A realistic multi-sheeted potential energy surface for NO2(2A′) from the double many-body expansion method and a novel multiple energy-switching scheme

Experimental and Theoretical Studies of Hyperthermal N + O2 Collisions

The dynamics of hyperthermal N(4S) + O2 collisions were investigated both experimentally and theoretically. Crossed molecular beams experiments were performed at an average center-of-mass (c.m.) collision energy of ⟨Ecoll⟩ = 77.5 kcal mol-1, with velocity- and angle-resolved product detection by a rotatable mass spectrometer detector. Nonreactive (N + O2) and reactive (NO + O) product channels were identified. In the c.m. reference frame, the nonreactively scattered N atoms and reactively scattered NO molecules were both directed into the forward direction with respect to the initial direction of the reagent N atoms. On average, more than 90% of the available energy (⟨Eavl⟩ = 77.5 kcal mol-1) was retained in translation of the nonreactive products (N + O2), whereas a much smaller fraction of the available energy for the reactive pathway (⟨Eavl⟩ = 109.5 kcal mol-1) went into translation of the NO + O products, and the distribution of translational energies for this channel was broad, indicating extensive internal excitation in the nascent NO molecules. The experimentally derived c.m. translational energy and angular distributions of the reactive products suggested at least two dynamical pathways to the formation of NO + O. Quasiclassical trajectory (QCT) calculations were performed with a collision energy of Ecoll = 77 kcal mol-1 using two sets of potential energy surfaces, denoted as PES-I and PES-II, and these theoretical results were compared to each other and to the experimental results. PES-I is a reproducing kernel Hilbert space (RKHS) representation of multireference configurational interaction (MRCI) energies, while PES-II is a many-body permutation invariant polynomial (MB-PIP) fit of complete active space second order perturbation (CASPT2) points. The theoretical investigations were both consistent with the experimental suggestion of two dynamical pathways to produce NO + O, where reactive collisions may proceed on the doublet (12A') and quartet (14A') surfaces. When analyzed with this theoretical insight, the experimental c.m. translational energy and angular distributions were in reasonably good agreement with those predicted by the QCT calculations, although minor differences were observed which are discussed. Theoretical translational energy and angular distributions for the nonreactive N + O2 products matched the experimental translational energy and angular distributions almost quantitatively. Finally, relative yields for the nonreactive and reactive scattering channels were determined from the experiment and from both theoretical methods, and all results are in reasonable agreement.

Formation of N(2D) from Hyperthermal Collisions between O(3P) and NO(X2Π)

Hyperthermal collisions between O(3P) and NO(X2Π) could lead to the formation of the first electronically excited atomic nitrogen (N(2D)), which plays a key role in plasma formation in shock-heated air. This process is facilitated mainly by four doublet states, and to a much lesser extent by two quartet states. In this work, we report quasi-classical trajectory studies of this reactive process using the four analytical adiabatic potential energy surfaces for the doublet states developed previously from fitting high-level ab initio data. The reactions were found to be strongly enhanced by vibrational excitation of the NO reactant, consistent with the existence of potential energy barriers in the exit channel. Despite the large endothermicity of the reaction, the rate coefficient is significant at high temperatures, suggesting a possible role of this reaction in the hyperthermal kinetics in the shock layer of a hypersonic (re)entry vehicle.

The long-lived reactive nitrogen species in the troposphere: DFTB model for atmospheric applications

The longest lived reactive NO₂ molecule formation in a dry and clean air environment under a high-temperature shock wave was investigated under three basic reactions (R2 for the O + NO system, R6 for the NO + NO₃ system, and R7 for the NO + O₃ system) in the atmospheric environment. With certain approaches, a DFTB3 model was used, which gave results close to the density functional theory. In the calculations, the related reactions up to 250 ps were examined at individual specific temperatures, and the temperature ranges that contributed to the formation of the NO₂ molecule were determined. Moreover, a shock wave with both heating and cooling channels was applied only on R2 to see whether molecular concentrations were in good agreement with atmospheric information. The reaction products were examined under a shock wave of about 20 ps. At the end of the study, the applicability of the DFTB model to atmospheric systems was demonstrated by comparing it with experimental data and information. QCT approach was also used for the calculation of reaction rate constants of only O₂-formation on the O + NO system. Here, all systems are focused on nitrogen species containing oxygen. In particular, the highest-population NO molecule that emerged in the lightning flash event was used as the reactant, while systems existing with the longest lived NO₂ in the atmosphere after the lightning flash were focused in the product channel. As a result of the study, the hypothesis of geophysicists that almost all NO₂ formed in the lightning flash event originates from the NO + O system was disproved. It has been proven that the presence of NO₃ molecules that can withstand high temperatures in such systems should be evaluated.

Oxygen Molecule Formation and the Puzzle of Nitrogen Dioxide and Nitrogen Oxide during Lightning Flash

Unlike the compounds of the natural air atmosphere, the lightning systems are primarily focused on NO(X²Π), NO₂(1²A'), and O(³P) concentrations that occurred newly and highly in the ground electronic structure. While the NO/NO₂ concentrations ratio is about 2000 during the lightning flash, this ratio becomes about 0.8 right after the lightning flash. The reason for this decrease in the ratio is the disappearance of the high temperature that prevents the formation of NO₂ (with the combination of NO and O) and of the photon energy that causes its dissociation (NO₂ + hv → NO + O) right after the lightning flash. However, this study will focus on the reactions that contribute to the NO concentration, except for the combination of N and O atoms during lightning flash. To do this, it was focused on the reactive scattering states (especially the NO-exchange) of the NO + O collision and the photo-dissociation of NO₂, which provide the formation of the NO molecule in the ground electronic state. This case raises important questions. To what extent do the NO-exchange reaction and the photo-dissociation of NO₂ contribute to the atmospherically observed NO molecules? or how can the vibrational quantum states of the NO molecules formed by the photo-dissociation be effected on the NO + O¹ collision to produce a NO¹ molecule? These conditions may contribute to the concentrations of NO high during lightning flashes. Under low collision energy (between 0.1 and 0.3 eV), the NO (v = 0) population dissociated by a photon can act as reactants in the NO-exchange reactive scattering on the doublet electronic state. Since it is assumed that all of the NO₂ molecules are due to NO in the lightning flash system, this is one of the reasons that makes the NO population so high during lightning flash. Therefore, in the light of considering that the lightning system supports the formation of highly vibrating molecular groups, it might also support the formation of O₂ molecules. In particular, it was shown that the v = 4 quantum state of the NO molecule over the doublet state between collision energies of 0.9-1.5 eV and the v = 5 quantum state of the NO molecule over the quartet state between collision energies of 1.0-1.5 eV contribute to O₂ formation.

Reactive and Nonreactive Collisions between NO(X2Π) and O(3P) under Hyperthermal Conditions

Quasiclassical trajectory calculations are performed for hyperthermal collisions between NO(X²Π) and O(³P) on recently developed potential energy surfaces for the lowest doublet and quartet states of the NO₂ system. Three product channels are investigated, and their branching fractions are in reasonably good agreement with the recent crossed molecular beam study at 84 kcal/mol of collision energy. The dominant inelastic channel has a strong forward scattering bias and a high translational energy distribution with limited internal excitation in the scattered NO. The exchange channel has significantly higher NO internal excitation and is also forward biased. The abstraction channel producing internally excited O₂ has the smallest branching fraction and a broader angular distribution also with a forward peak. The angular and translational energy distributions in the three channels are consistent with experiment, but the agreement is not always quantitative. The sources of the differences are discussed. Finally, the impact of NO vibrational excitation on the reactive channels and the corresponding rate coefficients are reported.

Reaction of the N Atom with Electronically Excited O2 Revisited: A Theoretical Study

The kinetics of the reaction of N with electronically excited O₂ (singlet a¹Δ_g and b¹Σ_g⁺ states), potentially relevant for NO_x formation in nonthermal air plasma, is theoretically studied using the multireference second-order perturbation theory. The corresponding thermodynamically and kinetically favored reaction pathways together with possible intersystem crossings are identified. It has been revealed that the energy barrier for the N + O₂(a¹Δ_g) → NO + O reaction is approximately twice the barrier height for the counterpart process with O₂(X³Σ_g^-). The molecular oxygen in the b¹Σ_g⁺ state, in turn, proved to be even less reactive to atomic nitrogen than O₂(a¹Δ_g). Appropriate thermal rate constants for specified reaction channels are calculated by the variational transition-state theory incorporating corrections for the tunneling effect, nonadiabatic transitions, and anharmonicity of vibrations for transition states and reactants. The corresponding three-parameter Arrhenius expressions for the broad temperature range (T = 300-4000 K) are reported. At last, post-transition-state molecular dynamics simulations indicate that the N + O₂(a¹Δ_g) reaction produces vibrationally much colder NO molecules than the N + O₂(X³Σ_g^-) process.

