Complexity surrounding an apparently simple Fermi resonance in p -fluorotoluene revealed using two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is a powerful tool allowing overlapped features in an electronic spectrum to be separated, and interactions between vibrations and torsions to be identified. Here the technique is employed to assign the 790–825 cm -1 region above the origin of the S 1  S 0 transition in para -fluorotoluene ( p FT), which provides insight into the unusual time-resolved results of Davies and Reid [Phys. Rev. Lett. 109 , 193004 (2012)]. The region is dominated by a pair of bands that arise from a Fermi resonance; however, the assignment is complicated by contributions from a number of overtones and combinations, including vibration-torsion (“vibtor”) levels. The activity in the 2D-LIF spectra is compared to recently reported zero-electron-kinetic-energy (ZEKE) spectra [Tuttle et al. J. Chem. Phys. 146 , 244310 (2017)] to arrive at a consistent picture of the energy levels in this region of the spectrum.


I. INTRODUCTION
Understanding the internal energy level structure in molecules is a key quest of chemical and molecular physicists. In particular, vibrations underpin our knowledge of the motion of the nuclei, which drives the making and breaking of bonds in chemistry. Chemistry can be further affected by the rotation of the molecule and the torsional motion of hindered rotor groups. All of these motions can couple, although this coupling can usually be treated as a perturbation on the overall vibrational energy structure.
In previous work, we have studied the lower-wavenumber regions of the S1  S0 transition in parafluorotoluene (pFT) using resonance-enhanced multiphoton ionization (REMPI) and zero-kineticenergy (ZEKE) spectroscopy; 12,13,17,20 while both we 13,20 and the Lawrance group 16 have also employed the technique of two-dimensional laser-induced fluorescence (2D-LIF). 21 The low-wavenumber region has been shown to be rich in interactions, involving torsional, vibrational and vibrational-torsional levels. (Since we work under jet-cooled conditions, and since we only partially resolve rotational structure, we do not directly consider interactions involving rotations.) Earlier work on the S1  S0 transition in pFT has been reported by Cave and Thompson 22 , Cvitaš and Hollas 23 , Seliskar et al. 24 and Okuyama et al. 25 The latter two studies presented laser-induced fluorescence (LIF) spectra under jet-cooled conditions, giving assignments of some of the vibrational bands. Some of the low-wavenumber bands have been reassigned to vibration-torsion (vibtor) levels by Zhao,3 and confirmed in recent work by our group 15 and that of Lawrance et al. 16 In an earlier paper from our group, 14 we had used the assignments of Okuyama et al. 25 in assigning ZEKE spectra recorded via various levels, unaware that some of the assignments of the lower-wavenumber features had been superseded by those in Zhao's thesis 3 -some of those latter reassignments are implicit in Ref. 2. In our earlier work, 14 we assigned the two levels at~800 cm -1 to different totally-symmetric fundamentals on the basis of Okuyama et al's work, 25 but one of these was reassigned to an overtone level in Ref. 26. In Ref. 27, time-resolve photoelectron spectroscopy (tr-PES) was employed, and these same two features were assigned as a Fermi resonance (FR), involving the same levels noted in Ref. 26, although it was suggested that at least one other state might be interacting.

II. EXPERIMENTAL
The 2D-LIF apparatus has been described recently. 13 The vapour above room temperature parafluorotoluene (99% purity, Alfa Aesar) was seeded in~5 bar of Ar and the gaseous mixture passed through a General Valve pulsed nozzle (750 μm, 10 Hz, opening time of 180-210 μs) to create a free jet expansion. This was intersected at X/D~20 by the frequency-doubled output of a single dye laser, operating with C540A. The fluorescence was collected, collimated and focused onto the entrance slits of a 1.5 m Czerny Turner spectrometer (Sciencetech 9150) operating in single-pass mode, dispersed by a 3600 groove/mm grating, and~300 cm -1 windows of the dispersed fluorescence collected by a CCD camera (Andor iStar DH334T). At a fixed grating angle of the spectrometer, the excitation laser was scanned, and at each excitation wavenumber the image was accumulated for 2000 laser shots. This produced a 3D surface of fluorescence intensity versus the excitation laser wavenumber and the wavenumber of the emitted and dispersed fluorescence, termed a 2D-LIF spectrum. 21 We have also recorded separate dispersed fluorescence (DF) spectra with higher averaging to get better signal to noise than simply taking a vertical slice through the 2D-LIF image. These DF spectra were recorded with the same spectrometer as for the 2D-LIF spectra, and were recorded three times accumulating over 5000 shots each time, and an average taken of these.

III. RESULTS AND ASSIGNMENTS
A. Nomenclature and labelling

Vibrational and Torsional Labelling
Since neither Wilson 28 12,20 ) Since the G12 molecular symmetry group (MSG) is appropriate for vibtor levels, we shall use these symmetry labels throughout.
In addition, torsional levels will be labelled via their m quantum number. (The reader may find it useful to refer to previous work 9, 10,11,15,18 if they are not familiar with these labels.) The correspondence between the C2v point group labels and the G12 MSG ones are given in Table I. To calculate the overall symmetry of a vibtor level, it is necessary to use the corresponding G12 label for the vibration, and then find the direct product with the symmetry of the torsion ( Under the free-jet expansion conditions employed here, the molecules are all expected to be cooled to their zero-point vibrational level and thus all S1  S0 pure vibrational excitations are expected to be from this level. In contrast, owing to nuclear-spin and rotational symmetry, the molecules can be in one of the m = 0 or m = 1 torsional levels. 18,34

Coupling and transitions
If an anharmonic fundamental is close in wavenumber to one or more combination or overtone vibrational levels that has the same overall symmetry, then "off-diagonal" anharmonic interactions can occur. The non-interacting levels are termed zero-order states (ZOSs), and their interaction leads to the formation of eigenstates that are linear combinations of these, and will be at different wavenumbers to the original ZOSs. 31 The simplest example of two interacting states is the classic Fermi resonance, 35 while for more than two levels we term this a complex Fermi resonance. For molecules that contain a hindered internal rotor, then the ZOSs can also be torsional or, if vibration-torsional coupling occurs, "vibtor" levels. The end result of such interactions is the formation of eigenstates which facilitate delocalization of energy through widespread motion of the molecule. Such couplings are only expected to be significant for small changes, v  3, of the vibrational quantum number, and also for changes, m, of 0, ±3 or ±6 in the torsional quantum number in descending order of likely strength. 10,15,18,36,37 In electronic spectroscopy, if we assume a non-coupled picture initially, then a zero-order vibrational, torsional or vibtor level can be bright (i.e. it has a significant transition intensity) or dark (i.e. it has no, or a very small transition intensity); these are often termed a zero-order bright (ZOB) state and a zeroorder dark (ZOD) state, respectively. Following interaction, the resulting eigenstates will be composed of mixtures of ZOB and ZOD state character and so more transitions will become observable in the spectrum as a result of the interaction.
