Photodissociation of ozone in the Hartley band. Exploratory potential energy surfaces and molecular dynamics

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

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.

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.

Photodissociation by Circularly Polarized Light Yields Photofragment Alignment in Ozone Arising Solely from Vibronic Interactions

We present a direct determination of photofragment alignment produced by circularly polarized light in photolysis of a planar polyatomic molecule. This alignment arises via a new mechanism involving coherent excitation of two mutually perpendicular in-plane transition dipole moment components. The alignment is described by a new anisotropy parameter γ_{2}^{'} that was isolated by a unique laser polarization geometry. The determination of the parameter γ_{2}^{'} was realized in ozone photolysis at 266 nm where dc slice images of O(^{1}D_{2}) atomic fragments were acquired. A model developed for interpretation of the photolysis mechanism shows that it can exist only in case of failure of the Born-Oppenheimer approximation when electronic and vibrational (vibronic) interactions have to be taken into account. This finding suggests that determination of the alignment parameter γ_{2}^{'} can be used as a key for direct insight into vibronic interactions in photolysis of polyatomic molecules. The results obtained for ozone photolysis via the Hartley band showed significant γ_{2}^{'} alignment but little recoil speed dependence, consistent with the notion that, as opposed to the situation for derivative coupling, under our experimental conditions, the vibronic contributions to the nonadiabatic dynamics are not dependent on recoil speed.

Single-root networks for describing the potential energy surface of Lennard-Jones clusters

Potential energy surface (PES) holds the key in understanding a number of atomic clusters or molecular phenomena. However, due to the high dimension and incredible complexity of PES, only indirect methods can be used to characterize a PES of a given system in general. In this paper, a branched dynamic lattice searching method was developed to travel the PES, which was described in detail by a single-root network (SRN). The advantage of SRN is that it reflects the topological relation between different conformations and highlights the size of each structure energy trap. On the basis of SRN, to demonstrate how to transform one conformation to another, the transition path that connects two local minima in the PES was constructed. Herein, we take Lennard-Jones (LJ) clusters at the sizes of 38, 55, and 75 as examples. It is found that the PES of these three clusters have many local funnels and each local funnel represents one morphology. If a morphology is located more frequently, it will lie in a larger local funnel. Besides, certain steps of the transition path were generated successfully, such as changing from icosahedral to truncated octahedral of the LJ₃₈-cluster. Though we do not exhibit all the parts of the PES or all transition paths, this method indeed works well in the local area and can be used more widely.

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 1(1)A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two (1)A1 states. In the present work, valence correlated energies of the 1(1)A1 state and the 2(1)A1 state were calculated at the 1(1)A1 open minimum, the 1(1)A1 ring minimum, the transition state between these two minima, the minimum of the 2(1)A1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1(1)A1 state, the present calculations yield the estimates of (ring minimum-open minimum) ∼45-50 mh and (transition state-open minimum) ∼85-90 mh. For the (2(1)A1-(1)A1) excitation energy, the estimate of ∼130-170 mh is found at the open minimum and 270-310 mh at the ring minimum. At the transition state, the difference (2(1)A1-(1)A1) is found to be between 1 and 10 mh. The geometry of the transition state on the 1(1)A1 surface and that of the minimum on the 2(1)A1 surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.

Excited-state wavepacket and potential reconstruction by coherent anti-Stokes Raman scattering

We propose a methodology for reconstructing polyatomic excited-state molecular wavepackets and potential energy surfaces by multiple pulse optical spectroscopy.

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.

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.

Optimal internal coordinates, vibrational spectrum, and effective Hamiltonian for ozone

In this paper the authors use the optimal internal vibrational coordinates previously determined for the electronic ground state of the ozone molecule to study the vibrational spectrum of the molecule employing the second empirical potential energy surface calculated by Tyuterev et al. [Chem. Phys. Lett. 316, 271 (2000)]. First, the authors compute variationally all the bound vibrational energy levels of the molecule up to the dissociation limit and state the usefulness of the optimal coordinates in this respect, which allows us to converge all the bound levels using relatively small anharmonic basis sets. By analyzing the expansion coefficients of the wave functions, they show then that a large portion of the vibrational spectrum of O3 can be structured in nearly separable polyadic groups characterized by the polyad quantum number N=n1+n2+n(theta) corresponding to the optimal internal coordinates. Accordingly, they determine an internal effective vibrational Hamiltonian for O3 by fitting the effective Hamiltonian parameters to the experimental vibrational frequencies, using as input parameters in the fit those extracted from an analytical second-order Van Vleck perturbation theory calculation. It is finally shown that the internal effective Hamiltonian thus obtained accurately describes the vibrational spectrum of ozone in the low and medium energy regimes.

