N(4S /2D)+N2: Accurateab initio-based DMBE potential energy surfaces and surface-hopping dynamics

Formation Mechanisms of Electronically Excited Nitrogen Molecules from N + N2 and N + N + N Collisions Revealed by Full-Dimensional Potential Energy Surfaces

This work reports six new full-dimensional adiabatic potential energy surfaces (PESs) of the N3 system (four 4A″ states and two 2A″ states) at the MRCI + Q/AVQZ level of theory that correlated to N2(X1Σg+) + N(4S), N2(X1Σg+) + N(2D), N2(A3Σu+) + N(4S), N2(B3Πg) + N(4S), N2(W3Δu) + N(4S), and N(4S) + N(4S) + N(4S) channels. The neural networks with a proper account of the nuclear permutation invariant symmetry of N3 were employed to fit the PESs based on about 4000 ab initio points. The accuracy of the PESs was validated by excellent agreement on the equilibrium bond length, vertical excitation energy, and dissociation energy with experimental values. Two possible mechanisms of the formation of N2(A) were found. One is that the collision occurs between N2(X) and N(4S) in the 14A″ state, followed by a nonadiabatic transition through the conical intersection with the 24A″ PES, resulting in the formation of the N2(A) + N(4S) product. The other takes place in the collision among three N(4S) atoms in the adiabatic 24A″ state, and then, N2(A) + N(4S) is formed. This is the first systematical research of the N3 system focusing on the formation of the excited states of N2 via both adiabatic and nonadiabatic pathways.

Quantum and semiclassical studies of nonadiabatic electronic transitions between N(4S) and N(2D) by collisions with N2

The dynamics and kinetics of spin-forbidden transitions between N(2D) and N(4S) via collisions with N2 molecules are investigated using a quantum wave packet (WP) method and the semi-classical coherent switches with decay of mixing (CSDM) method. These electronic transition processes are competing with exchange reaction channels on both the doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients are found in reasonable agreement with each other, and both reproduce the previous theoretical results. For the excitation process, the agreement between the two approaches is dependent on the treatment of the zero-point energy (ZPE) in the product, because the high endoergicity of this process leads to severe violation of the vibrational ZPE. The Gaussian-binning (GB) method is found to improve the agreement with the quantum result. The excitation rate coefficients are found to be two orders of magnitude smaller than that of the adiabatic exchange reaction, underscoring the inefficient intersystem crossing due to the weak spin-orbit coupling between the two spin manifolds of the N3 system.

Chemical versatility of azide radical: journey from a transient species to synthetic accessibility in organic transformations

The generation of azide radical (N₃˙) occurs from its precursors primarily via a single electron transfer (SET) process or homolytic cleavage by chemical methods or advanced photoredox/electrochemical methods. This in situ generated transient open-shell species has unique characteristic features that set its reactivity. In the past, the azide radical was widely used for various studies in radiation chemistry as a 1e^- oxidant of biologically important molecules, but now it is being exploited for synthetic applications based on its addition and intermolecular hydrogen atom transfer (HAT) abilities. Due to the significant role of nitrogen-containing molecules in synthesis, drug discovery, biological, and material sciences, the direct addition onto unsaturated bonds for the simultaneous construction of C-N bond with other (C-X) bonds are indeed worth highlighting. Moreover, the ability to generate O- or C-centered radicals by N₃˙ via electron transfer (ET) and intermolecular HAT processes is also well documented. The purpose of controlling the reactivity of this short-lived intermediate in organic transformations drives us to survey: (i) the history of azide radical and its structural properties (thermodynamic, spectroscopic, etc.), (ii) chemical reactivities and kinetics, (iii) methods to produce N₃˙ from various precursors, (iv) several significant azide radical-mediated transformations in the field of functionalization with unsaturated bonds, C-H functionalization via HAT, tandem, and multicomponent reaction with a critical analysis of underlying mechanistic approaches and outcomes, (v) concept of taming the reactivity of azide radicals for potential opportunities, in this review.

