Bachelor Thesis Chemistry

Pathways in Rotaxane Molecular Shuttles

 

   

by

Stan Papadopoulos      

26 August 2017    

Studentnumber 10722718 Research Institute Van ’t Hoff Institute for Molecular Sciences Research Groups Molecular Photonics & Computational Chemistry

Supervisors Prof. dr. A.M. Brouwer & Dr. ir. B. Ensing Daily Supervisor A. Tiwari MSc.

Acronyms

bam benzylic amide macrocycle

CMD Constrained MD

CV collective variable

DABCO 1,4-diazabicyclo[2.2.2]octane

FF Force Field

FPT Freeze-Pump-Thaw

MD Molecular Dynamics

ni naphtalimide

PES Potential Energy Surface

PrCN butyronitrile

RESP Restrained Electrostatic Potential

succ succinimide

TA Transient Absorption

i

Abstract

A rotaxane is a molecular machine consisting of multiple docks on a chain around which a macrocycle

is trapped by the bulky end stations, allowing only translational motion, which in this specific case

happens upon excitation. A computational study was performed to probe the shuttling mechanisms in

hydrogen-bonded [2]-rotaxanes followed by a short experimental study.

The computational part was conducted with Molecular Dynamics, because it allows us to follow the

system over time making it possible to observe the shuttling, of which the mechanism likely changes

with chain length. The longer the chain, the more flexible and easily bent it can become whereas a

short thread cannot bend much, therefore not allowing for harpooning in a small system; the focus was

on C5 and C16 - the rotaxanes as depicted in Scheme 1 with the number being the amount of carbons

between the two stations - due to time constraints. From equilibration simulations it is shown that in

the neutral state the ring favours the succinimide station and upon excitation followed by charge transfer

this preference switches, meaning that the ring is now docked at the naphthalimide station. Moreover, in

the charged/excited state the thread is mostly encountered in a bent configuration, because the ring can

hydrogen-bond to the succinimide station in addition to the naphthalimide station to which it is already

bonded.

Free energy plots also showed that in the neutral state the preferred station is the succinimide one,

which is supported by experiments. The energy curves from the charged state gave mixed results: for C5

the favoured dock changed from succinimide to naphthalimide, but in C16 nothing changed significantly,

which might be due to the end-to-end restrictions of the constrained runs that inhibited bending and

optimal formation of hydrogen bonds. Furthermore, all barriers derived from the energy curve were

approximately 4-5 kcal/mol, which equals the strength of two weak hydrogen bonds.

In the simulations, two mechanism of shuttling were observed. The random-walk happened in C5

and in C16 the shuttling occurred via harpooning. From this we might assume that the mechanism

changes depending on the length of the chain.

ii

Populair wetenschappelijke samenvatting

Rotaxanen zijn moleculaire systemen die arbeid kunnen verrichten, in het geval van rotaxanen is dit via

een shuttlebeweging. Ze zijn te vergelijken met een halter met een ring die om het handvat heen zit en

niet kan ontsnappen door de grote uiteindes. De ring kan hierom alleen maar heen en weer bewegen

tussen beide uiteindes. Aan deze uiteindes bevinden zich stations waar de ring kan ankeren. Normaliter

is de ring altijd gebonden aan een station, maar wanneer het andere station negatief geladen wordt, is

het gunstiger voor de ring om daar te ankeren, waardoor de ring zich naar het negatief geladen station

beweegt. Een toepassing zou een moleculaire schakelaar zijn en afhankelijk van waar de ring zich

bevindt kan je zeggen dat de schakelaar ”uit” of ”aan” staat.

De vraag is echter, wat voor mogelijkheden heeft de ring om zich langs het handvat te verplaat-

sen? Deze kwestie wordt onderzocht met behulp van een computationele methode die berekent hoe

het molecuul zal bewegen. Hierdoor kunnen we ons systeem in de tijd volgen en observeren hoe de

shuttlebeweging verloopt. Als eerste is een ”random walk” voorgesteld, wat inhoud dat de ring zich

willekeurig heen en weer over het handvat beweegt en toevallig bij het andere eind terechtkomt. Een

nieuw voorstel is gedaan die zegt dat de beweging vergelijkbaar is met het werpen van een harpoen en

het touw waar aan het vastzit terugtrekt. Bedoeld wordt dat de twee uiteindes naar elkaar toekomen en

