-1-An experimental and theoretical study of the photoelectron spectra of cis-dichloroethene: Valence shell vertical ionization and vibronic coupling in the low-lying cationic states

valence shell photoelectron spectrum of cis-dichloroethene has been studied both experimentally and theoretically. Photoelectron spectra have been recorded with horizontally and vertically plane polarized synchrotron


I. INTRODUCTION
The Born-Oppenheimer approximation, 1 which separates the electronic and nuclear motions, allows molecular processes to be described as being due to nuclei moving over the potential energy surfaces formed by the electrons. Each electronic state is characterized by its own potential energy surface which is decoupled from those of other electronic states. This picture of non-interacting states has proved highly successful in interpreting the photoelectron spectra of numerous molecules. [2][3][4] Under these conditions, the regular vibrational progressions associated with a specific photoelectron band can be simulated by using the Franck-Condon factors connecting the initial neutral and the final ionic states. 5 However, experiments have shown that in many molecules the vibrational structure becomes erratic, resulting in diffuse bands exhibiting no regular progressions. This irregular structure can be attributed to a breakdown of the Born-Oppenheimer approximation, and is often observed in polyatomic molecules where there is a large number of energetically close-lying electronic states and many nuclear degrees of freedom. [6][7][8][9][10][11][12] Non-adiabatic effects, due to the coupling between electronic and nuclear motions, can lead to the formation of a conical intersection between potential energy surfaces. Such vibronic coupling, by providing a highly efficient pathway between neighbouring electronic states, can lead to photoelectron bands displaying complex vibrational excitations involving not only the totally symmetric modes but also the non-symmetric modes which are normally forbidden (at least in odd quanta). The development of the theoretical aspects of vibronic coupling has been summarized in several reviews. 6,7,9,10 These show that vibronic coupling complicates ionization spectra and can result in photoelectron bands exhibiting irregular vibrational structure and also in the appearance of unexpected bands. 13 The present work concerns the photoelectron spectrum of cis-dichloroethene (C 2 Cl 2 H 2 , Figure 1), henceforth referred to simply as dichloroethene. Synchrotron radiation has been employed to record valence shell photoelectron spectra in the photon excitation range 19 -90 eV. The lowest energy band, assigned to the (3b 1 ) -1X 2 B 1 state, exhibits prolonged vibrational progressions which can be analyzed in terms of excitations involving the totally symmetric The next two states, (2b 1 ) -1D 2 B 1 and (8b 2 ) -1Ẽ 2 B 2 form a single photoelectron band with highly irregular vibrational structure.
The unusual photoelectron band shapes observed in the experimental spectra of dichloroethene arise from vibronic coupling and the breakdown of the adiabatic approximation. Such effects can be expected for two groups of cationic states, namely the (Ã 2 B 2 , B 2 A 1 , and C 2 A 2 ) and the (D 2 B 1 and Ẽ 2 B 2 ) states, due to the relatively small vertical energy gaps between the states within each group. In the first group, the states can be coupled via the b 1 , a 2 and b 2 non-totally symmetric modes (B 2 A 2 b 1 A 1 , A 2 A 1 a 2 A 1 , B 2 A 1 b 2 A 1 ), and in the second group via the a 2 modes (B 1 B 2 a 2 A 1 ).
We have investigated the vibronic coupling effects outlined above by employing the theoretical approach which has been applied previously to various vibronic coupling systems. 6,14 In this approach, the nuclear dynamics are described using model Hamiltonians assuming linear vibronic coupling (LVC) between the electronic states, expressed in the socalled diabatic basis. 6, 14 The parameters required for the LVC models are derived from ab initio calculations using the outer valence Green's function (OVGF) method [15][16][17]  Of relevance to the present work are photoelectron spectra of dichloroethene recorded with HeI, [21][22][23][24][25] HeII, 25 Al Kα, 26 and synchrotron, 27,28 radiation. Mass analyzed threshold ionization (MATI) 29 and pulsed field ionization photoelectron (PFI-PE) 30 spectra have been reported. Electron momentum spectroscopy has also been employed. 31 Theoretical predictions for the orbital energies 24,25,32 and the valence shell photoelectron spectra 25,32,33 have been obtained.