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.

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.

The photodissociation of ozone in the Hartley band: A theoretical analysis

Three-dimensional diabatic potential energy surfaces for the lowest four electronic states of ozone with 1A' symmetry-termed X, A, B, and R-are constructed from electronic structure calculations. The diabatization is performed by reassigning corresponding energy points. Although approximate, these diabatic potential energy surfaces allow one to study the uv photodissociation of ozone on a level of theory not possible before. In the present work photoexcitation in the Hartley band and subsequent dissociation into the singlet channel, O3X+hnu-->O(1D)+O2(a 1Deltag), are investigated by means of quantum mechanical and classical trajectory calculations using the diabatic potential energy surface of the B state. The calculated low-resolution absorption spectrum as well as the vibrational and rotational state distributions of O2(a 1Deltag) are in good agreement with available experimental results.

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

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.

The triplet channel in the photodissociation of ozone in the Hartley band: Classical trajectory surface hopping analysis

The triplet channel in the photodissociation of ozone in the Hartley band, O3 + hv-->O(3P) + O2(3sigma), is investigated by means of a classical trajectory surface hopping method using ab initio diabatic potential energy surfaces for the B and the R states. Because of the strong recoil in the R state along the breaking O-O bond, O2(3sigma) is produced with a high rotational energy. The nonadiabatic transition probability depends markedly on the coordinate along the crossing seam. As a consequence a unique correlation is found between the internuclear geometry at the crossing and the final vibrational state of O2(3sigma). The calculated distribution of the translational energy is in good accord with the measured distribution.

The Huggins band of ozone: Assignment of hot bands

The "hot bands" of the Huggins band of ozone are assigned, in both the 218 K and the 295 K spectrum. The assignment is based on intensities calculated with three-dimensional vibrational wave functions for the electronic ground state (X) and the excited state (B). The hot-band structures in the 218 K spectrum all can be assigned to transitions starting from vibrational states with one quantum of stretching excitation in the ground electronic state. The 295 K spectrum shows new structures, which are due to transitions originating from vibrational states in the X state with two quanta of excitation of the stretching modes--despite very small Boltzmann factors. All structures in the low-energy range of the 295 K spectrum, even the very weak ones, thus can be uniquely interpreted. The significance of hot bands results from the strong increase of Franck-Condon factors with excitation of the stretching modes in both the lower and/or the upper electronic states, whose equilibrium bond lengths differ significantly.

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).

The Huggins band of ozone: A theoretical analysis

The Huggins band of ozone is investigated by means of dynamics calculations using a new (diabatic) potential energy surface for the 3 (1)A'(1B2) state. The good overall agreement of the calculated spectrum of vibrational energies and intensities with the experimental spectrum, especially at low to intermediate excitation energies, is considered as evidence that the Huggins band is due to the two C(s) potential wells of the 1B2 state rather than the single C2v well of the 2 (1)A'(1A1) state. The vibrational assignment of the "cold bands," based on the nodal structure of wave functions, on the whole supports the most recent experimental assignment [J. Chem. Phys. 115, 9311 (2001)]. The quantum mechanical spectrum is analyzed in terms of classical periodic orbits and the structure of the classical phase space.

The Huggins band of ozone: Unambiguous electronic and vibrational assignment

The Huggins band of ozone is investigated by means of exact dynamics calculations using a new (diabatic) potential energy surface for the (1)B(2) state. The remarkable agreement with the measured spectrum strongly suggests that the Huggins band is due to the two C(s) potential wells of the (1)B(2) state. The vibrational assignment, based on the nodal structure of wave functions, supports the most recent experimental assignment.