Transient two-dimensional vibrational spectroscopy of an operating molecular machine

Synthetic molecular machines are promising building blocks for future nanoscopic devices. However, the details of their mechanical behaviour are in many cases still largely unknown. A deeper understanding of mechanics at the molecular level is essential for the design and construction of complex nanodevices. Here, we show that transient two-dimensional infrared (T2DIR) spectroscopy makes it possible to monitor the conformational changes of a translational molecular machine during its operation. Translation of a macrocyclic ring from one station to another on a molecular thread is initiated by a UV pulse. The arrival of the shuttling macrocycle at the final station is visible from a newly appearing cross peak between these two moieties. To eliminate spectral congestion in the T2DIR spectra, we use a subtraction method applicable to many other complex molecular systems. The T2DIR spectra indicate that the macrocycle adopts a boat-like conformation at the final station, which contrasts with the chair-like conformation at the initial station.

: a 1DIR spectrum of the bare thread and molecular shuttle. In the thread, the succ HB mode (green dot marked with T) is blue shifted with respect to the succ HB mode of the rotaxane (green dot marked with R). The thread also lacks the absorption bands associated with the macrocycle. b 2DIR spectrum (∆A) of the thread. c 2DIR spectrum (∆A) of the molecular shuttle. d T1DIR spectra (∆A) of the thread and molecular shuttle at t UV = 50 ns. e T2DIR spectrum (∆∆A) of the thread at t UV = 50 ns. f T2DIR spectrum (∆∆A) of the molecular shuttle at t UV = 50 ns. The 2DIR and T2DIR spectra are measured with a parallel ( ) polarised IR-pump pulse with respect to the probe pulse. The coloured closed and open circles correspond to the labeled components of the molecular shuttle in Fig. 1a of the main text.
Supplementary Figure 2: Comparison between the ground state 2DIR spectrum of a model compound and the T2DIR spectrum of the molecular shuttle at 50 ns after UV excitation. a Chemical structure of the ni model compound. b 1DIR spectrum of the model compound. c 2DIR (⊥ ∆A) spectrum of the model compound. d Chemical structure of the molecular shuttle in the triplet state. e T1DIR spectrum (∆A) of the molecular shuttle at t UV = 50 ns. The arrows indicate the shift in frequency caused by the excitation of the ni station. The coloured closed and open circles labelling the spectral features correspond to the coloured components of the molecules. f T2DIR (⊥ ∆∆A) spectrum of the molecular shuttle. The 2DIR and T2DIR spectra are measured with a pump pulse perpendicularly polarised with respect to the probe pulse.
Supplementary Figure 3: The constructed ni-free 1DIR (a) and 2DIR spectra (b) of the molecular shuttle measured with a parallel ( ) polarised IR-pump pulse with respect to the probe pulse. The constructed ni-free 1DIR (c) and 2DIR spectra (d) of the molecular shuttle measured with a perpendicularly (⊥) polarised IR-pump pulse with respect to the probe pulse. The dashed green lines denote the pump positions of the slices in e and f. The 2DIR spectra are measured with a perpendicularly (⊥) polarised IR-pump pulse with respect to the probe pulse e Cross section of the ni station-free 2DIR spectrum (∆A), where the yellow peak denotes the resonant excitation at 1,675 cm -1 . f Cross section of the ni station-free 2DIR spectrum (∆A), where the yellow peak denotes the resonant excitation at 1,627 cm -1 . In the slices, the red curve is the spectrum measured with a parallel ( ) polarised IR-pump pulse, and the blue curve is the spectrum measured with a perpendicularly (⊥) polarised IR-pump pulse with respect to the probe pulse. The perpendicular signal in both T2DIR cross sections is multiplied by a factor of three for an easy comparison with the parallel signal. The coloured closed and open circles correspond to the labeled components of the molecular shuttle in Fig. 2 of the main text.
