Mechanisms of IR amplification in radical cation polarons

Break down of the Born–Oppenheimer approximation is caused by mixing of electronic and vibrational transitions in the radical cations of some conjugated polymers, resulting in unusually intense vibrational bands known as infrared active vibrations (IRAVs). Here, we investigate the mechanism of this amplification, and show that it provides insights into intramolecular charge migration. Spectroelectrochemical time-resolved infrared (TRIR) and two-dimensional infrared (2D-IR) spectroscopies were used to investigate the radical cations of two butadiyne-linked conjugated porphyrin oligomers, a linear dimer and a cyclic hexamer. The 2D-IR spectra reveal strong coupling between all the IRAVs and the electronic π–π* polaron band. Intramolecular vibrational energy redistribution (IVR) and vibrational relaxation occur within ∼0.1–7 ps. TRIR spectra show that the transient ground state bleach (GSB) and excited state absorption (ESA) signals have anisotropies of 0.31 ± 0.07 and 0.08 ± 0.04 for the linear dimer and cyclic hexamer cations, respectively. The small TRIR anisotropy for the cyclic hexamer radical cation indicates that the vibrationally excited polaron migrates round the nanoring on a time scale faster than the measurement, i.e. within 0.5 ps, at 298 K. Density functional theory (DFT) calculations qualitatively reproduce the emergence of the IRAVs. The first singlet (S1) excited states of the neutral porphyrin oligomers exhibit similar IRAVs to the radical cations, implying that the excitons have similar electronic structures to polarons. Our results show that IRAVs originate from the strong coupling of charge redistribution to nuclear motion, and from the similar energies of electronic and vibrational transitions.


Introduction
Electronic transitions are typically promoted by photons with energies greater than 10 000 cm À1 (l < 1000 nm), and the associated electron density redistribution is faster than the response of the nuclei. On the other hand, low energy photons (500-3000 cm À1 ; l z 3000-20 000 nm) excite molecules to higher vibrational states, which are classically described by harmonic motions of nuclei. Electronic excitations generally have oscillator strengths 100-1000Â greater than those of vibrational transitions and UV-vis-NIR absorption bands are far more intense than IR bands in most organic compounds, despite the fact that IR bands are signicantly sharper.
Oxidation of a family of p-conjugated porphyrin molecular wires (Fig. 1a) has been shown to generate radical cations that exhibit IR vibrational transitions with intensities on the same order of magnitude as electronic transitions. [1][2][3][4] The behavior of these species can be explained by treating the charge or 'hole' as a polaron, which is understood as a geometrical reorganization localized over 2-3 porphyrin units. 3 The polaron exhibits a low energy electronic absorption band P 1 in the region 1500-6000 cm À1 corresponding to a transition between the highest occupied molecular orbital (HOMO) and the singly occupied molecular orbital (SOMO). 2,5,6 The IR bands of these cations (Fig. 1b) are much more intense than those of the neutral oligomers; they have molar attenuation coefficients 3 z 10-70 mM À1 cm À1 , far beyond the intensities expected for vibrational transitions. Here we present a study of the origin of this huge IR band intensication in both linear and cyclic p-conjugated porphyrin oligomers.
Similarly intensied IR bands have been observed in the polarons of doped conjugated polymers, 7,8 and mixed-valence coordination complexes, 9 where they are known as 'infrared active vibrations' (IRAVs). This terminology arose because they were attributed to infrared-activation of Raman modes by electric elds. 4,7,10 Their origin is attributed to two processes: coupling between charge redistribution and vibrational motion ( Fig. 2a), or mixing between low-lying electronic and vibrational transitions (Fig. 2b). 8,9,11,12 Either of these mechanisms could explain the IRAVs in doped butadiyne-linked porphyrin oligomers, especially as the energy of the formally electronic P 1 transition is similar to those of the classically vibrational IRAV transitions (Fig. 1b). 3 The radical cations of butadiyne-linked porphyrin oligomers are suitable systems to explore the behavior of IRAVs using advanced ultrafast spectroscopies including two-dimensional infrared spectroscopy (2D-IR) and time-resolved infrared spectroscopy (TRIR). Polarization-sensitive ultrafast spectroscopies 13 have been used previously to explore IRAVs in doped conjugated polymers, and 2D electronic spectroscopy has been used to explore optically generated polaron pairs in conjugated polymers. 14 The discrete molecular nature of our systems allows us to elucidate mechanistic insights into the behavior of polarons on a molecular wire.
