Ultrafast photodissociation dynamics of 1,4-diiodobenzene

The photodissociation dynamics of 1,4-diiodobenzene is investigated using ultrafast time-resolved photoelectron spectroscopy. Following excitation by laser pulses at 271 nm, the excited-state dynamics is probed by resonance-enhanced multiphoton ionization with 405 nm probe pulses. A progression of Rydberg states, which come into resonance sequentially, provide a fingerprint of the dissociation dynamics of the molecule. The initial excitation decays with a lifetime of 33 ± 4 fs, in good agreement with previous studies. The spectrum is interpreted by reference to ab-initio calculations at the CASPT2(18,14) level including spin-orbit coupling. We propose that both the 5B 1 and 6B 1 states are excited initially, and based on the calculations we identify diabatic spin-orbit coupled states corresponding to the main dissociation pathways.


INTRODUCTION
The addition of substituent atoms and groups to the archetypal aromatic benzene molecule has interesting and profound effects on its chemistry and photophysics. This ranges from the function of aromatic amino acid side chains involved in π stacking and hydrogenbonding interactions in biological environments, to fundamental spectroscopic events in the gas phase. The addition of a halogen atom to a benzene ring in particular introduces additional electronically excited states, leading to (π,σ*), (n,π*) and (n,σ*) transitions in the UV-Vis region of the spectrum of aryl halides. For the heavier halogens, spin-orbit coupling becomes a key factor in determining the electronic structure, and thus dynamics, in species such as iodobenzene and diiodobenzene (DIB).
As a consequence of the dense manifold of electronic states arising from the perturbations on the aromatic π system due to the substituent, the photodissociation of aryl halides exhibits a rich variety of phenomena. Early photofragment translational energy distribution studies by Bersohn, et. al. [1][2][3] identified an indirect dissociation (predissociation) pathway, where the system is directly excited to a bound (π, π*) state that undergoes a curve crossing (facilitated by spin-orbit coupling) to a repulsive (n, σ*) state. Later studies also identified an additional, direct dissociation pathway via a repulsive (n, σ*) state [4][5][6] . The branching ratio between the direct and indirect pathways is determined by the excitation energy and the nature of the substituents.
In monosubstituted benzenes, the effects of the different substituent halogen atoms manifest themselves in both mechanism and timescale. When excited at 266 nm, chlorobenzene features an indirect dissociation with a lifetime of ~1 ns 7 , while bromobenzene undergoes indirect dissociation in 26 ps 7,8 . In iodobenzene, the indirect dissociation pathway with a decay-time of ~600 fs is complemented by a direct dissociation on a faster, ~400 fs 6,7 time scale. In mono-halogenated benzenes, the substitution of heavier halogens apparently accelerates curve crossing, presumably via stronger spin-orbit coupling of the initially excited (π, π*) state to the (n, σ*) repulsive surface 7,8 . In addition, the appearance of a second reaction pathway in iodobenzene likely indicates a shift in the relative energies of the excited states, which brings the direct pathway into play.
Para-disubstituted benzenes have been found to demonstrate similar trends. Excitation of p-dichlorobenzene at ~266 nm results in only the predissociation pathway, with dissociation occurring in 122 ps 9,10 . The situation is similar in p-dibromobenzene, but with a faster decay of 18.2 ps 11 . Initial photofragment translational energy studies of p-diiodobenzene suggested that predissociation occurs on a timescale faster than the rotational period of the molecule 1 , and a recent ultrafast photoelectron study 12 suggests that the dissociation proceeds via curve crossing from an initially excited bound state. However, no ultrafast studies of the wavepacket motion along the dissociative surface have been reported.
Ultrafast spectroscopy has long been used to study dissociation reactions 13,14 , and photoelectron spectroscopy involving Rydberg states has more recently been shown to be an effective measure of structural dynamics [15][16][17][18] . The present investigation probes the photodissociation dynamics of p-diiodobenzene using time-resolved pump-probe photoelectron spectroscopy (see Figure 1). Following excitation at 271 nm, the dynamics of p-diiodobenzene is probed by multiphoton ionization via molecular Rydberg states using 405 nm photons. The photon energy matches the electronic transition energies between the dissociative states and the Rydberg resonances only at specific time delays. Consequently, measuring the travel times at which resonant ionization occurs can monitor the dissociation pathway.