Supplementary Figure 4: Example of the SVD-based reduction of uncertainty using the perpendicularly polarized T2DIR signal ν pump = 1,654 cm -1 . a The n measured points y(ω,t = 1 ps) and their meanȳ(ω,t = 1 ps). b Subtraction of the two most significant components (U t<0 , panel c) from y(ω,t = 1 ps) and the new mean. c Singular values (5 most significant marked in red, s), target (V )-and projection (U t<0 )-vectors of points y(ω,t < 0).    Fig. 2. b T2DIR spectrum cross section (∆∆A), where the yellow peak denotes the resonant excitation at 1,654 cm -1 . c T2DIR spectrum cross section (∆∆A), where the yellow peak denotes the resonant excitation at 1,592 cm -1 . In all spectra, the red curve is the spectrum measured with a parallel ( ) polarised IR-pump pulse, and the blue curve is the spectrum measured with a perpendicularly (⊥) polarised IR-pump pulse with respect to the probe pulse. The perpendicular signal in both T2DIR cross sections is multiplied by a factor of three to facilitate comparison with the parallel signal.   Table 1: Summary of the measured and calculated absorption bands. The vibrational modes with their corresponding frequencies and description of the molecular shuttle in the ground, triplet, and radical-anion state. s and as stand for the symmetric and antisymmetric CO stretch vibrations of the naphthalimide station in the electronic ground state, respectively; Ar stands for aromatic ring vibration; rad. anion for radical anion. The calculated frequencies were obtained from DFT at the B3LYP/6-31G(d) level (scaling factor 0.973) on the following model compounds: a n-propyl-naphthalimide station; a T n-propyl-naphthalimide station in the triplet state; a •− radical anion n-propyl-naphthalimide station; b methyl-succinamide station-macrocycle pseudo-rotaxane; c radical anion n-propyl-naphthalimide station-macrocycle pseudo-rotaxane; d methyl-succinamide station.   Fig. 4 of the main text. All numbers are in cm -1 ; multiple numbers are given for the computed vibrations because both n-butyl and n-pentyl chains were included, and because in many cases several modes contribute to the observed bands. A signal generated from the Ti:sapphire oscillator (80 MHz) output is amplified and frequency-divided to produce a 1 kHz signal. This signal triggers a pulse generator which provides the triggering for the YLF pump laser and Pockels-cell driver of the regenerative amplifier, an electronically gated amplifier used to record the signals of the MCT-detector array, and a computer-controlled electronic delay generator (Berkeley Nucleonics Corporation Model 575-4C). The latter provides the triggering for the Nd:YAG laser that generates the UV pump pulse. The maximum delay between the UV and mid-IR laser pulses is determined by the repetition rate of the Ti:sapphire laser (1 ms).
The 355 nm pulse length is determined from a cross-correlation with the mid-IR pulses obtained by differentiating the pump-probe signal in a Ge plate. From a fit to a gaussian function we obtain a FWHM of 3.6±0.4 ns for the pump pulse. The Nd:YAG laser is pumped at 500 Hz and Q-switched at 100 Hz. Using the amplified 800 nm output of the Legend and an optical setup described elsewhere 3 we obtain mid-IR pulses with a duration of ∼150 fs, a bandwidth of 200 cm -1 and an energy of 20 µJ. Probe and reference pulses are obtained from the mid-IR light by reflection off the front and back surfaces of a wedged BaF 2 window. The remainder is passed through an IR Fabry-Perot interferometer, resulting in pump pulses with a bandwidth of 25 cm -1 . The centre frequency of the light is varied by adjusting the distance between the parallel mirrors of the IR Fabry-Perot interferometer using a feedback-controlled piezoelectric mount. The polarisation of the IR pump pulse is set at 45 • with respect to that of the probe pulse using a MgF 2 zero-order λ -half plate. Subsequently, the polarisation of the measured spectrum is selected using a polariser situated directly after the sample set at either 0 • (parallel spectrum) or 90 • (perpendicular spectrum) with respect to the pump polarisation. The pump pulses have an intensity envelope that is approximately single-sided exponential with a FWHM of 800 fs, as determined from a cross correlation measured by using two-photon absorption in InAs placed in a sample cell similar to the one used in the T2DIR experiment.