A. Framework for treating nuclear dynamics
In the present work we study the vibrational structure associated with the (Ã 2 B 2 -B 2 A 1 -C 2 A 2 ) and the (D 2 B 1 -Ẽ 2 B 2 ) state photoelectron band systems within the framework of a general multistate multimode vibronic coupling problem, as described by Köppel et al. 6 Moreover, the actual computational protocol for the two-state problem, (D 2 B 1 -Ẽ 2 B 2 ), closely follows that described by Trofimov et al. 8 where the summation runs over the set of N vibronically coupled cationic electronic states, and r and Q denote the electronic and nuclear coordinates, respectively.  35 The normal modes required for the evaluation of the coupling constants were derived from the Cartesian normal modes computed, together with s  , using the MP2 method. 35 The ionization energies () i E Q at various nuclear configurations were obtained using the OVGF method. [15][16][17] The step  s =0.5 was used in the calculations.  36 The Lanczos method allows a sufficiently converged spectral envelope to be obtained prior to the full convergence of the individual transitions. This makes the Lanczos method especially useful in spectroscopic applications. In our case, 10 000 Lanczos iterations were performed to generate the spectra of each vibronic symmetry. The general multistate vibronic coupling code was used in these computations. 37 The theoretical spectral envelopes were obtained by convoluting the generated spectra with Lorentzians of 0.011 eV (FWHM).
Such a convolution yields line profiles closely matching the characteristics of the peaks observed in the experimental photoelectron spectra.

B. Ground state parameters
The equilibrium ground state geometrical parameters of neutral dichloroethene, computed in the present work using the MP2 method and the cc-pVTZ basis set, 38,39 are shown in Table I, together with the experimental data. 40 While the calculated C-Cl bond length and the C=C-Cl angle are in excellent agreement with the experimental values, the C=C bond length is slightly overestimated and the C-H bond length somewhat underestimated by the present calculations. There is also a discrepancy between the calculated and the experimental C=C-H angle.
The corresponding ground state vibrational frequencies, calculated in the harmonic approximation using the same level of theory (MP2/cc-pVTZ), are listed in Table II

C. Calculations of the vertical ionization spectra
The energies (E) and (relative) spectral intensities (pole strengths, P) of the vertical ionization transitions below ~18 eV were computed using the OVGF method [15][16][17] and the cc-pVTZ basis set, 38,39 as implemented in the GAUSSIAN program package. 44 The same OVGF/cc-pVTZ approach, as discussed in Sec. IIA, was employed for evaluation of the vibronic coupling constants. The OVGF method provides a consistent third-order description of the ionization processes in situations where the orbital picture of ionization 45 applies. Such processes normally include all the low-lying ionization transitions. For these transitions, an error of less than 0.2-0.3 eV, with respect to the experimental ionization energies, can be expected in OVGF calculations employing the cc-pVTZ, or better quality, basis set. Due to its high numerical efficiency, the OVGF method is very well suited to a large series of computations, such as that of the ionization energies at various nuclear configurations carried out in the context of the present work for the determination of the coupling constants (Eqs. (10) and (11)).
In order to calculate the vertical ionization spectrum of dichloroethene for the entire valence shell, including the inner valence region, the third-order algebraic diagrammatic construction (ADC(3)) approximation scheme for the one-particle Green's function 15,46,47 was employed. The ADC(3) calculations were performed using the cc-pVTZ basis set with Cartesian representation of the d-functions. The ADC(3) approximation not only describes the main "one-hole" (1h) electronic states through third-order in the residual electronic interaction, as does the OVGF method, but it also accounts for satellite "two-hole oneparticle" (2h-1p) electronic states, which are treated through first-order. The ADC(3) method is therefore applicable in situations where the breakdown of the orbital picture of ionization 45 takes place. The latter phenomenon manifests itself by a strong redistribution of spectral intensity from the main lines to satellites, and often occurs for inner valence transitions. The ADC(3) and OVGF methods have previously proven to be very successful in similar studies of halogenated molecules. [48][49][50][51][52][53][54] In addition, the outer valence vertical ionization energies were computed using the EOM-IP-CCSD method, [55][56][57][58] as implemented in the Q-Chem program package. 59 The cc-pVTZ basis set was also used in these calculations.
In all our electronic structure calculations of the ionization spectra, the carbon and