Potential energy surface for high-energy N + N2 collisions

Potential energy surface calculations yield physical insight into the structure of intermediates and the dynamics of molecular collisions, and they are the first step toward molecular simulations that provide physical insight into energy transfer, reaction, and dissociation probabilities. The potential energy surface for high-energy collisions of N₂ with N can be used for modeling chemical dynamics and energy transfer in atmospheric shock waves. Here we present an analytic ground-state. (⁴A'') potential energy surface for N₃ that governs electronically adiabatic collisions of N₂(¹Σ+g) with N(⁴S). The fitted surface consists of a pairwise potential based on an accurate diatomic potential energy curve plus a connected permutationally invariant polynomial (PIP) in mixed-exponential-Gaussian bond order variables (MEGs) for the three-body part. The three-body fit is based on multireference complete active space second order perturbation theory (CASPT2) calculations. The quality of the quartet N₃ fit is comparable to that for a previous fit of the NO₂ potential. We characterize two local minima of N₃, two tight transition structures, two van der Waals geometries, and the noncollinear reaction path for the symmetric exchange reaction. The nonreactive approach of an N atom to N₂ along the perpendicular bisector is more repulsive than the collinear reproach, but plots of the force on the bond versus the potential energy at the distance of closest approach allow us to infer that vibrational energy transfer should occur much more readily in high-energy collinear collisions than in high-energy perpendicular-bisector collisions.

Quantum and Classical Dynamics of the N(2D) + N2 Reaction on Its Ground Doublet State N3(12A″) Potential Energy Surface

The initial state-selected dynamics of the N(²D) + N₂(X¹∑) → N₂(X¹∑) + N(²D) exchange reaction on its electronic ground doublet state N₃(1²A″) potential energy surface (PES) has been studied here by time-dependent quantum mechanics (TDQM) and quasi-classical trajectory (QCT) methods. Dynamical attributes such as total reaction probabilities, state-selected integral cross sections, and initial state-selected rate constants have been calculated. The presence of metastable quasi-bound complexes in the collision process is confirmed by substantial oscillatory structures in the reaction probability curves. Also, rotational excitations of reagent N₂ on the reactivity have been examined by calculating the probabilities for the two-body rotational angular momentum up to j = 10. We conclude that the reagent rotational excitation increases the reactivity. The TDQM results are compared with QCT results.

Multiple conical intersections in small linear parameter Jahn-Teller systems: the DMBE potential energy surface of ground-state C3 revisited

A new single-sheeted DMBE potential energy surface for ground-state C3 is reported. The novel analytical form accurately describes the three symmetry-equivalent C2v disjoint seams, in addition to the symmetry-required D3h one, over the entire configuration space. The present formalism warrants by built-in construction the confluence of the above crossings, and the rotation-in-plane of the C2v seams when the perimeter of the molecule fluctuates. Up to 1050 ab initio energies have been employed in the calibration procedure, of which 421 map the loci of intersection. The calculated energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion, and fitted analytically with chemical accuracy. The novel form is shown to accurately mimic the region defined by the 4 conical intersections, while exhibiting similar attributes to the previously reported one [J. Chem. Phys., 2015, 143, 074302] at the regions of configuration space away from the crossing seams. Despite being mainly addressed to C3, the present approach should be applicable to adiabatic PESs of any X3 system experiencing similar topological attributes, in particular the small-linear-parameter Jahn-Teller molecules.

