Accurateab initiopotential energy curve of O2. II. Core-valence correlations, relativistic contributions, and vibration-rotation spectrum

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

Bond dissociation energy of O2 measured by fully state-to-state resolved threshold fragment yield spectra

We have determined the bond dissociation energy of O2 by measuring fully state-to-state resolved threshold fragment yield spectra in the XUV energy region, O2X3Σg-,N″,J″→O(PJ3)+O(S1o3)/O(S2o5). Our results have yielded a bond dissociation energy value of 41 269.19 ± 0.10 cm-1, which is consistent with previous measurements but exhibits a significantly lower uncertainty, approximately five times smaller. It is noteworthy that this study is the first to simultaneously achieve fine structure state resolution for the parent O2 molecule and spin-orbit state resolution for the O(3PJ) fragments in the measurement of O2 bond dissociation energy. As a result, our findings have established a solid foundation for the obtained data.

Self-consistent field method for open-shell systems within the density-matrix functional theory

The unrestricted Hartree-Fock method is extended to correlation calculation within the density-matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin-orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi-Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2 .

Dissociation cross sections and rates in O2 + N collisions: molecular dynamics simulations combined with machine learning

The collision-induced dissociation reaction of O2 (v, j) + N, a fundamental process in nonequilibrium air flows around reentry vehicles, has been studied systematically by applying molecular dynamics simulations on the 2A', 4A' and 6A' potential energy surfaces of NO2 in a wide temperature range. In particular, we have directly investigated the role of the 6A' surface in this process and discussed the applicability of the simplified approximate rate models proposed by Esposito et al. and Andrienko et al. based on the lowest two surfaces. The present work indicates that the state-selected dissociation of O2 + N is dominated by the 6A' surface for all except for the low-lying O2 states. Furthermore, a complete database of rovibrationally detailed cross sections and rate coefficients is a prerequisite for modeling the relevant nonequilibrium air flows in spacecraft reentry. Here, the combination of the quasi-classical trajectory (QCT) and the neural network (NN) has been proposed to predict all state-selected dissociation cross sections and further construct dissociation parameter sets. All NN-based models established in this work accurately reproduce the results calculated from QCT simulations over a wide range of rovibrational quantum numbers with R2 > 0.99. Compared with the explicit QCT simulations, the computational requirement for predicting cross sections and rates based on the NN models significantly reduces. Finally, thermal equilibrium rate coefficients computed from NN models match remarkably well the available theoretical and experimental results in the whole temperature range explored.

λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density

In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn–Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron–electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF.

Diagnostics of Air Purification Plasma Device by Spatially Resolved Emission Spectroscopy

A non-thermal plasma, air purification device (PlasmaShield®, MD250, Keswick, SA, Australia), was investigated using spatially resolved optical emission spectroscopy. The emission spectra were measured with two spatial dimensions to analyze and identify the transition lines of excited NO–γ (A2Σ–X2Π), N2 (C3Π–B3Π), and N2+ (B2Σ–X2Σ) systems. The N2 emission band at 337 and 316 nm were used to determine the spatially resolved vibrational temperature of N2 molecules, TvibN2. It was found that the average N2 vibrational temperatures in the x and y directions are almost the same. Two key operating parameters, supplied power and air flow, influence the N2 vibrational temperature. The results demonstrate that applying higher supplied power increases the vibrational temperature, while changes in air flow velocity do not affect the vibrational temperature values. The phenomenological plasma temperature (PPT) was also estimated from the N2 vibrational temperature. It was observed that PlasmaShield® generates excited N2 and NO only within a narrow region around the discharge electrode tip (with peak intensity below 100 µm from the tip). The study also shows no presence of excited OH*, O*, and other radicals.

Quantification of the Effect of an External Magnetic Field on Water Oxidation with Cobalt Oxide Anodes

Here, we quantify the effect of an external magnetic field (β) on the oxygen evolution reaction (OER) for a cobalt oxide|fluorine-doped tin oxide coated glass (CoO_x|FTO) anode. A bespoke apparatus enables us to precisely determine the relationship between magnetic flux density (β) and OER activity at the surface of a CoO_x|FTO anode. The apparatus includes a strong NdFeB magnet (β_max = 450 ± 1 mT) capable of producing a magnetic field of 371 ± 1 mT at the surface of the anode. The distance between the magnet and the anode surface is controlled by a linear actuator, enabling submillimeter distance positioning of the magnet relative to the anode surface. We couple this apparatus with a finite element analysis magnetic model that was validated by Hall probe measurements to determine the value of β at the anode surface. At the largest tested magnetic field strength of β = 371 ± 1 mT, a 4.7% increase in current at 1.5 V vs the normal hydrogen electrode (NHE) and a change in the Tafel slope of 14.5 mV/dec were observed. We demonstrate through a series of OER measurements at sequential values of β that the enhancement consists of two distinct regions. The possible use of this effect to improve the energy efficiency of commercial water electrolyzers is discussed, and major challenges pertaining to the accurate measurement of the phenomenon are demonstrated.

Potential energy surfaces for high-energy N + O2 collisions

Potential energy surfaces for high-energy collisions between an oxygen molecule and a nitrogen atom are useful for modeling chemical dynamics in shock waves. In the present work, we present doublet, quartet, and sextet potential energy surfaces that are suitable for studying collisions of O₂(³Σ_g ^-) with N(⁴S) in the electronically adiabatic approximation. Two sets of surfaces are developed, one using neural networks (NNs) with permutationally invariant polynomials (PIPs) and one with the least-squares many-body (MB) method, where a two-body part is an accurate diatomic potential and the three-body part is expressed with connected PIPs in mixed-exponential-Gaussian bond order variables (MEGs). We find, using the same dataset for both fits, that the fitting performance of the PIP-NN method is significantly better than that of the MB-PIP-MEG method, even though the MB-PIP-MEG fit uses a higher-order PIP than those used in previous MB-PIP-MEG fits of related systems (such as N₄ and N₂O₂). However, the evaluation of the PIP-NN fit in trajectory calculations requires about 5 times more computer time than is required for the MB-PIP-MEG fit.

Spin-Forbidden Branching in the Mechanism of the Intrinsic Haber-Weiss Reaction

The mechanism of the O₂^⋅− and H₂O₂ reaction (Haber–Weiss) under solvent‐free conditions has been characterized at the DFT and CCSD(T) level of theory to account for the ease of this reaction in the gas phase and the formation of two different set of products (Blanksby et al., Angew. Chem. Int. Ed. 2007, 46, 4948). The reaction is shown to proceed through an electron‐transfer process from the superoxide anion to hydrogen peroxide, along two pathways. While the O₃^⋅− + H₂O products are formed from a spin‐allowed reaction (on the doublet surface), the preferred products, O^⋅−(H₂O)+³O₂, are formed through a spin‐forbidden reaction as a result of a favorable crossing point between the doublet and quartet surface. Plausible reasons for the preference toward the latter set are given in terms of the characteristics of the minimum energy crossing point (MECP) and the stability of an intermediate formed (after the MECP) in the quartet surface. These unique results show that these two pathways are associated with a bifurcation, yielding spin‐dependent products.

An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (HxOy) Species

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO3 and H2O3 (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

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.

High resolution spectral analysis of oxygen. IV. Energy levels, partition sums, band constants, RKR potentials, Franck-Condon factors involving the X³Σg⁻, a₁Δg and b¹Σg⁺ states

We have updated the isotopically invariant Dunham fit of O2 with newly reported literature transitions to derive (1) the energy levels, partition sums, band-by-band molecular constants, and RKR potentials for the X(3)Σg(-), a(1)Δg, and b(1)Σg(+) states of the six O2 isotopologues: (16)O(16)O, (16)O(17)O, (16)O(18)O, (17)O(17)O, (17)O(18)O, and (18)O(18)O; (2) Franck-Condon factors for their a(1)Δg-X(3)Σg(-), b(1)Σg(+)-X(3)Σg(-), and a(1)Δg-b(1)Σg(+) band systems. This new spectroscopic parameterization characterizes all known transitions within and between the X(3)Σg(-), a(1)Δg, and b(1)Σg(+) states within experimental uncertainty and can be used for accurate predictions of as yet unmeasured transitions. All of these results are necessary to provide a consistent linelist of all transitions which will be reported in a followup paper.

Accurate calculations on the 22 electronic states and 54 spin-orbit states of the O2 molecule: potential energy curves, spectroscopic parameters and spin-orbit coupling

The potential energy curves (PECs) of 54 spin-orbit states generated from the 22 electronic states of O2 molecule are investigated for the first time for internuclear separations from about 0.1 to 1.0nm. Of the 22 electronic states, the X(3)Σg(-), A(')(3)Δu, A(3)Σu(+), B(3)Σu(-), C(3)Πg, a(1)Δg, b(1)Σg(+), c(1)Σu(-), d(1)Πg, f(1)Σu(+), 1(5)Πg, 1(3)Πu, 2(3)Σg(-), 1(5)Σu(-), 2(1)Σu(-) and 2(1)Δg are found to be bound, whereas the 1(5)Σg(+), 2(5)Σg(+), 1(1)Πu, 1(5)Δg, 1(5)Πu and 2(1)Πu are found to be repulsive ones. The B(3)Σu(-) and d(1)Πg states possess the double well. And the 1(3)Πu, C(3)Πg, A'(3)Δu, 1(5)Δg and 2(5)Σg(+) states are the inverted ones when the spin-orbit coupling is included. The PEC calculations are done by the complete active space self-consistent field (CASSCF) method, which is followed by the internally contracted multireference configuration interaction (icMRCI) approach with the Davidson correction. Core-valence correlation and scalar relativistic corrections are taken into account. The convergence of present calculations is evaluated with respect to the basis set and level of theory. The vibrational properties are discussed for the 1(5)Πg, 1(3)Πu, d(1)Πg and 1(5)Σu(-) states and for the second well of the B(3)Σu(-) state. The spin-orbit coupling effect is accounted for by the state interaction method with the Breit-Pauli Hamiltonian. The PECs of all the electronic states and spin-orbit states are extrapolated to the complete basis set limit. The spectroscopic parameters are obtained, and compared with available experimental and other theoretical results. Analyses demonstrate that the spectroscopic parameters reported here can be expected to be reliably predicted ones. The conclusion is obtained that the effect of spin-orbit coupling on the spectroscopic parameters are small almost for all the electronic states involved in this paper except for the 1(5)Σu(-), 1(5)Πg and 1(3)Πu.

Ab initio simulation of transport phenomena in rarefied gases

Ab initio potentials are implemented into the direct simulation Monte Carlo (DSMC) method. Such an implementation allows us to model transport phenomena in rarefied gases without any fitting parameter of intermolecular collisions usually extracted from experimental data. Applying the method proposed by Sharipov and Strapasson [Phys. Fluids 24, 011703 (2012)], the use of ab initio potentials in the DSMC requires the same computational efforts as the widely used potentials such as hard spheres, variable hard sphere, variable soft spheres, etc. At the same time, the ab initio potentials provide more reliable results than any other one. As an example, the transport coefficients of a binary mixture He-Ar, viz., viscosity, thermal conductivity, and thermal diffusion factor, have been calculated for several values of the mole fraction.