When designating excitations, we shall generally omit the lower level, since it will be obvious from the jet-cooled conditions; similarly, for emissions, we shall omit the upper level, as that will be obvious from the excitation and context. In the usual way, vibrational transitions will be indicated by the cardinal number, i, of the Di vibration, followed by the number of quanta; torsional transitions will be indicated by m followed by its value. Finally, vibtor transitions will be indicated by a combination of the vibrational and torsional transition labels. If no m values are specified, then the transition refers to m = 0 and m = 1 levels, whose transition wavenumbers are expected to be coincident at the present resolution. We give two examples: (i) When accessed via emission from the origin, 201m2 represents an excitation from the S0 zero-point m = 1 level to the m = 1 level in the S1 state, followed by emission to the m = 2 level of the D20 level in S0; and (ii) (29 2 , 91) represents a dual excitation from the m = 0 and m = 1 levels of the S0 zero-point level to both m levels of the S1 state D29 overtone level, followed by dual emission to the corresponding m levels of the D9 level in the S0 state -note that these transitions will be coincident with our resolution.
The wavenumbers of the levels will be given with respect to the relevant zero-point level in each state, but noting that some excitations will originate from the m = 1 level in S0 and those transition energies are given with respect to that level, as usual; the S1  S0 origin is located at 36860.0 cm -1 (Ref. 16).
Very frequently, the most intense transition is expected to be that for which no change in the vibrational or both vibrational and torsional quantum numbers occurs; these will be designated v = 0 and (v, m) = 0 transitions. As has become common usage, we will generally refer to a level using the notation of a transition, with the level indicated by the specified quantum numbers, with superscripts indicating levels in the S1 state and subscripts indicating levels in the S0 state; since we will also occasionally be referring to levels in the ground state cation, D0 + , we shall indicate those levels with a preceding superscripted + sign. Also, the eigenstates will usually be referred to by the dominant contribution from one of the ZOSs, with the context implying if an admixture of other ZOSs is present. 2D-LIF band positions can be indicated by a pair of (excitation, emission) wavenumbers, and corresponding transitions similarly.

Overall comments on the S1  S0 spectrum
In Figure 1, we show an overview of the excitation spectra across the region of interest recorded using both REMPI and fluorescence spectroscopies. To lower wavenumber it may be seen that there are two dominant features at 797 cm -1 and 804 cm -1 , with two other weaker features to higher wavenumber (one of which is not so clear in the integrated image, but features are evident in the 2D-LIF image in Figure   2). In Ref. 12 we discussed the assignment of this spectrum in detail, with the aid of ZEKE spectra and calculated vibrational wavenumbers, although some of the assignments were tentative. As noted above, the two intense bands have been assigned as arising from eigenstates that are dominated by one of 9 1 and 29 2 (Refs. 12, 26 and 27). Further, our ZEKE study 12 indicated a number of contributions to this region from overtones, combinations and vibtor levels, with many of these involving the three main levels (14 2 , 29 1 and 11 1 ) that give rise to features seen in the spectrum at~400 cm -1 , whose assignments were deduced from ZEKE 15,16 and, more recently, 2D-LIF spectra. 20 As well as 29 2 , the other overtones and combinations of these three levels, and also transitions involving combinations with the vibtor level 14 1 m 6(-) , and possibly others, are expected. In the ZEKE study 12 it was also concluded that, as well as spectroscopy will provide further evidence for or against these assignments and, as will be seen, give further insight into the activity and coupling.
In Figure 2 we present an overview of the recorded 2D-LIF spectrum across the 790-825 cm -1 excitation region. Vertical integration of the whole of this window of the spectrum gives a standard "LIF" spectrum, which is shown in Figure 1 where it is compared to the REMPI spectrum; it may be seen that both traces are very similar, indicating that the activity in this window of the 2D-LIF spectrum is a good representation of the overall activity of the transition. The 2D-LIF spectrum also shows a wealth of structure in the 0-300 cm -1 region, which is shown in Figure 3. In Figure 2, it will be noticed that there are two main vertical stripes of activity, corresponding to excitation via each of the two most intense bands in Figure 1 -this is in line with emissions arising from eigenstates that are composed of the same ZOSs. However, there are also cases where there is a pronounced difference in activity following excitation of one band and not the other, and such features are expected not to be associated with the two main eigenstates, but to arise from separate overlapping transitions. In addition, there is a third main stripe of emission activity to higher excitation wavenumber, with some common activity across the three main excitation features, with some weaker bands in between. Since we already have the assignments from our earlier ZEKE study, 12 we ought largely be able to assign the 2D-LIF spectrum by reference to the known S0 and S1 vibrational wavenumbers, 16,20,33 together with a knowledge of the positions of the torsional and low-wavenumber vibtor levels in the different states. 15,16 Although we can obtain a conventional DF spectrum at a particular excitation wavenumber by taking a vertical cut through the 2D-LIF spectrum, we have often recorded such DF spectra separately, covering a wider range of emission wavelengths with an increased number of shots. In Figures 4-8 we show expanded sections of the 2D-LIF spectra, together with corresponding sections of the DF spectra, recorded via the centre of each of the 797 cm -1 and 804 cm -1 bands. Much of the activity is very similar from both of the bands, again confirming that these mainly arise from eigenstates that are largely made up from the same ZOSs.