2D-IR is a technique used to elucidate equilibrium structural dynamics, vibrational mode coupling and energy transfer in complex molecular structures. [15][16][17][18] It offers simultaneous resolution of the pump and probe axes, as well as ultrafast time resolution (<1 ps), providing a snapshot of the coupling between vibrational modes at a given pump-probe delay time. 19 Recording data at varying delay times between pump and probe pulses extends the utility of the technique, enabling analysis of chemical dynamics and kinetic decay processes. TRIR offers similar benets to 2D-IR, at the expense of a resolved pump axis.
Previous work suggests the polaron (i.e. positive charge) in our systems is delocalized over 2-3 porphyrin units, 3 and that the charge is fully delocalized in the dimer radical cation (Robin-Day class III). 3 Consequently, we propose the linear dimer l-P2 + c as a model molecular polaron, and contrast its properties with those of the cyclic hexamer c-P6$T6 + c (Fig. 2a). The dimer radical cation l-P2 + c exhibits a broad P 1 absorption band of electronic origin in the region >3000 cm À1 ; a band around 2050 cm À1 which is characteristic of the C^C alkynyl stretch, observed as a discrete intensied vibrational-like absorption; and a series of IRAVs in the ngerprint region (1000-1600 cm À1 ).
The structurally well-dened C^C vibrational stretch absorption in l-P2 + c is isolated in energy between the formally electronic P 1 band and the IRAVs in the ngerprint region, providing an unambiguous handle with which to explore the behavior of the polaron and IRAVs. Conversely, c-P6$T6 + c shows a Fano-type anti-resonance at this energy, due to the overlap of the C^C vibrational alkynyl stretch with the lower-energy P 1 polaron electronic band (Fig. 2b). 3 This overlap causes a cancellation of oscillator strengths due to destructive quantum interference between the electronic continuum and discrete vibrational transition. 4,6,20 Experimental

Synthesis
The neutral porphyrin oligomers l-P2 and c-P6$T6 were synthesized as reported previously. 21,22 Decoration of porphyrins with meso-3,5-bis(trihexylsilyl)-phenyl substituents improves solubility and prevents aggregation in the absence of pyridine (exclusion of which is essential to avoid unwanted reactions between pyridine and the radical cations). 3,23,24 Sample preparation for spectroscopic investigation Experiments were performed in an optically transparent thinlayer electrochemical cell (OTTLE) tted with 2 mm CaF 2 windows; 25 path length: ca. 0.2 mm; solvent: CD 2 Cl 2 containing 0.1 M tetra-n-butylammonium hexauorophosphate (Bu 4 NPF 6 ) as supporting electrolyte. l-P2 + c and c-P6$T6 + c concentrations were adjusted to give a maximum optical density of 0.4-0.8 in  the P 2 bands (see Fig. S2 †) by NIR spectroscopy ($800-1000 nm), which is equivalent to optical densities of 0.2-0.5 in the ngerprint region, by adjusting the applied voltage with reference to the known oxidation potentials of the porphyrin radical cations (l-P2 + c E ox,1 ¼ 0.39 V, c-P6$T6 + c E ox,1 ¼ 0.20 V, both referenced to Fc/Fc + , see ESI † for further discussion on sample preparation). 3 This corresponds to a concentration of monocation of $0.1 mM.

