Harmonic Oscillator Approximation Research Articles

On Analytical Corrections for Restraints in Absolute Binding Free Energy Calculations.

Double decoupling absolute binding free energy simulations require an intermediate state at which the ligand is held solely by restraints in a position and orientation resembling the bound state. One possible choice consists of one distance, two angle, and three dihedral angle restraints. Here, I demonstrate that in practically all cases the analytical correction derived under the rigid rotator harmonic oscillator approximation is sufficient to account for the free energy of the restraints.

High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

Monohalogenated methyl- and methoxy-benzoic acids: A combined experimental and quantum chemical theoretical study on their structure, vibrational analysis and molecular parameters

In this paper, the molecules 3-fluoro-2-methylbenzoic acid; 3-chloro-2-methoxybenzoic acid; and 3-bromo-2-methylbenzoic were investigated using experimental and quantum chemical theoretical approach for vibrational and electronic properties from the optimized structure. Becke three parameter Lee–Yang–Parr density functionals along with 6-311++G(d,p) basis set were employed to compute their geometric optimization, fundamental frequencies and molecular parameters. The detected FT-IR and FT-Raman spectra were compared with their simulated spectra and the rms error between the detected and simulated vibrational frequencies was found at 6.17, 7.22 and 6.76 cm−1 for FMA, CMA and BMA, respectively. All the vibrational fundamentals were assigned unequivocally using potential energy distribution (PED) obtained in the computations. 1H and 13C NMR chemical shifts were evaluated by integrating the gauge-independent atomic orbital (GIAO) method with DFT and compared with corresponding experimental values. TD-DFT approach was followed to compare the simulated absorption maxima (λmax) in DMSO-d6 solvent with observed values and interpreted in terms of HOMO and LUMO. The global reactive descriptors were estimated from the associated energies of HOMO and LUMO which describe the reactivity and stability of the molecules. Molecular electrostatic potential (MEP) surface has been determined using the charge density distributions to demonstrate electrophilic and nucleophilic nature of the molecules. DFT computations also ascertained the applicability of the titled molecules as NLO materials from the computed values of dipole moment and hyperpolarizability. Thermodynamic parameters and rotational constants were also evaluated employing rigid rotor harmonic oscillator approximation. Natural bond orbital (NBO) analysis confirmed the charge delocalization due to intra-molecular interactions.

Effect of choosing coordinate systems on computationally predicting nonradiative transition rates of flexible thermally activated delayed fluorescence molecules

AbstractUnderstanding nonradiative transition mechanisms is important in various situations. However, compared with radiative processes where temporal profiles of photon emission can be monitored in a straightforward manner, experimentally accessing the rate information may not be an easy task with nonradiative transitions. Hence, applying theoretical tools toward predicting the rates can be a useful tactic. Such predictions become very useful in designing optoelectronic materials as in the molecules adopted for constructing organic light‐emitting diodes (OLEDs). The correlation function formalism is a method that can fulfill the purpose of designing OLED materials. The formalism requires information regarding the vibrational normal modes of the two electronic states before and after the transition. Because the method is also based on harmonic oscillator approximation, it can actually fail to provide high reliability when there is a large geometric distortion between the initial and the final states. In fact, the harmonic normal mode picture is more prone to lose reliability in the Cartesian coordinates than in the internal ones even at a small distortion, and hence adopting internal coordinates may be more preferable for practical calculations. This is because normal mode mixing becomes less severe when molecular coordinates are described with internal degrees of freedom such as bond stretching, bending, and torsion. In this regard, how much more reliable the nonradiative rate predictions in OLED materials become with the use of internal coordinate system deserves a close inspection. In this account, we review on the derivation of the correlation function formalism and provide how it can be adapted toward the use of the internal coordinates. As a demonstration, we evaluate the intersystem crossing and the internal conversion rates of a series of thermally activated delayed fluorescence (TADF) molecules with both Cartesian and internal coordinate systems. Overall, handling transitions involving substantial structural changes is improved indeed with the internal coordinates. However, limitations are still apparent for the TADF systems with a flexible donor–acceptor type construct especially when the inevitable inter‐domain twisting takes place with the electronic transition. Future prospect for handling the issue is commented as a concluding remark.

