The vibrational energies of ozone up to the dissociation threshold: Dynamics calculations on an accurate potential energy surface

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.

Heteroatom-Based Diradical(oid)s

Heteroatom-centered diradical(oid)s have been in the focus of molecular main group chemistry for nearly 30 years. During this time, the diradical concept has evolved and the focus has shifted to the rational design of diradical(oid)s for specific applications. This review article begins with some important theoretical considerations of the diradical and tetraradical concept. Based on these theoretical considerations, the design of diradical(oid)s in terms of ligand choice, steric, symmetry, electronic situation, element choice, and reactivity is highlighted with examples. In particular, heteroatom-centered diradical reactions are discussed and compared with closed-shell reactions such as pericyclic additions. The comparison between closed-shell reactivity, which proceeds in a concerted manner, and open-shell reactivity, which proceeds in a stepwise fashion, along with considerations of diradical(oid) design, provides a rational understanding of this interesting and unusual class of compounds. The application of diradical(oid)s, for example in small molecule activation or as molecular switches, is also highlighted. The final part of this review begins with application-related details of the spectroscopy of diradical(oid)s, followed by an update of the heteroatom-centered diradical(oid)s and tetraradical(oid)s published in the last 10 years since 2013.

High Resolution Infrared Spectroscopy in Support of Ozone Atmospheric Monitoring and Validation of the Potential Energy Function

The first part of this review is a brief reminder of general information concerning atmospheric ozone, particularly related to its formation, destruction, observations of its decrease in the stratosphere, and its increase in the troposphere as a result of anthropogenic actions and solutions. A few words are said about the abandonment of the Airbus project Alliance, which was expected to be the substitute of the supersonic Concorde. This project is over due to the theoretical evaluation of the impact of a fleet in the stratosphere and has been replaced by the A380, which is now operating. The largest part is devoted to calculations and observations of the transitions in the infrared range and their applications for the atmosphere based both on effective models (Hamiltonian, symmetry rules, and dipole moments) and ab initio calculations. The complementarities of the two approaches are clearly demonstrated, particularly for the creation of an exhaustive line list consisting of more than 300,000 lines reaching experimental accuracies (from 0.00004 to 0.001 cm-1) for positions and a sub percent for the intensities in the 10 microns region. This contributes to definitively resolving the issue of the observed discrepancies between line intensity data in different spectral regions: between the infrared and ultraviolet ranges, on the one hand, and between 10 and 5 microns on the other hand. The following section is devoted to the application of recent work to improve the knowledge about the behavior of potential function at high energies. A controversial issue related to the shape of the potential function in the transition state range near the dissociation is discussed.

Photoacoustic studies of energy transfer from ozone photoproducts to bath gases following Chappuis band photoexcitation

Photoacoustic spectroscopy (PAS) is a sensitive technique for the detection of trace gases and aerosols and measurements of their absorption coefficients. The accuracy of such measurements is often governed by the fidelity of the PAS instrument calibration. Gas samples laden with O3 of a known or independently measured absorption coefficient are a convenient and commonplace route to calibration of PAS instruments operating at visible wavelengths (λ), yet the accuracy of such calibrations remains unclear. Importantly, the photoacoustic detection of O3 in the Chappuis band (λ ∼ 400-700 nm) depends strongly on the timescales for energy transfer from the nascent photoproducts O(3P) and O2(X, v > 0) to translational motion of bath gas species. Significant uncertainties remain concerning the dependence of these timescales on both the sample pressure and the bath gas composition. Here, we demonstrate accurate characterisation of microphone response function dependencies on pressure using a speaker transducer to excite resonant acoustic modes of our photoacoustic cells. These corrections enable measurements of photoacoustic response amplitudes (also referred to as PAS sensitivities) and phase shifts with variation in static pressure and bath gas composition, at discrete visible wavelengths spanning the Chappuis band. We develop and fit a photochemical relaxation model to these measurements to retrieve the associated variations in the aforementioned relaxation timescales for O(3P) and O2(X, v > 0). These timescales enable a full assessment of the accuracy of PAS calibrations using O3-laden gas samples, dependent on the sample pressure, bath gas composition and PAS laser modulation frequency.