Photoelectron Spectroscopy
The experimental apparatus has been described in detail elsewhere 16,19,20

UV-Visible Absorption Spectrometry
A Shimadzu UV-1700 double-beam scanning spectrometer (20 W, halogen lamp) was used to obtain the UV-visible absorption spectrum of 1,4-diiodobenzene from 190 nm to 400 nm. A small amount of solid sample was placed in the bottom of a sealed quartz cuvette with a path length of 1 cm, and the pressure was allowed to equilibrate before measurement of the vapor. Figure 2. Molecular structure of DIB, with Cartesian axes labeled in accordance to Table 2.

Theory
All calculations described here are performed using the Molpro ab initio electronic structure program 21,22 and employ a correlation-consistent Dunning basis set of triple-zeta plus polarization quality (cc-pVTZ) for carbon and hydrogen atoms 23 . Iodine atoms are described by an effective core potential (ECP) for a 46-electron core, i.e. large-core [Kr]5d 10 , with the larger cc-pVTZ-PP basis set of Peterson et al. 24 to describe the seven valence electrons. The ECP for iodine contains terms for the evaluation of spin-orbit coupling for the valence electrons.
The geometry of the 1 1 A 1 ground state of DIB is optimized at the Complete Active Space Self-Consistent Field (CASSCF) level using a fourteen electrons in twelve orbitals active space, i.e. CASSCF (14,12), comprising the six benzene-like π orbitals and electrons and, for each iodine, the two C-I σ bond orbitals and electrons and the iodine p x (out-of-plane, see  Figure 2). The calculations are performed at the CASSCF (18,14) level with an active space that comprises all orbitals and electrons from the (14,12) space plus the iodine p y (inplane) lone pair for each iodine atom. Due to an orbital rotation between two orbitals in the B 2 irreducible representation (IR), specifically the C-C σ core orbital and the iodine p y (in-plane) lone pair orbital, during unconstrained CASSCF optimization of the (18,14) active space orbitals, the core orbitals are frozen following an initial CASSCF (14,12) calculation. This places the iodine p y orbitals correctly in the larger active space. The state-averaged (SA) CASSCF (18,14) calculation yields two roots in each IR of C 2v symmetry ( In principle, the ground state geometry of the molecule could be affected by the improved treatment of dynamical electron correlation in CASPT2. At the CASPT2 level, the optimized C-I bond length is R CI = 2.072 Å, as determined by a numerical fit to the CASPT2 ground state potential energy curve, which is slightly shorter than the CASSCF(14,12) optimized value of 2.102 Å. This finding is in line with similar observations for the 1 1 A 1 ground state in iodobenzene, where Sage et al. 5 found that MP2 predicted C-I bond lengths of 2.062 Å were somewhat shorter than the 2.120 Å predicted by CASSCF (12,10). Although the inclusion of spin-orbit coupling markedly changes the overall potential energy landscape, the position of the minimum of the SOC CASPT2 ground state is barely affected. The vertical transition properties listed in Table 1 are calculated at the CASSCF(14,12) optimized geometry, but with the two C-I bonds having the optimum CASPT2 bond length of 2.072 Å.