UV-vis-NIR and IR spectroscopy
The FTIR and UV-vis-NIR spectra of l-P2 + c and c-P6$T6 + c were reported previously. 3 FTIR spectra of l-P2 and c-P6$T6 were recorded using a FTIR Bruker Tensor 37 and a Shimadzu UV-1800 UV Spectrograph.

Time-resolved and 2D-IR measurements
Time-resolved and 2D-IR spectra were collected using spectrometers at the STFC Rutherford Appleton Laboratory, as described in detail elsewhere. 19 Ultrafast amplied lasers pump optical parametric ampliers to generate the tunable ultrafast pump and probe pulses. Experiments were performed on both ULTRA, a titanium sapphire amplier system with broadband, shorter pulse capability (10 kHz, >50 fs, >300 cm À1 ), and LIFEtime, a ytterbium laser system with narrower band, longer pulses (100 kHz, >180 fs, <200 cm À1 ). While the ULTRA system allows a broad IR spectrum to be probed, LIFEtime uses two IR probe beams, enabling the observation of two narrower separate spectral windows, denoted probe a and probe b. ULTRA's broader bandwidth also permits simultaneous pumping of a broader spectrum, which is important, for example, for simultaneously pumping the modes in the frequency range 1200-1600 cm À1 . Where necessary, we note in each section which system (broadband ULTRA or the narrower-band LIFEtime) has been used. In practice, ULTRA allows the recording of larger pump/probe regions but requires longer acquisition times. Kinetics were extracted from 2D-IR LIFEtime and ULTRA TRIR data.
The pump-probe pulse time-delay is controlled by optical delay stages and the pump and probe beams are focused to <150 and <75 mm diameter, respectively, at the sample. The probe beams are collimated aer the sample and delivered to MCTarray IR spectrometers, providing the probe frequency axis in the spectra.
The difference between the TRIR and 2D-IR experiments is that in 2D-IR, rather than modulating the pump pulse on-off with a chopper, the pump pulses pass through an acousto-optic pulse shaper. 18 This device generates a pulse pair with varying delay, mimicking a rapid scanning interferometer, with phase cycling capability. Collected probe spectra at a range of interpulse delays are Fourier-transformed through this parameter to give the frequency-resolved pump spectrum axis in the 2D-IR spectra.
All samples measured in this set-up had optical densities of 0.2-0.5 in P 1 and ngerprint regions, to allow qualitative comparison between data sets, in lieu of known exact concentrations of monocation species. Polarization experiments were conducted by rotating the pump relative to the probe by a l/2 plate, measuring angles 0 , 54.7 and 90 at each time delay. Randomizing time delays, and recording concurrent spectra of parallel and perpendicular pump-probe orientations at a given delay time, allowed the calculation of anisotropies while minimizing the effect of uctuations in the concentration of the electrochemically generated radical cations.
The polarization dependent response of the detectors was tested using a W(CO) 6 standard, and compared to anisotropy values reported in the literature (Fig. S24 †). 26

2D-IR spectroscopy
(1) Fingerprint region (1200-1600 cm À1 ). Broadband ULTRA was used to record 2D-IR spectra of the ngerprint region (1200-1600 cm À1 ) for a range of time delays (400-1500 fs). The 2D-IR spectra of the oxidized species l-P2 + c and c-P6$T6 + c (at 500 fs, Fig. 3a and b) show signicant coupling between the majority of the modes as evidenced by the appearance of off-diagonal features at early times.
In the spectrum of l-P2 + c the on-diagonal features appear as pairs of signals, consisting of negative ground-state bleach signals (GSB, blue) with associated positive excited-state absorptions (ESA, black) corresponding to n 2 ) n 1 transitions at lower energy. The ESAs are red-shied from the GSB by the vibrational anharmonicity.
