Variations in Duschinsky rotations in m-fluorotoluene and m-chlorotoluene during excitation and ionization.

We investigate Duschinsky rotation/mixing between three vibrations for both m-fluorotoluene (mFT) and m-chlorotoluene (mClT), during electronic excitation and ionization. In the case of mFT, we investigate both the S1 → S0 electronic transition and the D0 + ← S1 ionization, by two-dimensional laser-induced fluorescence (2D-LIF) and zero-electron-kinetic energy (ZEKE) spectroscopy, respectively; for mClT, only the D0 + ← S1 ionization was investigated, by ZEKE spectroscopy. The Duschinsky mixings are different in the two molecules, owing to shifts in vibrational wavenumber and variations in the form of the fundamental vibrations between the different electronic states. There is a very unusual behavior for two of the mFT vibrations, where apparently different conclusions for the identity of two S1 vibrations arise from the 2D-LIF and ZEKE spectra. We compare the experimental observations to the calculated Duschinsky matrices, finding that these successfully pick up the key geometric changes associated with each electronic transition and so are successful in qualitatively explaining the vibrational activity in the spectra. Experimental values for a number of vibrations across the S0, S1, and D0 + states are reported and found to compare well to those calculated. Assignments are made for the observed vibration-torsion ("vibtor") bands, and the effect of vibrational motion on the torsional potential is briefly discussed.


I. INTRODUCTION
An analysis of the vibrational activity in electronic and photoelectron spectra is often used as a signature of vibrational coupling between fundamentals, overtones, and combination levels. This occurs through anharmonic coupling, which leads to the dispersal, and so delocalization, of internal energy within a molecule -an important aspect to enhancing photostability. 1,2,3,4 Sometimes activity in fundamentals other than that excited can be seen in experimental spectra; however, to first order, vibrational fundamentals do not couple anharmonically. Such activity can be induced by changes in geometry that lead to significant Franck-Condon factors (FCFs), or as a result of a Duschinsky rotation,5 with cross-activity between vibrations being a signature of the latter. Understanding the intensities of vibrational features in electronic and photoelectron spectra is key to understanding electronic and geometric changes between electronic states. A Duschinsky rotation occurs when the vibrational motions and/or force constants vary significantly between two electronic states; then, each of the affected vibrations in one electronic state has a motion that can be expressed as a linear combination of more than one vibrational motion in the other electronic state. This is sometimes termed the Duschinsky effect, with the resulting vibrations said to have undergone Duschinsky mixing. This would mean, for example, that activity arising when exciting from a particular vibration would be more extensive than expected, owing to the excitation of further vibrations in the final electronic state. Of course, both Franck-Condon (FC) and Duschinsky effects will operate simultaneously, which can complicate the interpretation of the spectra.
Very recently, we published resonance-enhanced multiphoton ionization (REMPI) and zero-electronkinetic-energy (ZEKE) studies of the low-wavenumber regions of m-fluorotoluene (mFT) 6 and mchlorotoluene (mClT), 7 which mainly focused on torsions and vibration-torsion (vibtor) levels. The mFT study complemented the two-dimensional laser-induced fluorescence (2D-LIF) study of Stewart et al., who examined the first 350 cm -1 of the S1  S0 transition. 8 The spectra of both molecules were assigned in terms of torsion and vibtor levels in the S0 and S1 states. Earlier, Ito and coworkers 9,10,11,12 reported laser-induced fluorescence (LIF), dispersed fluorescence (DF), REMPI, and ZEKE spectra of the low-wavenumber region of mFT. In addition, Ichimura et al. 13 have published LIF and DF spectra of mClT, while Feldgus et al. 14 only reported REMPI and ZEKE spectra of mClT, restricted to the torsional region.
In the present work, we focus on a set of three vibrations that are active in the S1  S0 transition, and are found to have a high degree of cross-activity, as ascertained using 2D-LIF and ZEKE spectroscopy.
These three vibrations are designated D18, D19 and D20, as described in Ref. 15, and whose explicit motions will be discussed later.