Assignment of the main spectral activity
In our earlier ZEKE study, 12 a selection of spectra were recorded at excitation positions across the observed REMPI bands that are shown in Figure 1. From the changing activity, the make-up of the S1 levels was deduced. However, the activity was not always as expected and the present 2D-LIF spectra should be able to shed some light on this. If we assume that we can just sum the band positions of the levels seen at 400 cm -1 , then we can predict the excitation wavenumber at which we expect to see the relevant combination and overtone 2D-LIF bands. It is likely, however, as the ZEKE study confirmed, that levels are interacting with each other and also with the bright fundamental, 9 1 , that appears in this spectral region; as such, the excitations could appear at shifted positions. We will now briefly discuss both the positions of the observed 2D-LIF bands, and their activity.
Previous ZEKE, 12 fluorescence 26 and tr-PES 27 studies agree that the two main excitation bands at 797 cm -1 and 804 cm -1 ( Figure 1) correspond to eigenstates that largely correspond to contributions from 9 1 and 29 2 , and this is confirmed by the present DF and 2D-LIF spectra in Figure 5. At first sight, the v = 0 region shown at the top of Figure 5 is perplexing, as it indicates large contributions from 29 2 to both levels, with the spectra being consistent with those of Zhao and Parmenter. 26 Similar behaviour was seen in the ZEKE spectra, 12 but an explanation was found in that the Franck-Condon factors (FCFs) when exciting via 9 1 were non-diagonal. Thus, it was observed that the + 9 2 ZEKE band was the most intense when exciting via the 797 cm -1 eigenstate, supporting the fact that it was dominated by 9 1 , while the 804 cm -1 eigenstate is dominated by 29 2 . Similar behaviour is seen here -see next paragraph. Also, there are contributions from other ZOSs to the spectrum, some of which may contribute to form the main eigenstates -see later in this subsection. Additionally, the ZEKE study 12 concluded that there were two overlapping features at 818 cm -1 : 11 2 and 12 1 14 1 , but that these are not obviously in FRthese will be discussed later. Many of the other strong features in the 2D-LIF spectrum in Figure 2 may be deduced to arise from FC activity of the four main eigenstates dominated by each of 9 1 , 29 2 , 11 2 and 12 1 14 1 , with particularly rich structure apparent at both of the 797 cm -1 and 804 cm -1 excitation regions.
Indeed, occasionally the strong FC activity for certain features can obfuscate the assignment of the v = 0 band; however, considering the activity across the spectrum enables this to be achieved.
We first look at the v = 0 region of the 2D-LIF spectrum, at the top of Figure 5, together with the relevant sections of the DF spectra. The three pairs of bands here may be seen to correspond to three main emissions from each of the excitations, which may be assigned 16 to 142 (823 cm -1 ), 91 (843 cm -1 ) and 292 (850 cm -1 ). Furthermore, it is also pertinent to observe that in the S0 state, the two eigenstates made up from 91 and 292 are at 843 cm -1 and 850 cm -1 , while in the D0 + state, the two eigenstates are at 824 cm -1 and 832 cm -1 . 12 These levels are all close enough to be expected to be in Fermi resonance in each of the three electronic states, potentially complicating conclusions from DF or ZEKE spectroscopy regarding the make-up of the S1 eigenstates. This means that, in any of the electronic states, the given labels merely reflect the dominant contribution of a ZOS to the eigenstate. However, we have found that emissions from totally-symmetric fundamentals, such as 11 1 (see Ref. 20), and levels in other unpublished work, give a higher intensity for the 91 band than the 92 and 142 bands. From such spectra, we can conclude that the 843 cm -1 S0 eigenstate is made up of predominantly 91 character, but with some contribution from 292, and that the 850 cm -1 S0 eigenstate is dominated by 292, with some contribution from 91. It is difficult to be sure of the mixings with the 142 state, for which the emissions could also simply be arising from FC activity from the totally-symmetric fundamentals.
The immediate observation from Figure 5 is that the activity of the main emission bands is very similar, with the 850 cm -1 emission band dominating from both the 797 cm -1 and 804 cm -1 levels. If the ZOSs were not interacting in the S0 state, and if the FC intensity is dominant in the v = 0 region, then we would expect the emissions to the two S0 levels to switch intensity from the two S1 eigenstates, in contrast to the observations in Figure 5. As can be seen from Figure 7, however, the (9 1 , 92) emission is much stronger than (29 2 , 92), and hence the v = 0 intensities in Figure 5 are somewhat misleading.
Overall, we concur with the previous conclusions from our ZEKE work 12 and the tr-PES study 27 that the main S1 state eigenstates are each dominated by 9 1 and 29 2 to a similar extent, but that, as implied above, there is also the possibility of further interactions involving other ZOSs expected to be in this wavenumber region -see below.
A number of 2D-LIF bands appear with intensities that suggest they do not simply arise from FC activity. For example, we see significant non-totally-symmetric 291 and 281 bands ( Figure 4) when exciting at 797 cm -1 , with the (totally-symmetric) 281291 band being seen in Figure 5 -this is similar to behaviour seen when exciting via the origin (see Ref. 20). As we noted in Ref. 20, some caution is merited with the intensity of the 281 band, as this is at the expected wavenumber of the totally-symmetric 181201 level, which was concluded to be FC active via the origin, and likely also to be active via totally symmetric fundamentals; the 281291 band may also therefore have a contribution from 181201291. It is clear that the 291 band arises from Herzberg-Teller (HT) vibronic activity, and this would also apply to 181201291. Since these bands are seen to be present, but much weaker, when exciting at 804 cm -1 , the HT activity appears to be associated with the smaller 9 1 contribution to the latter eigenstate.
