Intermolecular Potential of the O2−O2 Dimer. An ab Initio Study and Comparison with Experiment

Thermodynamics of the van der Waals Dimers of O2, N2 and the Heterodimer (N2)(O2) and Their Presence in Earth's Atmosphere

The dimerization thermodynamics of N2 and O2, the principal components of Earth's atmosphere, have been determined from the respective second virial coefficients of the bound and metastable dimers calculated using the method of Stogryn and Hirschfelder that utilizes the Lennard-Jones (LJ) potential to account for intermolecular interactions. In addition, the thermodynamic properties of the heterodimer (N2)(O2) have been obtained using the same approach, employing combining rules to construct the LJ potential. Thus, Keq, ΔH, and ΔS for the three dimers are reported between 80-120 K. Over this temperature range, the ranking of Keq is (N2)(O2) > (O2)(O2) > (N2)(N2). The same trend is found for the exoethalpicity of dimer formation. For example, at 100 K, the Keq values are, respectively, 0.0406(14), 0.0215(5), and 0.0181(10), and the corresponding ΔH values are -2401(5), -2344(7), and -2279(1) J/mol. The mole fraction composition of the dimers in the atmosphere was calculated for altitudes up to 20 km. These calculations show that in the troposphere and the lower stratosphere (up to 20 km), the three dimers rank fifth to seventh in abundance, between CO2 and Ne. In this region, the average mole fractions of (N2)(N2), (O2)(O2), and (N2)(O2) are calculated to be 3.4(2) × 10-4, 2.80(9) × 10-5, and 1.95(7) × 10-4, respectively.

Molecular Oxygen Trimer: Multiplet Structures and Stability

We present a detailed theoretical study of the molecular oxygen trimer where the potential energy surfaces of the seven multiplet states have been calculated by means of a pair approximation with very accurate dimer ab initio potentials. In order to obtain all the states a matrix representation of the potential using the uncoupled spin representation has been applied. TheS = 0 ${S = 0}$ andS = 1 ${S = 1}$ states are nearly degenerate and low-lying isomers appear for most multiplicities. A crucial point in deciding the relative stabilities is the zero-point energy which represents a sizable fraction of the electronic well-depth. Therefore, we have performed accurate diffusion Monte Carlo studies of the lowest state in each multiplicity. Analysis of the wavefunction allows a deeper interpretation of the cluster structures, finding that they are significantly floppy in most cases.

An unrestricted approach for the accurate calculation of the intermolecular potential of (O2)4: Implications for the solid epsilon phase

Oxygen in its elemental form shows a variety of magnetic properties in its condensed phases; in particular, the epsilon solid phase loses its magnetism. These phenomena reflect the nature of the intermolecular forces present in the solid and the changes that arise with variations in pressure and temperature. In this study, we use intermolecular potentials obtained with unrestricted ab initio methods to model the singlet state of the oxygen tetramer [(O₂)₄], which is the unit cell, consistent with the non-magnetic character of this phase. To do this, we perform an analysis of the coupled-uncoupled representations of the spin operator together with a pairwise approximation and the Heisenberg Hamiltonian. We start from unrestricted potentials for the dimer calculated at a high level as well as different density functional theory (DFT) functionals and then apply a finite model to predict the properties of the epsilon phase. The results obtained in this way reproduce well the experimental data in the entire pressure range below 60 GPa. Additionally, we show the importance of calculating the singlet state of the tetramer as opposed to previous DFT periodic calculations, where the unrestricted description leads to a mixture of spin states and a poor comparison with the experiment. This point is crucial in the recent discussion about the coexistence of two epsilon phases: one where the identity of each O₂ with spin S = 1 is retained within the tetramer unit vs another at higher pressures where the tetramer behaves as a single unit with a closed-shell character.

An unrestricted approach for the accurate calculation of the interaction potentials of open-shell monomers: The case of O2-O2

The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of its associated properties stem from the fact that it is a very stable diradical. Its open-shell nature leads to low-lying multiplets with total electronic spin S = 0, 1, 2 in the case of the dimer, (O₂)₂, and the accurate calculation of the intermolecular potentials represents a challenge to ab initio electronic structure methods. In this work, we present intermolecular potentials calculated at a very high level, thus competing with the most accurate restricted potentials obtained to date. This is accomplished by drawing on an analogy between the coupled and uncoupled representations of angular momentum and restricted vs unrestricted methodologies. The S = 2 state can be well represented by unrestricted calculations in which the spins of the unpaired electrons are aligned in parallel; however, for the state where they are aligned in antiparallel fashion, it would seem that the total spin is not well defined, i.e., the well-known spin contamination problem. We show that its energy corresponds to that of the S = 1 state and perform unrestricted coupled cluster calculations for these two states. Then, we obtain the S = 0 state through the Heisenberg Hamiltonian and show that this is very reliable in the well region of the potentials. We make extensive comparisons with the best restricted potentials [Bartolomei et al., Phys. Chem. Chem. Phys. 10(35), 5374-5380 (2008)] and with reliable experimental determinations, and a very good agreement is globally found.