II. EXPERIMENTAL
The ZEKE 16 and 2D-LIF 17 apparatuses are the same as those employed recently. In both experiments for mFT, a free-jet expansion of mFT (Sigma-Aldrich, 98% purity) in 1.5 bar Ar was employed. For the ZEKE experiments on mClT, a free jet expansion was also used, consisting of mClT (Alfa Aesar, 98% purity) in 2 bar Ar, where the mClT sample was heated to ~50°C in order to introduce sufficient vapour to the expansion.
For the 2D-LIF spectra, the free-jet expansion was intersected at X/D ~20 by the frequency-doubled output of a single dye laser (Sirah CobraStretch), operating with Coumarin 503 and pumped with the third harmonic of a Surelite III Nd:YAG laser. The fluorescence was collected, collimated, and focused onto the entrance slits of a 1.5 m Czerny-Turner spectrometer (Sciencetech 9150) operating in singlepass 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 camera image was accumulated for 2000 laser shots. This allowed a plot to be produced of fluorescence intensity versus both the excitation laser wavenumber and the wavenumber of the emitted and dispersed fluorescence, termed a 2D-LIF spectrum. 18,19 For the ZEKE spectra, the focused, frequency-doubled outputs of two dye lasers (Sirah CobraStretch) were overlapped spatially and temporally, and passed through a vacuum chamber coaxially and counterpropagating, where they intersected the free jet expansion. The excitation laser operated with Coumarin 503 and was pumped with the third harmonic (355 nm) of a Surelite III Nd:YAG laser, while the ionization laser operated with Pyrromethene 597, pumped with the second harmonic (532 nm) of a Surelite I Nd:YAG laser. The jet expansion passed between two biased electrical grids located in the extraction region of a time-of-flight mass spectrometer, which was employed in the REMPI experiments. These grids were also used in the ZEKE experiments by application of pulsed voltages, giving typical fields of ~10 V cm -1 , after a delay of up to 2 s; this delay was minimized while avoiding the introduction of excess noise from the prompt electron signal. The resulting ZEKE bands had widths of ~5-7 cm -1 . Electron and ion signals were recorded on separate sets of microchannel plates.

III. RESULTS AND ASSIGNMENTS
A. Nomenclature and labelling

Vibrational and Torsional Labelling
We shall employ the Di labels 15  We shall also refer to the methyl torsional motion for mFT and mClT, for which the G6 molecular symmetry group (MSG) is appropriate, and we shall use those symmetry labels throughout. The torsional levels will be labelled via their m quantum number, 6,8

and the correspondence between the
Cs point group labels and the G6 MSG ones is given in Table I. To calculate the overall symmetry of a vibtor level, it is necessary to use the corresponding G6 label for the vibration, and then find the direct product with the symmetry of the torsion ( Under the free-jet expansion conditions employed here, almost all of the molecules are expected to be cooled to their zero-point vibrational level, and thus essentially all S1  S0 pure vibrational excitations are expected to originate 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, 24 with residual population in the m = 2 levels also seen. 6,7,8

Transitions
When designating excitations, we shall generally omit the lower level, since it will be obvious from either the jet-cooled conditions or the specified intermediate level. In the usual way, vibrational transitions will be indicated by the cardinal number, i, of the Di vibration, followed by a super-/subscript specifying the number of quanta in the upper/lower states, respectively; 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.

5
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, when required, subscripts indicating levels in the S0 state. Since we will also be referring to transitions and levels involving the ground state cation, D0 + , we shall indicate those as superscripts, but with a single, additional, preceding superscripted "+" sign. Relative wavenumbers of the levels will be given with respect to the relevant zero-point vibrational level with m = 0 in each electronic state.
For cases where the geometry and the torsional potential are both similar in the S1 and D0 + states, the most intense transition is usually expected to be that for which no changes in the torsional and/or vibrational quantum numbers occur: designated as m = 0, v = 0 or (v, m) = 0 transitions, as appropriate. However, as will be seen (and as reported in Refs. 6, 7, 12 and 14), the m = 0 and (v, m) = 0 transitions are almost always not the most intense bands in the ZEKE spectra for mFT and mClT, indicative of a significant change in the torsional potential upon ionization.