The Low-Lying Electronic States of NO2: Potential Energy and Dipole Surfaces, Bound States, and Electronic Absorption Spectrum

Nitrogen dioxide, NO₂, is a free radical composed of the two most abundant elements in Earth's atmosphere, nitrogen and oxygen, and is relevant to atmospheric and combustion chemistry. The electronic structure of even its lowest-lying states is remarkably complex, with various conical intersections and Renner-Teller pairings, giving rise to complex and perturbed vibronic states. Here we report some analysis of the 18 molecular states of doublet spin-multiplicity formed by combining ground-state N(⁴S_u) and O(³P_g) atoms. Three-dimensional potential energy surfaces were fit at the MRCI(Q)-F12/VTZ-F12 level, describing the lowest four (X̃, Ã, B̃, and C̃) electronic states. A properties-based diabatization procedure was applied to accommodate the intersections, producing energies in a quasidiabatic representation and yielding couplings that were also fit into surfaces. The low-lying vibrational levels on the ground X̃ state were computed and compared with experimental measurements. Compared to experiment, the lowest 125 calculated vibrational levels (up to 8500 cm^-1 above the zero-point energy) have a root-mean-squared error of 16.5 cm^-1. In addition, dipole moments for each of the lowest four electronic states-and the transition dipoles between them-were also computed and fit. With the coupled energy and dipole surfaces, the electronic spectrum was calculated in absolute intensity and compared with experimental measurements. Detailed structure in the experimental spectrum was successfully reproduced, and the total integrated intensity matches experiment to an accuracy of ∼1.5% with no empirical adjustments.

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.

The N(4S) + O2(X3Σ−g) ↔ O(3P) + NO(X2Π) reaction: thermal and vibrational relaxation rates for the 2A′, 4A′ and 2A′′ states

Cross sections, rates, equilibrium constants and vibrational relaxation times for the N(⁴S) + O₂(X³Σ−g) ↔ O(³P) + NO(X²Π) reaction from simulations on new, RKHS-based surfaces for the three lowest electronic states.

Modelling potential energy surfaces for small clusters using Shepard interpolation with Gaussian-form nodal functions

A new interpolation method based on Gaussian functions to reliably generate potential energy surfaces.

Ultrafast imaging of laser-controlled non-adiabatic dynamics in NO2 from time-resolved photoelectron emission

Imaging and controlling the ultrafast conical intersection dynamics in NO₂ using the latest advances in attosecond and light-synthesizer technology.

The O + NO( v) Vibrational Relaxation Processes Revisited

We have carried out a quasiclassical trajectory study of the O + NO( v) energy transfer process using DMBE potential energy surfaces for the ground-states of the ²A' and ²A″ manifolds. State-to-state vibrational relaxation rate constants have been computed over the temperature range 298 and 3000 K and initial vibrational states between v = 1 and 9. The momentum-Gaussian binning approach has been employed to calculate the probability of the vibrational transitions. A comparison of the calculated state-to-state rate coefficients with the results from experimental studies and previous theoretical calculations shows the relevance of the 1 ²A″ potential energy surface to the title vibrational relaxation process.

Cn (n=2-4): current status

The major aspects of the C₂, C₃ and C₄ elemental carbon clusters are surveyed. For C₂, a brief analysis of its current status is presented. Regarding C₃, the most recent results obtained in our group are reviewed with emphasis on modelling its potential energy surface which is particularly complicated due to the presence of multiple conical intersections. As for C₄, the most stable isomeric forms of both triplet and singlet spin states and their possible interconversion pathways are examined afresh by means of accurate ab initio calculations. The main strategies for modelling the ground triplet C₄ potential are also discussed. Starting from a truncated cluster expansion and a previously reported DMBE form for C₃, an approximate four-body term is calibrated from the ab initio energies. The final six-dimensional global DMBE form so obtained reproduces all known topographical aspects while providing an accurate description of the C₄ linear-rhombic isomerization pathway. It is therefore commended for both spectroscopic and reaction dynamics studies.This article is part of the theme issue 'Modern theoretical chemistry'.