Global potential energy surface of ground state singlet spin O4

A new global potential energy for the singlet spin state O₄ system is reported using CASPT2/aug-cc-pVTZ ab initio calculations. The geometries for the six-dimensional surface are constructed using a novel point generation scheme that employs randomly generated configurations based on the beta distribution. The advantage of this scheme is apparent in the reduction of the number of required geometries for a reasonably accurate potential energy surface (PES) and the consequent decrease in the overall computational effort. The reported surface matches well with the recently published singlet surface by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. In addition to the O₄ PES, the ground state N₄ PES is also constructed using the point generation scheme and compared with the existing PES [Y. Paukku et al., J. Chem. Phys. 139, 044309 (2013)]. The singlet surface is constructed with the aim of studying high energy O₂-O₂ collisions and predicting collision induced dissociation cross section to be used in simulating non-equilibrium aerothermodynamic flows.

Dimol Emission of Oxygen Made Possible by Repulsive Interaction

For the energy emitted in a textbook example of chemiluminescence, the peculiar red light produced by singlet molecular oxygen is about twice that of the spin-forbidden O₂(a¹Δ_g) → O₂(X³∑_g^-) transition. Theoretical studies suggest that the O₂(a¹Δ_g)-O₂(a¹Δ_g) van der Waals interaction is weak, and at room temperature no long-lived complex is formed. Our high-level ab initio calculations show that in the bound domain of the dimer, the oscillator strength is very small, but increases at smaller intermolecular separations, where, however, the interaction is repulsive. We propose that the emission is induced by collisions: it takes place "on-the-fly", when the collision energy allows the system to access the repulsive part of the potential energy surface where the oscillator strength is relatively large. The contribution of different orientations of the two O₂ molecules to the emission has been evaluated with a simple semiclassical model. The position of the emission peak is in accord with the experiment, and the estimated rate coefficient of collision-induced emission averaged over orientation is in reasonable agreement with the measurements.

On the role of the termolecular reactions 2O2 + H2 → 2HO2 and 2O2 + H2 → H + HO2 + O2 in formation of the first radicals in hydrogen combustion: ab initio predictions of energy barriers

We have investigated the role of termolecular reactions in the early chemistry of hydrogen combustion. We performed molecular chemical dynamics simulations using ReaxFF in LAMMPS to identify potential initial reactions for a 1 : 4 mixture of H₂ : O₂ in the NVT ensemble at density 276.3 kg m^-3 and ∼3000 K (∼4000 atm) and ∼4000 K (∼5000 atm), and then characterized the saddle points for those reactions using ab initio methods: CCSD(T) = FC/cc-pVTZ//MP2/6-31G, CCSD(T) = FULL/aug-cc-pVTZ//CCSD = FC/cc-pVTZ and CASSCF MP2/6-31G//MP2/6-31G. The main initial reaction is H₂ + O₂ → H + HO₂, frequently occurring in the presence of a second O₂ as a third body; that is, 2O₂ + H₂ → H + HO₂ + O₂. The second most frequent reaction is 2O₂ + H₂ → 2HO₂. We found three saddle points on the triplet PES of these termolecular reactions: one for 2O₂ + H₂ → H + HO₂ + O₂ and two for 2O₂ + H₂ → 2HO₂. In the latter case, one has a symmetric structure consistent with simultaneous formation of two HO₂ and the other corresponds to a bimolecular reaction between O₂ and H₂ that is "interrupted" by a second O₂ before going to completion. The classical barrier height of the symmetric saddle point for 2O₂ + H₂ → 2HO₂ is 49.8 kcal mol^-1. The barrier to H₂ + O₂ → H + HO₂ is 58.9 kcal mol^-1. The termolecular reaction will be competitive with H₂ + O₂ → H + HO₂ only at sufficiently high pressures.

Ab initio study of the O4H(+) novel species: spectroscopic fingerprints to aid its observation

A detailed ab initio characterization of the structural, energetic and spectroscopic properties of the novel O4H(+) species is presented. The equilibrium structures and relative energies of all multiplet states have been determined systematically by analyzing static and dynamical correlation effects. The two and three body dissociation processes have been studied and indicate the presence of conical intersections in various states including the ground state. Comparison with available thermochemical data is very good, supporting the applied methodology. The reaction, H3(+) + O4→ O4H(+) + H2, was found to be exothermic ΔH = -19.4 kcal mol(-1) and therefore, it is proposed that the product in the singlet state could be formed in the interstellar medium (ISM) via collision processes. To aid in its laboratory or radioastronomy detection in the interstellar medium we determined spectroscopic fingerprints. It is estimated for the most stable geometry of O4H(+) dipole allowed electronic transitions in the visible region at 429 nm and 666 nm, an intense band at 1745 cm(-1) in the infrared and signals at 40.6, 81.2 and 139.2 GHz in the microwave region at 10, 50 and 150 K respectively, relevant for detection in the ISM.