B. Overview of REMPI spectra
In Figure 1 we show the REMPI spectra of the first 500 cm -1 above the origin of the S1  S0 transition in mFT and mClT. The 0-350 cm -1 region of the mFT spectrum has been discussed in detail previously, in terms of 2D-LIF and ZEKE spectroscopy, 6,8 while the corresponding region of the mClT spectrum has also been discussed relating to ZEKE spectroscopy. 7 Because of the consistent vibrational labelling used for both molecules, 15 it can be seen that the activity in both spectra is similar. In the present work, we shall concentrate on the two expanded regions of Figure 1, between 400-480 cm -1 for mFT and 350-470 cm -1 for mClT. In the case of mClT, the spectrum was recorded in two mass channels, corresponding to the 35 Cl and 37 Cl isotopologues, where some bands around 370 cm -1 can be seen to undergo isotopic shifts (compare the red and black traces in the expanded region in the lower portion of Figure 1), but there are essentially no shifts for the lower-wavenumber bands. 7 For both mFT and mClT, these regions are dominated by activity involving three vibrations, D18, D19 and D20. As we shall see below, these vibrations are significantly Duschinsky mixed in the S1 state.
We shall firstly concentrate on the assignment of the 2D-LIF and ZEKE spectra of mFT, before moving on to the ZEKE spectrum of mClT (no 2D-LIF spectra were recorded for this molecule). We shall then discuss the observations for both molecules.

