The cage fragmentation of doubly ionized norbornane: A Born-Oppenheimer molecular dynamics study

Chemical Physics Letters 584 (2013) 24–29

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The cage fragmentation of doubly ionized norbornane: A Born-Oppenheimer molecular dynamics study S. Knippenberg a,b,⇑, B. Hajgató c a

Service de Chimie des Matériaux Nouveaux, Université de Mons, Place du Parc 20, B-7000 Mons, Belgium Département de Chimie, B6c, Université de Liège, B-4000 Liège, Belgium c Eenheid Algemene Chemie, Vrije Universiteit Brussel (VUB), Faculteit Wetenschappen, Pleinlaan 2, B-1050 Brussels, Belgium b

a r t i c l e

i n f o

Article history: Received 26 July 2012 In final form 31 July 2013 Available online 7 August 2013

a b s t r a c t Results are reported of Born-Oppenheimer molecular dynamics calculations performed on the singlet dication of norbornane, starting from the neutral ground state geometry. Intramolecular rearrangements and charge dissociation processes, which probably take place in the innermost valence ionization spectrum, are discussed and an analysis by means of natural bond orders and Wiberg bond indices has been performed. The outcome of these simulations and the observed cage fragmentation might explain a tremendous rise of electron-impact (e, 2e) ionization cross sections of norbornane at electron binding energies around the double-ionization threshold. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The electronic structure of the hydrocarbon norbornane, which is a highly strained cage compound also known as bicyclo [2.2.1] heptane, has been a few years ago subject to rather remarkable experimental studies employing electron momentum spectroscopy (EMS), which enables an analysis of ionization intensities in binary (e, 2e) electron impact ionization experiments (M þ e ! M þ þ 2e ) at high kinetic impact energies by virtue of a combination of the principles of scattering and ionization experiments. In the experimental spectra and related momentum distributions, a particularly broad and intense band at 25 eV was seen, of which no evidence could be found in previous and contemporary calculations and ionization experiments [1]. In literature, this is referred to as the ’band 12 issue’. One of the first attempts to investigate the outer-valence electronic structure of this molecule was performed by Bischof et al. [2] in 1969. In the late 90s, these He I photoemission spectra were ameliorated by Getzlaff and Schönhense [3]. Using Ultraviolet Photoelectron Spectroscopy (UPS) along with a He II photon beam, Bieri et al. investigated the inner valence ionization bands up to  24 eV [4]. To achieve more information on the energy range of band 12, J. H. D. Eland (Oxford University, United Kingdom) employed a 256 Å photon beam for binding energies up to 40 eV [5]. He only noticed a barely visible increase of the spectral background at  26 eV that has been ascribed to the double-ionization thresh-

⇑ Corresponding author. at: Service de Chimie des Matériaux Nouveaux, Université de Mons, Place du Parc 20, B-7000 Mons, Belgium. E-mail addresses: [email protected] (S. Knippenberg), hajgato@ vub.ac.be (B. Hajgató). 0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.07.083

old. Evaluating both the UPS and EMS experiments, the band 12 issue has to be related to ionization processes from the neutral ground state with characteristic time scales in between those of EMS and UPS [5]. In the meantime, one-particle Green’s function (1p-GF) calculations along with the third order algebraic diagrammatic construction scheme [ADC(3)] [6–9] were performed and – except for the region of the band 12 issue – the simulated spectra and related momentum distributions were found to confirm the EMS experiments [1]. Band 12 could not be related to the lower lying bands which originate from ionization out of the 1b1 and 1b2 orbitals as the momentum distributions have clearly a different shape, while the energy difference and the lack on recovered intensity prevent a direct assignment with respect to the higher lying 1a1 band, too. Later [10], the dependence on the inclusion of double electronic excitations in the shake-up excitation operator was investigated. The 3h–2p states were only found to play a minor role in the spectral region. It was therefore reasonable that the band 12 issue of norbornane is not due to a vertical ionization transition and a tentative description in terms of ultrafast nuclear dynamical effects and autoionization processes has become more plausible [10,11]. In the current study, Born-Oppenheimer molecular dynamics calculations are therefore performed on doubly ionized norbornane using its C2v ground state geometry. In the following section of this Letter, we briefly discuss the computational methods. In Section 3, the calculations and the obtained dynamics of the charged molecule are discussed, based on selected time windows between 0 and 1200 fs after double ionization. Before concluding, the shift of charges within the molecule is investigated reverting to a natural population analysis.