Ultrafast time-resolved photoelectron spectroscopy
The time-resolved, pump-probe photoelectron spectrum of DIB excited at 271 nm and probed with 405 nm photons is displayed in Figure 3. The spectral coordinate is the binding energy, which is the difference between the ionizing photon energy (3.06 eV) and the measured kinetic energy of the ejected electrons.
where E B is the binding energy, Ry is the Rydberg constant (13.6 eV), n is the principal quantum number, and  is the quantum defect. Given that typical quantum defect values are ~0.1 for nd Rydberg states, ~0.3-0.5 for np, and ~0.8-1 for ns states 28 , the observed resonances can be assigned based on their experimentally measured quantum defects. It should be noted that these values are typical for second row elements. In the following assignments, we consider 4p 4s 3p' 3p 3s excitation from the HOMO, which belongs primarily to the pi system of the aromatic carbon ring, and thus we refer to the aforementioned values. This ignores possible excitation of the iodine lone pair, from which we would access Rydberg states with n ≥ 6.
The  16 . The model assumes that optical excitation leads initially to a state that is not involved in the dissociation of the bond. This model was found to be a better fit to the present experimental data than an alternate model that we have tested and that assumes direct excitation to a dissociative surface. The model used here is also in agreement with a previous study 12 To adequately describe the experimental signals, I Ry (t) is then combined with a baseline that grows in at t=0 (arising from nonresonant ionization of the dissociating molecule), and convoluted with a Gaussian instrument function  IF , .
In the experiment, the resonance windows were found to be shorter than the temporal resolution and are therefore represented as Gaussian functions with a nominal width of σ = 1 fs.
It is important to keep in mind that both Equation 2 and Equation 3 pertain to the indirect dissociation whereby the molecule is initially excited into a bound state.
The parameters of the best fits to this model are listed in Table 1 Ground-state 8.41 Table 2 Fig. 2), and vertical excitation energies in eV. The data provided pertains to the SA(32)-CASPT2 (18,14) SOC potential energy curves, with the vertical ionization energy taken from the SOF CASPT2 (17,14) ground state energy of the DIB + cation. Energies are evaluated at the CASPT2 optimized geometry, with a C-I bond length of 2.072 Å.

. Electronic state labels, the main character of the dominant spin-orbit free (SOF) component of each electronic transition (with two characters provided if the second largest SOF component has a weight >20%), percentage weights of the dominant SOF components of each spin-orbit coupled (SOC) state at equilibrium geometry (only states with contributions larger than 1% are included), total transition dipole moments (TDM) in Debye (with the main axis identified in accordance to
The calculated adiabatic CASPT2 (18,14) potential energy curves (PECs) along the C-I bond distance are shown in Figure 4. Figure 4A shows the spin-orbit free (SOF) adiabatic states, while Figure 4B shows the spin-orbit coupled (SOC) states. The calculations retain C 2v symmetry throughout, preserving planarity and assuming that the dissociation proceeds along the z-axis. The non-adiabatic coupling between excited states of different symmetries is zero.
This allows the dissociation dynamics to be viewed as four independent processes occurring in  Table 2 is only valid at the CASPT2/cc-pVTZ-PP optimized ground state geometry; at other geometries the composition changes. The states are coupled by non-adiabatic coupling, which is known to be fairly localized and which manifests itself in sharply peaked non-adiabatic coupling matrix elements (NACMEs) at the pseudo avoided-crossings. The singlet and triplet manifolds are further connected by spin-orbit coupling, which is less localized, varies slowly and shows an asymptotic behavior at infinite R C-I that correlates with the coupling in atomic iodine.
At large internuclear separation, seven excited states and the ground state (two of each symmetry in total) correlate with the I( 3 P 3/2 ) + IPh(X, 2 A 1 ) asymptotic limit, whereas four states (one of each IR) correlate with the I( 3 P 1/2 ) + IPh(X, 2 A 1 ) limit.