C. 2D-LIF and ZEKE spectra of mFT
In Figure 2, the 2D-LIF spectrum of mFT in the range 412-464 cm -1 is presented, while ZEKE spectra recorded at various excitation positions across the same region are shown in Figure 3. Calculated wavenumbers for a selection of pertinent vibrations for both molecules, and for the three different electronic states considered, are presented in Table II -the level of theory utilized has generally been shown to be sufficient for these molecules in our previous work.
It will be seen in the discussion below that the D19 and D20 vibrations become very mixed in the S1 state. For this reason, we have designated the S1 mixed vibrations, DX and DY in the following. The strongest features in the 2D-LIF spectrum ( Figure 2) are seen when exciting via 18 1 , X 1 and Y 1 , each comprising m = 0 and m= 1 components, as indicated; significant cross-activity is evident. The strong emission bands seen when exciting via 18 1 are partially overlapped with those seen when exciting via Y 1 . Associated with each of the strong emission bands is a series of vibtor transitions, which have distinctive structure, as seen in the low wavenumber region. 8 These consist of strong m3(+) and weaker m3(-) bands when exciting via the m = 0 components, as well as a strong m2 band, with weaker m4 and m5 bands, when exciting via the m = 1 components -some of these are overlapped by other features in the 2D-LIF spectrum.
In Figure 3, we present the ZEKE spectra recorded via the m = 0 and m = 1 components of the 18 1 , X 1 and Y 1 vibrations of mFT. It can be seen from Figure 1 that the X 1 m 0 and 18 1 m 1 transitions overlap, and so the ZEKE spectrum recorded for these overlapped features is included in both the upper and lower portions of Figure 3, but located on the correct scale in each case. Again, significant cross activity is seen when exciting via 18 1 , X 1 and Y 1 , for both m levels.
To aid in the understanding of the activity of the spectra, Duschinsky matrices were calculated (using the FC-LAB II program) 25 for a selection of the vibrations. This was done for the three pairings of the S0, S1, and D0 + electronic states for mFT, and these are shown in Figure 4. Additionally, we show the calculated motions of the three Duschinsky-mixed vibrations of interest, in each of the three electronic states. First, we point out that the Di labels are defined with respect to the S0 motion. (The motions of meta-disubstituted benzenes in the S0 state, on which the Di labelling is based, were discussed in detail in Ref. 15.) Secondly, the S0/D0 + matrix indicates that the vibrational motions in the ground state cation are very similar to those in the ground state neutral molecule, so that the S0 vibrational labels, Di, can also be used for the cationic vibrations to a very good approximation. (It is highlighted that the wavenumber ordering of the D19 and D20 vibrations have switched in the cation relative to the S0 state -see Table II.) We now turn to the S0/S1 matrix for mFT in Figure 4. This indicates that the motions of the S1 vibrations corresponding to the D18, D19, and D20 S0 vibrations are significantly altered, and each of these S1 vibrations can be thought of as being significant admixtures of the corresponding S0 ones, i.e. they are Duschinsky mixed; a similar picture holds when these S1 vibrations are expressed in terms of the D0 + vibrations. In contrast, the D17 and D21 vibrations exhibit extremely similar motions in the three electronic states, and so are not considered to be Duschinsky mixed. We now point out that the S1 D18 vibration is dominated by the same motion as in the S0 state (and D0 + state) and so these are recognizably the same vibration, even though the S0 and S1 motions are not precisely the same, with a noteworthy contribution in S1 from D19. Hence, we retain the D18 label for this vibration across the three electronic states. This is not true for the D19 and D20 vibrations, where the two S1 vibrations have motions that can be expressed as significant admixtures of the corresponding S0 (or D0 + ) vibrations; as such, the D19 and D20 labels cannot be used for these two S1 vibrations, which is why we have designated them DX and DY, in increasing wavenumber order.
We now look at the activity in the 2D-LIF and ZEKE spectra in more detail. In Figure 2, we can see that there is significant cross activity in the 2D-LIF spectrum involving the D18, D19 and D20 vibrations, as indicated by the (X 1 , 181), (X 1 , 191) and (X 1 , 201) bands, together with (Y 1 , 181), (Y 1 , 191) and (Y 1 , 201), which appear for each of the two m levels. A definite (18 1 m 0 , 191m0) band can be seen, as well as (18 1 m 0 , 181m0), but there is only the faintest activity for (18 1 m 0 , 201m0); there do, however, appear to be (Y 1 m 0,1 , 181m0,1) bands, albeit overlapped by (Y 1 m 1 , 201m4); indicating a lesser contribution of D18 to the S1 state Y 1 vibration, compared to the X 1 vibration -see further discussion below.
With regard to the mFT ZEKE spectra in Figure 3, clear + 19 1 and + 20 1 activity can be seen when exciting via each of X 1 and Y 1 , for both m = 0 and m = 1 levels, with the + 19 1 wavenumber being lower than that of + 20 1 , i.e. the opposite order to the S0 and S1 states -see Table II. (There is also + 18 1 activity, but this is less prominent.) The + 19 1 m x vibtor activity is greatest when exciting via Y 1 and that of + 20 1 m x when exciting via X 1 , with this being most clear from the + 19 1 m 3(+) and + 20 1  At this point, we note that for a symmetric, disubstituted benzene, such as mDFB, the point group is C2v, where the D19 and D20 vibrations are both of b2 symmetry, while D18 is of a1 symmetry; thus, D19 and D20 can be thought of as mixing with one another during their evolution as the mass of the substituents changes, 15 while D18 cannot. In the asymmetric mFT, we note that the masses of CH3 and a fluorine atom are very similar, and this may be an explanation of why there is strong Duschinsky mixing between D19 and D20. Also, as the mass difference between the two substituents increases for an asymmetric disubstitution, D18 and D19, , evolve into localized motions containing symmetric and asymmetric stretches, respectively, each involving the substituents, both being of a symmetry (in the Cs point group). 15 In the present case, this is exhibited as the mixing between the D18 and D19 modes, for which the localization of the motion is not complete, and the extent of this varies between the electronic states (see Figure 4). We now compare and contrast the activity in the 2D-LIF and ZEKE spectra seen when exciting via the 18 1 , X 1 and Y 1 levels.
The initial interpretation of the 2D-LIF spectrum (Figure 2) is that DY in the S1 state is dominated by S0 D20 character, with a sizeable contribution from D19 and a smaller one from D18; furthermore, DX has the largest contribution from D19 but with large contributions from D18 and (to a lesser extent) D20. We can also see that D18 in the S1 state has a significant contribution from S0 D19. These conclusions are largely in line with the calculated S0/S1 Duschinsky matrix (Figure 4).
If we now look at the ZEKE spectra in Figure 3, then we would reach a different conclusion, in that exciting via Y 1 gives the largest contribution from + D19 (i.e. the D19 vibration in the cation) with a significant contribution from + D20, while exciting via X 1 gives the largest contribution from + D20, with a significant contribution from + D19. Again, these conclusions are in line with the calculated S1/D0 + Duschinsky matrix -see Figure 4. As a consequence, at first sight it seems that the conclusions from the 2D-LIF and ZEKE spectra are contradictory with regards to the make-up of the DX and DY S1 vibrations. This must arise from the small, but notable, differences in the motions of the D18, D19 and D20 vibrations in the S0 and D0 + electronic states, which cause the expression of the S1 motions as admixtures of these vibrations in the different electronic states to differ. In addition, the Franck-Condon factors between the vibrations and associated vibtor levels will differ for the S1  S0 and D0 +  S1 transitions, depending on the main geometry changes between the respective pair of electronic states. These have been discussed previously 6,7 for mFT and mClT, where the changes are very similar.
Notably, for mFT, the C-CH3 and C-F bond lengths both increase significantly during the S1  S0 transition; however, the C-CH3 bond length is almost unchanged during the D0 +  S1 ionization, while the C-F bond shortens. Also, a shortening of all ring C-C bond lengths occurs during the S1  S0 transition, while there is an asymmetric change in those bond lengths during the D0 +  S1 ionization.
These are consistent with the 18 1 , X 1 and Y 1 activity seen during the S1  S0 and S1  S0 transitions ( Figure 1 and Figure 2, respectively) and the activity of + 18 1 in the ZEKE spectra via the vibrationless m 0 and m 1 levels (see Ref. 6).
We now consider the calculated motions of these three vibrations. Looking first at D18 and D19 ( Figure   4), we see motions in the S0 and D0 + states that have significant in-phase C-CH3 and C-F stretches for D18, but these are out-of-phase for D19; moreover, the motions of the other atoms are very similar for these states. For D18 in the S1 state, although the motion of the methyl group, and that of some of the ring carbon atoms, is different than those of the other two electronic states, it is dominated by the inphase C-CH3 and C-F stretches: this is our justification for employing the same vibrational label.
Similarly, for D20 in the S0 and D0 + states, the motion can be identified by the in-phase, in-plane bending of the C-CH3 and C-F bonds. However, in the S1 state, the motions of two of the vibrations, the ones labelled X and Y, can be seen to be significant mixtures of the motions of the D19 and D20 vibrations. In particular, the motions of the C-CH3 and C-F bonds for DX and DY are similar to those of D19 and D20, respectively, while the motions of the carbon atoms in the aromatic rings for DX and DY largely resemble D20 and D19, respectively. Thus, different aspects of the DX and DY motions resemble different parts of the D19 and D20 vibrations. This shows that the D19 and D20 motions have indeed become mixed in S1, in line with the Duschinsky matrices ( Figure 4) and this is reflected in the activity in the 2D-LIF and ZEKE spectra (Figure 2 and Figure 3). Of course, each entry in the Duschinsky matrix is a distillation of the comparisons of all angular and radial displacements between two vibrations; nonetheless, even though the subtleties of the different changes are not necessarily evident, the entry is expected to reflect the most important geometry changes for a particular electronic transition. This case shows that in fact the Duschinsky matrix does give a good qualitative picture of the observed spectral activity, although, for very mixed vibrations, caution is merited in the interpretation of the matrix in establishing how vibrations of one electronic state map onto another. Clearly, for the S1  S0 emission, it is the motions of the C-CH3 and C-F bonds that dominate the overlap of the S1 DX and DY vibrations with the S0 D19 and D20 ones; while for the D0 +  S1 ionization, the relative motions of the carbon atoms in the aromatic ring are the more important in determining the activity.
Summarizing, we conclude that the D18, DX and DY vibrations are heavily mixed in the S1 state, with the D19 and D20 contributions to X 1 and Y 1 each being particularly significant; however, when distilled into Duschinsky matrix entries, these are different when expressed in terms of the S1 or D0 + vibrations, but in agreement with the observed vibrational activity.  Figure 6 indicates that although the D18, D19, and D20 vibrations of the D0 + state are mixed versions of the corresponding S0 ones, there is sufficient dominant character to employ the same labels for both states, notably with respect to the motions of the C-CH3 and C-Cl bonds. With regard to the aromatic ring carbon atoms, although the motions are not the same in the S1 state as the other two states, they are largely correspondent with that expected for the D19 or D20 vibrations and this gives a more diagonal Duschinsky matrix, allowing the same vibrational labels to be used in the three states. Although the 2D-LIF spectrum was not recorded, the S0/S1 Duschinsky matrix indicates that there would likely be significant cross activity between the 191 and 201 emissions, but with 181 being largely pure. We comment that the activity seen in the ZEKE spectra when exciting via 19 1 m 0 and 19 1 m 1 is similar to that observed 7 via the pure torsional levels, m 0 and m 1 , although the + 19 1 m x bands are relatively more intense here, as expected. We highlight that no evidence was seen for the + 18 1 m x bands observed via the pure torsional levels; 7 additionally, there was a similar lack of + 20 1 m x band activity.