We now highlight the 1636 cm -1 emission band (Figure 7), which appears strongly when exciting at 804 cm -1 , but is much weaker when exciting at 797 cm -1 . This is assigned to 144, and indicates that the 14 2 /29 1 overlap seen at~400 cm -1 is analogously present at 804 cm -1 , now involving 14 4 and 29 2 ; these are shifted up in wavenumber from the expected excitation positions, and this is consistent with interactions with 9 1 . We might, therefore, also expect to see one or more 2D-LIF features corresponding to 142291, which is expected at 1248 cm -1 . We see 142291 clearly at 1243 cm -1 when exciting via 29 1 (see Ref. 20), but unfortunately such features are likely to be obscured by the strong 51 band seen in this region of the present spectra (see Figure 6), precluding definitive deductions regarding 142291 activity.
Other excitations being seen to contribute to the~400 cm -1 region 20 were 14 1 m 6(-) and 14 1 20 2 m x and so we might expect to see combinations of these with 14 2 , 29 1 and 11 1 . (Note that the assignment of the m level associated with 14 1 20 2 was unclear, but was thought to be 1 or 2 -see Ref. 20.) Considering this, 143m6(-) would be expected at 1443 cm -1 , and can be assigned to a band seen at 1449 cm -1 when exciting via 804 cm -1 (see Figure 6) which appears more weakly at 797 cm -1 ; 142291m6(-) is expected at 1043 cm -1 , and can be assigned to a weak feature seen at 1040 cm -1 when exciting via 804 cm -1 (see Figure  5). The 111141m6(-) vibtor band is expected at 1072 cm -1 (which is at the same wavenumber as a weak feature seen 20 when exciting at 398 cm -1 ). Although a clear emission band is seen at this wavenumber ( Figure 5), it is unexpectedly only seen when exciting at 797 cm -1 -indeed, this band will be assigned to a different transition below.
We note that the 111 band is more intense via the 804 cm -1 eigenstate (Figure 4), and associate this with additional FC activity from the various other levels contributing to this feature, as well as that from the 9 1 ZOS contribution.
There are three other ZOSs expected to contribute to this spectral region: 11 2 , 11 1 14 2 and 11 1 29 1 . We see a clear (11 2 , 112) band at (818, 906) cm -1 (Figure 8) which is slightly shifted up from the expected excitation position of~816 cm -1 . Exciting at 818 cm -1 , it is also possible to see extremely weak 111 activity on expanded views of Figure 8, but more sizeable 113 activity is evident. There is some 112 activity when exciting at 797 cm -1 , with very faint activity at 804 cm -1 , which is consistent with FC activity.
Weak 111291 emission is seen at 877 cm -1 , as expected (see Figure 8), and has two islands of activity: one at 809 cm -1 , and one at 797 cm -1 . The latter is likely related to the 291 HT activity at that wavenumber, suggesting the former is the v = 0 band, and this is close to the expected position. Note that the 11 1 29 1 level is of a1 symmetry, and so unable to couple to the 9 1 band anharmonically, explaining its weakness; there are, however, possibilities of other vibtor levels with which it could interact and this, together with intrinsic anharmonicity in forming the combination band, could explain the slightly shifted position.
The 111142 band is expected at~1277 cm -1 , and clear features are seen at 1276 cm -1 (see Figures 6 and 8). There are four islands of activity, at 797, 804, 811 and 818 cm -1 , with the first two being far stronger than the latter two. We note that the latter may contain some contribution from 293, which can be seen when exciting via 29 1 (Ref. 20), but this is expected to be significantly weaker for the present excitation, owing to symmetry. The ZEKE spectra 12 show + 11 1 14 2 activity at 804 and 818 cm -1 , but not obviously so at 797 cm -1 . One complicating factor is FC activity from the two main 797 cm -1 and 804 cm -1 eigenstates, and it can be seen that there are clear 142 bands at these excitation positions ( Figure 5), and so it is not unexpected to see 111142 bands also; hence, these are assigned to FC activity, together with the (818, 1276) cm -1 band. These arguments are also supported by the clear FC activity from 182 at the two lower wavenumber positions (see Figure 5); this emission is also seen weakly when exciting at 818 cm -1 -see Figure 8). From this, we conclude that the 111142 band is demonstrating FC activity from 9 1 , 29 2 and 12 1 14 1 /11 2 . We thus conclude that the band at (811, 1276) cm -1 is likely to be the v = 0 band. The reasons noted above for the very weak 111291 band also apply to 142291 and explain why it is not obviously seen in our spectra, although, as noted, it could be overlapped with the strong 51 band. These reasons do, however, makes it surprising that the 141291m6(-) band is seen at 1042 cm -1 , suggesting that this could arise by other coupling mechanisms, perhaps involving 29 2 .
We now discuss the 121141 activity -see Figure 8. This appears at three positions with the v = 0 band clearly seen at 818 cm -1 , and the other islands of emission activity being via excitations at 797 and 804 cm -1 . It is seems likely these last two features must arise from FC activity from the two main eigenstates, as it is difficult to see that 9 1 and 29 2 are interacting so strongly with 12 1 14 1 that the resulting eigenstates end up so far apart; moreover, we do not see any evidence of 91 nor 292 activity when exciting via 12 1 14 1 -see Figure 8. Interestingly, the same islands of activity for 121141 occur with the much weaker 113, although the activity at 804 cm -1 seems stronger than that at 797 cm -1 , which is the opposite of the 121141 activity. The 113 activity can be contrasted with that of 112, which is actually stronger when exciting at 797 cm -1 than 804 cm -1 . We also remark that there is a curious coincidence here, whereby in the S1 state the 11 2 and 12 1 14 1 levels are almost isoenergetic, while in the S0 state the 113 and 121141 levels almost coincide; it is also the case that the latter corresponding cation levels are similarly very close in energy. 12 There is not, however, any unambiguous evidence of interactions between the noted levels in any of the three electronic states.
