Theory of the photodissociation of ozone in the Hartley continuum: Potential energy surfaces, conical intersections, and photodissociation dynamics

Quantum Dynamics of Photodissociation: Recent Advances and Challenges

Recent advances in constructing accurate potential energy surfaces and nonadiabatic couplings from high-level ab initio data have revealed detailed potential landscapes in not only the ground electronic state but also excited ones. They enabled quantitatively accurate characterization of photoexcited reactive systems using quantum mechanical methods. In this Perspective, we survey the recent progress in quantum mechanical studies of adiabatic and nonadiabatic photodissociation dynamics, focusing on initial state control and product energy disposal. These new insights helped to understand quantum effects in small prototypical systems, and the results serve as benchmarks for developing more approximate theoretical methods.

Ozone Photodissociation in the Singlet Channel at 226 nm

We report the rotational state distribution and vector correlations of the O₂(a ¹Δ_g, v = 0) fragments arising from the 226 nm photodissociation of jet-cooled O₃. Consistent with previously reported trends, the rotational distribution is shifted to higher rotational states with decreasing wavelength. We observe highly suppressed odd rotational state populations due to a strong Λ-doublet propensity. The measured rotational distribution is in agreement with classical trajectory calculations for the v = 0 products, although the distribution is slightly narrower than predicted. The spatial anisotropy follows the previously observed trend of decreasing β with increasing photon energy with β = 0.72 ± 0.14 for v = 0, j = 38. As expected for a triatomic molecule, the v-j correlation is consistent with v perpendicular to j, but the measured correlation is nonlimiting due, in part, to rotational and translational depolarization. The j-dependent line width of the O₂(a ¹Δ_g) REMPI spectrum is also discussed in connection with the lifetime of the resonant O₂(d ¹Π_g) state due to predissociation via the II ¹Π_g valence state.

Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States. Application to Ozone and Sulfur Dioxide

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1¹B₂ and 2¹A₁ are the challenging ones. As the 1¹A₂, 1¹B₁, and 1¹B₂ states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2¹A₁ states and the 1¹A₁ ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1¹B₂ states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2¹A₁ ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2¹A₁ state of ozone and predicting some diradical character in the so-called "ionic" 1¹B₂ states.

Origin of the "odd" behavior in the ultraviolet photochemistry of ozone

The origin of the even-odd rotational state population alternation in the ¹⁶O₂(a ¹Δ_g) fragments resulting from the ultraviolet (UV) photodissociation of ¹⁶O₃, a phenomenon first observed over 30 years ago, has been elucidated using full quantum theory. The calculated ¹⁶O₂(a ¹Δ_g) rotational state distribution following the 266-nm photolysis of 60 K ozone shows a strong even-odd propensity, in excellent agreement with the new experimental rotational state distribution measured under the same conditions. Theory indicates that the even rotational states are significantly more populated than the adjacent odd rotational states because of a preference for the formation of the A' Λ-doublet, which can only occupy even rotational states due to the exchange symmetry of the two bosonic ¹⁶O nuclei, and thus not as a result of parity-selective curve crossing as previously proposed. For nonrotating ozone, its dissociation on the excited B¹A' state dictates that only A' Λ-doublets are populated, due to symmetry conservation. This selection rule is relaxed for rotating parent molecules, but a preference still persists for A' Λ-doublets. The A''/A' ratio increases with increasing ozone rotational quantum number, and thus with increasing temperature, explaining the previously observed temperature dependence of the even-odd population alternation. In light of these results, it is concluded that the previously proposed parity-selective curve-crossing mechanism cannot be a source of heavy isotopic enrichment in the atmosphere.