D. ZEKE spectra of mClT
This suggests that the D19 vibration in the cation has a very similar motion to that of the S1 state, which is largely supported by the Duschinsky matrix shown in Figure 6 and D20 vibrations undergo Duschinsky mixing between the S1 state and the cation, in line with the presented S1/D0 + Duschinsky matrix.
From Figure 1, the 20 1 m 0 transition is expected to be largely coincident with the 19 1 m 1 transition for the 35 Cl isotopologue. The strongest ZEKE band expected from 20 1 m 0 is + 20 1 m 3(+) ; this can be seen as a shoulder on the lower wavenumber side of the + 19 1 m 4 band in Figure 5, providing evidence for this overlap. Similarly, the 19 1 m 0 band for the 37 Cl isotopologue is mostly overlapping the same band for the 35 Cl isotopologue; but since we do not expect significant isotopic shifts for the + 19 1 m x bands, then there is not expected to be any obvious evidence expected for this overlap, and indeed none is seen.
We also note that the 20 1 m 0 band for the 37 Cl isotopologue is expected to coincide with the 20 1 m 1 band for the 35 Cl isotopologue, and there is a slight broadening of the main + 20 1 m 4 band, but this is merely consistent with + 20 1 m 3(+) activity from the 37 Cl isotopologue, rather than being definitive.
Comparing the vibrational motions of the three vibrations shown in Figure 4 and Figure 6, it is clear that in the S0 and D0 + states, the C-CH3 and C-Cl stretches have become more localized for mClT -as per the discussion given in Ref. 15 -see the forms of the D18 and D19 modes; however, there is more bending motion of the methyl group in D19 of mClT caused by the more pronounced asymmetry in mass in the molecule.
In summary, between the S1 and D0 + states for mClT, the corresponding Duschinsky matrix suggests that all three of the D18, D19 and D20 states undergo a small amount of Duschinsky mixing so that activity in each of the three modes is expected in the cation, whichever is excited, and this will, of course, apply to both of the m = 0 and m = 1 components. The spectra recorded when exciting via 18 1 m 0,1 do support a greater mixing between D18 and D20. The spectra recorded when exciting via 19 1 m 0,1 appear to show little evidence of activity involving the other two vibrations, while those recorded via 20 1 m 0,1 suffer from significant overlap, but do not exclude involvement of activity of the other two vibrations.
Hence, these observations are only qualitatively in line with the Duschinsky matrices. Overall, however, the situation for mClT appears to be clearer cut than for mFT. We note our discussion of the geometry changes for mFT in Section III.C, which complicates the expected vibrational activity, and which also applies, but to a more limited extent, to mClT. We highlight the consistency between the molecules with the activity of 18 1 , 19 1 and 20 1 in the S1  S0 excitation ( Figure 1). Further, we saw activity of both + 18 1 and + 19 1 when exciting via the vibrationless m 0 and m 1 levels, 7 which is expected from the anticipated changes in bond lengths; note that only + 18 1 was active in the case of mFT, 6 again illustrating activity differences between two very similar molecules.

