States Of NO Research Articles

Diabatic neural network potentials for accurate vibronic quantum dynamics-The test case of planar NO3.

A recently developed scheme to produce high-dimensional coupled diabatic potential energy surfaces (PESs) based on artificial neural networks (ANNs) [D. M. G. Williams and W. Eisfeld, J. Chem. Phys. 149, 204106 (2019)] is tested for its viability for quantum dynamics applications. The method, capable of reproducing high-quality ab initio data with excellent accuracy, utilizes simple coupling matrices to produce a basic low-order diabatic potential matrix as an underlying backbone for the model. This crude model is then refined by making its expansion coefficients geometry-dependent by the output neurons of the ANN. This structure, strongly guided by a straightforward physical picture behind nonadiabatic coupling, combines structural simplicity with high accuracy, reproducing ab initio data without introducing unphysical artifacts to the surface, even for systems with complicated electronic structure. The properties of diabatic potentials obtained by this method are tested thoroughly in the present study. Vibrational/vibronic eigenstates are computed on the X̃ and à states of NO3, a notoriously difficult Jahn-Teller system featuring strong nonadiabatic couplings and complex spectra. The method is investigated in terms of how consistently it produces dynamics results for PESs of similar (fitting) quality and how the results depend on the ANN size and ANN topography. A central aspect of this work is to understand the convergence properties of the new method in order to evaluate its predictive power. A previously developed, high-quality model utilizing a purely (high-order) polynomial ansatz is used as a reference to showcase improvements of the overall quality which can be obtained by the new method.

An ab initio investigation of non-adiabatic couplings and conical intersections among the lowest five electronic states of the NO3 radical

ABSTRACTIn order to explore spectroscopic properties of a floppy molecule, it is necessary to compute accurate diabatic potential energy surfaces (PESs) around the Franck–Condon region of nuclear configuration space. In such cases, it is desirable to include the non-adiabatic coupling terms (NACTs) through Jahn–Teller (JT) and pseudo Jahn–Teller (PJT) effects as well as other accidental conical intersections (CIs) prevailing among the electronic states of the molecule. In this work, we investigate NACTs among the five lowest doublet electronic states of NO3 radical [ and 22B2)], in which all those effects (JT, PJT and CIs) have prominent contributions. The study is carried out in terms of normal modes (Qis) of NO3 and the CIs (JT and accidental) are located in a plane of nuclear configuration space of two such coordinates (Qi and Qj). We have calculated ab initio adiabatic PESs and NACTs of those five states of NO3 at the MRCI level as functions of pairwise Qis. Further, to explore the nature of a given CI in terms of normal coordinates contributing to NACTs within a particular plane Qi-Qj, we have performed CP-MCSCF study computing analytic NACTs and characterised their contributions along various Qks.

Modeling cusps in adiabatic potential energy surfaces using a generalized Jahn-Teller coordinate

A recent generalization of the Jahn-Teller coordinate proposed for modeling cusps on single-sheeted adiabatic potential energy surfaces for triatomics is extended to any type of crossing seam. The model is applied to the 2A″ state of NO2 and the more complicated HN2(2A′) system, which shows permutationally equivalent and strongly curved seams.

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.

Accurate double many-body expansion potential energy surface for the 2(1)A' state of N2O.

An accurate double many-body expansion potential energy surface is reported for the 2(1)A' state of N2O. The new double many-body expansion (DMBE) form has been fitted to a wealth of ab initio points that have been calculated at the multi-reference configuration interaction level using the full-valence-complete-active-space wave function as reference and the cc-pVQZ basis set, and subsequently corrected semiempirically via double many-body expansion-scaled external correlation method to extrapolate the calculated energies to the limit of a complete basis set and, most importantly, the limit of an infinite configuration interaction expansion. The topographical features of the novel potential energy surface are then examined in detail and compared with corresponding attributes of other potential functions available in the literature. Exploratory trajectories have also been run on this DMBE form with the quasiclassical trajectory method, with the thermal rate constant so determined at room temperature significantly enhancing agreement with experimental data.

N2O ionization and dissociation dynamics in intense few cycle femtosecond laser radiation

Using few cycle pulses, uniform-electric-field-ion imaging spectrometer and Dalitz plotting, we can identify two new stepwise processes, in the dissociation of the 3+ and 4+ states of N2O in intense few cycle pulses at 4 × 1015 Wcm−2. We observe suppression of selective channels at longer pulse length, which we attribute to molecular dynamics on the 2+ state and the shape of the 3+ potential, which influences propagation of the dissociating wave packet.