The T2DIR experiment is performed by focusing the 355 nm output 3 cm before the sample with an f = 300 mm CaF 2 lens. The changes induced in the sample are monitored by the two mid-IR probe pulses, which are spatially overlapped with the pump beam, at various time delays between the UV-pump and mid-IR pulses. The mid-IR reference beam passes through an area of the sample not influenced by the pump. The mid-IR pump, probe and reference beams are focused through the sample by means of an f = 100 mm off-axis parabolic mirror. At the sample, the UV and mid-IR beam diameters are 1 mm and 200 µm, respectively. The polarisation of the UV-pump and mid-IR probe are perpendicular with respect to one another. Transient absorption changes are measured by frequency-dispersed detection of the mid-IR pulses using a 2 × 32 HgCdTe (MCT) array detector (Infrared Associates).

The T2DIR experiment
The T2DIR spectrum, ∆∆A (ω 1 , ω 2 ,t UV ,t IR ), is the difference between the 2DIR spectrum of the electronic excited state species, ∆A UV,IR (ω 1 , ω 2 ,t UV ,t IR ), and the 2DIR spectrum of the electronic ground state species, ∆A IR (ω 1 , ω 2 ,t IR ): A 0 (ω 1 , ω 2 ) is the absorption of the sample when neither pump pulse is present. The signals are measured in terms of transmission with A = − log 10 (T /T 0 ). This yields the following: where T 0 is the transmission of the sample in the absence of a pump pulse, a is the fraction of molecules excited by the UV pump, ω 1 the pump frequencies, ω 2 the probe frequencies, t UV the delay between the UV-pump and 2DIR pulse pair, and t IR the delay between the IR-pump and IR-probe pulses. The terms in the square brackets are observed at the same time by the probe when both UV and IR pump pulses are acting on the sample. We use the timing scheme shown in Supplementary Fig. 10 to obtain the signals necessary to construct ∆∆A as shown in equation 3: the sample is probed at a repetition rate of 1 kHz. The mid-IR pump pulse is optically chopped at a frequency of 250 Hz such that two sequential pulses are allowed to pass and the following two sequential pulses are blocked, effectively pumping the sample at 500 Hz. The UV laser is run at a repetition rate which is not a divider of 250 Hz (we choose 100 Hz). In this manner, the following absorption spectra required for the generation of the T2DIR spectrum can be recorded: the ground state absorption, A 0 , is measured at each laser shot where both UV and IR pumps are off (occurring at 450 Hz). The vibrationally excited state absorption, A IR at a certain pump frequency and delay time, is measured at each shot where only the IR pump pulse acts on the sample (occurring at 450 Hz). The electronic excited state absorption, A UV at a certain delay time, is measured at each shot where only the UV pump pulse acts on the sample (occurring at 50 Hz). The vibrationally excited absorption of the electronic excited state species, A UV,IR at a certain IR-pump frequency and delay time, is measured at each shot where both IR and UV pumps act on the sample (this occurs at 50 Hz).

Baseline correction
The absorption of the sample y observed with a certain pixel (corresponding to a frequency ω), at a certain delay (t) is determined by the meanȳ(ω,t) of all individual shots y i , and the corresponding error is determined by the standard deviation σ (ω,t) of these points: where n is the total number of repeats of the measurement. The T2DIR measurements contain random baseline fluctuations which can be averaged out by performing a sufficient number measurements, thereby revealing the T2DIR signal (see Supplementary Fig. 4a).
In order to reduce the spread of the measurements caused by stochastic baseline fluctuations, we employed a singular-value-decomposition (SVD) based method developed by Haldrup 4 . Briefly, an SVD is performed on the measurements before t UV = 0, which yields the projection vectors, singular values, and target vectors (U, s, and V T respectively) of the baseline fluctuations (see Supplementary  Fig. 4c). Next, the contribution of each baseline component a i (ω,t < 0) to each measurement y i (ω,t) is obtained from a least-squares fit of the target vectors U t<0 to the measurements at delay points t > 0, y(ω,t > 0). We subtract the most significant of the componentsŨ t<0 from the dataset, thereby reducing the spread of the individual measurements ( Supplementary Fig. 4b): Subsequently, we employ robust statistics to further reduce the uncertainty of the measured points 5 .