Spin Crossover and Magnetic-Dielectric Bistability Induced by Hidden Pseudo-Jahn–Teller Effect

In a semi-review paper, we show that the hidden Jahn–Teller effect (JTE) and pseudo-JTE (PJTE) in molecular systems and solids, under certain conditions lead to the formation of two coexisting stable space configurations with different magnetic and dielectric properties, switchable by external perturbations. One of the stable configurations has a high space symmetry and a non-zero or higher spin (HS) (non-zero magnetic moment), the other being distorted, but with zero or lower spin (LS). The number of systems with hidden JTE or PJTE is innumerable; we demonstrate this on the (no exhaustible, too) group of systems with half-filed closed-shell degenerate electronic (orbital or band) configurations e2 and t3. The spin-crossover-change from the high symmetry HS arrangement to the low-symmetry LS geometry is accompanied by (driven by the PJTE) orbital disproportionation, in which the system prefers spins-paired states with two electrons on the same orbital (and lower symmetry charge distribution) over the Hund’s spin-parallel arrangement involving several orbitals. Ab initio calculations previously carried out on a series of molecular systems and clusters in crystals, including CuF3, Si3, Si4, Ge4, C4H4, Na4−, C603−, CuO6 (in two crystal environments, LiCuO2 and NaCuO2), etc., confirmed the general theory and allowed for estimates of the parameter values including relaxation times. The hidden JTE and PJTE are thus general tools for search and studies of polyatomic systems with bistabilities.

Diagonal Born-Oppenheimer corrections to the ground electronic state potential energy surfaces of ozone: improvement of ab initio vibrational band centers for the 16O3, 17O3 and 18O3 isotopologues

Mass-dependent diagonal Born-Oppenheimer corrections (DBOCs) to the ab initio electronic ground state potential energy surface for the main ¹⁶O₃ isotopologue and for homogeneous isotopic substitutions ¹⁷O₃ and ¹⁸O₃ of the ozone molecule are reported for the first time. The system being of strongly multiconfigurational character, multireference configuration interaction wave function ansatz with different complete active spaces was used. The reliable DBOC calculations with the targeted accuracy were possible to carry out up to about half of the dissociation threshold D₀. The comparison with the experimental band centers shows a significant improvement of the accuracy with respect to the best Born-Oppenheimer (BO) ab initio calculations reducing the total root-mean-squares (calculated-observed) deviations by about a factor of two. For the set of ¹⁶O₃ vibrations up to five bending and four stretching quanta, the mean (calculated-observed) deviations drop down from 0.7 cm^-1 (BO) to about 0.1 cm^-1, with the most pronounced improvement seen for bending states and for mixed bending-stretching polyads. In the case of bending band centers directly observed under high spectral resolutions, the errors are reduced by more than an order of magnitude down to 0.02 cm^-1 from the observed levels, approaching nearly experimental accuracy. A similar improvement for heavy isotopologues shows that the reported DBOC corrections almost remove the systematic BO errors in vibrational levels below D₀/2, though the scatter increases towards higher energies. The possible reasons for this finding, as well as remaining issues are discussed in detail. The reported results provide an encouraging accuracy validation for the multireference methods of the ab initio theory. New sets of ab initio vibrational states can be used for improving effective spectroscopic models for analyses of the observed high-resolution spectra, particularly in the cases of accidental resonances with "dark" states requiring accurate theoretical predictions.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (¹⁸O¹⁶O¹⁸O) and asymmetric (¹⁸O¹⁸O¹⁶O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (¹⁶O¹⁸O¹⁶O) and asymmetric (¹⁶O¹⁶O¹⁸O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Localized and delocalized bound states of the main isotopologue 48O3 and of 18O-enriched 50O3 isotopomers of the ozone molecule near the dissociation threshold

Knowledge of highly excited rovibrational states of ozone isotopologues is of key importance for modelling the dynamics of exchange reactions, for understanding longstanding problems related to isotopic anomalies of the ozone formation, and for analyses of extra-sensitive laser spectral experiments currently in progress. This work is devoted to new theoretical study of high-energy states for the main isotopologue 48O3 = 16O16O16O and for the family of 18O-enriched isotopomers 50O3 = {16O16O18O, 16O18O16O, 18O16O16O} of the ozone molecule considered using a full-symmetry approach. Energies and wave functions of bound states near the dissociation threshold are computed in hyperspherical coordinates accounting for the permutation symmetry of three identical nuclei in 48O3 and of two identical nuclei in 50O3, using the most accurate potential energy surface available now. The obtained vibrational band centers agree with observed ones with the root-mean-squares deviation of about 1 cm-1, making the results appropriate for assignments and analyses of future experimental spectra. The levels delocalized between the three potential wells of ozone isomers are computed and analyzed. The states situated deep in the three (for 48O3) or two (for 50O3) equivalent potential wells have similar energies with negligible splitting. However, the states situated just below the potential barriers separating the wells, are split due to the tunneling between the wells resulting in the splitting of rovibrational sub-bands. We evaluate the amplitudes of the corresponding effects and consider possible perturbations in vibration-rotation bands due to interactions between three potential wells. Theoretical predictions for the splitting of observable band centers are provided for the first time.

