Photoelectron angular distributions from resonant two-photon ionisation of adiabatically aligned naphthalene and aniline molecules

ABSTRACT Photoelectron images have been measured following the ionisation of aligned distributions of gas phase naphthalene and aniline molecules. Alignment in the adiabatic regime was achieved by interaction with a 100 ps infrared laser pulse, with ionisation achieved in a two-photon resonant scheme using a low intensity UV pulse of ∼6 ps duration. The resulting images are found to exhibit anisotropy that increases when the alignment pulse is present, with the aniline PADs peaking along the polarisation vector of the ionising light and the naphthalene PADs developing a characteristic four-lobed structure. Photoelectron angular distributions (PADs) that result from the ionisation of unaligned and fully aligned distributions of molecules are calculated using the ePolyScat ab initio suite and converted into two-dimensional photoelectron images. In the case of naphthalene excellent agreement is observed between experiment and the simulation for the fully aligned distribution, showing that the alignment step allows us to probe the molecular frame, but in the case of aniline it is clear that additional processes occur following the one-photon resonant step. GRAPHICAL ABSTRACT


Introduction
Photoelectron angular distributions (PADs) are uniquely sensitive to electronic structure and dynamics, to nuclear configuration and dynamics, and to the chirality and Of particular interest have been techniques that enable PADs to be measured 'from the point of view of a molecule'; so-called molecular frame (MF) PADs [1,2]. Although rich information on photoionization dynamics can be achieved for light polyatomic molecular systems by exploiting polarisation geometries in multiphoton ionisation experiments [3], MFPADs provide a means of obtaining comparable information on the photoionization dynamics of heavier and more complex molecular systems.
There are two main techniques that have been used to access MFPADs. The first of these relies on a dissociative ionisation process in which the emitted photoelectron is detected in coincidence with one or more ionic fragments [4][5][6][7][8][9]. This technique requires either the availability of dissociative ionisation pathways in which fragments are ejected in the axial recoil limit or the use of an intense electric field to fragment the molecule in a Coulomb explosion. The second technique, employed in this work, uses a moderately strong laser field to create an aligned distribution of molecules prior to ionisation [10]. Alignment can be achieved in either one dimension (confinement of a single molecular axis in the laboratory frame) or three dimensions (confinement of all three principal molecular axes in the laboratory frame). The alignment is generally characterised by the value of cos 2 θn , where θn is the angle between the polarisation vector of the alignment pulse and the molecular axis being considered. Using this terminology, cos 2 θn = 1 represents complete alignment (coincidence of the molecular frame and laboratory frame axes) and cos 2 θn = 1/3 represents an isotropic distribution. The measured PADs will converge on the molecular frame if the degree of alignment is very high (typically cos 2 θn > 0.9) [11]. The technique applies to most molecules that can be delivered in a cold molecular beam, as long as they possess an anisotropic polarizability tensor.
Laser-induced alignment falls into two limiting regimes; the nonadiabatic and the adiabatic. In the nonadiabatic regime, alignment is induced by a laser pulse, which is short with respect to the molecular rotational period(s), or by a rapidly truncated pulse of longer duration. The rotational wave packets thus created lead to molecular alignment in regularly spaced, narrow time windows termed revivals. A major advantage of the revivals is that they occur after the laser pulse is turned off, such that the influence of the laser field on any observed dynamics of the aligned molecules is eliminated. Photoelectron angular distributions measured from aligned molecules under the field-free conditions provided by rotational revivals have been used to explore strong-field ionisation [12], femtosecond time-resolved photodissociation [13], molecular orbital dynamics [14], and single photon ionisation with VUV pulses [15][16][17][18]. However, revivals typically provide efficient alignment for only a few hundred femtoseconds, which prevents observations of the dynamics of longer-lived molecular processes. Furthermore, a high degree of alignment at a revival is normally only possible for linear and symmetric top molecules, and the best alignment requires pulseshaping and quantum state selection [19]. For asymmetric top molecules, the irregular rotational level structure hampers sharp alignment at revivals [20] and, in particular, makes it challenging to achieve efficient field-free 3D alignment [21][22][23].