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S. Knippenberg, B. Hajgató / Chemical Physics Letters 584 (2013) 24–29

2. Computational details Norbornane in its singlet ground state has been optimized using density functional theory (DFT) in conjunction with the non-local hybrid and gradient corrected Becke three-parameter Lee–Yang– Parr functional (B3LYP) [12,13], an approach which is known to deliver excellent results for equilibrium geometries [14,15]. Dunning’s correlation-consistent polarized valence double f basis set have been used, augmented by a set of diffuse s; p and s; p; d functions on hydrogen and carbon atoms, respectively (aug-cc-pVDZ) [16,17]. A study of nuclear dynamical effects and the molecular relaxation in the final doubly ionized state is based on Born-Oppenheimer molecular dynamical (BOMD) calculations [18–22], at the same B3LYP/aug-cc-pVDZ level, of the evolution in time of the system immediately after ionization. The trajectory step size was set to 0.250 au, the Bulirsch–Stoer method was used for the integration scheme [23,24], along with an integration step size of 0.2 fs. A fifth-order polynomial fit was applied in the integration correction scheme. All BOMD trajectory calculations have been performed at 0 K. We thereby neglect thermal motions in the final doubly ionized state, that is, we assume that the only source of kinetic energy immediately after ionization exclusively arises from potential energy gradients. This approximation is justified when comparing the extent of thermal fluctuations at room temperature (kB T  25 meV) with double ionization energies larger than 10 eV and an energy resolution on the order of 0.6 eV, which corresponds with the specifications of the set-up in the EMS group of Flinders University [1]. Starting from 200 fs and up to 1200 fs after the double ionization, the alterations that the electronic wave function undergo during the nuclear relaxation processes have been quantified at the same level with intervals of 100 fs, according to calculations of atomic charges and Wiberg bond orders [25], within the framework of a natural bond orbital (NBO) analysis [26,27]. Total bond orders have been calculated by summing the values derived from the a- and b-spin electron densities in the matrix of Wiberg indices [28]. The current approach of both DFT and molecular dynamics is among the best ones which can be employed to study a system with the size of norbornane and is therefore in line with other recent studies upon reaction dynamics [29–32]. Furthermore, at this moment, we cannot perform non-adiabatic ab initio molecular dynamics due to the complexity of the problem and the computational demand of these kind of simulations on ionization processes. As a consequence, we have to restrict ourself to an adiabatic approximation, that still gives profound insight. All results presented in the current study have been obtained using GAUSSIAN 09 [33].

comes into play. With respect to the ultrafast time scale of such a cage fragmentation, the BOMD calculation has been performed on the geometry of the neutral singlet ground state of norbornane (see Figure 1). The pathway obtained by the BOMD run, of which snapshots are given in Figures 2 and 3, yields indeed an ultrafast cage fragmentation, which leaves contra-intuitively the C2 —C1 —C3 bridge intact: from  127 fs after the double ionization, the C7 —C3 and C5 —C2 bonds get broken and an ethylene-like structure, involving these two carbon atoms and the hydrogens H12 ; H10 ; H8 and H6 , detaches from the remaining carbon five ring. After 1200 fs, the distance between C7 and C3 has increased and exceeds 30 Å. During this process, the orientation of the ethylene fragment changes and charge rearrangements together with proton shifts take place. It can be remarked that the current study confirms the results of 2þ the previous work on norbornane [11] in the sense that the compound pulls apart, although the fragments found in both studies differ; by manually scanning the potential energy surface at the þ time, species with bruto formula C5 Hþ 7 ¼ CH2 and CH3 were found. To verify the charge distribution, a natural population analysis of the electronic density has been performed (see Table 1). It can be seen that already in the neutral ground state the charges on C2 and C3 are slightly distinguishable from the other five carbons, as the partial charges on these two atoms amount to 0.265 in stead of 0.444. After double ionization, at t ¼ 0 fs, the double positive charge is quite homogeneously distributed among the molecular system: an increase of 0.070–0.090 elementary charges has been seen, except for the bridgehead C1 atom, which keeps or even slightly augments its partial negative charge. The outermost hydrogen atoms H7 ; H8 ; H11 and H12 , and in lesser extent H3 and H4 gather a relatively enlarged share of the positive charge; together, these six atoms are responsible for collecting a bit more than 50% of the released charge after double ionization. It is noted that the charge of the atoms of the ethylene-like fragment prior to double ionization amounts only to +0.018. At the instant of double ionization (0 fs) however, the partial charge of these atoms equals +0.774, while at the end of the simulation, at 1200 fs, the ethylene fragment has a charge of +0.531, or a bit more than a quarter of the total charge of norbornane. The fragmentation can clearly be seen when the charge of the C2 and C3 bridgehead atoms is considered: it changes from 0.086 at 100 fs for both atoms to +0.184 and +0.313, respectively. As a small side effect, the negative charge on C1 increases; it is this local spatial distribu-