A. Duschinsky rotation
The assumed linear and orthogonal relationship between the vibrations of different electronic states, 5 is only an approximation 26 and neither of these conditions strictly holds; moreover, when the geometries of the electronic states differ from each other, axis switching can occur, 27 which can further complicate the matter. On top of this, the entries in a Duschinsky matrix are a single number summarizing all of the changes in angular and radial motions of the bonds between two electronic states. If the vibrational motions are largely similar, then the diagonal entries will be the largest. If some of the vibrations become very mixed, then significant off-diagonal elements will be present, but still the diagonal elements would be expected to be the largest. The case is unusual here in that some off-diagonal elements are the largest for particular vibrations. Normally, this would suggest a misassignment of the vibrational labels; however, here these labels have been established from the S0/D0 + Duschinsky matrix. Hence we interpret these large off-diagonal elements as reflecting particular aspects of the geometry changes that occur as a result of the electronic excitation. In such a scenario, as happens here for mFT, there is no longer a clear 1:1 correspondence between the vibrations in the S1 state and the other two states. This is indeed largely borne out by the calculated matrices and the experimental observations as discussed in the present work, with the strong mixing between the D19 13 and D20 modes for mFT being the most notable, and that between D18 and D20 being significant for mClT. Different Duschinsky mixings between the molecules will arise from the slightly different motions of the vibrations, owing to the different masses of the halogen atoms in the two cases, plus slightly different electronic effects caused by the different electronegativities of the halogen atoms, and the different overlap of the halogen orbitals with the aromatic π system. For mFT, the motions of two of the S1 vibrations become strong mixtures of the S0 (and D0 + ) vibrations, preventing the same labels being used; although the mixing is also significant for mClT, the motions are similar enough to employ the same labels. These changes in motions are reflected in the activity in the ZEKE spectra and, for mFT, also in the 2D-LIF spectra.