Evidence for lambda doublet propensity in the UV photodissociation of ozone

The photodissociation of O₃ at 266 nm has been studied using velocity mapped ion imaging. We report temperature-dependent vector correlations for the O₂(a¹Δ_g, v = 0, j = 18-20) fragments at molecular beam temperatures of 70 K, 115 K, and 170 K. Both the fragment spatial anisotropy and the v-j correlations are found to be increasingly depolarized with increasing beam temperature. At all temperatures, the v-j correlations for the j = 19 state were shown to be reduced compared to those of j = 18 and 20, while no such odd/even rotational state difference was observed for the spatial anisotropy, consistent with previous measurements. We find that temperature-dependent differences in the populations and v-j correlations between the odd and even rotational states can be explained by a Λ-doublet propensity model. Although symmetry conservation should lead to formation of only the A' Λ-doublet component, and only even rotational states, out-of-plane rotation of the parent molecule breaks the planar symmetry and permits the formation of the A″ Λ-doublet component and odd rotational states. A simple classical model to treat the effect of parent rotation on the v-j correlation and the odd/even rotational population alternation reproduces both the current measurements and previously reported rotational distributions, suggesting that the "odd" behavior originates from a Λ-doublet propensity, and not from a mass independent curve crossing effect, as previously proposed.

Nascent O2 (a 1Δg, v = 0, 1) rotational distributions from the photodissociation of jet-cooled O3 in the Hartley band

We report rotational distributions for the O₂ (a ¹Δ_g) fragment from the photodissociation of jet-cooled O₃ at 248, 266, and 282 nm. The rotational distributions show a population alternation that favors the even states, as previously reported for a 300 K sample by Valentini et al. [J. Chem. Phys. 86, 6745 (1987)]. The alternation from the jet-cooled precursor is much stronger than that observed by Valentini et al. and in contrast to their observations does not depend strongly on the O₂ (a ¹Δ_g) vibrational state or photolysis wavelength. The odd/even alternation diminishes substantially when the ozone beam temperature is increased from 60 to 200 K, confirming its dependence on parent internal energy. The magnitude of the even/odd alternation in product rotational states from the cold ozone sample, its temperature dependence, and other experimental and theoretical evidence reported since 1987 suggest that the alternation originates from a Λ-doublet propensity and not from a mass independent curve crossing effect, as previously proposed.

Attosecond electronic and nuclear quantum photodynamics of ozone monitored with time and angle resolved photoelectron spectra

Recently we reported a series of numerical simulations proving that it is possible in principle to create an electronic wave packet and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds. We considered the ozone molecule: for this system the electronic wave packet leads to a dissociation process. In the present work, we investigate more specifically the time-resolved photoelectron angular distribution of the ozone molecule that provides a much more detailed description of the evolution of the electronic wave packet. We thus show that this experimental technique should be able to give access to observing in real time the creation of an electronic wave packet in a neutral molecule and its impact on a chemical process.

Intermediate photofragment distributions as probes of non-adiabatic dynamics at conical intersections: application to the Hartley band of ozone

Quantum dynamics at a reactive two-state conical intersection lying outside the Franck–Condon zone is studied for a prototypical reaction of ultraviolet photodissociation of ozone in the Hartley band.

Signatures of a conical intersection in photofragment distributions and absorption spectra: photodissociation in the Hartley band of ozone

Photodissociation of ozone in the near UV is studied quantum mechanically in two excited electronic states coupled at a conical intersection located outside the Franck-Condon zone. The calculations, performed using recent ab initio PESs, provide an accurate description of the photodissociation dynamics across the Hartley/Huggins absorption bands. The observed photofragment distributions are reproduced in the two electronic dissociation channels. The room temperature absorption spectrum, constructed as a Boltzmann average of many absorption spectra of rotationally excited parent ozone, agrees with experiment in terms of widths and intensities of diffuse structures. The exit channel conical intersection contributes to the coherent broadening of the absorption spectrum and directly affects the product vibrational and translational distributions. The photon energy dependences of these distributions are strikingly different for fragments created along the adiabatic and the diabatic paths through the intersection. They can be used to reverse engineer the most probable geometry of the non-adiabatic transition. The angular distributions, quantified in terms of the anisotropy parameter β, are substantially different in the two channels due to a strong anticorrelation between β and the rotational angular momentum of the fragment O2.