H7 H5

H11 C4

C6

H1 3. Results and discussion In line with our study on the potential energy surface of norbornane [11] published in 2007, which was also performed using the B3LYP functional and a (however non-diffuse) correlation consistent double f basis, the current investigation is built upon the question whether the structure of norbornane corroborates a charge fragmentation after double ionization: within a fully saturated hydrocarbon cage compound such as norbornane, all chemical bonds derive, according to a basic Lewis depiction, from the pairing of two electrons with opposite spins. In view of the importance of cyclic strains in the cage, it is therefore natural to expect, on intuitive chemical grounds, that a double-ionization event would induce the breaking of a single C–C bond. Severe intramolecular rearrangements are expected, once nuclear dynamics

H3

C2

H9 C3

C1

H4

H2

H6 H8

C5

H10

C7

H12

Figure 1. Norbornane in its neutral ground state. The nonredundant internal coordinates of this compound within the C2v symmetry point group (B3LYP/aug-ccpVDZ geometry) are as follows: RðC1 ; C2 Þ ¼ 1:55 Å; RðC2 ; C4 Þ ¼ 1:55 Å ; RðC4 ; C6 Þ ¼ 1:57 Å; RðC1 ; H1 Þ ¼ 1:10 Å; RðC2 ; H3 Þ ¼ 1:10 Å; RðC4 ; H5 Þ ¼ 1:10 Å; RðC4 ; H7 Þ ¼ 1:10 Å; hðC3 ; C1 ; C2 Þ ¼ 94:4 ; hðC1 ; C2 ; C4 Þ ¼ 101:5 ; hðC2 ; C4 ; C6 Þ ¼ 103:1 ; hðH1 ; C1 ; C2 Þ ¼ 109:0 ; hðH3 ; C2 ; C4 Þ ¼ 113:9 ; hðH5 ; C4 ; C6 Þ ¼ 112:6 ; hðH7 ; C4 ; C6 Þ ¼ 111:1 ; sðC2 ; C4 ; C6 ; C3 Þ ¼ 0:0 ; s ðC1 ; C2 ; C4 ; C6 Þ ¼ 35:3 ; sðH5 ; C4 ; C6 ; C3 Þ ¼ 120:8 ; sðH7 ; C4 ; C6 ; C3 Þ ¼ 118:7 ; sðH3 ; C2 ; C4 ; C6 Þ ¼ 160:8 .

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Figure 2. Selected frames from the Born-Oppenheimer molecular dynamics calculation on doubly ionized norbornane between 0 and 600 fs. The DFT/B3LYP functional is applied along with the aug-cc-pVDZ basis set.

Figure 3. Selected frames from the Born-Oppenheimer molecular dynamics calculation on doubly ionized norbornane between 700 and 1200 fs. The DFT/B3LYP functional is applied along with the aug-cc-pVDZ basis set.

tion of partial positive and negative charges over C1 —C2 —C3 which keeps the bridge of the original norbornane molecule intact after the double ionization. The increase in distance between the fragments induces a decrease in the absolute charge of the C7 and in lesser extent the C5 atoms, which is seen when a scan is performed from 100 to 400 fs. In the same time range, the positive charges upon H6 ; H8 ; H10 and H12 diminish: a bit less than one third of the initial value is lost for H6 and H10 , compared to almost fifty percent for H8 and H12 . The Wiberg bond indices (given in Table 2) visualize this cage fragmentation and reorientation. At this point it is good to note

that the Wiberg index is a covalent bond index; considering the cage of norbornane in its ground state, which exclusively consists out of covalent C—C bonds and attached hydrogens, the Wiberg tools are very appropriate to be used. Between 100 and 200 fs, the C2 —C5 and C3 —C7 Wiberg bond indices diminish from 0.821 to 0.243 and to 0.033, respectively (see Table 2). The C2 —C7 Wiberg bond index is barely 0.063 at the instance of double ionization, while it amounts to 0.189 and almost equals the C2 —C5 one at the end of the dynamics run. Inside the C5 H8 ring, charge relocations take place: the hole on C3 at 800 fs is redistributed to C6 at 900 fs (see Figure 3 and Table 1), and the proton H9 shifts equivalently from C6 to C3 . The