B. Vibtor coupling and torsional potential changes
In Table III and Table IV, we give the wavenumbers of the different vibtor transitions in the cation for mFT and mClT, respectively, and the separation of each of these levels from the m = 0 level of each vibration. Previously, 6,7 we have discussed the fact that the torsional potential of the out-of-plane D30 vibration and its first overtone in the cation is altered compared to the pure torsional potential for both mFT and mClT, while the potentials for the observed in-plane (totally-symmetric) vibrations were not affected. Here, we find that the vibtor spacings of the cation involving the in-plane D19 vibration are reduced compared to those of the pure torsional levels (Table IV) suggesting the torsional barrier experienced during this vibration is lower, while some of those involving D20 are largely unaltered.
However, it is difficult to rationalize, from the vibrational motions shown in Figure 4 and Figure 6, why the CH3 torsional barrier is particularly sensitive to the D19 vibrational motion in the cation, and this may reflect a more complicated explanation in terms of electronic-and vibration-induced steric interactions.

V. CONCLUSIONS
In this work, we have focused on the activity and character of three vibrations for the closely-related molecules, mFT and mClT. In particular, we examined the change in the character of a subset of the vibrations upon electronic excitation, S1  S0, which was deduced via the activity in ZEKE spectra, but also in 2D-LIF spectra for mFT. Even though the activity in the REMPI spectra was very similar for these two molecules, the details of the changing vibrational character showed that in fact there were significant differences in the mixings occurring as a result of electronic excitation and ionization. This could be seen from the calculated form of the vibrations, as well as the differences in the vibrational activity exhibited in the spectra. In general terms, the calculated Duschinsky matrices were in line with the observed spectral activity, even though such matrices are only expected to be approximate reflections of the vibrational character change between electronic states. Unusually, for mFT, if one were to deduce the correspondence between the S1 vibrations and those in the S0 and D0 + states, reverse conclusions would be reached. This was identified as being due to the motions of the carbon atoms in the aromatic ring pairing with the switched C-CH3 and C-F bond motions in the S1 state for two of the vibrations. Remarkably, the Duschinsky matrices picked up the subtlety of the different electronic transitions affecting different geometric aspects of the molecule, and, in a qualitative way, correctly predicted the switched intensities of the transitions involving the D19 and D20 vibrations. We conclude that Duschinsky matrices, even though they are a rather coarse distillation of all of the changes in atomic motions between electronic states, are actually very sensitive to the aspects of the geometry that are most affected by the electronic transition.
Understanding such changes in detail, via assignment of vibrational structure as a result of electronic excitation and photoionization, are clearly key to understanding photo-physico-chemical behaviour.  c The + m 0 and + m 1 levels are degenerate at our resolution. Levels with m ≠ 3n have degenerate + and -levels.    isotopologues are presented. Note that for mFT, the region around the origin to lower wavenumber than the indicated break has been scaled by a factor of 0.5.      26 Figure 6