Including vibrational effects in magnetic circular dichroism spectrum calculations in the framework of excited state dynamics.

In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4- and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements.

An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene.

We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.

Approximate Energy Spectra of the Quantum Gaussian Well: A Four-parameter Potential Fitting

Abstract: In this work, we present a detailed study of a one-dimensional Schrödinger equation in the presence of quantum Gaussian well interaction. Further, we investigate the approximate solutions by using the harmonic oscillator approximation, variational principle, four-parameter potential fitting and numerical solution using the finite-difference method. The parabolic approximation yields an excellent energy value compared with the numerical solution of the Gaussian system only for the ground state, while for the excited states, it provides a higher approximation. Also, the analytical bound-state energies of the four-parameter potential under the framework of the Nikiforov-Uvarov (NU) method have been used after getting the suitable values of the potential parameters using numerical fitting. The present results of the system states are found to be in high agreement with the well-known numerical results of the Gaussian potential. Keywords: Gaussian potential, One-dimensional Schrödinger equation, Nikiforov- Uvarov (NU) method, Four-parameter potential. PACS: 03.65.−w; 02.90.+p; 12.39.Pn.

Comparative performance of theoretical tools in order to quantify the effect of the electric potential on the vibrational wavenumbers and intensities of the SERS of 2‐methylpyrazine adsorbed on a nanostructured silver electrode

AbstractThe effect of the electrode potential in surface‐enhanced Raman scattering (SERS) intensities and wavenumbers of 2‐methylpyrazine (2MP) was analyzed on the basis of a resonant charge transfer (CT) mechanism by using a simple theoretical model in which the metallic surface and its charge density were simulated by atomic silver clusters of different size (n) and charge (q), [Agn]q. Two linear silver atoms (n = 2) with zero charge (q = 0) and three linear silver atoms (n = 3) with positive and negative charges (q = ±1) linked to the two nonequivalent aromatic nitrogen atoms in 2MP were taken into account. The wavenumber shifts of the most intense bands and the SERS‐CT spectra of these two types of metal‐adsorbate supermolecule, [Agn‐N1]q and [Agn‐N4]q, were calculated by using a time‐dependent density functional theory (TD‐DFT) method and the independent mode displaced harmonic oscillator (IMDHO) approximation. A comparison of the effect of different levels of calculation, ab initio/DFT, on the predictions from the two theoretical models (isolated adsorbate/supermolecule) is also performed. Only DFT theoretical results of the metal‐adsorbate supermolecule allow to explain the main role of the pair of bands assigned to totally symmetric ring‐stretching 8a,b modes. The 8a vibration is the strongest band at any electrode potential, whereas the 8b mode reaches a maximum enhancement at −0.50 V and then decreases at −0.75 V. This model of a charged metal‐adsorbate interface allows for detecting the presence of a CT mechanism in a SERS record.

Franck‐Condon factors within damped displacement harmonic oscillators: Solvent‐enhanced absorption and fluorescence spectra

AbstractDamped harmonic oscillators that take into account local‐mode nuclear vibrations interacting with solvent molecules are developed into Franck‐Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling an unperturbed Hessian matrix that represents local modes of force constants for molecules in a gaseous phase, and then by diagonalizing the perturbed Hessian matrix it results in direct modification of Huang–Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. For highly symmetric polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in a solution can be scaled equally, one‐set scaling parameters constructed into damped Franck‐Condon factors can reproduce solvent‐enhanced absorption and fluorescence spectra in solution. However, for low symmetry molecules with atoms other than hydrogen and carbon atoms, multi‐set scaling parameters constructed into damped Franck‐Condon factors can also reproduce solvent‐enhanced absorption and fluorescence spectra in solution. Examples for high symmetry perylene in benzene solution with one‐set scaling parameters and for low symmetry carbazole in n‐hexane solution with multi‐set scaling parameters are given, in both cases, the present damped Franck‐Condon simulation can reproduce solvent‐enhanced absorption and fluorescence spectra in solution.