The adiabatic alignment regime is realised by turning on the alignment pulse slowly with respect to molecular rotation. In this way, the degree of alignment follows the intensity profile of the pulse and therefore reaches a maximum at the peak of the pulse. Here, it can be very high, approaching true fixed-in-space conditions. Adiabatic alignment applies to a broad range of molecules; it lasts as long as the pulse is on and it is straightforward to implement 3D alignment [24]. Furthermore, it is possible to achieve molecular orientation in which the direction of a permanent dipole moment in a polar molecule is defined [25]. These advantages of adiabatic alignment have been exploited in measurements of PADs following strong-field ionisation, which have been used to image nodal planes in molecular orbitals [24,26], to explore low energy structures with elliptically polarised pulses [27], and to demonstrate that 3D MFPADS can be obtained by controlled molecular rotation in combination with tomographic reconstruction methods [28]. PADs measured following ionisation of adiabatically aligned molecules with x-ray pulses, which are aimed at structural imaging through electron diffraction, have also been reported [29]. The advantages of adiabatic alignment, however, come at a price, namely that the alignment occurs in the presence of the laser field. For the strong-field ionisation studies referred to above, this was not observed to cause significant complications, but molecules in electronically excited states are likely to be perturbed by an alignment pulse whose intensity is > 10 11 W/cm 2 . In the present work, we study weak-field ionisation of electronically excited naphthalene and aniline that have been adiabatically aligned, and in the case of aniline only we observe unwanted complications from the alignment pulse.
In what follows, we present experimental measurements of photoelectron images following two-photon ionisation of adiabatically aligned naphthalene and aniline molecules. In both cases, the two-photon process is resonant at the one-photon level with the S 1 electronically excited state. In order to interpret these results, we present numerical simulations that project limiting case PADs, computed using ab initio scattering calculations, into two-dimensional photoelectron images.

Experimental method
Schematics of the key elements in the experimental setup are given in Figure 1(a,b). More details can be found in Ref. [30]. A molecular beam is formed by expanding a gas mixture of 80 bar of helium and 2 mbar of aniline or 1 mbar of naphthalene into a vacuum chamber through an Even-Lavie valve EL-7-4-2015-HRR,HT [31]. In the case of aniline (naphthalene), the valve was heated to 36°C (50°C). After passage through a 4-mm diameter skimmer, the molecular beam enters a velocity map imaging (VMI) spectrometer where it is crossed at 90°b y two collinearly focused, pulsed laser beams, one to align the molecules and one to ionise them. The electrons produced by the ionisation pulse are extracted with the static electric field (140-150 V/cm) in the VMI spectrometer, and projected onto a two-dimensional imaging detector consisting of a microchannel plate detector with an active diameter of 41.5 mm backed by a phosphor screen; see Figure 1(b). The electron hits on the detector are recorded by a CCD camera (Prosilica GE 680, Allied Vision) and on-line software analysis determines and saves the coordinates of each individual electron hit. Thus, the basic experimental observables are twodimensional velocity images of the photoelectrons. The repetition rate of the experiment is 200 Hz, limited by the pump speed in the vacuum chamber for the Even Lavie valve.
A schematic of the laser set-up is shown in Figure  1(a). Both laser beams originate from the same pulsed Ti:Sapphire laser system (customised Solstice ACE, model 80L-35F-1K-HP-T Spectra-Physics, 1 kHz, 6 W, 40 fs). A part of the uncompressed 800 nm output of the laser system provides the alignment beam. These laser pulses have a duration of 110 ps (FWHM, see Figure  1(c) for pulse profile) and a pulse energy up to 700 μJ. The beam used to ionise the molecules is obtained from an optical parametric amplifier (TOPAS, model TP8U1, Light Conversion, pumped by 3 mJ from the compressed output of the Ti:Sapphire laser system) and subsequent nonlinear optical processes. The TOPAS idler output at ∼ 2215 nm is frequency-mixed with an 800 nm beam from the Ti-Sapphire laser in a 0.5-mm thick BBO crystal to generate a visible beam at ∼ 588 nm.