The relatively strong 1518 cm -1 emission band ( Figure 6) when exciting at 804 cm -1 can be assigned as 143202mx, and would be the counterpart of the 141202mx band (702 cm -1 ) seen when exciting at~400 cm -1 ; 20 this would be consistent with the clear 702 cm -1 emission seen at this excitation position ( Figure   4). (Recall from above that in Ref. 20 we could not definitively decide on the associated m level.) In the above, we have seen that most of the bands we observed 20 when exciting at~398 cm -1 also appear in this region, each in combination with 142 and 291, but with their (v, m) bands at 804 cm -1 . This is particularly surprising, since the expected band positions might suggest that these would appear close to 797 cm -1 . This appears to be the result of a remarkable coincidence caused by the movement of the various levels via their interaction with 9 1 , and possibly in tandem with the positive anharmonicity of the 14 n progression, seen for pDFB. 38,39 It is also evident that there is greater 142 activity when exciting at 804 cm -1 than there is at 797 cm -1 (see Figure 5), which would be consistent with these other S1 levels arising from 14 2 combinations lying at this wavenumber.
Above, we have noted that the 1071 cm -1 emission band ( Figure 5) is at the expected position for 111141m6(-), but that it is unexpected that this would be almost exclusively localized at 797 cm -1 , particularly given the spread of activity of 111142 across the spectrum (and noting that the 14 2 and 14 1 m 6(-) levels are almost isoenergetic and interacting 12,16,20 ). Since we would expect 11 1 14 1 m 6(-) to appear at an excitation position of 806 cm -1 , it seems unlikely that any interaction would be enough to cause it to lie very close to the 797 cm -1 eigenstate, and would not be consistent with the localized activity. Further, close inspection of the 141m6(-) band profile (seen at 618 cm -1 in Refs 16 and 20) shows these to be somewhat different, and additionally the 1071 cm -1 band is found not to be enhanced when exciting via 11 1 . Since the band appears relatively localized in excitation position, and being totally symmetric, this is likely to be the v = 0 band; hence, we sought another assignment of this band, with the most likely candidate being 151201. This would suggest that the wavenumber of D15 in the S1 state is 687 cm -1 , which is still in reasonable agreement with the calculated value, but would require our previous value 12 of 678 cm -1 to be revised. The latter came from a very tentative assignment of a (v, m) = 0 ZEKE band to + 15 1 m 3(-) . If we then cross-check with the ZEKE spectrum, we would expect the + 15 1 20 1 level to lie at~1109 cm -1 using the calculated value for D15 in the cation, which would excellently match the ZEKE band at 1112 cm -1 seen when exciting at these corresponding wavenumbers; 12 pleasingly, this also matches the extent of this feature to lower wavenumber where the 1112 cm -1 ZEKE band is prominent. That ZEKE feature was assigned to + 14 2 29 1 in Ref. 12, but as we have noted, we are unable to discern 142291 emission in our 2D-LIF spectra, but it may be masked by the strong 51 features -we shall come back to this later. Since we expect 11 1 14 1 m 6(-) to be interacting with 11 1 14 2 , and since the v = 0 band of the latter is weak, then the 111141m6(-) band is also expected to be weak, and presumably this is the reason for its non-observation; further, if it were interacting, then we would expect to see activity at different excitation wavenumbers.
In our previous ZEKE study, 12 we also assigned a band at 1171 cm -1 to + 12 1 m 6(-) , seen clearly when exciting at 794 cm -1 and at various positions across the 797 cm -1 band. The corresponding 2D-LIF band would be expected to have an emission of~1161 cm -1 , but there is no such band seen when exciting at 797 cm -1 . (The only possible candidate is a feature at~1174 cm -1 , which lies just above the 101111 band, and appears to be wholly localized around 797 cm -1 , but this seem too distant in wavenumber to be likely; further, the S1 excitation position for 12 1 m 6(-) would be expected to be significantly higher than 797 cm -1 in the absence of any significant interactions.) There are a number of pure vibrational assignments for the 1174 cm -1 feature, with 141191291 perhaps being the most likely on the grounds that it is totally symmetric (and so could be FC active), and contains 291 character (given the activity of 291 at this excitation position). Although, we find little enhancement of this feature when exciting via 29 1 , this may be because of the difference in symmetry. Alternatives such as a HT-active a1 symmetry level, e.g. 141201302, would not be expected to be so intense. Either way, the reassignment of the ZEKE band meets the expectation that the 12 1 m 6(-) state would not be expected to lie so far from 12 1 14 1 , since the 14 1 and m 6(-) , and 14 2 and 14 1 m 6(-) , pairs of levels are each close together in the S1 state, 12,16 and so it is difficult to see what could displace the 12 1 m 6(-) level so far away from 12 1 14 1 . Further inspection of the spectra reveals a very weak 2D-LIF feature at (820, 1159) cm -1 that would be consistent with being the (12 1 m 6(-) , 121m6(-)) band. We now, however, would need to reassign the 1171 cm -1 ZEKE band.
One possibility is + 7 1 FC activity from totally symmetric levels such as 15 1 20 1 and 9 1 . However, this ZEKE band appears clearly across the 797 cm -1 and 804 cm -1 excitation regions and it is unclear why it would be so relatively intense when exciting at~797 cm -1 . Another possibility is + 9 1 14 1 , which would tie in with the activity of + 14 1 commonly seen in ZEKE spectra of substituted benzenes, and discussed in our recent paper on p-difluorobenzene; 39 additionally, the + 9 1  while the 1171 cm -1 ZEKE band, rather than indicating 12 1 m 6(-) activity at 797 cm -1 , is merely reflecting FC activity of + 7 1 or + 9 1 14 1 m 1 The 14 4 activity was difficult to pin down in the ZEKE study, but there was evidence for the + 14 4 ZEKE band appearing across the 804 cm -1 excitation region, and this seems to be confirmed in the 2D-LIF. It is difficult to pick out ZEKE bands arising from + 14 3 m 6(-) , expected at 1237 cm -1 , + 29 1 14 1 m 6(-) expected at 953 cm -1 , nor + 11 1 14 1 m 6(-) expected at 977 cm -1 . The lack of + 11 1 14 2 ZEKE bands in the 797 cm -1 excitation region are consistent with the S1 level not interacting significantly with 9 1 , but with other ZOSs that are contributing to the 804 cm -1 band.