Photodissociation of ozone from 321 to 329 nm: the relative yields of O(3P2) with O2(X 3Σg(-)), O2(a 1Δg) and O2(b 1Σg(+))

Product imaging of O((3)P2) following dissociation of ozone has been used to determine the relative yields of the product channels O((3)P2) + O2(X (3)Σg(-)) of ozone. All three channels are prominent at all wavelengths investigated. O2 vibrational distributions for each channel and each wavelength are also estimated assuming Boltzmann rotational distributions. Averaged over wavelength in the measured range, the yields of the O((3)P2) + O2(X (3)Σg(-)), O((3)P2) + O2(a (1)Δg), and O((3)P2) + O2(b (1)Σg(+)) channels are 0.36, 0.31,and 0.34, respectively. Photofragment distributions in the spin-allowed channel O((3)P) + O2(X (3)Σg(-)) are compared with the results of quantum mechanical calculations on the vibronically coupled PESs of the singlet states B (optically bright) and R (repulsive). The experiments suggest that considerably more vibrational excitation and less rotational excitation occur than predicted by the quantum calculations. The rotational distributions, adjusted to fit the experimental images, suggest that the dissociation takes place from a more linear configuration than the Franck-Condon bending angle of 117°. The dissociation at most wavelengths results in a positive value of the anisotropy parameter, β, both in the experiment and in the calculations. Calculations indicate that both nonadiabatic transitions and intersystem crossings substantially reduce β below the nominal value of 2.

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Ab initio quantum mechanical study of the O((1)D) formation in the photolysis of ozone between 300 and 330 nm

Spin-allowed production of O((1)D) in the near-UV photolysis of ozone is studied using ab initio potential energy surfaces and quantum mechanics. The O((1)D) quantum yield, reconstructed from the absolute cross sections for eight initial vibrational states in the ground electronic state, is shown to agree with the measurements in a broad range of photolysis wavelengths and temperatures. Relative contributions of one- and two-quantum stretching and bending initial excitations are quantified, with the contribution of the antisymmetric stretch being dominant for lambda < 330 nm. Large scale structures in the low-resolution quantum yield are shown to reflect excitations in the high-frequency short bond stretch in the upper electronic state. Spin-forbidden contribution to the O((1)D) quantum yield at wavelengths lambda > 320 nm is estimated using ab initio energies of the triplet states and their spin-orbit couplings.

Speed dependent rotational angular momentum polarization of the O2 (aΔg1) fragment following ozone photolysis in the wavelength range 248–265nm

The translational anisotropy and rotational angular momentum polarization of a selection of rotational states of the O2 (a 1Deltag; v=0) photofragment formed from ozone photolysis at 248, 260, and 265 nm have been determined using the technique of resonance enhanced multiphoton ionization in combination with time of flight mass spectrometry. At 248 nm, the dissociation is well described as impulsive in nature with all rotational states exhibiting similarly large, near-limiting values for the bipolar moments describing their angular momentum alignment and orientation. At 265 nm, however, the angular momentum polarization parameters determined for consecutive odd and even rotational states exhibit clear differences. Studies at the intermediate wavelength of 260 nm strongly suggest that such a difference in the angular momentum polarization is speed dependent and this proposal is consistent with the angular momentum polarization parameters extracted and reported previously for longer photolysis wavelengths [G. Hancock et al., Phys. Chem. Chem. Phys. 5, 5386 (2003); S. J. Horrocks et al., J. Chem. Phys. 126, 044308 (2007)]. The alternation of angular momentum polarization for successive odd and even J states may be a consequence of the different mechanisms leading to the formation of the two O2 (a 1Deltag) Lambda doublets. Specifically, the involvement of out of plane parent rotational motion is proposed as the origin for the observed depolarization for the Delta- relative to the Delta+ state.

New theoretical investigations of the photodissociation of ozone in the Hartley, Huggins, Chappuis, and Wulf bands

We review recent theoretical studies of the photodissociation of ozone in the wavelength region from 200 nm to 1100 nm comprising four major absorption bands: Hartley and Huggins (near ultraviolet), Chappuis (visible), and Wulf (near infrared). The quantum mechanical dynamics calculations use global potential energy surfaces obtained from new high-level electronic structure calculations. Altogether nine electronic states are taken into account in the theoretical descriptions: four 1A', two 1A'', one 3A' and two 3A'' states. Of particular interest is the analysis of diffuse vibrational structures, which are prominent in all absorption bands, and their dynamical origin and assignment. Another focus is the effect of non-adiabatic coupling on lifetimes in the excited states and on the population of the specific electronic product channels.