This beam is then frequency doubled in 40-mm thick KDP crystal to yield the final UV probe beam, which is linearly polarised. The intensity profile of the probe pulse, obtained by cross correlation with a 40-fs-long 800 nm pulse, is shown in the inset of Figure 1(c). The width at half maximum of the pulse is 0.6 ps but there is a long tail extending to ∼ 5 ps. This asymmetric shape as well as the bandwidth of the probe pulse, ∼ 0.06 nm, is due to the thick KDP crystal used for the frequency doubling.
For the aniline measurements, the pulses were centred at 293.85 nm, and the pulse energy was up to 0.2 μJ. For the naphthalene measurements, the pulses were centred at 293.53 nm and the pulse energy was 2 μJ.
A dichroic mirror (DM) is used to overlap the probe beam and the alignment beam, followed by a plano-convex lens (FL, f = 30 cm) which focuses the two collinear beams into the vacuum chamber via the entrance window (EW). The foci of the laser beams are positioned at the point where the laser paths cross the molecular beam. The focal spot size, ω 0 , of the alignment (probe) beam is 35 μm (20 μm). The intensity of the alignment pulses is controlled by the combination of a half-wave plate (HWP) and a thin film polariser (TFP). The alignment pulse polarisation is controlled by passing it through a rotatable half-wave plate (HWP), followed by a quarter-wave plate (QWP) with its fast axis fixed in the horizontal plane.
In most of the measurements, the alignment pulse is linearly polarised corresponding to 1D alignment of the molecules. Photoelectron images were then recorded for the following three cases: (i) no alignment pulse, i.e. randomly aligned molecules, (ii) the polarizations of the alignment pulse and probe pulse parallel to each other, (iii) the polarizations of the alignment pulse and probe pulse perpendicular to each other. In the case of naphthalene, measurements were also conducted on 3D aligned molecules, obtained by using an elliptically polarised alignment pulse.
Before travelling through the dichroic mirror (DM), the pulses in the alignment beam are spectrally truncated by a long-pass transmission filter (LPTF). This leads to a temporal truncation where the intensity drops by more than a factor of 100 over ∼ 10 ps [32,33]. The resulting intensity profile of the alignment pulse, obtained by cross correlation with the probe pulse, is shown in the inset of Figure 1(c). The timing of the probe pulse with respect to the alignment pulse is controlled by a delay stage (DS2) in the probe beam, placed after the KDP crystal.
The experimental procedure yields raw images that result from a 3D distribution of photoelectrons impacting on a 2D detector. Because cylindrical symmetry has been maintained in the experiment the 3D distribution can be recovered through Abel inversion and this was achieved using the BASEX software [34]. Radial and angular distributions were extracted from the 3D distribution, with the radial distribution converted to a photoelectron spectrum (kinetic energy distribution) using the appropriate Jacobian and following calibration. The angular distribution for a given photoelectron peak was obtained by summing the intensity as a function of angle over the whole peak area. This distribution was then fit to a series of even Legendre polynomials, P L (cosθ LF ), up to L = 10, where 'LF' denotes the laboratory frame.

Theory
The various axes and angles that are referred to throughout this section and in the rest of this paper are defined in Figure 2. Molecular frame photoelectron angular distributions (MFPADs) were generated using radial dipole matrix elements calculated by performing quantum scattering calculations using the ePolyScat package [35,36]. In order to generate the initial and final state electronic wavefunctions for the scattering calculations the molecular orbitals were generated on geometry-optimized S 0 structures at the HF/aug-cc-pVDZ level using the GAMESS software package [37,38]. The scattering calculations produced radial dipole matrix elements in the form shown in Equation (1) [35,36].
(1) In Equation (1)  The radial dipole matrix elements were rotated into the frame needed to define a specific geometry of interaction between the molecule and electric field according to Equation (2); Here T (θk, φk, θn, φn) is the resulting matrix element, Y * lm (θk, φk) is a spherical harmonic function and D 1 μ,−μ 0 (Rn) is the Wigner rotation matrix. The emission direction of the photoelectron is denoted by (θk, φk), whereas (θn, φn) denotes the angle between the polarisation vector of the probe pulse and the highest symmetry axis, which in this case is also the most polarisable axis (MPA). In the case of aniline this is the principal molecular axis indicated by the black dashed line in Figure 1(b). The MFPADs are determined by the square of these matrix elements, I p i ,p f μ 0 (θk, φk, θn, φn), according to Equation (3).
In the case of aniline, the initial wavefunction was taken to be the molecular orbital with the largest contribution to the S 1 excited state [39] and the final ionic state populated is the initial state minus a single electron. The naphthalene calculations are complicated by the fact that the excited state has mixed electronic character [40]. Here we have performed the calculations for the S 2 component, which in turn we have represented as arising from a single excitation which in fact contributes only 76% [41]. Details of the method can be found in Ref. [42]. The continuum wavefunction, and hence the MFPAD, was then calculated at a series of photoelectron kinetic energies and angles (θn, φn) Full computational results can be found online, via the ePSdata project [43,44].
The MFPAD depends on the photoelectron kinetic energy, E, and on (θn, φn) (see Figure 2); because of the 3D structure of the molecules the MFPAD will not be cylindrically symmetric. Therefore, the MFPAD can be expressed as [45] where the number of terms depends only on the maximum orbital angular momentum, l max , carried away by the ejected photoelectron; L max = 2l max . The ePolyScat calculations also provide values of β, the coefficient of P 2 (cos θ LF )n the photoelectron angular distribution that arises following ionisation of an isotropic distribution of MPAs. In the case of aniline, the trend in these values as a function of photoelectron kinetic energy can be compared with the trend in the values of the equivalent coefficient that have been determined in (1 + 1) two-photon ionisation experiments by Qu et al. [46] and by Thompson et al. [47] Although the experimental values will be influenced by the small anisotropy introduced in the two-photon ionisation process, in both cases the coefficient of P 2 (cos θ LF )ecreases from a positive value at ∼ 0 eV to zero at ∼ 0.5 eV and is then increasingly negative from ∼ 0.5 eV to ∼ 1 eV. This comparison therefore enables us to verify the computational results and that the calculated energies are in good agreement with the experimental energies.
Two separate processes were used to generate the simulated photoelectron images, one for ionisation of a 'completely aligned' sample ( cos 2 θn = 1 or cos 2 θn = 0) and one for ionisation of an isotropic sample cos 2 θn = 1/3 . For the completely aligned sample, a full 3D velocity distribution for a single component of the ionisation continuum (a u /b 1u for naphthalene; a 2 /b 1 for aniline) was created in the molecular frame using the radial dipole matrix elements at the chosen photoelectron kinetic energy. The molecular frame PAD was then rotated so that the most polarisable axis was aligned vertically (a u /a 2 ) or horizontally (b 1u /b 1 ) and then azimuthally averaged. The resulting 3D distribution was then projected onto a 2D plane to create simulated photoelectron images. For the isotropic sample a 3D laboratory frame PAD was created using the β parameter calculated by ePolyScat at the chosen photoelectron kinetic energy and then projected onto a 2D plane to create simulated photoelectron images.