The Role of Ozone Vibrational Resonances in the Isotope Exchange Reaction 16O16O + 18O → 18O16O + 16O: The Time-Dependent Picture

We consider the time-dependent dynamics of the isotope exchange reaction in collisions between an oxygen molecule and an oxygen atom: ¹⁶O¹⁶O + ¹⁸O → ¹⁶O¹⁸O + ¹⁶O. A theoretical approach using the multiconfiguration time-dependent Hartree method was employed to model the time evolution of the reaction. Two potential surfaces available in the literature were used in the calculations, and the results obtained with the two surfaces are compared with each other as well as with results of a previous theoretical time-independent approach. A good agreement for the reaction probabilities with the previous theoretical results is found. Comparing the results obtained using two potential energy surfaces allows us to understand the role of the reef/shoulder-like feature in the minimum energy path of the reaction in the isotope exchange process. Also, it was found that the distribution of final products of the reaction is highly anisotropic, which agrees with experimental observations and, at the same time, suggests that the family of approximated statistical approaches, assuming a randomized distribution over final exit channels, is not applicable to this case.

Formation of ozone by solid state reactions

We studied the isotopic composition of ozone formed at low (3-10 K) temperature via O + O2 solid state reactions using a partially dissociated 16O/16O2 : 18O/18O2 = 1 : 1 mixture. The ozone ice has an isotopic abundance that differs from the statistical one and from gas phase studies. Ozone formation is influenced by the competition of the production of O2 (O + O or O + O3) vs. O3 (O + O2) and by the energy released in the O + O reaction. The exothermicity of the O + O reaction helps to overcome the barrier of the O + O2 reaction. Heating the ozone ice past 50 K brings about a transformation from amorphous to crystalline ice. The formation of ozone on water ice yields a blue shift of IR bands, and the yield of formed O3 increases up to the sample temperature of 100 K. When 18O/18O2 is deposited on H216O ice, formation of 18O18O16O is detected. We propose that the exothermicity of the reaction 18O + 18O drives water dissociation (16O + H2) followed by ozone formation (16O + 18O2 → 16O18O18O).

Dissociation cross section for high energy O2-O2 collisions

Collision-induced dissociation cross section database for high energy O₂-O₂ collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O₄ potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.

Dissociation cross sections for N2 + N → 3N and O2 + O → 3O using the QCT method

Cross sections for the homo-nuclear atom-diatom collision induced dissociations (CIDs): N₂ + N and O₂ + O are calculated using Quasi-Classical Trajectory (QCT) method on ab initio Potential Energy Surfaces (PESs). A number of studies for these reactions carried out in the past focused on the CID cross section values generated using London-Eyring-Polanyi-Sato PES and seldom listed the CID cross section data. A highly accurate CASSCF-CASPT2 N₃ and a new O₃ global PES are used for the present QCT analysis and the CID cross section data up to 30 eV relative energy are also published. In addition, an interpolating scheme based on spectroscopic data is introduced that fits the CID cross section for the entire ro-vibrational spectrum using QCT data generated at chosen ro-vibrational levels. The rate coefficients calculated using the generated CID cross section compare satisfactorily with the existing experimental and theoretical results. The CID cross section data generated will find an application in the development of a more precise chemical reaction model for Direct Simulation Monte Carlo code simulating hypersonic re-entry flows.

Rovibrational energy transfer and dissociation in O2-O collisions

A set of state-specific transition rates for each rovibrational level is generated for the O2(X(3)Σ(g)(-))-O(3)P system using the quasi-classical trajectory method at temperatures observed in hypersonic flows. A system of master equations describes the relaxation of the rovibrational ensemble to thermal equilibrium under ideal heat bath conditions at a constant translational temperature. Vibrational and rotational relaxation times, obtained from the average internal energies, exhibit a pattern inherent in a chemically reactive collisional pair. An intrinsic feature of the O3 molecular system with a large attractive potential is a weak temperature dependence of the rovibrational transition rates. For this reason, the quasi-steady vibrational and rotational temperatures experience a maximum at increasing translational temperature. The energy rate coefficients, that characterize the average loss of internal energy due to dissociation, quickly diminish at high temperatures, compared to other molecular systems.