The spectrum of c-P6$T6 + c is similar to that of l-P2 + c showing signicant coupling between all IRAV modes in the frequency range 1300-1600 cm À1 . A major difference in intensity is observed between the GSB and ESA signals. In c-P6$T6 + c, the GSBs dominate the spectrum with little evidence of ESA at early times, whereas in l-P2 + c the ESA signals are more pronounced, albeit still weaker than corresponding GSB. At later times the GSB/ESA pair are of similar intensities (Fig. S7 †). The GSB of c-P6$T6 + c are expected to be more intense due to the quadratic dependence of signal intensities on the molar absorption coefficient. 18 The on-diagonal peak at $1480 cm À1 appearing in both monocation spectra (Fig. 3) results from residual neutral species, which show a strong on-diagonal peak at this frequency ( Fig. S6 †).
(2) Triple-bond stretch region (1300-2150 cm À1 ). The IRAV band centered at 2080 cm À1 in l-P2 + c is strong ($20 mM À1 cm À1 ) and easily assigned to the C^C alkynyl stretch (Fig. 1b). The narrowness, isolation and well-characterized nature of this band make it an ideal handle with which to explore the structure-property relationships of the IRAVs. Consequently, 2D-IR experiments were undertaken using the narrower pump bandwidth (full-width half-maximum, FWHM $ 80 cm À1 ) of the LIFEtime instrument centered on the C^C stretch (u pump ¼ 2080 cm À1 , Fig. 4).
A full population time delay series was recorded for probe regions 1300 to 2150 cm À1 , taking advantage of the short acquisition times of LIFEtime. 19 In these experiments, a narrowband pump was centered at 2050-2100 cm À1 , in direct resonance with the C^C stretch of l-P2 + c and with the Fano-type anti-resonance in the P 1 band of c-P6$T6 + c. The molecular responses were probed by selecting two spectral windows: probe a and probe b. Probe a was set to one of four spectral regions centered at $1370 cm À1 , 1520 cm À1 , 1650 cm À1 or 1800 cm À1 . Probe b was set to the on-diagonal region centered at 2025 cm À1 , giving a shared spectral window between each experiment and allowing normalization. In the resulting 2D-IR spectra ( Fig. 4a and b), off-diagonal signals appear immediately (within 200 fs) for all the IRAVs in the FTIR spectra. Each IRAV probed below 1600 cm À1 appears as a GSB with associated ESA as a result of vibrational mode anharmonicity. The GSB signals (blue) are much stronger at earlier times compared to the anharmonic ESA signals (black), commensurate with the 2D-IR spectra shown in Fig. 3.
One major difference between the two species is the absence of a positive ESA signal in the on-diagonal region of the c-P6$T6 + c spectra at early times. We observe a broad positive ESA band that extends across the whole spectrum, which appears to be primarily electronic (like the P 1 band). The absence of signicant ESA signals for c-P6$T6 + c indicates that the IRAV amplication effect is suppressed in the excited polaron. In l-P2 + c, the GSB and ESA are well resolved as a result of the discrete C^C stretch vibrational mode, although there is still a broad positive ESA feature extending across the whole ngerprint region. The presence of this feature, even in the absence of direct P 1 pumping, suggests some degree of vibronic coupling in l-P2 + c, as conrmed by the observation of the coupling of P 1 to all of the IRAVs in TRIR, as discussed below.
The evolution of the 2D-IR signals over time showed little change in the peak positions and shapes, with the exception of the l-P2 + c on-diagonal ESA/GSB pair at u pump ¼ 2070 cm À1 and u probe ¼ 2045/2078 cm À1 which appears to shi to higher frequencies within about 1 ps. To explore this time-dependence  This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 2112-2120 | 2115 of the peak position, a sum of two Voigt proles was tted to the slice at u pump ¼ 2070 cm À1 for the l-P2 + c on-diagonal C^C stretch (Fig. 4c), because Voigt functions generally provide more accurate ts to IR data than purely Lorentzian or Gaussian proles. 27 The GSB Voigt was xed to a FWHM of 41.3 cm À1 centered at 2084 cm À1 (values chosen from initial free ts at later times). The ESA Voigt was allowed to vary in both position and width. The Voigt prole peak positions for the ESA, n 2 ) n 1, shi to higher frequency over time, resulting in a decrease in the apparent anharmonicity Dn from 60 cm À1 to 20 cm À1 (Fig. 4d). This blue shi of $40 cm À1 follows a mono-exponential decay with a lifetime of 0.48 AE 0.01 ps. The FWHM of the ESA stays fairly consistent over time around 50-55 cm À1 . It is not clear whether this evolution reects a true decrease in anharmonicity over time, or the decay of overlapping ESA bands.