Ab initio constructed diabatic surfaces of NO2 and the photodetachment spectra of its anion

A thorough investigation has been performed for electronic structure, topological effect, and nuclear dynamics of NO2 molecule, where the adiabatic potential energy surfaces (PESs), conical intersections between the ground (X(2)A1) and the first excited state (A(2)B2), and the corresponding non-adiabatic coupling terms between those states are recalculated [Chem. Phys. 416, 11 (2013)] to achieve enough accuracy in dynamics. We employ beyond Born-Oppenheimer theory for these two state sub-Hilbert space to carry out adiabatic to diabatic transformation (ADT) to obtain the ADT angles and thereby, to construct single-valued, smooth, and continuous diabatic PESs. The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photo-electron spectra of its anion. It appears that not only Jahn-Teller type coupling but also Renner-Teller interaction contributes significantly on the overall spectrum. The coupling between the electronic states (X(2)A1 and A(2)B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear.

Accurate ab initio potentials at low cost via correlation scaling and extrapolation: Application to CO(AΠ1)

A recently proposed scheme that enables high quality molecular potentials to be obtained from small basis set calculations via scaling and extrapolation of the electron correlation to the complete basis set limit plus extrapolation to the complete basis set limit of the complete-active-space self-consistent field energy has been applied to the A 1Pi electronic state of CO. Based on standard multireference configuration interaction raw energies calculated with correlation-consistent basis sets of the aug-cc-pVXZ and aug-cc-pCVXZ types for the scaling and extrapolation procedures, a barrier separating the equilibrium region from the dissociation asymptote of 594+/-46 cm(-1) has been predicted at an internuclear distance of 2.25+/-0.01 A in reasonable agreement with some previous theoretical work and a recent direct least-squares fit to available spectroscopic data, while being 38% smaller than an early experimental upper limit of 950+/-150 cm(-1). Good agreement with experiment is also obtained for the minimum well depth and location at equilibrium: 25,532+/-165 cm(-1) at 1.2346+/-0.0015 A (theoretical) versus 25,597 cm(-1) at 1.2346+/-0.0006 A (experimental). The method can be extended to other wave function models, providing a general strategy for accurate potentials of larger dimensionality at costs that can be drastically smaller than traditional ones.

Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.

Theoretical investigation of exchange and recombination reactions in O(P3)+NO(Π2) collisions

We present a detailed dynamical study of the kinetics of O(3P)+NO(2Pi) collisions including O atom exchange reactions and the recombination of NO2. The classical trajectory calculations are performed on the lowest 2A' and 2A" potential energy surfaces, which were calculated by ab initio methods. The calculated room temperature exchange reaction rate coefficient, kex, is in very good agreement with the measured one. The high-pressure recombination rate coefficient, which is given by the formation rate coefficient and to a good approximation equals 2kex, overestimates the experimental data by merely 20%. The pressure dependence of the recombination rate, kr, is described within the strong-collision model by assigning a stabilization probability to each individual trajectory. The measured falloff curve is well reproduced over five orders of magnitude by a single parameter, i.e., the strong-collision stabilization frequency. The calculations also yield the correct temperature dependence, kr proportional, T-1.5, of the low-pressure recombination rate coefficient. The dependence of the rate coefficients on the oxygen isotopes are investigated by incorporating the difference of the zero-point energies between the reactant and product NO radicals, DeltaZPE, into the potential energy surface. Similar isotope effects as for ozone are predicted for both the exchange reaction and the recombination. Finally, we estimate that the chaperon mechanism is not important for the recombination of NO2, which is in accord with the overall T-1.4 dependence of the measured recombination rate even in the low temperature range.

W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions

In an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys. 120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations (T4), inclusion of connected quintuple excitations (T5), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemical network. The recent CCSDT(Q) method offers a cost-effective way of estimating T4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T4, and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ-CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)cc-pVTZ+CCSDTQcc-pVDZ-CCSDT(Q)cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit T4 contribution. The T5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T5 contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOCs are significant at the 0.1 kcal/mol level in hydride systems. Post-CCSD(T) contributions to the core-valence correlation energy are only significant at that level in systems with severe nondynamical correlation effects. Based on the accumulated experience, a new computational thermochemistry protocol for first- and second-row main-group systems, to be known as W4 theory, is proposed. Its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. Lower-cost variants are proposed: the sequence W1-->W2.2-->W3.2-->W4lite-->W4 is proposed as a converging hierarchy of computational thermochemistry methods. A simple a priori estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed.