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.

Enhancing the branching ratios in the dissociation channels for O(16)O(16)O(18) molecule by designing optimum laser pulses: A study using stochastic optimization

We propose a strategy of using a stochastic optimization technique, namely, simulated annealing to design optimum laser pulses (both IR and UV) to achieve greater fluxes along the two dissociating channels (O(18) + O(16)O(16) and O(16) + O(16)O(18)) in O(16)O(16)O(18) molecule. We show that the integrated fluxes obtained along the targeted dissociating channel is larger with the optimized pulse than with the unoptimized one. The flux ratios are also more impressive with the optimized pulse than with the unoptimized one. We also look at the evolution contours of the wavefunctions along the two channels with time after the actions of both the IR and UV pulses and compare the profiles for unoptimized (initial) and optimized fields for better understanding the results that we achieve. We also report the pulse parameters obtained as well as the final shapes they take.

Does the "reef structure" at the ozone transition state towards the dissociation exist? New insight from calculations and ultrasensitive spectroscopy experiments

Since the discovery of anomalies in ozone isotope enrichment, several fundamental issues in the dynamics linked to the shape of the potential energy surface in the transition state region have been raised. The role of the reeflike structure on the minimum energy path is an intricate question previously discussed in the context of chemical experiments. In this Letter, we bring strong arguments in favor of the absence of a submerged barrier from ultrasensitive laser spectroscopy experiments combined with accurate predictions of highly excited vibrations up to nearly 95% of the dissociation threshold.

Investigation of 3-fragment photodissociation of O3 at 193.4 and 157.6 nm by coincident measurements

Photodissociation of the ozone molecule at 193.4 nm (6.41 eV) and 157.6 nm (7.87 eV) is studied by fast-beam translational spectroscopy. Coincident detection of the dissociation products allows direct observation of the 3-fragment channel and determination of its kinematic parameters. The results indicate that at each wavelength, 3-fragment dissociation proceeds through synchronous concerted bond breaking, but the energy partitioning among the fragments is different. The branching fraction of the 3-fragment channel increases from 5.2(6)% at 193.4 nm to 26(4)% at 157.6 nm, in agreement with previous studies. It is shown that vibrational excitation of the symmetric stretch mode in O3 molecules created by photodetachment of O(3)(-) anion enhances the absorption efficiency, especially at 193.4 nm, but does not have a strong effect on the 3-fragment dissociation.

Theory of mass-independent fractionation of isotopes, phase space accessibility, and a role of isotopic symmetry

Key experimental and theoretical features of mass-independent fractionation (MIF) of isotopes, also known as the η-effect, are summarized, including its difference from the exit channel zero-point energy difference effect. The latter exactly cancels in the MIF. One key experimental result is that the MIF for O3 formation is a low-pressure phenomenon and, moreover, that it decreases with increasing pressure of third bodies at pressures far below the "Lindemann fall-off" pressures for three-body recombination of O and O2. A possible origin of the MIF is discussed in terms of a role for isotopologue symmetry in intramolecular energy sharing. An explanation is suggested for the large difference in the fall-off pressure for recombination and the pressure for a large decrease in MIF, in terms of a difference between deactivating collisions and what we term here "symmetry-changing collisions". It is noted that the theory of the MIF involves four recombination rate constants and an equilibrium constant, for each trace isotope, seven rate constants in all and two equilibrium constants. A conceptual shortcut is noted. Experimental and computational information that may provide added insight into the MIF mechanism and tests is described.

Improved Potential Energy Surface of Ozone Constructed Using the Fitting by Permutationally Invariant Polynomial Function

New global potential energy surface for the ground electronic state of ozone is constructed at the complete basis set level of the multireference configuration interaction theory. A method of fitting the data points by analytical permutationally invariant polynomial function is adopted. A small set of 500 points is preoptimized using the old surface of ozone. In this procedure the positions of points in the configuration space are chosen such that the RMS deviation of the fit is minimized. New ab initio calculations are carried out at these points and are used to build new surface. Additional points are added to the vicinity of the minimum energy path in order to improve accuracy of the fit, particularly in the region where the surface of ozone exhibits a shallow van der Waals well. New surface can be used to study formation of ozone at thermal energies and its spectroscopy near the dissociation threshold.

Mixed quantum-classical theory for the collisional energy transfer and the rovibrational energy flow: application to ozone stabilization

A mixed quantum-classical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zero-point energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantum-classical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally.