Towards Quantitative Reaction Dynamics of O3

Abstract

The reaction dynamics of O(3P) + O2(3Sigma_g-) collisions in the O3(1A') electronic ground state is characterized on a high-level MRCI+Q/aug-cc-pVQZ potential energy surface represented as a reproducing kernel. For the atom exchange reactions involving the ^{16}O and ^{18}O isotopes as the atomic collision partner, associated with rates k6(T) and k8(T), respectively, a negative temperature-dependence of k(T), consistent with experiments was found. The absolute rates typically underestimate measured rates by 50 percent, depending on the experiment considered. For the ratio R(T) = k8(T)/k6(T), the measured T-dependence was found, including a cusp at lower temperatures. The differences between experiments and computations are primarily due to neglect of quantum effects, primarily zero-point effects. For the atomization reaction, leading to 3O(3P), the rates is lower by approximately one order of magnitude compared with experiments, which is a clear improvement over simulations using previous potential energy surfaces computed with smaller basis sets. Non-adiabatic effects are deemed minor for the atom exchange reactions.

Figures (5)

• Figure 1: Performance of the RKHS-represented reactive, three-dimensional PES for the [OOO] system with the zero of energy at the O($^3$P)+O($^3$P)+O($^3$P) asymptote. (A) Correlation between single-channel RKHS representation and reference energies for on-grid training data. (B) Correlation between 3D mixed RKHS representation and reference energies for the on-grid training data. (C) Performance of the 3D mixed RKHS representation on the mixing region. (D) Performance of the 3D mixed RKHS representation for 1188 off-grid points not used in constructing the PES. The RMSD between the RKHS representation and the reference data and the corresponding $r^{2}$ are given in each panel.
• Figure 2: Panel A: Two-dimensional potential energy surface (PES) for a fixed internuclear distance $r = 2.46$ a.u. as a function of the Jacobi coordinates $(R,\theta)$, computed at the AVQZ level. The color scale represents the energy in kcal/mol. Solid black contour lines correspond to AVQZ energies, while dashed red contours indicate AVTZ results for comparison. The inset illustrates the definition of the Jacobi coordinates: $r$ is the diatomic bond length between ${\rm O}_{\rm A}$ and ${\rm O}_{\rm B}$, $R$ is the distance from the diatomic center of mass $Q$ to atom ${\rm O}_{\rm C}$, and $\theta$ is the angle between $\vec{r}$ and $\vec{R}$. Panel B: Energy difference surface $E_{\mathrm{AVTZ}} - E_{\mathrm{AVQZ}}$ as a function of $(R,\theta)$. The color map highlights regions where AVTZ overestimates (red) or underestimates (blue) the AVQZ energies. Contour lines are drawn at uniform intervals. The minimum energy in the reactant well region is found to be $E^{\mathrm{\min}}_{\rm AVQZ} = -29.6$ kcal/mol and $E^{\mathrm{\min}}_{\rm AVTZ} = -26.4$ kcal/mol within the selected $(R,\theta)$ window.
• Figure 3: Temperature dependence of the thermal rate coefficients $k(T)$ for the natural and heavy isotope of the incoming oxygen atom. Panel A: Results for $k(T)$ obtained from the RKHS-based PESs using the AVTZ and AVQZ basis sets and for oxygen isotopic substitutions as indicated in the legend. Earlier wave packet simulations using the SSB PES (black triangles) illustrate the negative $T-$dependence a number of previous studies reported.siebert2001spectroscopy The measured ratesanderson:1997 (blue and violet filled circles) are shown together with the reported uncertainties. Other measured rates are represented by the shaded uncertainty regions: blue and violetfleurat:2003 for $^{18}\mathrm{O} + ^{16}\mathrm{O}_2$ and $^{16}\mathrm{O} + ^{18}\mathrm{O}_2$, respectively, while the graywiegell1997temperature region applies to both. Panel B: $T-$dependence of the isotopic rate ratio $R(T) = k_8(T)/k_6(T)$. Theoretical predictions obtained with the AVQZ RKHS-PES (blue symbols) are compared with measurementsfleurat:2003anderson:1997 (grey and black symbols).
• Figure 4: Thermal rate coefficients $k(T)$ for the dissociation reaction using $g_{\mathrm{diss}} = 1/27$. The rate constants are shown as a function of inverse temperature ($10000/T$) on the lower horizontal axis, while the corresponding temperature scale (in K) is displayed on the upper axis. Simulation results obtained with different potential energy surfaces are shown as colored symbols, including statistical error bars estimated via bootstrapping. Results based on the RKHS-PES constructed with the AVTZMM.o3:2025 and AVQZ (present work) basis sets are shown as red open circles and dark red symbols, respectively, while those using the PIP-PESMM.o3:2025varga:2017 are the blue symbols. To visually emphasize the temperature dependence, the AVTZ and AVQZ simulation results were fitted and are represented by dashed lines in their respective colors. Experimental measurementsbyron:1959shatalov:1973 are shown as black open circles. A linear regression of the experimental data is indicated by the dashed black line.
• Figure 5: Potential energy curves of the five lowest $^1{\rm A}'$ electronic states ($1\,^1{\rm A}'$ (blue), $2\,^1{\rm A}'$ (orange), $3\,^1{\rm A}'$ (green), $4\,^1{\rm A}'$ (red), and $5\,^1{\rm A}'$ (purple)) as functions of the dissociation coordinate $R$ for fixed angles $\theta = 156.6^\circ$, $\theta = 129.9^\circ$ and $\theta = 90.1^\circ$ (panels A to C). The O--O bond distance was $r = 2.65\,a_0$. The zero of energy is the minimum of the ground-state surface (panel B). In A to C, colored symbols denote adiabatic ab initio MRCI energies, while solid black lines represent the corresponding diabatic potential energy curves. Panel D: Projection of the distribution $P(R,\theta)$ (green) from 1500 trajectories run at 100 K, leading to atom exchange onto the adiabatic ground-state potential energy surface $V(R,\theta; r = 2.65\,a_0)$. Inset: Angular distribution $P(\theta)$ for $R = 3.0\,a_0$ (blue), $R = 3.5\,a_0$ (orange), $R = 4.0\,a_0$ (green), and $R = 7$ a$_0$ (red). Note the near-symmetry of $P(\theta)$ with respect to $\theta = 90^\circ$.