability to predict the life-time of the metastable state is very important for further design and application of molecular motors, especially when studied in environments which strongly differ in temperature such as biosystems (usually room temperature to body temperature), when used in surface assemblies (often at very low temperatures), or as catalysts in reactions (often at elevated temperatures). Here we have presented a much simpler method of finding the transition state by scanning over an appropriate dihedral, which allows for the calculation of the energy of activation of the barrier for thermal helix inversion.
Acknowledgements
The hairpin switch project was conceived by Anouk Lubbe,[49] who is also thanked
for her extensive review of this chapter. The synthesis and experimental measurements of the molecular stirrers was performed by Jiawen Chen.[51]
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