As explained in Supplementary Equation 4: we take the mean of the dataȳ(ω,t) to determine the value of y, and the uncertainty is determined via the median absolute deviation (MAD) of the spread of the data points y i (ω,t): The MAD is converted to a standard deviation using the relationship σ = 1.4826 · MAD.
In the case of the initial state of the molecular shuttle (see main text Fig. 1a ), we did not record data points at delays t < 0. The 1 st and 2 nd projection vectors can therefore manifest mixing of both signal and baseline artifacts (see Supplementary Fig. 9) which is especially the case with the T2DIR signals. As a consequence, we would severely distort our data if we naively applied the SVD-based baseline reduction method as described above. We therefore remove the signal contribution (1 st projection vector) from the 2 nd projection vector. The 1 st component of the U t<0 of the final state T2DIR signal in Supplementary Fig. 4c is predominantly a featureless baseline artefact compared to the T2DIR signal. For the following analysis, we use the fact that the 2 nd component of the initial state T2DIR should be of a similar nature to the 1 st component of the U t<0 of the final state and that the 1 st component of the initial state predominantly contains signal. The 2 nd derivative with respect to frequency is a measure with which to evaluate only the structured part of the 2 nd component, and ignore featureless baseline artefacts. To remove structured features from the 2 nd component U m=2 (where m specifies a component), we first take the 2 nd derivative of all the components with respect to frequency U = d 2 U dω 2 . The magnitude b m =2 of the projection vectors U m =2 in U m=2 is determined by a least-squares fit of the first four U m =2 to U m=2 . The corrected 2 nd projection vector U c m=2 is obtained as follows: where, in our case, k = 5. The result is shown in Supplementary Fig. 9. We subsequently continue with the SVD-based baseline removal as described above. The baseline fluctuation target vectors V m =1 are randomly distributed about 0, whereas the signal component target vector V m=1 is predominantly either positive or negative. This is probably caused by laser-power fluctuations or changing pump-probe beam overlap due to ambient temperature fluctuations of over the course of hours. A final reduction in the spread of y i (ω,t) is achieved by reconstituting y i (ω,t) with the normalised 1 st projection vector U N m=1 to the median of the corresponding target vector V m=1 as follows:

Materials
All experiments on the molecular shuttle were carried out on a solution of the rotaxane (5×10 −4 M) and 1,4-diazabicyclo[2.2.2]octane (DABCO, 5×10 −2 M) in CD 3 CN (Eurisotop, >99.8% D purity). Neither the solvent nor DABCO has absorption bands in the spectral region of interest. Argon was bubbled through the sample for >15 min in order to remove dissolved oxygen from the solution. The sample was kept in a thermostatted sealed IR cell consisting of two CaF 2 windows separated by a 5 mm spacer. The sample cell was constantly moved in a Lissajous pattern to avoid residual heating and photochemical degradation of the sample. All steady-state Fourier-transform infrared (FTIR) spectra were measured on a Bruker Vertex 70 spectrometer (resolution 2 cm -1 ).