Quantum mechanical investigations of the N(S4)+O2(XΣg−3)→NO(XΠ2)+O(P3) reaction

The reaction between energetic nitrogen atoms and oxygen molecules has received important attention in connection with nitric oxide chemistry in the lower thermosphere. We report time-independent quantum mechanical calculations of the N(4S)+O2-->NO+O reaction employing the X 2A' and a 4A' electronic potential energy surfaces of Sayos et al. [J. Chem. Phys. 117, 670 (2002)]. We confirm the production of highly vibrationally excited NO molecules, consistent with previous semiclassical and more recent time-dependent quantum wave packet studies. Calculations are carried out for total angular momentum quantum number J=0 and cross sections and rate coefficients are extracted using the J-shifting approximation. The results are in good agreement with available experimental and theoretical data.

A quasiclassical trajectory study for the N(4S)+O2(X 3Sigmag-)-->NO(X 2Pi)+O(3P) reaction on the new 2A' and 4A' potential-energy surfaces

A quasiclassical trajectory study with the sixth-order explicit symplectic algorithm of the N(4S)+O2(X 3Sigmag-)-->NO(X 2Pi)+O(3P) atmospheric reaction has been performed by employing the new 2A' and 4A' potential-energy surfaces reported by Sayos et al. [J. Chem. Phys. 117, 670 (2002)]. For the translational temperature considered up to 10,000 K, the larger relative translational energy and the higher rovibrational levels of O2 molecule with respect to the previous works have been taken into account, and a clearer database about the character of the total reaction cross section has been presented in this work. The dependence of microscopic rate constants on the vibrational level of O2 molecule at T=3000, 5000, and 10,000 K has been exhibited, and we can see that the values of log10 k(T,v,J) vary almost linearly with the vibrational level of O2 molecule. The thermal rate constants at the translational temperature between 300 and 10,000 K have been evaluated and compared with the experimental and previous theoretical results. It is found that the thermal rate constants determined in this work have a better agreement with the experimental data and can provide a more valid theoretical reference at the translational temperature considered for the title reaction.

New Double Many-Body Expansion Potential Energy Surface for Ground-State HCN from a Multiproperty Fit to Accurate ab Initio Energies and Rovibrational Calculations

An accurate single-sheeted double many-body expansion potential energy surface has been obtained for the ground electronic state of the hydrogen cyanide molecule via a multiproperty fit to ab initio energies and rovibrational data. This includes 106 rovibrational levels and 2313 discrete points, which are fit with a rmsd of 4 cm(-1) and 2.42 kcal mol(-1), respectively, and seven zero first-derivatives that are reproduced at three stationary points. Since the potential also describes accurately the appropriate asymptotic limits at the various dissociation channels, it is commended both for the simulation of rovibrational spectra and reaction dynamics.

Dissociative multiphoton ionization of NO[sub 2] studied by time-resolved imaging

We have studied dissociative multiphoton ionization of NO2 by time-resolved velocity map imaging in a two-color pump-probe experiment using the 400 and 266 nm harmonics of a regeneratively amplified titanium-sapphire laser. We observe that most of the ion signal appears as NO+ with approximately 0.28 eV peak kinetic energy. Approximately 600 fs period oscillations indicative of wave packet motion are also observed in the NO+ decay. We attribute the signal to two competitive mechanisms. The first involving three-photon 400 nm absorption followed by dissociative ionization of the pumped state by a subsequent 266 nm photon. The second involving one-photon 400 nm absorption to the 2B2 state of NO2 followed by two-photon dissociative ionization at 266 nm. This interpretation is derived from the observation that the total NO+ ion signal exhibits biexponential decay, 0.72 exp(-t/90+/-10)+0.28 exp(-t/4000+/-400), where t is the 266 nm delay in femtoseconds. The fast decay of the majority of the NO+ signal suggests a direct dissociation via the bending mode of the pumped state. .