dat de ring bindingen kan maken met het andere station waar het aan vast blijft zitten en het initiele

station, dat zich terugtrekt, verlaat. Uit de berekeningen blijkt dat, ongeacht de grootte van de rotaxaan

de ring altijd gestationeerd is bij het beginstation, maar dat na het toevoegen van lading de ring aan de

andere kant van de halter is geankerd. De manier van bewegen verschilt wel afhankelijk van hoe lang

het handvat is. Bij de korte handvatten verloopt het via een ”random walk”, maar bij het grotere systeem

werd geobserveerd dat het shuttlen gebeurde volgens het harpoenmechanisme.

iii

Contents

Abstract ii

Populair wetenschappelijke samenvatting iii

1 Introduction 1

2 Computational Methods 2

3 Experimental Methods 53.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Results & Discussion 64.1 Computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1.1 NVT-simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1.2 Constrained MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.1.3 Mechanism of shuttling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Conclusion 16

6 Outlook 17

7 Acknowledgements 17

8 Bibliography 18

Appendix 1: NPT-simulations 20

Appendix 2: Constrained MD Indices 22

Appendix 3: TA-spectra 26

iv

1 Introduction

Molecular machines have recently been a topic of great interest, as the 2016 Nobel Prize in Chemistry

was awarded to Ben Feringa, Jean-Pierre Sauvage and James Fraser Stoddart for the design and synthesis

of these machines. They are a class of molecules that consist of at least one component which produce

quasi-mechanical work in response to (photo)chemical stimuli.1 Numerous of these nanomachines have

already been synthesized due to the recent developments in supramolecular chemistry, but this research

will only be about one type of machinery, the shuttle based on rotaxanes. The first synthetic shuttle was

discovered by Stoddart et al., which was based also a rotaxane.2 It is a mechanically interlocked molec-

ular architecture in which a dumbbell shaped molecule is threaded through a macrocycle (Scheme 1).

The ring is trapped, since both ends of the thread consist of docks, end-groups which are larger than the

diameter of the macrocycle and to which the ring can bond, thus allowing only translocation and pre-

venting dislocation. The applications for this process are particularly relevant to nanotechnology if used

as a molecular switch for nanoscale electronic components, as it has been shown that a rotaxane-based

device can be used to store data by electrochemically switching the states of the rotaxane.3

Rotaxanes based on hydrogen-bonding interactions (Scheme 1) have been studied for a considerable

time.4–7 The benzylic amide macrocycle (bam) is usually docked at the succinimide (succ) station, be-

cause it can nestle itself between two peptide moieties to form four hydrogen bonds. Upon photoinduced

excitation of the system an electron is donated by DABCO, which creates the naphtalimide (ni) radical

anion thereby changing the relative binding affinity, because the electron density on the carbonyl moi-

eties will be increased as a result. The macrocyle then shuttles to the charged station and docks there.

After charge recombination, the ring will move to its original station.

Scheme 1. Reaction scheme of the molecular shuttle. In the stable (top left), the system is activated by

a photochemical electron transfer, producing the ni radical anion (green). The bam ring (red) then

leaves the succ station (blue), to which it is bound initially and binds to the ni radical anion.

To be able to finetune this machine for practical purposes, such as increasing the shuttling rate by

1

adjusting the properties of the docks, it is important to understand the mechanism of the translocation.

The first proposal was that the ring unbinds from its initial succ station and then moves along the thread

via a random walk until it encounters the reduced ni, which then traps the ring.4 However, an alternate

mechanism should be considered in which the ring makes one or more hydrogen bonds to the final

station before it unbinds from the initial one.6 If the random walk mechanism is correct the shuttling

rate should be independent of the acceptor station and only depend on the length of the alkyl chain, since

the ring does not necessarily know what this station looks like, but it does take longer to reach the other

site if the thread is longer. However, it has been proven that the acceptor station does have an impact

in the shuttling rate, pointing towards the fact that the random walk might not be the actual shuttling

mechanism.6

The alternate pathways will be investigated for different lengths of the hydrocarbon chain by means

of Molecular Dynamics (MD) simulations. Different chain lengths will likely influence the preferred

mechanism of shuttling, because the end stations can more easily approach each other by bending if the

thread is somewhat longer, thus promoting harpooning. For a short chain this will not be energetically

favourable, so most likely a random walk will happen there. If the alkyl chain becomes too long, though,

the odds of the two station coming together will be small, since an incredible amount of conformations is

possible relatively few of which composed of a bent state, and in this case the shuttling would comprise

of two parts: the first will be the ring leaving the station and then shuttling will occur via harpooning.