Kinetic analysis
The time-resolved nature of the 2D-IR data presented in Fig. 4 allows the decay of the GSB and ESA to be tted to mono, bi or tri-exponential functions, convoluted with the instrument response function (IRF), providing information on the lifetimes of vibrational/electronic excited-states. 28 These functions are hereaer referred to as mono-, bi-or tri-exponential, for simplicity. The evolution of the spectral features is complicated by large initial GSBs, multiple recovery processes and crowded spectra, especially at early times (time-resolved surface plots are presented in Fig. S14-S23 †). The decay proles are categorized into four types: (1) on-diagonal GSB, (2) off-diagonal GSB, (3) ESA peaks (anharmonic bands of the GSBs) and (4) the broad ESA stretching across the whole spectrum (most visible around 1550-1750 cm À1 ). In order to describe the salient features of the spectra along with their time dependence as simply as possible, we decided to t the observed peaks to as few shared time constants as possible. The tting process is described in detail in the ESI (see eqn (S1), Fig. S9, S10, Tables S3 and S4 †).
We determined that the kinetic data for each species (l-P2 + c or c-P6$T6 + c) can be modeled in terms of three decay times, s 1 , s 2 and s 3 . Here we summarize the features of these decay processes and their associated states: (a) s 1 : intramolecular energy redistribution. This is a very fast process (l-P2 + c: s 1 ¼ 0.15 AE 0.02 ps; c-P6$T6 + c: s 1 ¼ 0.29 AE 0.01 ps) and it is mainly observed through the decay of the GSB (ondiagonal for l-P2 + c; both on-and off-diagonal for c-P6$T6 + c). It sits within the instrument response, but the good t to the decay prole at early times for every on-diagonal GSB and the agreement with previously reported values of the instrument response for this spectrometer 19 (s $ 200 fs) enable us to condently detect this fast decay component. s 1 appears as a rise-time for the ESA signals that decay with time-constants s 2 and s 3 (Fig. S11-S13 †). This process is consistent with intramolecular vibrational energy redistribution (IVR), as described by Rubtsov and coworkers in their work on acetylproline-NH 2 and relaxation-assisted 2D-IR spectroscopy (RA-2D-IR). [29][30][31] (b) s 2 : relaxation from an "electronic" excited state (l-P2 + c: s 2 ¼ 0.92 AE 0.01 ps; c-P6$T6 + c: s 2 ¼ 0.74 AE 0.07 ps). This process is mainly observed through the decay of the extremely broad featureless ESA band extending from 1300-2000 cm À1 ; in l-P2 + c, this decay is also detected as a component in the GSB. The resemblance of this ESA to the P 1 absorption band suggest that this decay originates from a nominally electronic excited state that lacks the IRAVs of the P 1 ground state.
(c) s 3 : relaxation from a "vibrational" excited state (l-P2 + c: 0.3 ps). This component appears in most of the signals and it is the dominant relaxation process for the sharper ESA signals. It resembles a normal vibrational relaxation process and it originates from a state populated by IVR that shows ESA/GSB pairs of similar intensity.

TRIR spectroscopy and anisotropy
A series of TRIR spectra of l-P2 + c and c-P6$T6 + c were recorded by pumping the regions around 2100 cm À1 , 2500 cm À1 or 3250 cm À1 and probing 2100 cm À1 or the ngerprint region. In the ngerprint region, the TRIR spectra of both l-P2 + c and c-P6$T6 + c are similar for times >1 ps, irrespective of whether the pump excites the C^C stretch (in l-P2 + c), the Fano-type antiresonance (in c-P6$T6 + c) or P 1 polaron band (both) (Fig. 5a  and b). Higher frequency pumps in general lead to more intense initial bleach features, disappearing rapidly within 1 ps. The presence of such features is less pronounced when the pump is applied at 2100 cm À1 .