Comment on “Theory of photodissociation of ozone in the Hartley continuum; effect of vibrational excitation and O(1D) atom velocity distribution” by E. Baloïtcha and G. G. Balint-Kurti, Phys. Chem. Chem. Phys., 2005, 7, 3829

In this Comment we present quantum mechanical absorption spectra of the Hartley band originating from the four vibrationally excited levels of the ground electronic state. The calculations are performed using the diabatic B-state potential energy surface and the transition dipole moment vector constructed from the ab initio data of the title paper. The calculated spectra are multimodal (for the symmetric stretch pre-excitation) and strongly structured (for the symmetric stretch and bending pre-excitations). These results agree with the previous theoretical analysis and with the predictions of a simple model based on the reflection principle, but contradict the findings of Baloïtcha amd Balint-Kurti thus questioning the accuracy of their calculations.

The photodissociation dynamics of ozone at 193nm: An O(D21) angular momentum polarization study

Polarized laser photolysis, coupled with resonantly enhanced multiphoton ionization detection of O(1D2) and velocity-map ion imaging, has been used to investigate the photodissociation dynamics of ozone at 193 nm. The use of multiple pump and probe laser polarization geometries and probe transitions has enabled a comprehensive characterization of the angular momentum polarization of the O(1D2) photofragments, in addition to providing high-resolution information about their speed and angular distributions. Images obtained at the probe laser wavelength of around 205 nm indicate dissociation primarily via the Hartley band, involving absorption to, and diabatic dissociation on, the B 1B2(3 1A1) potential energy surface. Rather different O(1D2) speed and electronic angular momentum spatial distributions are observed at 193 nm, suggesting that the dominant excitation at these photon energies is to a state of different symmetry from that giving rise to the Hartley band and also indicating the participation of at least one other state in the dissociation process. Evidence for a contribution from absorption into the tail of the Hartley band at 193 nm is also presented. A particularly surprising result is the observation of nonzero, albeit small values for all three rank K = 1 orientation moments of the angular momentum distribution. The polarization results obtained at 193 and 205 nm, together with those observed previously at longer wavelengths, are interpreted using an analysis of the long range quadrupole-quadrupole interaction between the O(1D2) and O2(1Deltag) species.

Infrared spectrum of cyclic ozone: A theoretical investigation

The infrared absorption spectrum of cyclic ozone is calculated by means of a new ab initio potential energy surface, the dipole moment function, and exact quantum mechanical dynamics calculations. Five different isotopomers are considered. The absorption line for excitation of the bending fundamental near 800 cm(-1) is by far the strongest band; all other bands are more than one order of magnitude less intense. This spectral pattern as well as the isotope shifts for the various isotopomers are important for identifying cyclic ozone. Several possibilities for accessing the ring minimum of cyclic ozone are also discussed on the basis of recent electronic structure calculations.

Theory of the photodissociation of ozone in the Hartley continuum; effect of vibrational excitation and O(1D) atom velocity distribution

The effect of vibrational excitation on the photodissociation cross section of ozone in the Hartley continuum is examined. The calculations make use of newly computed potential energy and transition dipole moment surfaces. The initial vibrational states of the ozone are computed using grid based techniques and the first few ab initio computed vibrational energy level spacings agree to within 10 cm(-1) with experimental values. The computed total absorption cross sections arising from different initial vibrational states of ozone are discussed in the light of the nature of the transition dipole moment surface. The computed cross section for excitation from the ground vibrational-rotational state is in good agreement with the experimentally measured cross section. Excitation of the asymmetric stretching vibration of ozone has a marked effect on both the form and magnitude of the photodissociation cross section. The velocity distributions of highly reactive O(1D) atoms arising from the photodissociation process in different wavelength ranges is also presented. The results show that the O(1D) atoms travel with a most probable translational velocity of 2.030 km s(-1) corresponding to a translational energy of 0.342 eV or 33.0 kJ mol(-1).