In addition, the activation energies for the shuttling will be determined experimentally by means

of Transient Absorption (TA) measurements, which is a type of time-resolved spectroscopy. A pulsed

laser promotes a fraction of the molecules to an electronically excited state and a weak probe pulse is

sent thereafter with a certain time delay.8 A decay curve can be obtained by plotting λmax versus the

time. The Eyring equation could then be used to calculate the energy barrier with the rate obtained from

experiments.9

2 Computational Methods

Completely soluted systems as large as the [2]rotaxanes cannot be studied using ab initio MD, which

uses DFT, which is why Force Field MD simulations are necessary as they are computationally less

demanding. With Force Field MD the equilibrium and transport properties of a classical many-body

system are computed.10 Classical is meant in the sense that the assumption is made that the atoms obey

the laws of classical mechanics.

To calculate all these properties Newton’s equations of motion are solved until the time averages of

these have equilibrated.10 The atoms in the system each have an initial position and velocity and from

those and the Force Field (FF), forces can be calculated. These forces induce an acceleration with which

new velocities can be calculated; these can be used to determine the new positions (Scheme 2).

2

Scheme 2. Visual concept of a MD algorithm. The arrowhead points towards the physical quantity that

can be calculated using the quantity/quantities displayed at the origin of the arrow.

A Force Field is one of the main necessities of MD and is a set of functions and parameters, derivable

from experiments or quantum mechanical calculations, which describe all molecular interactions to

calculate the Potential Energy Surface (PES) (Equation 2.1).

V =∑

Vbonds +∑

Vangles +∑

Vtorsion +∑

Vvdw +∑

Vcoul (2.1)

The first three terms of the equation denote the bonded interactions and the latter two are nonbonded

ones. A great number of FF’s have been made, most optimized for specific systems and the one used in

this study is an OPLS FF, which is optimized for liquid simulations and since it has been used in several

other computational studies on rotaxanes.11–14

The simulations were set up by creating a topology file of an acetonitrile solvated cubic box with

one rotaxane inside in which all the parameters are defined according to the OPLS FF with the Desmond

package.15 This data file was converted to a topology file usable by LAMMPS, another MD package

which was used to carry out the simulations.16 LAMMPS was chosen over Desmond, because it can

be combined with PLUMED, which allowed us to bias our simulations and perform Constrained MD

(CMD).17

Figure 1. Naphthalimide molecule as used in the Gaussian charge calculations.

Since the shuttling process is initiated with photoinduction, resulting in a negatively charged moiety,

3

a topology file needs to be created with extra charge on the naphthalimide. It was necessary to separate

the station from the rest of the rotaxane for the charge calculation, because in reality the charge is

localized only on that part. The only downside to this is that an extra hydrogen needed to be added

to comply to covalency which was lost due to separation and this atom will also obtain charge. That

charge was put on the carbon which was attached to the supplementary hydrogen. The calculations were

done with the Restrained Electrostatic Potential (RESP) method, which comprises of two steps: first,

the electrostatic potential is calculated with DFT, followed by assigning partial charges to every atom to

best reproduce this DFT potential.18 The charges were then replaced in a copy of the topology file from

the neutral systems to create the topology files for the charged rotaxanes.

With these converted files as a basis for the calculations, NPT-simulations were first performed to

determine the optimal box size by keeping the amount of particles, pressure and temperature constant,

while varying the volume of the box (Appendix 1). Once the box size converges it is considered equi-

librated and the average of all the sizes from that point onward is chosen as the optimal box size. We

then chose the frame with a box size closest to that average and used that as the starting frame for the

NVT-simulations in which the box size is kept constant instead of the pressure. This method is compu-

tationally less demanding, since the box size is kept the same, if not additional equations of motion are

needed to take the periodic boundary conditions into account as is the case with NPT.