Quasiclassical trajectory studies of 18O(3P) + NO2 isotope exchange and reaction to O2 + NO on D and D1 potentials

We report quasiclassical trajectory calculations for the bimolecular reaction (18)O((3)P) + NO2 on the recent potential energy surfaces of the ground (D0) and first excited (D1) states of NO3 [B. Fu, J. M. Bowman, H. Xiao, S. Maeda, and K. Morokuma, J. Chem. Theory. Comput. 9, 893 (2013)]. The branching ratio of isotope exchange versus O2 + NO formation, as well as the product angular distributions and energy and rovibrational state distributions are presented. The calculations are done at the collision energy of relevance to recent crossed beam experiments [K. A. Mar, A. L. Van Wyngarden, C.-W. Liang, Y. T. Lee, J. J. Lin, and K. A. Boering, J. Chem. Phys. 137, 044302 (2012)]. Very good agreement is achieved between the current calculations and these experiments for the branching ratio and final translational energy and angular distributions of isotope exchange products (16)O((3)P) + NO2 and O2 + NO formation products. The reactant (18)O atom results in (18)O(16)O but not N(18)O for the O2 + NO formation product channel, consistent with the experiment. In addition, the detailed vibrational and rotational state information of diatomic molecules calculated currently for the (34)O2 + NO formation channel on D0 and D1 states are in qualitative agreement with the previous experimental and theoretical results of the photodissociation of NO3 and are consistent with older thermal bimolecular kinetics measurements.

A general analytical expression for the two-dimensional Franck–Condon integral and simulation of the photoelectron spectra of nitrogen dioxide

On the basis of the harmonic oscillator approximation, the two-dimensional four-mode Franck–Condon vibrational overlap integral under mode-mixing effects has been reduced to a product expression of one-dimensional Gaussian integrals with the aid of expanding Hermite polynomials. A more general analytical expression for the calculation of the two-dimensional four-mode Franck–Condon overlap integrals was derived by directly calculating the Gaussian integrals. This analytical expression was applied to investigate the photoelectron spectra of considering mode-mixing and hot band effects. Geometry optimizations and harmonic vibrational frequency calculations were performed on the 2A1 state of NO2 and the 1A1 state of . Franck–Condon analyses and spectral simulations were carried out on the NO2( 2A1)–( 1A1) photodetachment processes. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectra. In addition, the equilibrium geometric parameters of the 1A1 state of were obtained in the spectral simulations: bond length R(ON) = 1.248 ± 0.005 Å and bond angle ∠ (ONO) = 116.8 ± 0.5°.

A study of the structure of high-energy states of nitrogen trioxide and the (NO)2 dimer: DFT calculations within the symmetrized Kohn-Sham formalism

The electronic structure, geometry, and thermodynamic parameters of the high-energy states of NO3 and the (NO)2 dimer are calculated at the DFT B3LYP/6–311++G(3df) level within the symmetrized Kohn-Sham formalism. The results of the DFT calculation of the excited states of NO3 well agree with the experimental data and precise ab initio calculations. The reactivity of high-energy nitrogen trioxide in the activation of molecular nitrogen and nitrogen protoxide is analyzed. The assumption is substantiated that the Karavaev effect (gain of nitrogen oxides in an air mixture with nitric acid vapors) is due to the photochemical activation of molecular nitrogen in the presence of an NO3 high-energy state as a decomposition product of nitric acid.

Theoretical studies on N-loss predissociation mechanisms of N2O+ (A 2Σ+) in C s symmetry

The N-loss predissociation mechanisms of the A 2Σ+ (2 2A′) state of N2O+ to the first and second dissociation limits were studied in the Cs symmetry. The potential energy curves (PECs) and minimum energy crossing points (MECPs) for the Cs states of N2O+ were calculated at the CAS levels. On the basis of our CAS calculation results (CASPT2 energetic results and CASSCF spin orbit couplings), we suggest two processes for N-loss predissociation mechanisms of A 2Σ+ (2 2A′) to the first and second limits. The first two steps in the two processes are the same: A 2Σ+ passes through the 2 2A′/1 4A″ MECP and then reaches the 1 4A″ (1 4Σ−) PEC. The 2 2A′/1 4A″ MECP has a bent geometry and is slightly higher in energy than the transition state along the 1 4A″ PEC. Our mechanisms are different from the previously suggested mechanisms (via 1 4Π).

