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Experimental and numerical studies were performed on the vibrational energy relaxation in shock-heated CO/N2/Ar mixtures. A laser absorption technique was applied to the time-dependent rovibrational temperature time-history measurements. The vibrational relaxation data of reflected-shock-heated CO were summarized at 1720–3230 K. In shock-tube experiments, the rotational temperature of CO quickly reached equilibrium, whereas a relaxation process was found in the time-dependent vibrational temperature. For the mixture with 1.0% CO and 10.0% N2, the vibrational excitation caused a decrease in the macroscopic thermodynamic temperature of the test gas. In the simulations, the state-to-state (StS) approach was employed, where the vibrational energy levels of CO and N2 are treated as pseudo-species. The vibrational state-specific inelastic rate coefficients of N2–Ar collisions were calculated using the mixed quantum–classical method based on a newly developed three-dimensional potential energy surface. The StS predictions agreed well with the measurements, whereas deviations were found between the Schwartz–Slawsky–Herzfeld formula predictions and the measurements. The Millikan–White vibrational relaxation data of the N2–Ar system were found to have the most significant impact on the model predictions via sensitivity analysis. The vibrational relaxation data of the N2–Ar system were then modified according to the experimental data and StS results, providing an indirect way to optimize the vibrational relaxation data of a specific system. Moreover, the vibrational distribution functions of CO and N2 and the effects of the vibration–vibration–translation energy transfer path on the thermal nonequilibrium behaviors were highlighted. [ABSTRACT FROM AUTHOR]

A merged potential energy surface (PES) is introduced for CO + CO collisions by combining a recent full-dimensional ab initio PES [Chen et al. J. Chem. Phys. 153, 054310 (2020)] and analytical long-range multipolar interactions. This merged PES offers a double advantage: it retains the precision of the ab initio PES in describing the van der Waals well and repulsive short range while providing an accurate physical description of long-range interaction; it significantly reduces the computational time required for trajectory integration since the long-range portion of the ab initio PES (involving numerous neural network fitting parameters) is now replaced by the analytical model potential. Based on the present merged PES, mixed Quantum-Classical (MQC) calculations, which capture quantum effects related to vibrational motion, align with a range of experimental data, including transport properties, vibrational energy transfer between CO and its isotoplogues, as well as rate coefficients for V–V and V–T/R processes. Notably, the original ab initio PES yields V–T/R rate coefficients at low temperatures that are significantly higher than the experimental data due to the artificial contribution of its unphysical long-range potential. In addition to conducting extensive MQC calculations to obtain raw data for V–V and V–T/R rate coefficients, we employ Gaussian process regression to predict processes lacking computed MQC data, thereby completing the considered V–V and V–T/R datasets. These extensive rate coefficient datasets, particularly for V–T/R processes, are unprecedented and reveal the significant role played by V–T/R processes at high temperatures, emphasizing the necessity of incorporating both V–V and V–T/R processes in the applications. [ABSTRACT FROM AUTHOR]

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110–2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau–Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO–Ar, CO–He, CO–CO, and CO–H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau–Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan–White vibrational relaxation data of the CO–Ar and CO–H2 systems to improve the performance of the Landau–Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted. [ABSTRACT FROM AUTHOR]

A new spin-averaged potential energy surface (PES) for non-reactive O2( Σ g − 3 ) + O2( Σ g − 3 ) collisions is presented. The potential is formulated analytically according to the nature of the principal interaction components, with the main van der Waals contribution described through the improved Lennard-Jones model. All the parameters involved in the formulation, having a physical meaning, have been modulated in restricted variation ranges, exploiting a combined analysis of experimental and ab initio reference data. The new PES is shown to be able to reproduce a wealth of different physical properties, ranging from the second virial coefficients to transport properties (shear viscosity and thermal conductivity) and rate coefficients for inelastic scattering collisions. Rate coefficients for the vibrational inelastic processes of O2, including both vibration-to-vibration (V–V) and vibration-to-translation/rotation (V–T/R) energy exchanges, were then calculated on this PES using a mixed quantum–classical method. The effective formulation of the potential and its combination with an efficient, yet accurate, nuclear dynamics treatment allowed for the determination of a large database of V–V and V–T/R energy transfer rate coefficients in a wide temperature range. [ABSTRACT FROM AUTHOR]

Molecular dynamics calculations of inelastic collisions of atomic oxygen with molecular nitrogen are known to show orders of magnitude discrepancies with experimental results in the range from room temperature to many thousands of degrees Kelvin. In this work, we have achieved an unprecedented quantitative agreement with experiments even at low temperature, by including a non-adiabatic treatment involving vibronic states on newly developed potential energy surfaces. This result paves the way for the calculation of accurate and detailed databases of vibrational energy exchange rates for this collisional system. This is bound to have an impact on air plasma simulations under a wide range of conditions and on the development of Very Low Earth Orbit (VLEO) satellites, operating in the low thermosphere, objects of great technological interest due to their potential at a competitive cost. [ABSTRACT FROM AUTHOR]

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows. [ABSTRACT FROM AUTHOR]

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110–2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau–Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO–Ar, CO–He, CO–CO, and CO–H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau–Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan–White vibrational relaxation data of the CO–Ar and CO–H2 systems to improve the performance of the Landau–Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted. [ABSTRACT FROM AUTHOR]