NVT-simulations are performed to let the system sample the PES and observe what changes occur in

the configuration of the rotaxane, but since the photoinduced translation of the macrocycle to the second

station occurs with a rate of 1.35 · 106 s−1 and the simulations are conducted on nanosecond scale it is

considered a rare-event, which is why CMD is used.4 Moreover, CMD is used to create a free energy

profile, which is not possible with regular MD, because there is no control over the reaction coordinates.

With CMD a collective variable (CV) is used to bias a simulation by applying a restraining potential,

which is achieved by constraining the output of the CV, a mathematical expression of an observable, to

a certain value.19

I =∑

i ∈ chain atoms

i · w(i) (2.2)

w(i) =e−γ·r(i)∑j e

−γ·r(j) (2.3)

For this project a new CV was designed as shown in equation 2.2, enabling us to track the position

of the ring on the chain in which the lowercase i represents every atom defined in the chain and w(i)

is a weight function which increases in value if the atom i is closer to the ring. The weight function is

defined as a fraction in which in the numerator is an exponential term specific to one atom and in the

denominator a summation of those exponential terms for all atoms, resulting in a relative weight. The

r(i) term in the weight function is the absolute distance of the atom to the geometrical centre of the ring,

so if that distance is closer the weight will naturally be higher; the other term in the exponent, γ, is the

weight factor, which influences how much the weight changes per distance unit and for this project 3

was benchmarked to be an optimal value. The output I of this CV is the index of the ring, which is

equivalent to the number assigned to an atom on the chain, but the index can also have a non-integer

4

value, meaning that the centre of the macrocycle is between two atoms. For instance if the ring is exactly

between index 12 and 13, the weights of those indices will both be 0.5 while the rest of the indices will

have a weight of approximatily 0; the resulting summation will be 12 ∗ 0.5 + 13 ∗ 0.5 = 12.5, which is

the correct index.

< Fconstr >=1

n− a

n∑i=a

κ(Ii − Iconstr) (2.4)

∆A =

∫ I

1< Fconstr > dI (2.5)

With the CV implemented in PLUMED, multiple CMD simulations were set up for C5 and C16,

both in the neutral and charged state and with an end-to-end constraint to create the PE curves along

the reaction coordinate. In every run the CV was constrained to one integer index, ranging from 1 to

n + 6 with the first integer index the nitrogen of the succ station closest to the biphenyl moiety and the

final one being the carbon before the nitrogen of the ni station. The timespan of each simulation was 10

ns, which was assumed to be long enough for the forces to be equilibrated. This fact was made visible

by plotting the indices versus time to verify if they were fluctuating around the set value (Appendix 2).

From those indices the average force during the simulation can be calculated as described in equation

2.4 with a force constant κ of 100 kcal/mol/A2. Then, with integration according to equation 2.5 the

PE curves can be created. In some cases, such as C5 and C5-1, the resolution of these curves was not

sufficient around the minima, which is why CMD runs with broken indices around the minima were

performed to smoothen the graph.

3 Experimental Methods

3.1 Procedure

A UV/VIS-spectrum was measured of a 100 mM C5 solution in butyronitrile (PrCN). 1,4-

diazabicyclo[2.2.2]octane (DABCO) (113.60 mg, 1.01 mmol) was then dissolved in PrCN (10 mL)

and diluted three times before adding it (1 mL, 33mM) to the C5-solution (2 mL). Another UV/VIS-

spectrum was measured. The Freeze-Pump-Thaw (FPT) procedure was executed 3 times on that solution

and then another five times after adding the stirring bar. Again an absorption spectrum was measured.

Finally TA measurements were conducted and another UV/VIS-spectrum of the same sample was mea-

sured afterwards to check for degradation.

The same procedure was executed for the C32 system, except that the DABCO solution was reused,

instead of prepared again.

5

4 Results & Discussion

4.1 Computational

Four variants of the rotaxane were studied using MD, but only the smallest two (C5 & C16) were

continued with, because the larger two would take too long to fully analyze due to the sheer simulation

time. The numbers refer to the number of carbons on the chain between the two stations.

4.1.1 NVT-simulations

Figure 2. Histogram of the distance (R) between the stations, defined as shown in Figure 3, and the

respective distance of the ring to each station as obtained from a NVT-simulation of C5 without a bias

potential.

Figure 3. C5 with arrows indicating the atoms defined as the stations for the histogram.