Dissociation cross sections for N2 + N → 3N and O2 + O → 3O using the QCT method

Cross sections for the homo-nuclear atom-diatom collision induced dissociations (CIDs): N₂ + N and O₂ + O are calculated using Quasi-Classical Trajectory (QCT) method on ab initio Potential Energy Surfaces (PESs). A number of studies for these reactions carried out in the past focused on the CID cross section values generated using London-Eyring-Polanyi-Sato PES and seldom listed the CID cross section data. A highly accurate CASSCF-CASPT2 N₃ and a new O₃ global PES are used for the present QCT analysis and the CID cross section data up to 30 eV relative energy are also published. In addition, an interpolating scheme based on spectroscopic data is introduced that fits the CID cross section for the entire ro-vibrational spectrum using QCT data generated at chosen ro-vibrational levels. The rate coefficients calculated using the generated CID cross section compare satisfactorily with the existing experimental and theoretical results. The CID cross section data generated will find an application in the development of a more precise chemical reaction model for Direct Simulation Monte Carlo code simulating hypersonic re-entry flows.

The Jahn-Teller plus pseudo-Jahn-Teller vibronic problem in the C3 radical and its topological implications

The combined Jahn-Teller plus pseudo-Jahn-Teller [(E'+A1')⊗e'] problem is discussed for the tricarbon radical (C3) by means of ab initio calculations at the multireference configuration interaction level of theory. For the (1)E' electronic state arising from a e'(2) valence configuration, three additional symmetry-equivalent C2v seams are found to lie in close proximity to the D3h symmetry-required seam over the entire range of the breathing coordinate here considered. As the perimeter of the molecule increases, the C2v disjoint seams approach the D3h one almost linearly and ultimately coalesce with it at Q1 = 5.005 a0, thence forming an intersection node or confluence. By further increasing the size of the molecular triangle, the C2v seams get rotated by ±π in the g-h plane. A three-state vibronic Hamiltonian is also proposed to model locally the title system and shown to accurately mimic the calculated data over the region close to the minimum energy crossing point. No net geometric phase effect is observed when the associated electronic wave functions are adiabatically transported along closed paths encircling the four singularity points. For all paths enclosing the intersection node, the sign reversal criterion is shown to be not fulfilled, even for infinitesimal loops. The results so obtained are expected to be valid for other ring systems experiencing similar topological attributes.

Modeling cusps in adiabatic potential energy surfaces

A method for modeling cusps on adiabatic potential energy surfaces without the need for any adiabatic-to-diabatic transformation is presented and shown to be successfully applied to the (2)A″ state of NO2. The more complicated case of a system with permutationally equivalent crossing seams is also examined and illustrated by considering the two first (2)A' states of the nitrogen trimer.

Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections

Analytical and numerical solutions describing Born–Oppenheimer breakdown in a simple, widely applicable, model depict shortcomings in modern computational methods.

Electronic Quenching in N((2)D) + N2 Collisions: A State-Specific Analysis via Surface Hopping Dynamics

The electronic quenching reaction N((2)D) + N2 → N((4)S) + N2 is studied using the trajectory surface hopping method and employing two doublet and one quartet accurate potential energy surfaces. State-specific properties are analyzed, such as the dependence of the cross section on the initial quantum state of the reactants, vibrational energy transfer, and rovibrational distribution of the product N2 molecule in thermalized conditions. It is found that rotational energy on the reactant N2 molecule is effective in promoting the reaction, whereas vibrational excitation tends to reduce the reaction probability. For initial states and collision energy thermalized in an initial bath, it is found that the products are "hotter", both vibration and rotation wise.

Accurate study of the two lowest singlet states of HN3: stationary structures and energetics at the MRCI complete basis set limit

The two lowest singlet potential energy surfaces of the hydrazoic acid are explored using high-level quantum chemistry calculations, revealing isomeric forms, transition states, and a new path for the nitrogen ring-closing mechanism in the ground state. The reaction of cyc-N3 with hydrogen is shown to proceed through a barrierless path that dissociates to N2 + NH((1)Δ) without reaching the HN3 global minimum. Several intersections between the two states are localized for both N3 isomers near the N3 + H dissociation. The energies of stationary structures and dissociation asymptotes are obtained with the multireference configuration interaction method at the complete basis set limit. A comparison with recent experimental data regarding the H-N3 bond strength and the dissociation barrier in the excited state shows that the present results are of chemical accuracy (~1 kcal mol(-1)).