Knowledge of energy exchange rate constants in inelastic collisions is critically required for accurate characterization and simulation of several processes in gaseous environments, including planetary atmospheres, plasma, combustion, etc. Determination of these rate constants requires accurate potential energy surfaces (PESs) that describe in detail the full interaction region space and the use of collision dynamics methods capable of including the most relevant quantum effects. In this work, we produce an extensive collection of vibration-to-vibration (V–V) and vibration-to-translation/rotation (V–T/R) energy transfer rate coefficients for collisions between CO and N 2 molecules using a mixed quantum-classical method and a recently introduced (A. Lombardi, F. Pirani, M. Bartolomei, C. Coletti, and A. Laganà, Frontiers in chemistry, 7, 309 (2019)) analytical PES, critically revised to improve its performance against ab initio and experimental data of different sources. The present database gives a good agreement with available experimental values of V–V rate coefficients and covers an unprecedented number of transitions and a wide range of temperatures. Furthermore, this is the first database of V–T/R rate coefficients for the title collisions. These processes are shown to often be the most probable ones at high temperatures and/or for highly excited molecules, such conditions being relevant in the modeling of hypersonic flows, plasma, and aerospace applications. [ABSTRACT FROM AUTHOR]

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 O 4 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+O 3 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 O 2 -O 2 collisions., (© 2024 Wiley-VCH GmbH.)

Experimental and numerical studies were performed on the vibrational energy relaxation in shock-heated CO/N2/Ar mixtures. A laser absorption technique was applied to the time-dependent rovibrational temperature time-history measurements. The vibrational relaxation data of reflected-shock-heated CO were summarized at 1720-3230 K. In shock-tube experiments, the rotational temperature of CO quickly reached equilibrium, whereas a relaxation process was found in the time-dependent vibrational temperature. For the mixture with 1.0% CO and 10.0% N2, the vibrational excitation caused a decrease in the macroscopic thermodynamic temperature of the test gas. In the simulations, the state-to-state (StS) approach was employed, where the vibrational energy levels of CO and N2 are treated as pseudo-species. The vibrational state-specific inelastic rate coefficients of N2-Ar collisions were calculated using the mixed quantum-classical method based on a newly developed three-dimensional potential energy surface. The StS predictions agreed well with the measurements, whereas deviations were found between the Schwartz-Slawsky-Herzfeld formula predictions and the measurements. The Millikan-White vibrational relaxation data of the N2-Ar system were found to have the most significant impact on the model predictions via sensitivity analysis. The vibrational relaxation data of the N2-Ar system were then modified according to the experimental data and StS results, providing an indirect way to optimize the vibrational relaxation data of a specific system. Moreover, the vibrational distribution functions of CO and N2 and the effects of the vibration-vibration-translation energy transfer path on the thermal nonequilibrium behaviors were highlighted., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110-2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau-Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO-Ar, CO-He, CO-CO, and CO-H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau-Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan-White vibrational relaxation data of the CO-Ar and CO-H2 systems to improve the performance of the Landau-Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

In this study, complete ( i.e. , including all vibrational quantum numbers in an N 2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N 2 -N 2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100-9000 K. To reach this goal, we improved a mixed quantum-classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique ( i.e. , the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.

The energy transfer, dissociations, and chemical reactions between O 2 and N 2 play an important role in the re-entry process of aircraft and many atmospheric, combustion, and plasma processes. Recently, Varga et al. ( J. Chem. Phys ., 2016 , 144 , 024310) developed a full-dimensional high-precision potential energy surface (PES) of the ground triplet electronic state for the O 2 and N 2 system based on ca. 55,000 data points, whose energies were calculated by multi-state complete-active-space second-order perturbation theory/minimally augmented correlation-consistent polarized valence triple-zeta electronic structure calculations plus dynamically scaled external correlation. The fitting function adopted the many-body expansion form with the four-body interactions fitted by the permutationally invariant polynomial in terms of bond-order functions of the six interatomic distances (MB-PIP). In this work, we refit the PES of the N 2 O 2 system by two methods based on the same data set that was used by Varga et al. The first uses the permutation invariant polynomial-neural network (PIP-NN) method to fit the entire energy of the 55,000 data points. In the second approach, the PIP-NN method is used to fit only the four-body interaction component, a similar treatment in the MB-PIP method, and the resulting PES is named MB-PIP-NN. Then, the performances of these new PESs and the MB-PIP PES are comprehensively and systematically compared, such as comparisons of various scans, properties of stationary points, and dynamics simulations. Possible improvements for the PES of N 2 O 2 are suggested. A more reliable PES of the system can be constructed in terms of data sampling range, electronic structure calculation level, and fitting method for high-temperature calculation and simulation in the future.

A modification in the potential energy surface (PES) for N 2 -N 2 interactions, reported in the literature [D. Cappelletti et al., Phys. Chem. Chem. Phys., 2008, 10, 4281], has been presented to improve its description of, particularly, the short range behavior for specific configurations, with the aim of producing a large database of vibration to vibration (V-V) and vibration to translation/rotation (V-T/R) energy transfer rate coefficients, with an increased accuracy extended to large temperature ranges relevant to the modeling of hypersonic gas flows. The modifications were introduced in a physically meaningful fashion and they are shown to improve the performance of the PES in a wide temperature range, not only for calculating rate coefficients, but also for determining a variety of physical properties. This new PES was then used to calculate V-V and V-T/R rate coefficients for inelastic N 2 -N 2 collisions through a mixed quantum-classical method, based on the quantum treatment of molecular vibrations, for vibrationally excited states up to v = 40. Such a large V-T/R coefficient database is quite unprecedented, and the comparison of the efficiency of the related processes with the corresponding V-V coefficients shows that vibrational relaxation plays a very relevant role in high temperature regimes.