6

From the NVT-simulations histograms can be obtained like in Figure 2 to quantify certain observables

of the calculation. The three curves correspond to the distance between the geometrical center of the

ring and the ni station (taken as the nitrogen), the ring and the succ station (taken as the first nitrogen

with respect to the diphenyl moiety) and the distance between the two stations (same atoms are used)

(see Figure 3 for indications). An intuitive choice for the succ station would be the center of the two

middle carbon atoms, but the geometrical center of the ring is sometimes also situated left of that.

A histogram created with those definitions would result in a cut-off graph, whereas defining the succ

station as the first nitrogen does result in a histogram which nears 0 at the beginning. Instead of a

normalized histogram as is usually the case, it was opted to produce one with the frequencies, since

this would actually quantify what configuration is preferred from the area under each curve. Because

these distances are calculated from single atoms, one should carefully interpret the position of the ring.

Furthermore, at larger distances the frequencies for the bam-station distances are non-zero, which is due

to the periodic boundary conditions. If the rotaxane crosses the boundary, the ring and opposing dock are

suddenly situated at the edges of the box and are ’far apart’. This issue is encountered in all histograms.

It can be concluded from Figure 2 that after equilibration the bam ring is docked at the succ station and

not at the ni one. Furthermore, the end-to-end distance (blue line) shows two bands, one representing

the stretched state and the other the bent state (Figure 4 & Figure 5 respectively).

Figure 4. C5-rotaxane in a stretched state obtained from a 20 ns NVT-simulation. The hydrogens are

omitted for clarity.

Figure 5. C5-rotaxane in a bent state obtained from a 20 ns NVT-simulation. The hydrogens are

omitted for clarity.

7

Figure 6. Histogram of the distance (R) between the stations, defined as shown in Figure 3, and the

respective distance of the ring to each station as obtained from a NVT-simulation of C5 with the

negatively charged ni (C5-1) without a bias potential.

When Figure 6 is compared with Figure 2, it is apparent that after equilibration, the tables have

turned, as expected, meaning that the ring is now docked at the ni station. Moreover, if the succ-

ni distance is compared, it becomes clear that in the charged state the thread slightly favours a bent

configuration. This is likely due to the fact that that the ring now has 4 free carbonyl groups that can

make hydrogen bonds with the hydrogens of the succinimide station by bending the thread a bit. As

seen in Figure 2, the reverse situation will not occur as much in the neutral state, because the carbonyl

groups of the naphthalimide are not strong enough as hydrogen bond acceptors.

8

Figure 7. Histogram of the distance (R) between the stations, defined as shown in Figure 3, and the

respective distance of the ring to each station as obtained from a NVT-simulation of C16 without a bias

potential.

Moving on to C16, from Figure 7 it is clear that it is entirely different from C5 after equilibration

regarding the configuration of the thread. The ring is docked nicely on the succ station, but the end-

to-end-distance is a wider spread, which shows that the thread explores many configurations without a

clear preference for either a bent or stretched state. This distribution of configurations changes when the

rotaxane is reduced, which is shown in Figure 8.

9

Figure 8. Histogram of the distance (R) between the stations, defined as shown in Figure 3, and the

respective distance of the ring to each station as obtained from a NVT-simulation of C16 with the

negatively charged ni (C16-1) without a bias potential.

There is now a minor preference for the bent configuration in the excited state, which becomes

apparent from the fact that there is now only one distinct peak of the succ-ni distance at a small value,

even though it is still able to extend itself. This shift in tendency is most likely because the carbonyl

groups of the ring are free to make hydrogen bonds with the succ station while being docked at ni,

forcing a bent structure. A similar occurrence will not be extraordinarily stable in the neutral state,

because that would mean the the carbonyl moieties of the ni station would have to make hydrogen

bonds. As is known, in the neutral state, it is not a strong hydrogen bond acceptor, thus the ring will not

have a definitive preference to be bonded in such a way and form a bent configuration.6

4.1.2 Constrained MD

As explained in Section 2 CMD simulations were performed on C5 and C16 in the neutral and the

charged state. For C5(-1) 10 ns simulations were carried out with each simulation constraining the ring

along the atoms on the chain, the indices of which are shown in Figure 9; the same applies to C16(-1)

(see Figure 12 for labeling). During each of those simulations the output of the CV, which is the index,

is tracked during the entire simulation to determine if the forces have equilibrated (Appendix 2), which

is necessary for creating the free energy plots that were constructed using the method descript in Section

2.

10

In all simulations the end-to-end distance was fixated at a distance the chain would be stretched

because of time constraints of the project. This would increase the equilibration of the forces put onto

the ring, as this would decrease the interactions the ring could have with both stations if the chain was

bent, thus preventing extra external forces.

Figure 9. The index labeling of C5 as used in the CMD simulations. Each index represents one 10 ns

CMD run in which the geometrical center of the ring is constrained to that index.

Figure 10. The free energy curve as obtained from the 14 CMD runs of C5.

11

Figure 11. The free energy curve as obtained from the 13 CMD runs of C5-1.

Figure 10 is a prime example of a free energy plot in the neutral state, with the lowest minimum

around the indices of the succinimide and the other, somewhat higher, minimum at the indices of the

naphthalimide.5,20 One intriguing aspect of it is that the barrier for the shuttling even in the neutral

state is approximately 4 kcal/mol, which is in the range of the breaking of a hydrogen bond.21,22 This

implies that shuttling could happen with thermal fluctuations around room temperature even while not

being excited, but this has not been reported yet as it is difficult to observe. It has been reported for

similar systems that the barrier is approximately 3 times larger.4 A reason would be that the restriction

on the end-to-end distance is decreasing the thermodynamic barrier, since the entropy becomes lower as

a result of a lower amount of possible configurations.

Upon reduction of the ni station the energy surface (along the reaction coordinate) changes in a

way that the ring now favours the charged moiety in the sense that the minimum at the naphthalimide

is lower in energy than the succinimide, but the barrier height is retained. The energy required to go

back to the succ station is approximately 2 kcal/mol higher, but should not be adequate to withhold

the macrocyle to shuttle back. Therefore it is likely that the end-to-end restriction distorts the energy

landscape considerably. The reason being that the rotaxane cannot explore all its configurations leading

to the fact that the ring cannot hydrogen bond to the opposing dock, which in turn would influence the

forces.

12

Figure 12. The index labeling of C16 as used in the CMD simulations. Each index represents one 10

ns CMD run in which the geometrical center of the ring is constrained to that index.

Figure 13. The free energy curve as obtained from the CMD runs of C16.

13

Figure 14. The free energy curve as obtained from the CMD runs of C16-1.

The energy curve of C16 (Figure 13) looks similar to that of C5 (Figure 10) albeit more stretched out.

Also in this case the barrier has a low value of 5 kcal/mol, enabling a shuttling motion rather effortlessly,

but once on the other side the system will be in a metastable state due to the ni station not being a well

defined minimum, because the barrier to go back is 1 kcal/mol; upon the ring’s arrival at the other side

it should move back almost instantaneously to the succ dock. Moreover, there is a tendency to always

go back to the succinimide, since the top of the barrier resides closer to the naphthalimide, allowing the

ring to have more possibilities to move backwards.

In the case of the reduced C16 the energy plot barely changed (Figure 14), but the minima became

less broad. Furthermore, in the proximity of the ni station (index 20) an extra peak has arisen, which

distorts the smooth surface. No oddities were encountered in the trajectory and the forces were equili-

brated. One thing to note is that a one dip in the index occurred (Figure 27, but since the calculated force

is an average calculated over 106 frames obtained from a 10 ns simulation and this distortion equates

only to 2% of the entire run the force should not be influenced significantly. Finally, no switch in dock-

ing preference has been observed after adding the charge. Because of the histogram (Figure 8) it is valid

to say that the charges were added correctly, since the ring shuttled to the other side via harpooning and

stayed docked there. The same reason as C5-1 likely applies to C16-1 as well: due to the constraint on

the end-to-end distance the state obtained from CMD is strained too much and is not as stable as it could

have been without the restrictions. However it is possible for the bam ring to be docked at the reduced

ni in the stretched state proven by Figure 8, showing that the ring is docked at the ni station while also

spending a considerable amount of time in stretched states.

14

4.1.3 Mechanism of shuttling

To probe the shuttling mechanism of the rotaxanes all these simulations were performed. The tendency

to shuttle upon reduction is confirmed by the histograms and the energy plots (except the free energy

curve of C16-1), but these are derived from equilibrated states and do not provide information about the

mechanism. Only during the NVT-simulation of C5-1 and C16-1 shuttling was observed, C26-1 and

C32-1 remained unchanged. The fact that in the larger systems no translocation took place during the

equilibration simulation is understandable, since the simulation time was in the order of nanoseconds

while in reality the shuttling takes microseconds.4 Within the simulations the shuttling can be regarded as

a rare-event, thus it is more likely to occur in the smaller systems, because the amount of configurations

are less decreasing the entropic factor.

It might be concluded that the shuttling mechanism changes depending on the length of the thread.

Shuttling in C5 went according to the random walk, likely because the thread is too short to bend without

which harpooning cannot occur. In C16 first the bam ring left the station after which the thread assumed

a bent configuration which resulted in harpooning. From these simulations it might be assumed that

shorter chains prefer shuttling via a random-walk mechanism, whereas longer chains prefer harpooning.

4.2 Experimental

To study the shuttling of the hydrogen-bonded [2]rotaxanes TA measurements were conducted on the

C5- and C32-systems. These had already been synthesized and isolated, thus they could immediately

be dissolved in butyronitrile. This solvent was used first, instead of acetonitrile, which was used in

the simulations, because the larger systems dissolve better in it. UV/VIS-spectra were taken after the

solvation to determine if the correct transitions could be observed and if the absorbance (∼1.5) at λmax(353 nm) was suited for the TA. This would indeed be the case after the addition of DABCO, because

then the rotaxane sample would be diluted 1.5 times, thus decreasing the absorbance by a factor of 1.5

according to Lambert-Beer’s law. DABCO was added to act as an electron donor during the shuttling

process to create the ni·− radical anion, which causes that station to be a strong H-bond acceptor.4 The

UV/VIS-spectrum of the solution after DABCO was added was similar to the previous one, but the

absorbance had decreased to approximately 1. To prepare the sample for TA the solution needed to be

degassed, since a radical is formed during the shuttling and if molecular oxygen (a biradical species)

would be present, it would quench the triplet state and oxidize the radical anion if formed, thus inhibit

the shuttling. After this step another UV/VIS-spectrum was measured to verify if nothing was out of the

ordinary because of the FPT; this was the case.

15

Figure 15. Decay curve of the population of the ni radical anion in C32

From the TA-spectra (Appendix 3, Figure 28 & Figure 29) it would be possible to deduce the trans-

lation by the shift of λmax over time, which has been proven to happen on a microsecond scale.4,23

However, if the corrected absorption at λmax is plotted a decay curve of the population of ni·− is ob-

tained(Figure 15), which shows that the population decreases much too rapidly for shuttling to occur.

Moreover, the original shape of the spectrum is lost after multiple timesteps, which indicates that the

sample might not be photostable anymore or has degraded, as it as an old sample. Indeed such was the

case, since another UV/VIS-spectrum was taken and the absorbance at λmax had decreased.

5 Conclusion

A study has been done on the shuttling mechanism of hydrogen-bonded [2]rotaxanes. First of all, from

the NVT-simulations we can conclude that in C5 and C16 naphthalimide becomes the favoured sta-

tion after reduction as expected. Furthermore, the chain spends a considerable amount of time in bent

configurations due to more hydrogen bonds being available if the ring is docked at naphthalimide, since

hydrogen-binding with two stations is now available, which was not the case in the neutral state, because

the hydrogen bonds with the naphthalimide were not strong enough.

Secondly, a collective variable has been developed to track the position on the ring, which allowed

us to perform Constrained Molecular Dynamics on the rotaxane. Using this, free energy curves were

obtained and in C5 confirmed the shift in preference; in C16 this could not be confirmed as the energy

minimum at the naphthalimide dock in the reduced state did not become lower than the one at the

succinimide station. The reason for it being the end-to-end distance restraint, which limited the hydrogen

bonding. This was necessary for this project, however, because the project duration was a limiting factor

and this approach would be the fastest way of converging the forces, which is necessary for producing

an accurate energy plot. The barriers of shuttling could also be determined from the energy plot and they

were rather small. In all cases (C5 & C16, neutral & charged) it was approximately 4-5 kcal/mol, which

16

is equivalent to two weak hydrogen bonds, and implies that shuttling is possible even in the neutral

state due to thermal fluctuations even though barriers thrice as large have been reported in previous

experiments. It is possible that the fixation of the end-to-end distance distorts the energy surface too

much.