III. EXPERIMENTAL APPARATUS AND PROCEDURE
The photoelectron spectra were recorded with a VG Scienta R4000 hemispherical electron energy analyzer mounted on the soft X-ray undulator-based PLÉIADES beamline at the SOLEIL synchrotron radiation facility. Detailed descriptions of the beamline and station instrumentation have been reported previously, 64,65 so only a summary is given here.
Synchrotron radiation, emitted by an electromagnetic undulator, is dispersed by a modified Petersen type monochromator, 66 incorporating varied line spacing and varied groove depth gratings, and delivered into the electron spectrometer. The spectrometer is mounted in a fixed position such that the electron detection axis lies perpendicular to the storage ring orbital plane. The undulator allows the plane of the linearly polarized radiation to be chosen to lie either parallel or perpendicular to the orbital plane. The electron spectra were recorded using an analyzer pass energy of 10 eV. The photoelectron anisotropy parameters, β, characterizing the angular distribution, were obtained from spectra recorded using parallel and perpendicularly polarized radiation, as described previously. 65 The electron spectra were corrected for the transmission efficiency of the analyzer as a function of kinetic energy. 67 19-07-18 The electron binding energy scale was calibrated by comparing a simulation, which included hot-band excitations, of the X 2 B 1 state photoelectron band 68 with the adiabatic ionization energy determined in the MATI experiment.
The highest occupied orbital, 3b 1 , can be assigned as a -type C=C double bond.
However, the Mulliken populations show that the chlorine character in the 3b 1 orbital is substantial and almost comparable with the carbon content. This implies that the 3b 1 orbital only nominally represents the carbon-carbon double bond and has features similar to that of the -type orbital describing the chlorine lone-pairs ( Figure 2).
A related orbital, 2b 1 , is constructed in a manner similar to the 3b 1 orbital ( Figure 2).
According to the Mulliken populations, this orbital should nominally be referred to as a chlorine lone-pair ( Cl LP ), since the chlorine character slightly exceeds the carbon character.
The difference between the 3b 1 and 2b 1 MOs can be understood from the plots shown in Figure 2. For the 3b 1 orbital a nodal plane occurs between the C and Cl atoms, while the 2b 1 orbital is fully bonding. In contrast to the 2b 1 MO, the 2a 2 orbital contains no contribution from the carbons and can be considered as a pure -type combination of chlorine lone pairs ( Cl LP ).
The 9b 2 and 10a 1 -type orbitals are also practically pure chlorine lone-pair orbitals ( Cl LP ). As can be seen from the plots in Figure 2, these orbitals differ only in the sign of the combination of the atomic chlorine p-orbitals.
According to the present analysis (Table III and Figure 2), the 8b 2 and 9a 1 orbitals are also chlorine -type lone-pairs and are involved in the C-Cl bonding. The 8a 1 , -type orbital, describes bonding between all the atoms.

B. Assignment of the photoelectron spectrum of dichloroethene
The present HF, OVGF, ADC(3) and EOM-IP-CCSD results for the vertical outer valence ionization transitions, obtained with the cc-pVTZ basis sets, are listed in Table IV together with the experimental values. The orbital picture of ionization is fulfilled for the six lowest ionization transitions.
According to our ADC(3) calculations, the lowest 2h-1p-satellite appears at 14.58 eV (P ~ 0.01) and represents a transition to a -* excited state of the cation having 2 A 2 symmetry. This excited state is predicted to have a dominant electronic configuration of 3b 1 2 3a 2 and to acquire its intensity from the 2a 2 ( CL LP ) orbital. The next satellite occurs at 15.68 eV (P ~ 0.27) and is a shake-down transition with the final state 2 A 1 (9b 2 1 2b 1 1 3a 2 ). Our ADC(3) calculations predict that this satellite is related to the ionization of the 9a 1 () MO whose main (1h-) line appears at 15.79 eV (P ~ 0.60). Satellites become more numerous at higher energy, but the orbital picture of ionization 45 generally holds below ~ 20 eV (Figure 3), thereby allowing the experimental spectrum to be interpreted in terms of the main lines.
Hence, the assignment of the observed structure is fairly straightforward. Our theoretical results (Figure 3), indicate that satellites also contribute to the next two bands in the experimental spectrum, due to the 8a 1 () -1 and 7b 2 () -1 states, with maxima at 16.9 and 18.9 eV, respectively. The corresponding peak maxima at 17.38 and 19.10 eV, respectively, are shifted slightly from the experimental values, apparently due to the increased 2h-1p-character of the final states. The bands at binding energies above 20 eV are affected substantially by break-down phenomena and can no longer be described by the orbital picture of ionization. 45 Here, the experimental spectrum becomes increasingly diffuse since groups of overlapping satellite states, covering a wide energy range, replace the dominant main line transitions. Although the structure in this region is extremely complex, a few bands can be assigned. The prominent maximum observed at 22.56 eV can be attributed to states gaining their intensity from the ionization of the 7a 1 orbital. A further calculated peak maximum at 23.38 eV (Figure 3) corresponds to an intense satellite (P = 0.34) of a complex nature containing contributions from configurations such as 7b 2 1 3b 1 1 3a 2 .
At higher energy, the spectrum shows two broad peaks centered at ~25.4 and 26.9 eV.
The interpretation of these peaks is less conclusive as the theoretical spectral profile appears more structured than the experimental spectrum. However, it seems that the two peaks are mainly due to transitions related to the 6b 2 and 6a 1 orbitals.