Polarization experiments were performed to study the relative orientations of the IRAV modes. Experiments of this type are oen used to establish the relative orientation between pumped and probed processes. 32,33 The vibrational anisotropy r was calculated using eqn (1). 13,33 In isotropic solution, the anisotropy is expected to be in the range À0.2 < r < 0.4, considering extremes with the transition dipole moment of induced absorption perpendicular or parallel to the excitation, respectively.
TRIR spectra using the magic angle (54.7 ) orientation DA mag , were acquired and served as a check of the experimental setup. Measurements with this orientation obeyed the expected relation (eqn (2)) to data obtained from parallel DA k and perpendicular DA t setup (Fig. S26 †).
Since l-P2 + c and c-P6$T6 + c are large molecules with molecular weight of 4.0 kDa and 11 kDa, respectively, no anisotropy decay due to rotational reorientation is expected on the experimental time scale.
Anisotropy of all TRIR signals in the ngerprint region against the time for both l-P2 + c and c-P6$T6 + c are plotted in Fig. 6a and b, respectively, showing no signicant change over the time. Due to instrument response effects at early times, the anisotropy is analyzed at probe delays >0.5 ps.
Investigation of all probe regions with a signal-to-noise above a selected threshold (Fig. S27-S32 †) showed that the anisotropy values for each ESA/GSB pair have similar values in the range r ¼ 0.28-0.38 for l-P2 + c and r ¼ 0.03-0.12 for c-P6$T6 + c ( Fig. 5c and d).
The fact that the anisotropies are independent of pump frequency allows the values to be averaged across the whole spectrum for each system, resulting in anisotropies of r ¼ 0.31 AE 0.07 for l-P2 + c and r ¼ 0.08 AE 0.04 for c-P6$T6 + c, both these average values are constant over time, as seen in Fig. 6.

Excited states of neutral oligomers
Electronic excitation of neutral porphyrin oligomers leads to population of the S 1 excited state. Probing the IR region of S 1 excited states reveals absorption spectra similar to those of the radical cations (Fig. 7), implying that the photoexcited state has a similar electronic structure to the polaron. A similar congruence between excited states and polaronic states has been observed in the excited states of polymer blends, colloidal quantum dots and perovskites. 34,35 There appears to be a broad electronic absorption band at 2000-2400 cm À1 , together with an intensied C^C stretch signal at 2050-2100 cm À1 , and other IRAVs in the nger print region at 1300-1600 cm À1 . The GSBs are very weak, since the ground state IR absorption is weak in the neutral molecules. In contrast, the ESAs are relatively strong, consistent with the presence of IRAVs in the S 1 excited state of the neutral porphyrin oligomer. Similar intense IR transitions have been observed in the neutral excited states of donor-acceptor systems. 36

DFT calculations
We sought to assign the observed IRAVs by carrying out DFT calculations using the range-separated LC-uPBE functional [37][38][39] and the 6-31G* basis set (which method was empirically found to correlate well with experimental observations in porphyrin oligomers monocations) 3 using the Gaussian09 soware. 40 Models of l-P2 + c and c-P6$T6 + c (without solubilizing groups in l-P2 + c and without solubilizing groups and template in c-P6$T6 + c) were built and geometries were minimized with charge 1+ and doublet multiplicity. Frequency calculations on the neutral and cationic models correctly predicted that several IR absorptions are intensied by a factor of 50-100 in the cations, including the C^C bond stretch and several bands in the ngerprint region ( Fig. 8a and b).