Note that in our recent paper on the 400 cm -1 region, 20 we assigned a 489 cm -1 2D-LIF emission band to 202m6(+) arising from interaction with 14 2 . We can see a weak feature at (805, 1308) cm -1 , which can be assigned to 142202m6(+) -expected at 1311 cm -1 . The 14 2 20 2 m 6(+) level would analogously be expected to interact with 14 4 , but we noted in Ref. 20 that such an interaction is likely to be weak and be highly dependent on the levels being extremely close in energy; indeed, this feature does have a localized intensity.

Comments on other selected features
In Figure 4, we see a very weak feature at (797, 558) cm -1 , assigned to 141201, that is barely visible when exciting at 804 cm -1 ; this is consistent with a corresponding emission observed in Ref. 16. A weak band at 633 cm -1 seems to be the same band seen when exciting at 364 cm -1 , 20 assigned to 141201m4 and can be expected to be active from 14 3 20 2 m 1 . The band at 670 cm -1 is 192 consistent with an emission reported by Gascooke et al. 16 An emission band at 731 cm -1 is seen clearly when exciting at 797 and 804 cm -1 (see Figure 4) and was also seen via the origin, 20 and it has been assigned to 101. A second very close emission feature is evident at 733 cm -1 when exciting via 797 cm -1 , which can be discerned in the DF spectra; the most likely assignment is 291301, and ties in with the observed stronger 281291/181201291 band when exciting at 797 cm -1 . It is interesting to note that 291301 is not enhanced when exciting via 29 1 (Ref. 20), which can be attributed to its different symmetry; this could thus be evidence for the enhancement of the 281291/181201291 band when exciting via 29 1 , 20 as being due to a significant 181201291 contribution.
There is a weak emission band at 863 cm -1 that is active across the three main regions of the spectrum.
A possible assignment is 292m2, accessed via a m = 3 transition, but this would be expected to be weak.
Other possibilities are 141203m2 or 111141m1, and we favour the latter as there is a weak secondary feature at 870 cm -1 , which seems likely to be 111191m4. Then these two bands are analogous to the 141m1191m4 interaction seen by Gascooke et al. 16 and the 142m1141191m4 interaction seen in our recent work. 20 A weak emission band at 895 cm -1 also appears at the three main excitation positions, and suggests assignments as 91m3(+) or 111291m2, with the latter favoured as the band is more intense when exciting at 797 cm -1 , as is the 291 band; also, since the level has e symmetry, it is symmetry-allowed at the three main positions from the m = 1 levels of the dominant ZOSs; the absence of 91 emission when exciting at 818 cm -1 makes the 91m3(+) assignment unlikely. There are several weak bands around 900 cm -1 , and although one of these is clearly 112, as noted in the above, the assignments of the others are uncertain, with vibtor levels related to 91 and 292 being candidates for some of these.
In the 1200-1300 cm -1 emission region (see Figure 6)  bands. To slightly higher wavenumber are the overlapped 111142 and 293 bands, whose presence can be ascertained from the differing activity when exciting via different intermediate levels. 20 We find that the 111142 band is more intense via 11 1 and 797 cm -1 , while the 293 band is more intense via 29 1 , 20 but we expect the contributions from the latter to be minimal in this excitation region. At 1294 cm -1 is 91111, and at 1301 cm -1 we see 111292, with the latter being most intense when exciting via 797 cm -1 and 804 cm -1 , consistent with the v = 0 region. There are three other prominent features to higher wavenumber in this region: 1364 cm -1 , which is assigned to 121141; 1394 cm -1 , which is assigned to 172; and 1487 cm -1 , which is assigned to 91281, and can be seen to be more intense via 797 cm -1 . Lastly, there appears to be a double band with maxima at 1515 cm -1 and 1519 cm -1 ; the latter has already been assigned to 143202mx (see above). Taking into consideration the expected activity of various combination bands via different intermediates, our favoured assignment of the 1515 cm -1 band is to 141161301, but this is tentative.
The 1600-1750 cm -1 emission region (see Figure 7) is not initially straightforward to assign as there are multiple overlapping bands, with possible interactions between the contributing S0 levels. DF spectra recorded from different intermediate levels (see Figures 7 and 9) are, however, very useful. This region is complicated since it is expected to show overtones and combination bands of the levels that contribute to the v = 0 (~800 cm -1 ) region; it is also where 111 and 291 combinations with the S0 levels seen at 1200-1300 cm -1 are expected to appear; and there is also the possibility of new fundamentals and other combinations and overtones. Furthermore, there is the likelihood of overlapping features and interactions between levels. In Figure 9 we show spectra recorded via six different intermediate levels:

IV. DISCUSSION
In Figure 3, we show the 0-310 cm -1 region of the DF spectra obtained when exciting via the origin, and each of the 797 cm -1 and 804 cm -1 bands. The features have been assigned and discussed in depth in Ref. 16, to which the reader is referred. It may be seen that the structure is very similar in all three cases, and in particular that there are features that arise from both the m = 0 and m = 1 levels, with similar relative intensities in each case.
We have noted that in the picosecond tr-PES 27 study, the two S1 eigenstates at 797 cm -1 and 804 cm -1 were concluded to arise from a Fermi resonance, as deduced from monitoring the time-dependent signal from ionization to the origin using photoelectron spectroscopy, and that is consistent with the deductions here and in Ref. 12. Of particular interest, however, is the observation that a large amount of the intensity was lost rapidly (over 30 ps) when these two eigenstates were excited coherently -this was interpreted as rotational dephasing involving one of the torsional levels in each of the two vibrational eigenstates.