Figure 5. Experimentally measured UV absorption spectrum of DIB, together with the calculated spectrum according to data in Table 2. The left panel gives the overall spectrum, while the right panel shows the region close to the excitation energy used in the current time-resolved experiment (vertical dashed lines in both panels).
Taking into account the oscillator strengths and vertical excitation energies in Table 2, there appears to be a reasonable correspondence between the theoretical spectrum and the experimentally measured optical absorption spectrum, see Figure 5. For this figure, the calculated vertical transitions from Table 2 are scaled by the square of the transition dipole moment and convoluted with a spectral width of σ = 0.2 eV. The experimental absorption spectrum is scaled to match the most intense peak near 240 nm. The absorption spectrum is dominated by the transition to the 6A 1 state at ~240 nm, which has an oscillator strength an order of magnitude greater than all other states in this energy region. Note that the experimental spectrum has a peak at ~200 nm that is even more intense than the 240 nm peak. In our calculations, there is a reasonably intense peak at ~201 nm due to 8A 1 . It could be that our calculations, which do not account for the effect of nuclear motion on the absorption spectrum, underestimate the intensity of that absorption, or that there is a nearby state at that energy that is not included in our calculations, since 8A 1 is the highest energy state in our calculations.
Based on the good agreement between the calculated and the observed absorption spectra of DIB, we conclude that the accuracy of the predicted vertical excitation energies and transition dipole moments is reasonable.
From Finally, taking into account the pump pulse energy and the magnitude of the TDMs, we conclude that the initial absorption most likely excites the 5B 1 and 6B 1 states. This assignment agrees with a previous study 12 , which suggested that the initially excited state is a bound electronic state. Although the pump pulse bandwidth (0.05 eV) is less than the calculated energy difference between the 5B 1 and 6B 1 states in the Franck-Condon region (E=0.19 eV), these bound states support vibrational levels and are thus expected to have a Franck-Condon envelope larger than the laser bandwidth. Absorption into the 5B 2 state is also possible, but this is dismissed here due to the comparatively small transition strength compared to the B 1 states.
In the adiabatic picture, the energy difference between the initially populated 5B 1 and 6B 1 states and the dissociative states 1B 1 , 2B 1 and 3B 1 states indicates that dissociation proceeds via a cascade of non-adiabatic transitions leading to one of the repulsive states.
However, a physically more intuitive picture is encoded in the 1-8B semi-diabatic states shown in Figure 6. These states are defined such that their SOF composition varies smoothly.
Computationally this is realized by maximizing the overlap between the eigenvectors of the SOF to SOC transformation between successive points on the curves. The semi-diabatic states are admixtures of SOF states, whose contribution varies along the carbon-iodine bond distance, R CI . In instances where the spin-orbit coupling is weak, these states can significantly resemble or even match the SOF states from which they originate. However, the semi-diabatic curves are not character-preserving, i.e. they formally behave like the SOF adiabatic curves exhibiting pseudo-avoided crossings. A mathematically rigorous formulation of the corresponding diabatic states is in principle possible via a transformation of the non-adiabatic coupling matrix elements (NACMEs) to the SOC basis 29 . Presently, the diabatic SOC 5B and 6B , which follow the character of the 5B and 6B in the FC region, are formed by inspection of the ab initio configuration interaction coefficients, and are presented in Figure 6. These diabatic states give an intuitive view of the dissociation pathway. could be explored using on-the-fly dynamics simulations [30][31][32] . However, for this to be feasible more efficient electronic structure calculations would be required. We also note that the constriction of the C-I bond, 0.032 Å, is smaller than the FWHM of the ground state v=0 wavefunction, which is about 0.09 Å.