The dipole derivatives of the modes with the most intensied absorptions show 100% alignment with the C^C axis along the length of the l-P2 + c molecule (Fig. 8c, for more details see ESI Section 5 †). The DFT calculated spectra do not exactly match the experimental spectra suggesting a dissimilarity between the modes in neutral and oxidized species as seen in doped conjugated polymers. 41

Discussion
The 2D-IR spectra reveal strong coupling in the radical cations l-P2 + c and c-P6$T6 + c. All of the IRAVs in the ngerprint region are coupled to the C^C stretch vibration and to the P 1 polaron band, as evidenced by the appearance of 2D-IR off-diagonal Fig. 6 Average anisotropy of all analyzed signals (greyed areas in Fig. 5a and b) of l-P2 + c (a) and c-P6$T6 + c (b) pumped both at 2100 cm À1 and 3250/2500 cm À1 as a function of probe time delay. signals at early times ( Fig. 4 and S14-S23 †). The TRIR show that pumping the C^C stretch or the higher energy polaron P 1 bands yields identical TRIR spectra. The spectra do not exhibit signicant differences in kinetic response or in anisotropy, suggesting that the species generated by excitation of a classically vibrational mode (C^C stretch) or a classically electronic transition (the polaron band) are identical, which conrms that the polaron absorption and vibrations must be strongly coupled. This result conrms that the Born-Oppenheimer approximation is an unsuitable framework from which to consider the nature of substantially delocalized polarons.
The kinetic evolutions of the 2D-IR spectra t a model with just three decay times: s 1 for IVR, s 2 for relaxation from an "electronic" excited state and s 3 for relaxation from a "vibrational" excited state. This "electronic" excited state is unusual: it exhibits a featureless ESA band, extending from 1300-2000 cm À1 , with no apparent IRAVs in c-P6$T6 + c. One explanation for this lack of IRAVs might be that they are suppressed by the same Fano-type anti-resonance that occurs with overlap of electronic and vibrational transitions in the ground state (Fig. 1). 3 The TRIR anisotropy measurements show similar anisotropies for all of the signals in the ngerprint regions of l-P2 + c and c-P6$T6 + c ( Fig. 5 and 6). The anisotropy value of 0.31 found for l-P2 +c is not far from the theoretical limit of 0.4 expected for a simple linear transition dipole, while the value of 0.08 found for c-P6$T6 +c is near the limit of 0.1 expected for 2D delocalization. 22 l-P2 + c is a linear molecule and its high TRIR anisotropy demonstrates that the intensied vibrations can be assigned to transitions parallel with the length of the molecule, i.e. parallel to the P 1 transition and C^C stretch vibrations.
At rst sight, the low anisotropy measured for c-P6$T6 + c, which implies that the vibrationally-excited polaron is delocalized around the whole nanoring, is surprising because previous results indicated that the polaron is only delocalized over 2-3 porphyrin units. Together, these results imply that, on IR-excitation, the polaron migrates around the circumference of the nanoring faster than the TRIR measurement, i.e. within 0.5 ps, at 298 K. In contrast, polaron migration is slow on the timescale of linear electronic and vibrational measurements ($fs) at 298 K, and on the EPR timescale ($100 ns) at 80 K. 3 The time-independence of the anisotropies supports the assignment of IRAVs to being within the porphyrin framework, as this assignment xes the relative orientations of the pumped and probed transitions. This contrasts with systems that have coupled bonds capable of rotating in relation to each other, which in turn causes a change in anisotropy over time. 42 The apparent observation of IVR effects in l-P2 + c is also consistent with the assignment of the IRAV modes to transitions along the C^C axis of the molecule, as IVR is known to occur efficiently between modes having strong spatial mode overlap (i.e. between modes that share vibrating atoms). 31 The evidence presented above implies that all the IRAV modes in l-P2 + c are aligned along the long axis of the butadiynecontaining skeleton, i.e. along the porphyrin-porphyrin axis and the C^C stretch direction. This, together with the assignment of ngerprint vibrations by DFT, is consistent with the polaron redistribution mechanism as proposed by Zamadar et al. (Fig. 2a) and the explanation for previously observed infrared 'marker bands' in porphyrin monomers where inten-sied infrared transitions are assigned to contracting and expanding breathing modes with transition dipole moments passing through opposed meso positions. 