Communication: Ab initio study of O4H+: a tracer molecule in the interstellar medium?

The structure and energetics of the protonated molecular oxygen dimer calculated via ab initio methods is reported. We find structures that share analogies with the eigen and zundel forms for the protonated water dimer although the symmetrical sharing of the proton is more prevalent. Analysis of different fragmentation channels show charge transfer processes which indicate the presence of conical intersections for various states including the ground state. An accurate estimate for the proton affinity of O4 leads to a significantly larger value (5.6 eV) than for O2 (4.4 eV), implying that the reaction H3(+) + O4 → O4H(+) + H2 is exothermic by 28 Kcal/mol as opposed to the case of O2 which is nearly thermoneutral. This opens up the possibility of using O4H(+) as a tracer molecule for oxygen in the interstellar medium.

Nonadiabatic couplings in the collisional removal of O(2)(b (1)Sigma(g) (+),v) by O(2)

The effect of nonadiabatic couplings on the collisional removal of O(2)(b (1)Sigma(g) (+),v) by O(2)(X (3)Sigma(g) (-), v=0) is investigated. Two-dimensional adiabatic and quasidiabatic potential energy surfaces for the excited dimer states and the corresponding nonadiabatic radial couplings have been computed by means of ab initio calculations. Alternately, a two-state theoretical model, based on the Landau-Zener and Rosen-Zener-Demkov assumptions, has been employed to derive analytical forms for the nonadiabatic couplings and an adiabatic-to-diabatic transformation only depending on a reduced set of adiabatic energy terms. Compared to the ab initio results, the predictions of the model are found to be highly accurate. Quantum dynamics calculations for the removal of the first ten vibrational states of O(2)(b (1)Sigma(g) (+),v) indicate a clear dominant contribution of the vibration-electronic relaxation mechanism relative to the vibration-translation energy transfer. Although the present reduced-dimensionality model precludes any quantitative comparison with experiments, it is found that the removal probabilities for v=1-3 are qualitatively consistent with the experimental observations, once the vibrational structure of the fragments is corrected with spectroscopical terms. Besides, the model served to show how the computation of the adiabatic PESs just at the crossing seam was sufficient to describe the nonadiabatic dynamics related to a given geometrical arrangement. This implies considerable savings in the calculations which will eventually allow for larger accuracy in the ab initio calculations as well as higher dimensional treatments.

Multireference quantum Monte Carlo study of the O4 molecule

Fixed-node diffusion quantum Monte Carlo (FN-DMC) calculations are performed to obtain the most accurate dissociation barrier and heat of formation with respect to dissociation into molecular oxygen for the chemically bound tetraoxygen molecule. Multireference trial wave functions were used and built from truncated CASSCF(16,12) through a weight-consistent scheme allowing to control the fixed-node error. Results are compared with the previous ab initio benchmark Complete Active Space SCF Averaged Coupled Pair Functional/aug-cc-pVQZ (CASSCF-ACPF/AVQZ) results. The FN-DMC barriers to dissociation and heat of formation obtained are 11.6+/-1.6 kcal/mol and 98.5+/-1.9 kcal/mol, respectively. These thermochemical energies should be taken as the theoretical references when discussing the relevance of tetraoxygen in a variety of experiments and atmospheric chemical processes.

Potential energy surfaces for small alcohol dimers I: Methanol and ethanol

Potential energy landscapes for homogeneous dimers of methanol and ethanol were calculated using counterpoise (CP) corrected energies at the MP26-311+G(2df,2pd) level. The landscapes were sampled at approximately 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of a relative monomer yaw, pitch, and roll and the spherical angles between the monomer centers (taken as the C atom attached to the O). The 19 different routes studied for methanol and the 22 routes examined for ethanol include 607 CP corrected energies. Both landscapes can be adequately represented by site-site, pairwise-additive models, suitable for use in molecular simulations. A modified Morse potential is used for the individual pair interactions either with or without point charges to represent the monomer charge distribution. A slightly better representation of the methanol landscape is obtained using point charges, while the potential energy landscape of ethanol is slightly better without point charges. This latter representation may be computationally advantageous for molecular simulations because it avoids difficulties associated with long-range effects of point-charge-type models.