C. Vibrational structure of the lowest photoelectron bands
As has been shown in Sec. IVB, our electronic structure calculations provide a reliable description of the cationic states responsible for the photoelectron bands observed below the onset, at ~14.5 eV, of the 2h-1p-satellites. According to our results, six cationic states occur in the binding energy range below this onset. The lowest of these states gives rise to an isolated band between ~9. 6  At the equilibrium ground state geometry of neutral dichloroethene, the lowest cationic state is separated from the higher lying states by a substantial energy interval (~1.9 eV, Table IV). Therefore the adiabatic approximation should be valid for the X 2 B 1 state, with the nuclear dynamics being described in terms of a single potential energy surface.
The key characteristics, such as the equilibrium geometry and the vibrational frequencies, of the X 2 B 1 state, as calculated in the present work at the MP2/cc-pVTZ level of theory, are listed in Tables I and II, respectively. The corresponding data for the neutral ground state are also given. As can be seen, the most important changes in the geometry of the X 2 B 1 state in comparison with that of the ground state include a slight increase in the C=C bond length and a decrease of about the same amount in the C-Cl bond length (Table I).
Thus, except for the  2 (a 1 ),  4 (a 1 ) and  7 (a 2 ) modes, with the first two being associated with changes in the C=C and C-Cl bond lengths, there are only minor changes in the frequencies of most of the harmonic vibrations. The frequencies for the  2 and  7 modes are strongly reduced in the X 2 B 1 state (Table II). A pronounced modification to the C=C bond length in the X 2 B 1 state is also predicted by the large intrastate coupling constant  obtained for the  2 mode (Table V). The elongation of the C=C bond can be expected since the X 2 B 1 state is obtained by ionization of the 3b 1 () orbital which is bonding with respect to the carbon atoms. The antibonding character of this orbital with respect to the carbon-chlorine pair of atoms is responsible for the reduction in the C-Cl bond lengths (Sec. IVA, Figure 2), which leads to a noticeable increase in the frequency of the 4 mode.
The intrastate coupling constants  for the totally symmetric modes in the X 2 B 1 state (Table V), and the corresponding ground state vibrational frequencies (Table II) (Table VI).
Since the adiabatic approximation holds for the X 2 B 1 state, a more rigorous approach can be employed to generate the theoretical spectrum. The Franck-Condon factors can be computed at a level beyond the LVC approximation using the harmonic potential energy surfaces obtained at the MP2/cc-pVTZ level of theory for the neutral ground state and the X 2 B 1 cationic state (Fig 4(b)). The explicit evaluation of the Franck-Condon factors was performed using the pre-screening scheme 70,71 as implemented in the GAUSSIAN package. 44 In contrast to the LVC/Poisson spectrum, the final state (X 2 B 1 ) vibrational frequencies were used to generate the spectral intensities. The Franck-Condon spectrum obtained in this way ( Figure 4(b)) is in excellent agreement with the experimental data (Figure 4(a)), and the predicted adiabatic transition energy of 9.64 eV is in accord with the measured value. This closer agreement reflects the importance of the more accurate vibrational frequencies and of the improved description of the vibrational modes in the modeling of the spectrum. We note also that the Duschinsky effect 72 of the normal mode mixing in the final state, which is not treated in the LVC model, is now taken into account.
The present theoretical results indicate that the X 2 B 1 state photoelectron spectrum can be explained satisfactorily in terms of only the totally symmetric modes, in agreement with the Franck-Condon principle. According to our predictions, the most active modes are  2 through to  5 (Table V), and the observed peaks can be assigned to excitations involving these modes ( Figure 2 state photoelectron bands should be affected strongly by non-adiabatic effects. 6 The intersection between the potential energy surfaces associated with the Ã 2 B 2 and C 2 A 2 states takes place at much higher energy and therefore should not be relevant to the spectrum (Table VI, Figure S1).
The interstate coupling constants  characterizing the interactions amongst the Ã 2 B 2 , B 2 A 1 and C 2 A 2 states, via various non-totally symmetric modes, are given in Table VII.
Here, the derivation of the constants was complicated by the specific shape of the potential energy surface of the B 2 A 1 state along the  9 ,  11 , and  12 modes, all of b 2 symmetry (Table   II). According to our ionization energies computed for the molecular geometries distorted along the corresponding vibrational coordinates, the potential energy surface of the B 2 A 1 state is flatter than that of the neutral ground state, whereas a steeper potential energy surface is expected within the LVC approach for non-zero coupling to the potential energy surface of to compute the coupling constants . In such situations, a higher-level model has to be adopted or an additional 2 B 2 state has to be introduced in order to make the fitting possible.
However, since the lower (Ã 2 B 2 state) potential energy surface has the expected shape (which is also flatter than that of the neutral ground state), reflecting the existence of a nonzero coupling along the  9 (b 2 ),  11 (b 2 ), and  12 (b 2 ) modes, one can try to estimate this coupling in an approximate manner. To do this we stay within the LVC level of approximation and assume that the potential energy surface of the  (Table VII) can then be considered as upper bound estimates describing the coupling between the   The results of our vibronic modeling of the (Ã 2 B 2 -B 2 A 1 -C 2 A 2 ) state band system are shown in Figure 5 where the theoretical spectrum accounting for vibronic coupling amongst all three states ( Figure 5(b)) is compared with the Poisson spectrum which is obtained using an approximation where vibronic coupling is not treated (Figure 5(c)). The experimental spectrum is also shown ( Figure 5(a)). The most striking spectral feature, namely the splitting of the second band, observed between ~11.9 and 12.3 eV, into two strong components, cannot be reproduced assuming non-interacting cationic states, but is reproduced qualitatively by the vibronic coupling calculations. This confirms that the present vibronic treatment has been performed at a suitable level, and it also demonstrates the extent to which vibronic interaction can modify spectral structure.
By comparing the spectra shown in Figure 5 it can be seen that the onset of irregularity in the experimental Ã 2 B 2 state photoelectron band above 11.7 eV can be attributed to an additional vibrational excitation (indicated as red bars in Figure 5 Figure 5(b)). The second progression mentioned above (red lines in Figure 5(b)) can be interpreted as excitations of the Ã 2 B 2 -B 2 A 1 coupling modes, namely the  10 (CH bend) and  11 (CCl stretch) modes. This discussion implies that in the energy range below 11.9 eV one does not have nonadiabatic coupling effects, but rather effects of vibronic intensity borrowing. The latter effects are possible below the conical intersection [6], which, according to our results for the Ã 2 B 2 and B 2 A 1 states, occurs at 11.87 eV (Table VI).
According to our theoretical predictions, the photoelectron bands associated with the  (Figure 5(c)). However, some small discrepancies between the predicted and observed profiles still remain, indicating that a refinement to the present vibronic model might be needed. The vertical separation of only ~0.4 eV (Table IV)  suggests that these two states may couple vibronically via the two a 2 modes ( 6 and  7 ), (B 1 B 2 a 2 A 1 ). In the present work, an appropriate two-state LVC model was set up and its parameters were evaluated (Tables V and VII).