Those time-resolved experiments made use of picosecond lasers, whose linewidth is~15 cm -1 . As such, more than one eigenstate is excited coherently, forming a wavepacket -i.e. a coherent superposition of more than one eigenstate. As with the nanosecond experiments, projection of the excited state eigenstates (in that case, a wavepacket) onto those of another state (in that case, the cation) can, in principle, allow the ZOS make-up to be ascertained, particularly if the corresponding ZOSs are well-  27 and these should, of course, be consistent with the separation of corresponding bands seen in a REMPI or LIF experiment. Such a Fourier transform was performed in that work, 27 and two peaks were seen, one at 6.7 cm -1 and one at 6.2 cm -1 , with the former being the more intense and sharp, while the latter was much weaker with a broader structure. The 6.7 cm -1 separation matches that between the 797 cm -1 and 804 cm -1 excitation bands in Figure 1. The 6.7 cm -1 separation was hypothesised as arising from a particular m level of the two vibrations, with the 6.2 cm -1 separation arising from the other populated m level in the same levels (recalling that both m = 0 and m = 1 levels will be populated). The separation was suggested as being caused by the m = 0 and m = 1 levels having slightly different rotational constants. It was then suggested that the rapid loss of intensity within the first 30 ps arose from rotational dephasing, which was suggested as arising from a rotational-level dependent coupling term -it was noted that such a coupling could not be simply anharmonic, since this would not have a rotational dependence. The rotational dephasing would occur as a result of destructive interference between the many coherently excited rotational levels corresponding to the same m level in the two different vibrational eigenstates, caused by an m-specific (and J, K-dependent) interaction.
Since this effect is expected to be very small, it would be consistent with the small difference in the two spacings of the eigenstates reported in Ref. 27. Further, this would explain why, in Figure 3, we see the whole set of torsional levels via both the 797 cm -1 and 804 cm -1 levels at what appear to be identical emission wavenumbers -the dephasing only occurs as a result of the two eigenstates being coherently excited. At the resolution in our spectra, we are unable to see any obvious difference in spacings of the various torsional levels in Figure 1, nor in the separation of the various (v, m) = 0 bands. As noted in Ref. 27, what is required is for there to be one or more interactions with nearby ZOSs that is m specific, and which causes a sufficient perturbation to lead to a J, K-dependent perturbation to the rotational energy levels, which we now explore.
In the above, we have noted several levels that are coincident with one or more of the main two eigenstates at 797 cm -1 and 804 cm -1 ; however, we also require the levels to be interacting for the mspecific interaction to occur. Hence, for example, the 15 1 20 1 level could not be a cause of the perturbation in rotational constants as it is not interacting to any noticeable extent, and there would be no reason why the interaction would not take place in both m levels. The latter comment also applies to levels such as 11 1  It is clear, however, that the loss of intensity in the tr-PES study cannot be incipient dissipative intramolecular vibrational redistribution (IVR), as then we would expect a significant, broad underlying background in the present nanosecond excitation spectra, but this is not seen.
Coming back to our recent work 20 on the bands at~400 cm -1 , we there noted that there are a significant number of bands involving the low-wavenumber, out-of-plane modes, D14 and D20, commensurate with these modes coupling to the torsional motion of the methyl group, and this is also the case in the higher wavenumber region focused on in the present work. These modes, and to some extent D19, seem to be key in providing routes for the methyl group to couple to the vibrational motions. Because of symmetry constraints, the main routes are coupling with the m = 3(-) level for D20 and D19 and the m= 6(-) level for D14. Coupling between in-plane vibrations also occurs -for example, D29 with m = 3(+).
In Refs. 13 and 20, we also highlighted the role of the m = 1 levels in enhancing the coupling between levels, something that is implicit in the energy level diagrams of Ref. 16. These open up routes to coupling between vibtor levels arising from vibrations of different C2v symmetry, which lead to a rapid rise in the possibilities for interactions, albeit somewhat sporadically at low energy. 17 We have seen that there is strong evidence for the interaction between 9 1 and 29 2 , both from the tr-PES study, 27 and also from the corresponding FC activity, but with differing intensities in both the ZEKE study 12 and the present 2D-LIF study. Furthermore, other activity in the ZEKE and 2D-LIF spectra indicate that there are contributions from other ZOSs, and that these have moved from their expected positions, providing evidence of interactions. We also see that for "clean" emission features, such as 1518 cm -1 and 1636 cm -1 , there is weak activity at 797 cm -1 as well as the very dominant activity at 804 cm -1 , and this confirms the interactions of some of the ZOSs with 9 1 . In contrast, although we see clear 121141 activity when exciting at 797 cm -1 and 804 cm -1 , the lack of any partnering activity of 91 or 292 when exciting via 12 1 14 1 suggests no interaction with those levels, and the former activity is FC in nature. Although a quantitative picture is not straightforward to extract, we believe the picture of the interactions is qualitatively as follows. The 29 2 ZOS lies above 9 1 , and this is the main interaction. The 14 4 level also lies above 9 1 , which may arise as part of the overall set of interactions, including 9 1 29 2 , or because of positive anharmonicity in the 14 n progression; either way, the 14 4 and 9 1 levels also interact. The result is that 29 2 -dominated and 14 4 -dominated eigenstates are essentially at the same energy (804 cm -1 ). Since 14 2 and 14 1 m 6(-) interact strongly 12,15,16 then this gives some rationale as to why the 14 3 m 6(-) level also appears at 804 cm -1 (since 14 2 and 14 1 m 6(-) are almost isoenergetic) 16,20 although there is no a priori reason to expect the interactions of different ZOSs with 14 4 and 14 3 m 6(-) to be the same. In contrast, the 11 1 14 2 level appears at a lower wavenumber, implying that the interactions between 9 1 and this level are weaker; the appearance of 11 1 29 1 to lower wavenumber is consistent with its different symmetry from 9 1 . It is surprising that the 14 1 29 1 m 6(-) level also appears at 804 cm -1 , and this is likely the result of a number of interactions. We cannot be definitive about the positions of 11 1 14 1 m 6(-) and 14 2 29 1 , as unambiguous emission bands are not seen for these. We might expect 11 1 14 1 m 6(-) to be close to 11 1 14 2 and 14 1 29 1 m 6(-) to be close to 14 2 29 1 , but as noted above, the interactions could be different for these ZOSs. We assigned an emission band at 1071 cm -1 to 151201, even though this was at the wavenumber expected for 111141m6(-), and noted that the 15 1 20 1 level does not appear to be interacting with 9 1 or 29 2 . As commented above, via the 797 cm -1 and 804 cm -1 eigenstates we see 121141 FC emission, and we conclude the 12 1 14 1 level is not interacting with 9 1 . Moreover, even though 11 2 and 12 1 14 1 are almost degenerate, they do not seem to be interacting in S1, as their activity across the spectra is different; similar comments apply to 121141 and 113 in S0. Finally, we have concluded that the + 12 1 m 6(-) band was misassigned in our previous ZEKE study, 12 and we tentatively conclude that the corresponding S1 level may be located close to 12 1 14 1 .