12,43 The intensication in those monomers arises as the contraction of one side of the porphyrin results in charge redistribution to minimize antibonding interactions on the contracted side. DFT calculations of l-P2 + c support the assignment of the intensied vibrations to similar contracting and expanding modes, and the calculated dipole derivatives of the most intensied vibrations are oriented along the long axis of l-P2 + c (Fig. 8). The coupling between vibrational modes and charge redistribution can be appreciated by calculating the distribution of the SOMO at distorted geometries, at which the molecule is mechanically compressed/expanded during a vibration to the extent of 10 times the energy of the rst vibrational transition (Fig. 8d). The mechanism of vibronic coupling can thus be explained in the case of l-P2 + c: as one porphyrin ring contracts, the anti-bonding orbital lobes are brought closer together. In response to this, the mobile polaron redistributes to the expanded ring, causing a large change in the dipole moment. The electron density in these systems is effectively moving from one porphyrin ring to another, in a way analogous to an electronic transition, providing an explanation for the exceptionally high intensities observed for these vibrations. This mechanism relies on the polaron being mobile along the oligomer backbone and redistributing in response to vibrations. It follows that the polaron must be mobile in c-P6$T6 + c, as conrmed by the observed low anisotropy.
The delocalization length of polarons in conjugated polymers tends to be reduced by strong electron-phonon coupling. 11,44,45 The assignment of the IRAVs (by denition strongly coupled phonon modes) to those of breathing modes across two porphyrin rings is consistent with the previously reported delocalization length of 2-3 porphyrin units in the radical cations of butadiyne linked porphyrin oligomers. 3 DFT calculations predict a huge intensication of several vibrational bands, but they fail to reproduce the observed pattern of activated vibrations in the ngerprint region, even for the simpler system of l-P2 + c. DFT predicts only two IRAVs in the window 1100-1800 cm À1 compared to at least ve modes observed in the experimental IR spectrum.

Conclusions
Time-resolved IR spectroscopies have been used to probe the origins of IRAVs in the radical cations of porphyrin oligomers. 2D-IR studies of two compounds, l-P2 + c and c-P6$T6 + c, show that vibrational coupling occurs at early times between all of the IRAVs and with the P 1 polaron bands. The similarity between spectra arising from pumping in the classically vibrational C^C stretch and those arising from pumping the P 1 polaron bands demonstrates the presence of strong vibronic coupling between the P 1 band and IRAV modes. This result, in combination with results from DFT calculations and polarization-dependent TRIR experiments, suggest the IRAV modes have a substantial vector component in the direction of the C^C backbone of l-P2 + c. This assignment is consistent with the idea that IRAVs originate from polaron redistribution in response to, and on the time scale of, the vibration, which amplies the transition dipole moment of the vibrational mode.
Coupling between vibrational modes and charge transport is frequently an important factor determining the rate of electron transfer through molecular wires in single-molecule electronic devices. [46][47][48] If we assume that the vibrational modes in l-P2 + c are similar to those in c-P6$T6 + c, then the anisotropy of $0.08 recorded for c-P6$T6 + c suggests that, in the vibronic excited state, the polaron is mobile along the length of the molecular backbone, consistent with previous discussions of polarons in polymer chains. 11 Author contributions WJK, MJ and MDP collected and analyzed the 2D-IR and TRIR data. MDP synthesized the c-P6$T6. GMG, IVS, PMD and MT helped to design and implement the 2D-IR and TRIR experiments. MDP, AWP and HLA initiated the project. MJ and MDP carried out the computational work. All authors contributed towards interpretation of the data. WJK and MJ wrote the manuscript, with contributions from all authors.

Conflicts of interest
There are no conicts to declare.