Classical vs quantum corrections to jet broadening in a weakly-coupled Quark-Gluon Plasma

The transverse momentum broadening coefficient hat{q} receives both soft, classical and radiative, quantum corrections. The former are responsible for a large mathcal{O} (g) correction, whereas the latter enter at relative order αs, but are enhanced by a double logarithm of the length of the medium over the thermal wavelength. We analyze radiative corrections for a weakly-coupled quark-gluon plasma. We find that a thermal population of dynamical gluons changes the boundaries and reduces the size of the double-logarithmic phase space. It also provides new subdominant logarithmic corrections. We also show how the quantum, double-logarithmic and classical, soft phase spaces are smoothly connected once the radiated gluon becomes soft enough. Finally, we discuss a pathway to a determination of radiative corrections beyond the harmonic-oscillator approximation.

Room-Temperature Deep-UV Photoluminescence from Low-Dimensional Hexagonal Boron Nitride Prepared Using a Facile Synthesis.

Identification and evaluation of defect levels in low-dimensional materials is an important aspect in quantum science. In this article, we report a facile synthesis method of low-dimensional hexagonal boron nitride (h-BN) and study light emission characteristics due to the defects. The thermal annealing procedure is optimized to obtain clean multilayered h-BN as revealed by transmission electron microscopy. UV–vis spectroscopy shows the optical energy gap of 5.28 eV, which is comparable to the reported energy gap for exfoliated, clean h-BN samples. X-ray photoelectron spectroscopy reveals the location of the valence band edge at 2 eV. The optimized synthesis route of h-BN generates two kinds of defects, which are characterized using room-temperature photoluminescence (PL) measurements. The defects emit light at 4.18 eV [deep-UV (DUV)] and 3.44 eV (UV) photons. The intensity of PL has an oscillatory dependence on the excitation energy for the defect emitting DUV light. A series of spectral lines are observed with the energy ranging between 2.56 and 3.44 eV. The average peak-to-peak energy separation is about 125 meV. The locations of the spectral lines can be modeled using Franck–Condon-type transition and associated with displaced harmonic oscillator approximation. Our facile route gives an easier approach to prepare clean h-BN, which is essential for classical two-dimensional material-based electronics and single-photon-based quantum devices.

Estimation of Excited-State Geometries of Benzene and Fluorobenzene through Vibronic Analyses of Absorption Spectra

The parameters used in theoretical modeling of vibrational patterns within Franck–Condon (FC) approximation can be adjusted to match the vibrationally well-resolved experimental absorption spectrum of molecules. These simulation parameters can then be used to reveal the structural changes occurring between the initial and final states assuming the harmonic oscillator approximation holds for both states. Such a theoretical approach has been applied to benzene and fluorobenzene to disclose the first excited-state geometries of both compounds. The carbon–carbon bond length of benzene in the 1B2u state has been calculated as 1.430 Å, which is in very good agreement with the experimental bond length of 1.432 Å. The FC spectral fit method has been exploited to reveal the 1B2 state of fluorobenzene as well. Commonly employed density functional theory (DFT) and time-dependent DFT methods have been used to calculate the ground- and excited-state geometries of both compounds, respectively. The comparison of geometrical parameters and vibrational frequencies at the relevant states shows that frequently used hybrid functionals perform quite well in the ground state, whereas their performances drop considerably while predicting the excited-state properties. Among the hybrid functionals studied, TD-B3LYP with 6-31+G(d) basis set can be chosen to calculate the excited-state properties of molecules, albeit with much less anticipation of accuracy from the performance that B3LYP usually shows at the ground state.