Table 1 Natural population analysis of the electronic density for the snapshots of the BOMD calculation of the singlet dication of norbornane, starting from the neutral ground state geometry, compared to that of the neutral species.a

1200 fs 0.484 0.226 0.582 0.690 0.210 0.234 0.206 0.321 0.320 0.274 0.362 0.419 0.246 0.410 0.234 0.354 0.233 0.307 0.234

200 fs

300 fs

400 fs

500 fs

600 fs

700 fs

800

900 fs 0.504 0.086 0.086 0.386 0.385 0.386 0.385 0.305 0.305 0.330 0.330 0.328 0.328 0.409 0.409 0.328 0.328 0.409 0.409

0.622 0.184 0.313 0.555 0.424 0.604 0.265 0.389 0.363 0.314 0.306 0.358 0.280 0.379 0.252 0.400 0.268 0.428 0.236

0.704 0.212 0.308 0.556 0.358 0.553 0.193 0.440 0.439 0.281 0.306 0.367 0.211 0.341 0.247 0.348 0.237 0.379 0.247

0.621 0.173 0.218 0.525 0.276 0.449 0.232 0.377 0.381 0.291 0.321 0.346 0.237 0.338 0.209 0.395 0.241 0.336 0.241

0.608 0.208 0.265 0.537 0.231 0.557 0.206 0.354 0.409 0.289 0.299 0.337 0.249 0.326 0.221 0.347 0.254 0.353 0.228

0.607 0.249 0.181 0.554 0.227 0.547 0.202 0.396 0.350 0.318 0.288 0.333 0.244 0.363 0.241 0.341 0.245 0.348 0.239

0.644 0.246 0.223 0.581 0.192 0.546 0.197 0.391 0.397 0.279 0.287 0.368 0.223 0.360 0.231 0.330 0.235 0.363 0.227

0.621 0.133 0.249 0.564 0.232 0.519 0.244 0.384 0.373 0.297 0.311 0.344 0.244 0.350 0.242 0.408 0.237 0.354 0.250

0.543 0.244 0.566 0.620 0.225 0.161 0.224 0.373 0.391 0.294 0.351 0.380 0.229 0.406 0.238 0.363 0.232 0.287 0.228

1200fs C2 C3

1100 fs C2 C3

1000 fs C2 C3

900 fs C2 C3

800 fs C2 C3

700 fs C2 C3

600 fs C2 C3

500 fs C2 C3

400 fs C2 C3

300 fs C2 C3

200 fs C2 C3

100 fs C2 C3

0 fs C2 C3

0.1874 0.0072

0.1646 0.0065

0.1277 0.0078

0.0507 0.0095

0.2524 0.0207

0.1635 0.1566

0.0818 0.2494

0.2307 0.0917

0.2444 0.0217

0.2241 0.0699

0.2433 0.0197

0.8211 0.0623

0.8641 0.0629

C5

0.1894 0.0073

0.1655 0.0066

0.1282 0.0078

0.0510 0.0096

0.2581 0.0212

0.1633 0.1564

0.0792 0.2414

0.2208 0.0878

0.2274 0.0202

0.1793 0.0571

0.1477 0.0325

0.0623 0.8210

0.0629 0.8641

C7

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

H4 H9 H11

0.7652 0.8180 0.0024

0.8665 0.7759 0.0028

0.8307 0.8473 0.0020

0.7954 0.7858 0.0029

0.8807 0.1297 0.0213

0.8949 0.0290 0.0291

0.9015 0.0210 0.0154

0.8900 0.0179 0.0427

0.8767 0.1600 0.0117

0.8846 0.0001 0.0322

0.8851 0.0372 0.0666

0.8665 0.0017 0.0325

0.8522 0.0029 0.0290

C3

0.0502 0.0150 0.8876

0.0055 0.0551 0.8961

0.0162 0.0247 0.8933

0.0230 0.0158 0.8945

0.0033 0.6605 0.8198

0.0026 0.8312 0.7952

0.0019 0.8155 0.8212

0.0027 0.8263 0.7831

0.0027 0.6460 0.8531

0.0025 0.8270 0.7924

0.0034 0.7613 0.6972

0.0022 0.8629 0.6773

0.0029 0.8670 0.6685

C6

B3LYP/aug-cc-pVDZ results.