Next, the mechanism of the shuttling is shown to change depending on the chain length. Upon

charge addition to the naphthalimide station a random walk mechanism was observed for C5, but in C16

a mixed mechanism took place. First the ring explored the energy landscape with a random walk when

leaving the initial (succinimide) dock, continued by the chain bending, which allowed to translation to

finish via harpooning. Thus shorter chains likely prefer random walk, whereas the longer the thread

becomes, the more favourable harpooning gets until a certain length after which a mix will dominate the

translational motion.

Finally, transient absorption measurements were also performed on C5 and C32 in butyronitrile.

These were unfortunately inconclusive as the naphthalimide radical anion decayed within 1 microsec-

ond, disabling the shuttling. This might be due to degradation of the rotaxanes as the samples were quite

old.

6 Outlook

As mentioned in the beginning of the discussion, the two largest systems (C26 & C32) still need to be

analyzed using constrained MD in order to create a potential energy curve, which was not done due to

time constraints. In addition, the constrained MD which was performed had an end-to-end restriction,

which is of course not natural. The next step would be to do the constrained MD without the fixation of

the end-to-end distance. Another computational method would be metadynamics, which is another way

to explore the energy landscape and is able to find minima along the reaction coordinate of the CVs.

Finally, the original purpose of this project was also to compare the computational data to experimental

data, such as the activation energies. To further validate the calculations it would be advised to redo the

experiments for all systems, preferably in acetone as this was the solvent used in the simulations.

7 Acknowledgements

I thank Fred Brouwer and Bernd Ensing for allowing me to do a joint Bachelor Project, which made it

even more interesting. I also want to thank them for the valuable discussions and talks. Furthermore, I

want to thank Ambuj Tiwari for the daily supervision and for being a really nice guy who was always

available for questions and problem solving. Next, I want to thank Michiel Hilbers for helping with the

experimental/technical side of the project. Additionally, many thanks to Ferry, Rhea and Tamika for all

the time we’ve spent helping each other out. Finally, I want to thank both the Computational Chemistry

and Molecular Photonics Groups for the nice atmosphere, which made my time working on this project

really enjoyable and made the time fly by.

17

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19

Appendix 1: NPT-simulations

Figure 16. Box length of a cubic unit cell as obtained from NPT-simulations on C5.

Figure 17. Box length of a cubic unit cell as obtained from NPT-simulations on C5-1.

20

Figure 18. Box length of a cubic unit cell as obtained from NPT-simulations on C16.

Figure 19. Box length of a cubic unit cell as obtained from NPT-simulations on C16-1.

21

Appendix 2: Constrained MD Indices

Figure 20. The output of the CV of every constrained MD-simulation of C5 (14 in total) was tracked

during the entire simulation. The black lines represent the set value in the CMD run and the coloured

lines are the actual indices from the simulations.

Figure 21. The output of the CV of some constrained MD-simulation of C5-1 (13 in total) was tracked

during the entire simulation. The black lines represent the set value in the CMD run and the coloured

lines are the actual indices from the simulations.

22

Figure 22. The output of the CV at index 11.5 of C5-1 to increase the resolution around the minimum.

Figure 23. The output of the CV at index 11.8 of C5-1 to increase the resolution around the minimum.

The average index lies below the set value, since the ring was practically on the nitogren of the ni

station and the instability of that position outweighed the force constant of the bias potential.

23

Figure 24. The CV output of the first half of the constrained MD-simulation of C16 was tracked during

the entire simulation. The black lines represent the set value in the CMD run and the coloured lines are

the actual indices from the simulations.

Figure 25. The CV output of the second half of the constrained MD-simulation of C16 was tracked

during the entire simulation. The black lines represent the set value in the CMD run and the coloured

lines are the actual indices from the simulations.

24

Figure 26. The CV output of the first half of the constrained MD-simulation of C16-1 was tracked

during the entire simulation. The black lines represent the set value in the CMD run and the coloured

lines are the actual indices from the simulations.

Figure 27. The CV output of the second half of the constrained MD-simulation of C16-1 was tracked

during the entire simulation. The black lines represent the set value in the CMD run and the coloured

lines are the actual indices from the simulations.

25

Appendix 3: TA-spectra

Figure 28. TA-spectra of C5

Figure 29. TA-spectra of C32

26