The
The intrastate coupling constants  (Table V) (Table VII), the coupling between the two states, via the  6 (a 2 ) and  7 (a 2 ) modes, is rather plotted as a function of binding energy. The β-independent photoelectron spectrum, and the βvalues, were obtained using the procedure described by Powis et al. 65 It is noticeable that the β-parameter associated with the Ã 2 B 2 state is lower in the low binding energy portion of the photoelectron band than it is in the high energy portion, particularly around 11.8 eV. Our vibronic calculations show that the adiabatic approximation is valid for the low energy We have measured photoelectron spectra, and derived the corresponding β-parameters, in the photon energy range 19 -90 eV. 68 These measurements show that the value of the photoelectron anisotropy parameter for the peak occurring around 11.8 eV is always similar to those corresponding to the two main components of the Cooper minimum. 73 The effect of vibronic interactions on the electronic state photoelectron angular distributions and branching ratios of dichloroethene is considered in detail by Powis et al. 68

V. SUMMARY
The ADC(3) approach has been employed to calculate the complete valence shell ionization spectrum of dichloroethene. In addition, vertical ionization energies have been computed using the OVGF and the EOM-IP-CCSD methods. The theoretical results agree well with each other and with the measurements, thereby allowing assignments to be -26-proposed for most of the structure observed in the experimental spectra, including the innervalence regions dominated by satellite states.
The vibrational structure occurring in the lowest photoelectron bands has been studied using the LVC formalism for model Hamiltonians in the diabatic electronic basis. 6  a Peak maxima, as estimated from the present photoelectron spectrum. b The adiabatic transition energy is 9.659 eV.