27

NPA charge of C3 diminishes from +0.249 to 0.566 between 800 and 900 fs, while for C6 the charge increases from 0.519 to +0.161. In the same time interval, the accumulated positive charge of 0.354 on H11 diminishes to 0.287, too. At 700, 800 and 900 fs, Wiberg bond indices (Table 2) of 0.831, 0.661 and 0.016 are found for C6 —H9 ; for H9 —C3 , the indices are 0.029, 0.130, and 0.786, respectively. The evolution of the kinetic energy is given in Figure 4: from 0 eV at the instant of double ionization until  2:9 eV at the end of the simulated time window. Since the total energy is constant, the scheme for the potential energy does not contain more

a

Table 2 Selected Wiberg bond indices for the snapshots of the BOMD calculation of the singlet dication of norbornane.a

S. Knippenberg, B. Hajgató / Chemical Physics Letters 584 (2013) 24–29

B3LYP/aug-cc-pVDZ results. a

1100 fs 0.544 0.212 0.515 0.663 0.206 0.233 0.209 0.348 0.336 0.293 0.327 0.398 0.243 0.377 0.247 0.343 0.249 0.290 0.243

100 fs

0.455 0.171 0.171 0.368 0.368 0.368 0.368 0.291 0.291 0.335 0.335 0.317 0.317 0.438 0.438 0.317 0.317 0.438 0.438

0.562 0.226 0.515 0.679 0.188 0.212 0.193 0.350 0.346 0.288 0.334 0.437 0.230 0.406 0.233 0.313 0.228 0.297 0.236

0 fs

0.441 0.265 0.265 0.444 0.444 0.444 0.444 0.228 0.228 0.239 0.239 0.226 0.226 0.227 0.227 0.226 0.226 0.227 0.227

1000 fs Neutral

C1 C2 C3 C4 C5 C6 C7 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12

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S. Knippenberg, B. Hajgató / Chemical Physics Letters 584 (2013) 24–29

3.5

3

Kinetic energy (eV)

2.5

2

1.5

1

0.5

0 0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Time of simulated dynamics (fs) Figure 4. Evolution of the kinetic energy throughout the BOMD simulation (full line) along with a moving average curve obtained using 128 terms (dashed line).

information. From the very flat slope of the envelope between 900 and 1250 fs in Figure 4, it is clear that our Born Oppenheimer MD run is near to convergence with respect to kinetic energy. The rapid oscillations in the kinetic energy evolution especially below 100 fs are due to a rapid convertion of vibrational to kinetic energy right after double ionization. A distinct band is seen between  140 and  340 fs, which is not primarily related to the breakdown of the C2 —C5 and C3 —C7 bonds (see Table 2), but whose cause should be searched in the rotation of the C2 H4 and C5 H7 fragments with respect to each other (see Figure 2). No other barrier has been seen in the current analysis. We further note that the adiabatic relaxation energy of doubly ionized norbornane in its singlet spinstate under C2v symmetry amounts to 2.4 eV. It can be remarked that at 0 K only the zero pointenergy contributes to the vibrational energy since all vibrational modes are in ground state. However, if the simulations were performed at e.g. room temperature, influences of thermal distributions of the vibrations had to be taken into account. To get more insight into the increased intensity of band 12, we note the operator V, which describes the (e; 2e) ionization of a molecular target containing M nuclei and N electrons located at f~ Rg and f~ r i g, is the electron scattering potential [34,35]

V¼

M X

N X Z A 1 ; þ ~ ri  ~ r0 j r 0 j i¼1 j ~ A¼1 j RA  ~

with ~ r 0 the Cartesian coordinates characterizing the projectile. Within the framework of an EMS experiment performed at room temperature, it has to be kept in mind that the norbornane compound is already subject to slight structural distortions of its structure due to thermally induced rotational and vibrational transition in its electronic neutral ground state. The double ionization might cause an ultrafast Coulomb explosion, which manifests an ultrafast release of the C2v symmetry of the cage compound in the course of the binary electron-impact ionization experiment with scattering potential V, which is dependent on nuclear and electronic coordinates. As a consequence, a tremendous increase of (e; 2e) ionization