V. CONCLUSIONS
In this work, it has been seen that, although at first sight the REMPI/LIF excitation spectra appear to indicate a rather straightforward pairwise classic Fermi resonance interaction, in fact the picture is significantly more complicated, in agreement with the conclusions of the ZEKE study 12 and, in part, consistent with the conclusions of the tr-PES study. 27 It is clear, however, that although there are a fair number of ZOSs contributing to the 790-825 cm -1 region, the present results and those of Ref. 27 indicate that we are still in the restricted IVR regime, but with the situation being far more complicated than a simple Fermi resonance. In previous work, 40 we have discussed the factors that affect experimental observations relating to IVR, and one of these was the temperature of the molecules. This, we believe, underlies the indications of wider-ranging IVR implicit in the DF spectra obtained via 9 1 and even via the~400 cm -1 levels in a 300 K sample of pFT, 41 probably driven by thermally-populated torsional and rotational levels.
Lastly, as with the 14 2 14 1 m 6(-) interaction which has localized rotation-level dependent coupling, 16 we find that several other bands appear to show unexpected intensity profiles (e.g. bands at 973 cm -1 and 993 cm -1 ), and this may be evidence for similar effects.
In summary, we have shown that 2D-LIF is a powerful tool in revealing overlapping bands in an excitation spectrum and separating these to facilitate their assignments. The spectra also help to reveal interacting levels via the different intensities seen when exciting at different positions. In some cases, complications arise from separating FC activity from cross-activity arising from interacting ZOSs, but considering other activity can often clarify this. The technique is particularly useful in cases such as here, where a (not too large) number of ZOSs are interacting in complex Fermi resonances, and where the anharmonic shifts in levels cause levels to move, making it more difficult to identify them in a simple excitation spectrum. Further, the much more complete dataset represented by a 2D-LIF spectrum provides greater reliability regarding the interpretation of the activity; however, the "2D-ZEKE" spectra we have published 12 are complementary, as they project the S1 levels onto a different electronic state, and so help to confirm assignments.  b The Di labels are described in Ref. 33, where the vibration mode diagrams can also be found.

Figure List
1. Overview of the REMPI spectrum and integrated 2D-LIF spectrum over the range of interest -see text.
2. Overview of the 2D-LIF spectrum across the whole range of interest. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background.
3. Expanded view of the 2D-LIF spectrum of pFT in the 0-310 cm -1 region exciting via the 797 cm -1 and 804 cm -1 eigenstates. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. We also show the corresponding DF spectra from these two levels and the origin. This region covers the main torsion and vibtor levels associated with the D20, D19 and D30 vibrations. The appearance of the spectrum via the origin is very similar to that recently published by Gascooke et al. in Ref. 16, where it is discussed in detail. The relative intensities in the 2D-LIF spectrum are as recorded, while the DF spectra have been adjusted to be qualitatively in agreement with the 2D-LIF spectrum, but with some regard to presentational clarity. Thus, the relative intensities within the same DF trace will be reliable, but not necessarily when comparing between two traces.
4. Expanded views of the 2D-LIF and DF spectra for the 390-790 cm -1 region, exciting via the 797 cm -1 and 804 cm -1 eigenstates. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. See text for discussion of the assignments. The relative intensities in the 2D-LIF spectrum are as recorded, while the DF spectra have been adjusted to be qualitatively in agreement with the 2D-LIF spectrum, but with some regard to presentational clarity. Thus, the relative intensities within the same DF trace will be reliable, but not necessarily when comparing between two traces.
5. Expanded views of the 2D-LIF and DF spectra for the 790-1190 cm -1 region exciting via the 797 cm -1 and 804 cm -1 eigenstates. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. See text for discussion of the assignments. The relative intensities in the 2D-LIF spectrum are as recorded, while the DF spectra have been adjusted to be qualitatively in agreement with the 2D-LIF spectrum, but with some regard to presentational clarity. Thus, the relative intensities within the same DF trace will be reliable, but not necessarily when comparing between two traces.
6. Expanded views of the 2D-LIF and DF spectra for the 1190-1590 cm -1 region exciting via the 797 cm -1 and 804 cm -1 eigenstates. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. See text for discussion of the assignments. The relative intensities in the 2D-LIF spectrum are as recorded, while the DF spectra have been adjusted to be qualitatively in agreement with the 2D-LIF spectrum, but with some regard to presentational clarity. Thus, the relative intensities within the same DF trace will be reliable, but not necessarily when comparing between two traces. For the 143202mx level, we are unable to be definitive of the value of x, which is thought to be 1 or 2 -see text and Ref. 20. 7. Expanded views of the 2D-LIF and DF spectra for the 1590-1790 cm -1 region exciting via the 797 cm -1 and 804 cm -1 eigenstates. The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. See text for discussion of the assignments. The relative intensities in the 2D-LIF spectrum are as recorded, while the DF spectra have been adjusted to be qualitatively in agreement with the 2D-LIF spectrum, but with some regard to presentational clarity. Thus, the relative intensities within the same DF trace will be reliable, but not necessarily when comparing between two traces.
8. Expanded views of sections of the 2D-LIF spectra across the 790-825 cm -1 region demonstrating the activity when exciting via 797 cm -1 , 804 cm -1 and 818 cm -1 . The spectral intensities are represented by colours, with red being the most intense through to blue being the least; black represents the zero background. See text for discussion of the assignments.
9. DF spectra of 1600-1750 cm -1 regions via different intermediate levels. See text for discussion of the assignments. Each trace has been normalized to the most intense band; thus, the relative intensities within the same DF trace will be reliable, but to compare intensities between traces, refer to Figure 7.