Naphthalene
Naphthalene was ionised in a (1 + 1) scheme through thē 8 171 8 1 vibrational state [48] at 2052 cm −1 above the S 1 origin using ∼ 293.53 nm light linearly polarised along the Z direction ( Figure 3). The raw photoelectron image that is measured in the absence of the alignment pulse is shown in Figure 3a(ii). Two prominent rings are observed in the image, with a slight preference for photoelectron emission direction along the polarisation of the probe polarisation vector in both rings. The effect of introducing an alignment pulse that is linearly polarised along Z can be seen in Figure 3b(ii); this pulse is expected to induce 1D alignment, confining the long axis of the molecules along the Z as illustrated in Figure 3b(i). In Figure 3b(ii) it can be seen that, in the case of the outer ring, the intensity of the electron emission along the Zaxis decreases and a four-lobed structure appears. Measurements were also made with an elliptically polarised alignment beam to induce 3D alignment; in this case the major polarisation axis was directed along the Zaxis and the minor polarisation axis along the Y-axis with an ellipticity ratio of 3:1. The resulting alignment is illustrated schematically in Figure 3c(i). The outermost ring in the image shows the same characteristic four-lobed structure, see Figure 3c(ii), with the suppression of the photoelectron emission along the Z-axis a little more pronounced than when the molecules are 1D aligned.
Because cylindrical symmetry has been preserved to measure the images shown in Figure 3(a,b) the BASEX software can be used to invert the images. However, when the naphthalene molecules are aligned in three dimensions (Figure 3c) cylindrical symmetry is broken. Although alternative routines, such as FINA [49,50], do exist to deal with this situation, in this work we have not determined a kinetic energy distribution or angular distribution for the image shown in Figure 3(c) so this image will not be discussed in what follows.
The rings observed in the image appear as distinct peaks in the kinetic energy distribution, shown for randomly oriented molecules by the blue curve in Figure 4. The peak corresponding to the outermost ring is labelled peak 1 in Figure 4 and centred at 0.33 eV. This peak corresponds to the formation of the naphthalene cation in its vibrational ground state. Peak 2 corresponds to the next ring and is centred at 0.12 eV; this peak corresponds to the formation of the naphthalene cation in an excited vibrational state that is likely to be the8 1 7 1 state that was observed at an ion energy of 1503 cm −1 (photoelectron kinetic energy of 953 cm −1 ) by Cockett et al. [51] following ionisation of the8 1 8 1 state at 1135 cm −1 above the S 1 origin. The kinetic energy distribution extends almost to 2 eV, even with no alignment pulse present. Such high energies indicate that the naphthalene molecule can absorb three photons from the probe pulse. The kinetic energy distribution that results when the molecules are aligned in one dimension by the 800 nm pulse is shown by the red curve in Figure 4. It  Figure 3a(ii). The red curve corresponds to 1D aligned molecules and is obtained from the image in Figure 3b(ii). The baseline corresponds to zero intensity.
can be seen that the alignment pulse only causes minor changes in the photoelectron spectrum.
Angle-resolved photoelectron intensities, I LF (θ LF ), are obtained for the main photoelectron peaks, where θ LF is the polar angle between the electron emission direction in the detector plane and the laboratory frame (LF) axis defined by the polarisation of the probe beam. The angular distributions can be quantified by fitting I LF (θ LF ) to an expansion in Legendre polynomials: to obtain values of the coefficients b LF L . In Equation (5) b LF L is a normalised laboratory frame anisotropy parameter and P L (cosθ LF ) is a Legendre polynomial, both of degree L. In general, the number of terms required in the expansion depends on the experimental geometry, the number of photons, the degree of alignment, and the maximum orbital angular momentum associated with the departing photoelectron. Because the experiment has cylindrical symmetry and inversion symmetry there is no dependence on the azimuthal angle φ LF and only even values of L contribute to the series. In practice, we find that the inclusion of terms with L > 10 does not improve the fit. Fitting the photoelectron intensity (determined through reconstruction) as a function of angle enables b LF L parameters to be deduced for both rings in the images shown in Figure 3(a,b); these are shown in Table 1. The four-lobed structure associated with peak 1 when the alignment pulse is present means that the angular distribution must contain a significant non-zero contribution from b LF L coefficients with L ≥ 4. Inspection of Table 1 shows that the magnitude of b LF 4 is significant for both of the photoelectron peaks analysed in naphthalene, but that in the case of peak 1 |b LF 4 | |b LF 2 |, consistent with the characteristic four-lobed shape observed.
In order to gain insight into the measured photoelectron anisotropy we have performed ePolyScat calculations of the photoionization dynamics in order to determine MFPADs, as described in Section 3. In Figure 5 we show examples of the calculated MFPADs at different photoelectron kinetic energies and in two different geometries: (θn, φn) = (0, 0) and (θn, φn) = π 2 , π 2 . These geometries select photoelectron partial waves of a u and b 1u symmetry, respectively. The dramatic change in the MFPADs over the 0.13-4.0 eV range of kinetic energy can be attributed to the presence of a shape resonance by analogy with experimental observations on other similar molecules [52,53].
The MFPADs are relatively simple and have up-down symmetry at all kinetic energies. As the kinetic energy increases, more lobes appear in the MFPADs for both polarisation geometries. The LFPAD results from an average over all the possible directions of the MPA in the laboratory frame, weighted by any anisotropy in the distribution of MPAs that is introduced by the experiment by the alignment pulse. When the alignment pulse is introduced the distribution of MPAs is confined along the laboratory frame Z axis, according to the value of cos 2 θn . In the limit of cos 2 θn = 1 or cos 2 θn = 0 the LFPAD would converge on the a u or b 1u MFPAD, respectively. In order to establish how close to a molecular frame measurement we have achieved in the photoelectron images shown in Figure 3(b), we have used the output of the ePolyScat calculations at 0.33 eV photoelectron kinetic energy to create simulated photoelectron images in three limiting cases: (a) ionisation  of an isotropic distribution of naphthalene molecules cos 2 θn = 1/3 , (b) ionisation of a distribution of naphthalene molecules whose MPAs are completely aligned along the polarisation vector of the ionising beam ( cos 2 θn = 1; this selects the a u continuum), and (c) ionisation of a distribution of naphthalene molecules whose MPAs are completely aligned perpendicular to the polarisation vector of the ionising beam ( cos 2 θn = 0; this selects the b 1u continuum). The results of these simulations are shown in Figure 6 and can be compared with the equivalent experimental images; we have also included in Figure 6 the experimental photoelectron image that results when the polarisation of the alignment beam is perpendicular to the polarisation of the probe beam.
When an isotropic sample is ionised the photoelectron wave function will contain contributions from all of the possible ionisation continua which are defined by the photoelectron orbital angular momentum, l, and the irreducible representation χ . In the case of naphthalene, the possible continua are la u , lb 1u , and lb 3u . The PAD is determined by the relative magnitude of each component (dictated by the radial dipole matrix element) and the relative phase between components. Because the phase contribution is complicated, and controls the extent of constructive and destructive interference, it is not possible to simply predict what the laboratory frame PAD is expected to look like on the basis of the plots shown in Figure 5. However, the ePolyScat code determines β, the coefficient of P 2 (cos θ LF ) in the photoelectron angular distribution that arises following ionisation of an isotropic distribution of MPAs; this value is used to generate the image shown in Figure 6(d). In the experiment, a resonant two-photon ionisation scheme is used and so the sample ionised is not fully isotropic. Nonetheless, the photoelectron intensity peaks along the vertical axis in Figure 6(a), consistent with the simulation shown in Figure 6(d).
When a fully aligned sample is ionised a single irreducible representation is selected; la u when the ionisation beam is polarised along the MPA and, in our experimental setup, lb 1u when it is polarised perpendicular to the MPA. In the experiment we cannot achieve complete alignment, but as the alignment improves we expect to converge on the la u result in the parallel geometry and the lb 1u result in the perpendicular geometry. In Figure 6(e) we can see that the four-fold structure that appears in the outer ring of the experimental images when the alignment beam is introduced in the parallel geometry is reproduced in the simulations, suggesting that a high degree of alignment must have been achieved and that the measured PADs from naphthalene are close to the molecular frame result. Furthermore, the simulations also broadly reproduce the experimental image in the crossed polarisation case. This agreement is remarkable considering that (i) the complicated nature of the excited electronic state in naphthalene has not been fully accounted for in the calculations, and (ii) the experimental alignment is not perfect.

Aniline
A distribution of randomly oriented aniline molecules (Figure 7a(i)) was excited to the S 1 origin using light at 293.85 nm that is linearly polarised along Z and ionised following the absorption of a second photon from the same laser beam. The resulting raw photoelectron image is shown in Figure 7a(ii) and shows three prominent rings, labelled 1-3, with the photoelectron intensity approximately isotropic in all rings. Figure 7(b) shows the effect that introducing an alignment pulse, linearly polarised along Z, has on the observed photoelectron image. This pulse causes the molecules to align such that the distribution of MPAs is confined with respect to the polarisation direction of the probe pulse, as indicated in Figure 7b(i). The raw image is shown in Figure 7b(ii) and can be compared with the image in Figure 7a(ii) which was obtained without the alignment pulse. Two prominent changes can be seen: first, the rings are now clearly anisotropic with an enhanced intensity along the z-axis, and secondly, evidence of additional rings can be seen.
The resulting photoelectron spectra are shown in Figure 8. The spectrum arising from the unaligned sample is consistent with the spectrum obtained by Qu and coworkers [46], considering the differences in experimental conditions. In this figure it can be seen that the peak with maximum intensity is centred at 0.75 eV, in agreement with our expectation for the kinetic energy of photoelectrons associated with the formation of the cation in its vibrational origin [46]; the results discussed in this paper focus on these photoelectrons. The peaks at lower kinetic energies correspond to the formation of the cation in vibrationally excited states. The alignment pulse causes a significant effect on the photoelectron spectrum, as can be seen by comparing the red and blue lines in Figure 8. In particular, photoelectrons with kinetic energies up to 1.6 eV are detected; higher than energetically possible following the absorption of two probe photons. This can be explained if some of the electronically excited aniline molecules absorb an 800 nm photon from the alignment pulse before absorbing the second UV photon in a (1 + 1 + 1) ionisation scenario. If this occurs, then aniline molecules that are ionised to create cations in the ground vibrational state would release photoelectrons with a kinetic energy of ∼ 2.27 eV. As we will see, this process significantly affects the anisotropy observed in the photoelectron images.
In Figure 9 we show examples of the resulting MFPADs at different photoelectron kinetic energies and in two different geometries: (θn, φn) = (0, 0) and (θn, φn) = π 2 , π 2 . These geometries select photoelectron partial waves of a 2 and b 1 symmetry, respectively. The MFPADs change dramatically over the 0.1-4.1 eV range of kinetic energy, as expected from the experimental results presented by Qu et al. [46] As with naphthalene, we have used the output of the ePolyScat calculations, in this case at the experimental photoelectron kinetic energy (0.7 eV) corresponding to the outer ring in Figure 7(b), to create simulated photoelectron images in three limiting cases; (a) ionisation of  Figure 7a(ii). The red curve corresponds to 1D aligned molecules and is obtained from the image in Figure 7b(ii). The baseline corresponds to zero intensity.
an isotropic distribution of aniline molecules ( cos 2 θn = 1/3), (b) ionisation of a distribution of aniline molecules whose MPAs are completely aligned along the polarisation vector of the ionising beam ( cos 2 θn = 1; this selects the a 2 continuum), and (c) ionisation of a distribution of aniline molecules whose MPAs are completely aligned perpendicular to the polarisation vector of the ionising beam ( cos 2 θn = 0; this selects the b 1 continuum). The results of these simulations are shown in Figure 10 below the equivalent experimental images. We have also included in Figure 10 the experimental photoelectron image that results when the polarisation of the alignment beam is perpendicular to the polarisation of the probe beam.
In Figure 10 we can see that the simulated images do not reproduce what is seen in the experiment. In order to investigate whether this is caused by the fact that aniline does not align as well as naphthalene, a series of experimental photoelectron images was recorded at different intensities of the alignment pulse, with parallel polarizations of the alignment beam and the probe beam. In each case the angular distributions were fitted to Equation (5) and the anisotropy parameters obtained from the fits are presented in Figure  11. For the probe pulse only, the b LF L parameters are small with b LF 2 = −0.1 and b LF 4 = 0.06, consistent with the near circularly-symmetric electron image. As the intensity of the alignment pulse is increased, the values of b LF L with L > 2 remain close to zero. Conversely, the value of b LF 2 increases steadily to a value of ∼ 0.4, consistent with photoelectron intensity being concentrated along the direction of the polarisation direction of the probe pulse. At higher alignment intensities, the value of b LF 2 continues to increase but at a much lower rate.   The change in the experimental values of b LF 2 seen in Figure 11 can be attributed to an increased degree of alignment, i.e. an increased value of cos 2 θn , as the intensity increases [10]. The increasingly positive b LF 2 values tell us that, as the alignment improves, the experimental photoelectron emission peaks increasingly parallel to the polarisation vector of the probe beam. However, in Figure  10(f) we have seen that the simulation for completely aligned aniline molecules shows photoelectron emission peaking perpendicular to the polarisation vector of the probe beam. We can see that even for a high degree of alignment we do not expect the experimental images to converge on the molecular frame. We therefore attribute the discrepancy between the experimental and simulated images to the absorption of a 800 nm photon by aniline in its S 1 electronic state. The absorption of the 800 nm photon will lead to excitation of a higher-lying electronic (Rydberg) state and allow access to higher-lying vibrational states in the cation. The evidence for this process can be seen in Figure 8 where the photoelectron spectrum is qualitatively different when the alignment pulse is introduced.

Conclusion
We have presented photoelectron images measured following the ionisation of aligned distributions of gas phase naphthalene and aniline molecules. The resulting images are found to exhibit anisotropy that increases when the alignment pulse is present with the aniline PADs peaking along the polarisation vector of the ionising light and the naphthalene PADs developing a characteristic fourlobed structure. Comparison with calculated photoelectron images that result from the ionisation of unaligned and fully aligned distributions of molecules demonstrates that an excellent degree of alignment has been achieved in the case of naphthalene, and that the photoelectron images are largely determined by the photoelectron angular distribution in the molecular frame.
In many respects the aniline work represents a cautionary tale. It is clear that the presence of the alignment pulse provides an additional ionisation channel involving the absorption of 800 nm photons by molecules that have been resonantly excited to S 1 by the UV pulse. Many other electronically excited molecules are likely to be similarly susceptible to the absorption of photons from an alignment pulse. We offer two ways to eliminate these unwanted processes. The first is to ionise molecules through absorption of a single VUV photon. In these cases, because no electronically excited states are involved, the most effective adiabatic alignment techniques can be used, allowing the measurement of PADs from complicated asymmetric top molecules that are close to fixed in space. However, studies of photophysical processes in aligned molecules require the preparation of electronically excited states. In these cases, perturbations caused by the alignment field can be avoided by turning it off once a sufficiently high degree of alignment has been achieved. Recently this technique has been demonstrated for a range of complex molecules embedded in helium nanodroplets [32].
In these experiments a 150 ps long pulse, truncated to less than 10 ps at its peak, created sharp 1D or 3D alignment under field-free conditions lasting 10-20 ps. Although the field-free alignment will not last as long when created in gas phase molecules, it is expected to be sufficient to allow PADs from highly aligned molecules to be recorded [54].