intensity is very likely, especially when the scattering is regarded at larger distances. Equivalently, shifting the scope to the momentum of the electron prior to ionization, the effect of ultrafast nuclear dynamics in the final state, of which the current study is an elaborate example, is most likely to be seen at low electron momenta. Similar effects have been tentatively reported in recent investigations by means of EMS on ethanol [36–39] and cyclopropane [40]. In the latter study, Jahn-Teller distorsions, i.e. ultrafast nuclear dynamics in the final state, may be found to lead to significant and recognizable fingerprints in EMS momentum distributions of the highest orbitals around zero momentum. In the case of ethanol, the turn-up of the momentum distribution characterizing the HOMO is explained by an ultrafast reorganization of the molecular structure, which is related to the first stages of a fragmentation process of the ethanol radical cation into a methyl radical and a protonated form of formaldehyde [38]. In the current study on norbornane, we relate the tremendous rise at 25 eV in the EMS spectrum and its momentum distribution having a maximum at zero momentum to ultrafast processes and a cage fragmentation of the doubly ionized compound, as it is seen in the discussed BOMD calculations.

4. Conclusions Investigating the appearance of an elaborated band at 25 eV in the electron momentum spectrum of norbornane [1,5,10,11], Born Oppenheimer molecular dynamics simulations have been performed on the doubly ionized singlet state of this cage compound using initially its C2v ground state geometry. An accumulation of positive charge is noted at the bridgehead carbon atoms C2 and C3 until 800 fs. A molecular cage fragmentation persists from 127 fs, giving rise to a C5 H8 ring and a C2 H4 ethylene-like structure. After 1200 fs, the latter fragment is responsible for a gathered positive charge of 0.531. The results give therefore support to the thesis that autoionization processes and dissociating states induced by double ionization might also explain the tremendous rise of elec-

S. Knippenberg, B. Hajgató / Chemical Physics Letters 584 (2013) 24–29

tron-impact (e, 2e) ionization cross sections at electron binding energies around the double-ionization threshold and the band 12 issue. In the ring structure, charge redistributions and proton shifts occur. To verify experimentally the predictions made in the current study, Threshold PhotoElectron PhotoIon COincidence (TPEPICO) measurements on norbornane are highly welcomed [41,42].

[12] [13] [14] [15] [16] [17] [18] [19] [20]

Acknowledgement [21]

The authors are grateful to Prof. M.S. Deleuze (Hasselt University, Belgium) for various useful discussions on electron momentum spectroscopy and the band 12 issue of norbornane. S. K. acknowledges the Belgian science policy office (Belspo) and the Marie-Curie COFUND funding of the seventh European framework programme (FP7) for his research fellowship at the University of Mons; he is currently post-doctoral research fellow (Chargé de Recherches) of the Fonds National de la Recherche Scientifique, Belgium. The BOMD calculations as well as the NBO analyses have been performed at the CMN Daltoncity cluster at the University of Mons. References [1] S. Knippenberg et al., J. Chem. Phys. 121 (2004) 10525. [2] P. Bischof, J.A. Hashmall, E. Heilbronner, V. Hornung, Helv. Chim. Acta 52 (1969) 1745. [3] M. Getzlaff, G. Schönhense, J. Electron Spectrosc., Relat. Phenom. 95 (1998) 225. [4] G. Bieri, F. Burger, E. Heilbronner, J.P. Maier, Helv. Chim. Acta 60 (1977) 2213. [5] S. Knippenberg, M.S. Deleuze, T.J. Cleij, J.-P. François, L.S. Cederbaum, J.H.D. Eland, J. Phys. Chem. A 109 (2005) 4267. [6] J. Schirmer, L.S. Cederbaum, O. Walter, Phys. Rev. A 28 (1983) 1237. [7] J. Schirmer, G. Angonoa, J. Chem. Phys. 91 (1989) 1754. [8] H.G. Weikert, H.-D. Meyer, F. Tarantelli, L.S. Cederbaum, J. Chem. Phys. 104 (1996) 7122. [9] M.S. Deleuze, M.G. Giuffreda, J.-P. François, L.S. Cederbaum, J. Chem. Phys. 111 (1999) 5851. [10] S. Knippenberg, B. Hajgató, Spectr. Chim. Acta A 88 (2012) 102. [11] S. Knippenberg, B. Hajgató, J.-P. François, M.S. Deleuze, J. Phys. Chem. A. 111 (2007) 10834.

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