DISCUSSION
Inspection of the quantum defects of the experimentally observed Rydberg resonances (Table 1) shows that the value for the 3p peak (0.42) is almost identical to that of the 4p peak (0.43). The different observation times of those peaks therefore implies that their quantum defects are not strongly affected by the dissociation of the C-I bond. It is likely, then, that these Rydberg orbitals have nodes along the C-I axis, making them less sensitive to structure changes along the dissociation coordinate 33,34 . This suggests that they could be either p x or p y orbitals. It is furthermore important to note that the probe pulses are polarized perpendicularly relative to the pump pulse. The computational results show that the initial excitation has a transition dipole moment oriented perpendicular to the plane of the molecule (x direction, see Figure 2), and so the out-of-plane p x orbital is preferentially probed at short delay times, before the molecule has time to rotate (assuming C 2v symmetry). Combining the two arguments, we conclude that the 1.07 eV and 1.85 resonances can be identified as the 4p x and 3p x resonances, respectively. The 3p' peak has a quantum defect that is significantly different from the 3p and 4p resonances. There are several possible explanations for this observation, which will be discussed below.
The resonance observed with the longest time delay, the 3s peak, has a quantum defect that differs notably from that of the 4s peak (0.73 vs. 0.98). This is consistent with the fact that ns Rydberg states have significant electron density in the region of the dissociating C-I bond, so that the quantum defect is expected to change as the molecular structure evolves.
We find that most travel times ∆t listed in Table 1 increase monotonically with the binding energies of the Rydberg resonances. This is rational since Rydberg states with larger binding energies are lower in total energy, and therefore come later into resonance with the energy of the dissociative state given the fixed probe photon energy. It is then interesting to observe that the 3p' peak with a binding energy of 1.85 eV is seen after the 3p peak with a binding energy of 2.05 eV. The most natural explanation is that the 3p' transient arises from ionization out of a different dissociative surface, as illustrated in Figure 7. The temporal sequence of the binding energy transients therefore indicates that the 3p' resonance arises from a higher energy dissociative valence state than the 4s, 3p, and 3s resonances. This is in excellent agreement with the CASPT2 calculations, which show that the initial excitation may lead to either of two close-lying B 1 states. Specifically, the initial excitation most likely populates both the 5B 1 and 6B 1 states. Those states eventually couple to the dissociative 3B 1 and 2B 1 states, respectively. Thus, it is possible that the 3p' resonance arises from the dissociation on the 2B 1 state accessed via the 6B 1 state, while the 4s, 3p, and 3s resonances show the dissociation on 3B 1 state, which is accessed from excitation to the 5B 1 state (see Figure 7).  Based on the valence state assignments discussed above, we can combine the experimental results with the calculated potential energy curves to determine the C-I distance of the dissociating molecule as a function of time. For each Rydberg resonance, we fit the sum of the experimental binding energy and the probe photon energy to the calculated energy difference between the ion ground state and the assigned valence state (see Table 3), thus correlating the measured ∆t with the dissociating C-I distance. The 4p resonance, arising from a superposition of bound states, was placed at the ground state equilibrium bond length of 2.072 Å. For this state, the sum of the experimental binding energy and the probe photon energy is found to be 0.30 eV larger than the calculated energy difference between the ion ground state and the initial excitation energy. Given that the valence-Rydberg absorption occurs between two bound electronic surfaces, it is reasonable to attribute this to the deposition of vibrational energy in the Rydberg state, which is then preserved in the ionization step.
The fit of the experimentally measured travel time ∆t to the dissociating C-I bond distance outlined in Table 3 allows us to track the wavepacket motion along the 3B 1 surface.
Finally, we note that the differing quantum defect of the 3p' peak as compared to the 3p and 4p resonances is not yet definitively explained. The two involved repulsive surfaces (2B 1 and 3B 1 ) have the same symmetry, so that the selection rules for Rydberg transitions are the same in the C 2v picture. This means it is unlikely that the 3p' peak is a 3p y or 3p z orbital if the molecule retains C 2v symmetry. It is possible that, because the 2B 1 state (from which the 3p' resonance is accessed) is of mixed singlet/triplet character, the 3p' resonance arises from a singlet Rydberg series, whereas the other resonances belong to a triplet series. Alternatively, it is possible that the avoided crossing from the 5B 1 to 2B 1 surface breaks the C 2v symmetry, so that transitions to the 3p y and 3p z resonances are allowed.

CONCLUSION
Upon excitation with a 4.58 eV laser pulse, 1,4-diiodobenzene is found to dissociate via an ultrafast indirect dissociation pathway. The initially excited 5B 1 and 6B 1 bound states decay into the repulsive 2B 1 and 3B 1 states with a 33 ± 4 fs time constant. As the molecule travels down the repulsive surfaces, the probe laser pulse comes into resonance with molecular Rydberg states in a sequential fashion. The assignment of the dissociative states based on CASPT2 calculations is tentative but in good agreement with the observed binding energy transients as well as with a previous study 12 .
The observation of the fast indirect dissociation pathway as the dominant reaction mechanism is informative. The increase in spin-orbit coupling caused by the substitution by iodine as compared to lighter halogen atoms causes a significant increase in the rate of nonadiabatic internal conversion in p-diiodobenzene (33 fs) compared to p-dibromobenzene (18.2 ps 11 ) and p-dichlorobenzene (122 ps 9,10 ). In addition, the fact that direct dissociation is not observed indicates that the system exhibits qualitatively different behavior than the monosubstituted iodobenzene, which undergoes dissociation via both direct and indirect pathways 6,7 . The absence of an observed direct pathway could be the result of a shift in the energies of the repulsive surfaces relative to iodobenzene. The calculated semi-diabatic states 5 and 6 provide some indication of how these dissociations proceed through the network of adiabatic electronic states. In conclusion, diiodobenzene provides a stark reminder of the complexity of even apparently simple dissociation dynamics in molecules with a high density of states and strong spin-orbit coupling.

SUPPLEMENTARY MATERIAL
See supplementary material for calculated SOF and SOC potential energy curves, as well as the optimized ground state geometry of DIB and a summary of the calculated SOF excitation transitions.