The ground-state 1DIR spectrum of the molecular shuttle is shown in main text Fig. 3b. In addition to the peaks discussed previously, a peak is observed at 1,700 cm -1 which belongs to the symmetric CO-stretch vibration of the ni station (ni s ). The ni s mode is spectrally isolated and we can therefore use it as a measure for the amount of ni present in the spectrum. The corresponding 2DIR spectrum is shown in main text Fig. 3c. The diagonal absorption of the ni s mode is observed at (1,700 cm -1 , 1,700 cm -1 ). Cross peaks between the ni s and the ni as and ni Ar modes are clearly visible at (1,700 cm -1 , 1,663 cm -1 ), (1,700 cm -1 , 1,632 cm -1 ), (1,663 cm -1 , 1,700 cm -1 ), and (1,632 cm -1 , 1,700 cm -1 ). The remaining features are discussed in the main text. As stated in the main text, the ground-state 2DIR spectrum of the shuttle contains overlapping absorptions of the ni station with both the macrocycle and succ station which makes direct conformational determination impossible. Supplementary Fig. 3 shows the ni-free 2DIR spectrum of the molecular shuttle from which we obtained the angle θ i j between the mc HB···succ and succ HB modes. In order to obtain θ i j , we need to eliminate the contribution from the ni station. The 1DIR ni-free spectrum ( Supplementary Fig. 3a and c) is constructed by subtracting the 1DIR spectrum of the ni station ( Supplementary Fig. 2b) from that of the molecular shuttle. The spectra are normalised on the ni s mode before subtraction. The remaining peaks are the mc HB···succ (1,663 cm -1 ) and the succ HB (1,632 cm -1 ) modes. The ni-free 2DIR spectra (Supplementary Fig. 3b and d) are generated in a similar fashion as the 1DIR spectra, with the added benefit that we do not need record a separate ni station spectrum. The T2DIR spectrum of the triplet species contains the ground-state 2DIR depletion-spectrum of the ni station. By comparing intensities at 1,700 cm -1 we determine that in order to eliminate the contribution of the ni station, one needs to add the depletion spectrum multiplied by a factor of 3.5 to the ground-state 2DIR spectrum. The result for both pump polarisations is shown in Supplementary  Fig. 3. The peaks observed in the 2DIR spectra have been discussed in the main text. Supplementary Fig. 3e and f show cross-sections of the ni-free 2DIR spectra at the pump frequencies 1,675 cm -1 and 1,627 cm -1 respectively, indicated by the green dashed lines. The macrocycle and succ station absorptions overlap moderately. For the determination of the angle θ i j between the vibrational modes, we choose to use cross-sections where the central frequency of the pump is slightly off-resonance. In this manner, we avoid direct excitation of both modes. When pumping at 1,675 cm -1 ( Supplementary Fig. 3e), we observe a large resonant feature with v = 0→1 = 1,668 cm -1 and v = 1→2 = 1,654 cm -1 . A polarisation-dependent ∆A feature is observed on the flank of the v = 1→2 transition at 1,627 cm -1 . This is the positive part of the cross-peak, indicative of coupling between the macrocycle and the succinamide station. The cross-section of the ni-free 2DIR spectrum with ν pump = 1,627 cm -1 shows (Supplementary Fig. 3f) a diagonal peak with v = 0→1 = 1,654 cm -1 and v = 1→2 = 1,623 cm -1 . A negative polarisation-dependent off-diagonal feature is observed at 1,668 cm -1 , which corresponds to the v = 0→1 transition of the macrocycle amide I mode. This is the complementary cross peak which indicates coupling between the succ HB and mc HB···succ modes. We determined the cross-peak anisotropy in the same fashion as was done for the switched state. The maximum change in absorption of the cross peaks were used for the values of ∆A and ∆A ⊥ . Using equation 2 of the main text, we obtain two independent determinations of θ i j , one from each off-diagonal feature, which allows us to estimate the uncertainty of the measurement in the value obtained.

DFT calculations with different functionals and basis sets
In Supplementary Table 2 we compare the IR frequencies in the investigated spectral ranges as predicted by DFT calculations with different functionals and basis sets. In the model system (see Figure 4 of the main text), all features are included which we found to have an effect on the calculated frequencies of the vibrations of interest. We obtain good agreement between the experimental and calculated data (see next section). Furthermore, we find that the calculations with the B3LYP and B97D functionals using the 6-311G(d,p) basis set reproduce the experimental vibrational frequencies only slightly better than the B3LYP/6-31G(d) calculations. The results of the M062X/CC-pVDZ calculation are in substantially worse agreement with experiment. We can link the computed and experimental frequencies in order to achieve the best possible agreement after simple linear scaling (scaling factor 0.973).

Comparison of calculated and experimental transient spectra
In Supplementary Fig. 5a we compare the calculated transient 1D spectrum after charging the ni station with the experimental transient 1D spectrum (t UV = 50 ns). In Supplementary Fig. 5b we compare the calculated transient 1D spectrum after shuttling (i.e., with the macrocycle hydrogen-bonded to the ni •− station), and compare it with the experimental transient 1D spectrum at t UV = 4000 ns. The calculated and experimentally observed IR frequencies are listed in Supplementary  Table 2. The good agreement supports the boat-like co-conformation in the final state, which was also derived from the T2DIR spectrum.