Toward the modeling of the NO2(2A″) manifold

AbstractGlobal diabatization angles are obtained to construct a 3 × 3 diabatic potential matrix for the 2A″ states of NO2. Over 12,500 energies have been calculated to map ab initio, the configuration space of (at least) the first 3 adiabatic sheets. With the level of theory used, such angles could be modeled such as to ensure a proper description of all involved crossing seams as well as the merging of the diabats into the adiabats at the asymptotic limits. This result provides an extension to the 3‐state case of the method proposed earlier (Mota and Varandas, J Phys Chem A 2008, 112, 3768), and illustrates the essential steps toward the modeling of the NO2(2A″) manifold via double many‐body expansion theory. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

ChemInform Abstract: Examination of the 2A′2 and 2E′′ States of NO3 by UV Photoelectron Spectroscopy of NO- 3.

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A theoretical study on the mechanisms of the N2(X1 ) + O+(4Su) reaction involving the 14A″ and X2Π states of the N2O+ ion and the predissociation of the X2Π state

The adiabatic path for the N2(X1 ) + O+(4Su) → NO+(X1Σ+) + N(4Su) reaction is presented based on the CASPT2 O- and N-loss dissociation potential energy curves (PECs) of the 14A″ (not 14Σ−) state of N2O+ and it has a small barrier of 0.45 eV (0.34 eV with the CASSCF zero-point energy corrections) in good agreement with the experimental value of 0.33 ± 0.08 eV. Based on the CASPT2 O- and N-loss dissociation PECs of the X2Π state of N2O +and the calculated energies and spin-orbital coupling values at the located MECPs (minimum energy crossing points) for the X2Π/14A″ state pairs, a nonadiabatic path via the 14A″/12A″ O-loss MECP, X2Π minimum, and 12A″/14A″ N-loss MECP is presented. The CASPT2 energetic results indicate that this nonadiabatic process can occur without external energy. Based on the adiabatic and nonadiabatic paths, we explain the experimental facts for the reaction: small cross-section at low energy and an onset of a strong increase in cross-section at a certain energy value. Mechanisms for O- and N-loss predissociation of the X2Π state by 14A″ via the 12A″/14A″ O- and N-loss MECPs, respectively, are described, and the experimental facts are explained using the results of our energetic and spin–orbit coupling calculations.

Computed lifetimes of metastable states of the NO2+ dication

Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v<or=2 vibrational states of the B 2Sigma+ electronic state, the calculated radiative lifetimes of the excited electronic states are longer than their predissociation lifetimes, hence, accounting for the failure of the attempts which have been made so far to observe any emission from the latter states.

Born−Oppenheimer Symmetry Breaking in the C̃ State of NO2: Importance of Static and Dynamic Correlation Effects

A systematic theoretical treatment is performed with highly correlated ab initio theoretical methods to establish the structural nature of the C state of NO2. We predict the C state to have an asymmetric structure (point group C(s)). Spin-restricted and spin-unrestricted configuration interaction (CISD), coupled cluster [CCSD and CCSD(T)], multireference complete active space self-consistent field (CASSCF), and internally contracted multireference configuration interaction (ICMRCI) methods were used in conjunction with very large correlation-consistent polarized valence zeta cc-pVXZ and aug-cc-pVXZ [X = T, Q, 5] basis sets. The asymmetric C 2A'' state is predicted to lie T(e) = 47.5 kcal/mol (2.06 eV, 16,600 cm(-1)) above the X 2A1 state at the aug-cc-pV5Z/UCCSD(T) level of theory, with T0 = 46.0 kcal/mol (2.00 eV, 16,100 cm(-1)), in good agreement with the experimental values of 46.77 kcal/mol (2.028 eV, 16,360 cm(-1)) by Weaver and 46.42 kcal/mol (2.013 eV, 16,234 cm(-1)) by Aoki. The symmetric structure (in C(2v) symmetry) with re(NO) = 1.274 A and theta(e) (ONO) = 109.9 degrees is a transition state between the two equivalent asymmetric (in C(s) symmetry) structures and is located only 1.53 kcal/mol (0.066 eV, 540 cm(-1)) above the asymmetric structure. The asymmetric structure is predicted to have structural parameters r(e)(NOl) = 1.489 A, r(e)(NOs) = 1.169 A, and theta(e)(ONO) = 109.7 degrees with the same method, aug-cc-pV5Z/UCCSD(T). The averaged NO bond distance is 1.329 A, and the difference between the two NO bond distances is 0.320 A. The three harmonic vibrational frequencies for the C 2A'' state are 1656 (in-phase stretch), 759 (bend), and 378 (out- of-phase stretch) cm(-1). While these theoretical results further corroborate the previous predictions concerning the asymmetric nature of the C state, there remains discrepancy between the theoretical and experimental symmetric stretching mode omega1 (1656 and 923 cm(-1), respectively). It is possible, however, that this disagreement could be resolved by a reassignment of the corresponding lines in the experimental spectrum, though additional vibronic simulations of the spectrum are required to confirm this proposition.

Observation of alignment of the ground state of NO2 under laser excitation

A Hanle signal is observed in the absorption of a cell filled with nitrogen dioxide NO2 at room temperature. The excitation was performed by an Ar+ laser at a wavelength of 476.4 nm.

Complete double photoionisation spectrum of NO

Abstract A new time-of-flight photoelectron–photoelectron coincidence technique, which gives complete two-dimensional e−–e− spectra in single-photon double photoionisation, is applied to nitric oxide. Direct double photoionisation is the major process at photon energies of 40.8, 48.4 and 50 eV, but dissociative ionisation with autoionisation of atomic fragments is also significant at these wavelengths and is dominant at 38.7 eV photon energy. The energy of the v=0 level of the A2Π state of NO2+ is corrected, leading to a new prediction of the wavelength of optical emission. The electron energy distributions in formation of the bound states of NO2+ are smooth, lacking sharp autoionisation features. Broad peaks found in the photoelectron distributions coincident with autoionisations of atomic oxygen are at different energies for each different O* state, indicating the involvement of several distinct dissociative superexcited states of NO+.

Role of the middle and long range parts of the NO2 potential energy surfaces: anomalous density of states and recombination rate constant

Using an accurate ab initio potential energy surface of NO2, the density of vibrational states of NO2 has been calculated up to the dissociation threshold. It is shown that the semi-classical approach, based on phase space volume derivation, cannot be used in the vicinity of the dissociation threshold, due to long-range interactions. Consequently, a new adiabatic method is introduced that benefits from the quantum nature of the NO intramolecular mode, while properly taking into account the C2v symmetry. Finally, the spin–orbit interactions are shown to play an important role for the observed anomalous density of states just below the dissociation threshold. On the other hand the effect of the middle and long range parts of the potential energy surface on the high pressure limit of the recombination rate constant is investigated within adiabatic capture theory. It is shown that the middle range forces are crucial to reproduce the law of variation of the experimental rate coefficient as a function of temperature and that the spin-orbit interactions play a role only at very low energy.

Analytical global potential energy surfaces of the two lowest 2A′ states of NO2

Download options Please wait... Supplementary files Fortran computer codes TXT (34K) Article information DOI https://doi.org/10.1039/B101507I Article type Paper Submitted 15 Feb 2001 Accepted 11 May 2001 First published 25 Jun 2001 Download Citation Phys. Chem. Chem. Phys., 2001,3, 2726-2734 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Analytical global potential energy surfaces of the two lowest 2A′ states of NO2 D. Reignier, T. Stoecklin, P. Halvick, A. Voronin and J. C. Rayez, Phys. Chem. Chem. Phys., 2001, 3, 2726 DOI: 10.1039/B101507I To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author D. Reignier T. Stoecklin P. Halvick A. Voronin J. C. Rayez

High resolution spectrum of NO2 loosely bound states: densities of states and long range forces

More than 1700 rovibronic states of low angular momentum (J = 1/2–7/2) have been observed by laser induced fluorescence (LIF) at high precision and resolution, ≃0.004 cm−1, in a range covering 133 cm−1 below the NO2 lowest photodissociation threshold D0. This allowed us to significantly improve and complete previous experimental results devoted to the states lying in the vicinity of D0 (A. Delon, S. Heilliette and R. Jost, Chem. Phys., 1998, 238, 465). The density of loosely bound vibronic levels exceeds the expected density over the entire observed energy range and exhibits an abrupt increase in the last 30 cm−1 below D0. The number of observed vibronic levels between D0 − 133 cm−1 and D0 is about twice the expected number of levels. The rovibronic eigenstates cannot be assigned any other quantum numbers than J and the overall symmetry. This indicates strong intramolecular couplings, and this is consistent with the fact that the densities of observed rovibronic states J = 1/2, 3/2, 5/2 and 7/2 have reached their maximum value, as compared with the density of vibronic levels. Moreover, R0/P2 intensity ratios, involving the same upper levels, scatter around their average value by four orders of magnitude. The above mentioned anomalous properties of the loosely bound states of NO2 (density and intensity ratios) are assumed to be the consequences of the long range electrostatic forces between the fragments NO and O. To quantify this hypothesis, we propose a simple analytic relation between the isotropic contribution of the long range part of the potential energy surface and the density of observed loosely bound states.