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C+.

We introduce ULYSSES, a user-friendly and robust C++ library for semiempirical quantum chemical calculations. In its current version, ULYSSES is equipped with a large set of different semiempirical models, most of which are based on the Neglect of Diatomic Differential Overlap (NDDO) approximation. Empirical corrections for dispersion and hydrogen bonding are available for most methods, so that higher quality is achieved in the calculation of energies of nonbonded complexes. The library is furthermore equipped with geometry optimization, as well as modules for calculating molecular properties of general interest. Ideal gas thermodynamics is available and allows single structure as well as conformer (multistructure) averaged properties to be calculated. We offer the possibility to use several vibrational partition functions according to the nature of interactions being studied: for covalent systems, the traditional harmonic oscillator approximation is available; for nonbonded complexes, we systematically extended the partition function proposed by Grimme for all thermodynamic functions. The library is also capable of running Born-Oppenheimer molecular dynamics.

Universal anharmonic potential energy surfaces for XY2-type molecules

An approach to generate anharmonic potential energy surfaces for both linear and bent XY2-type molecules from their equilibrium geometries, Hessians, and total atomization energies alone is presented. Two key features of the potential energy surfaces are that (a) they reproduce the harmonic behavior around the equilibrium geometries exactly and (b) they have the correct limiting behavior with respect to total bond dissociation. The potentials are constructed from two diatomic potentials, for which both the Morse or Varshni potentials are tested, and a triatomic potential, for which modified forms of the Anderson-n potential are tested. Potential energy surfaces for several linear and bent molecules are constructed from ab initio data, and the third-order derivatives of these surfaces at their equilibrium geometries are compared to the results of finite difference computations. For bent molecules, the vibrational spectra predicted by vibrational configuration interaction calculations on these surfaces are compared to experiment. A modified version of the Anderson-n potential, in combination with the Varshni potential, is demonstrated to predict vibrational frequencies associated with bond angle bending an average of 20 cm−1 below the harmonic oscillator approximation and with a fourfold reduction in the root-mean-square deviation from experiment compared to the harmonic oscillator approximation.

Anharmonicity in partially filled skutterudites YbxCo4Sb12

We report an experimental investigation of Yb filler ion dynamics in partially filled skutterudite samples YbxCo4Sb12 (x=0.26 and x=0.4). From extended x-ray absorption fine structure (EXAFS) measurements at the Yb L2-edge, the mean-square displacements of the Yb fillers were extracted over a wide temperature range from 10 to 500 K. We found that the low-temperature dynamics of Yb fillers are described well using a harmonic oscillator approximation with Einstein temperatures of 70±5 K for both samples. This finding is consistent with the observed low-energy phonon mode at 5.3(5) meV in the inelastic x-ray scattering (IXS) data. However, the temperature dependence deviates from the harmonic approximation at high temperatures due to significant cubic anharmonicity, which was revealed in the EXAFS cumulant analysis. Our study also demonstrates that complementary information on filler dynamics in skutterudites can be acquired using EXAFS and IXS.

A general analytical expression for evaluation of an arbitrary n-dimensional Franck-Condon overlap integral including the Duschinsky effect

Evaluations of the multidimensional Frank-Condon (FC) overlapping integrals are needed theoretically to investigate the mechanism of radiative and non-radiative processes among the different electronic states of polyatomic molecules. We extended our recently reported approach to calculate an arbitrary n-dimensional Franck–Condon overlapping integrals based on harmonic oscillator approximation and taking into account the Duschinsky effects. An analytical formula was derived straightforwardly based on the Hermite polynomials expanding properties and directly evaluating Gaussian integrals. A method to determine the coefficient parameter matrices of four-dimensional Franck-Condon integrals by matrix operations was presented. In addition, as a practical application, we simulated and elucidated the vibrationally resolved peaks of the photodetachment spectra of SeO2‾. Moreover, in the spectral simulations, employing our iterative Franck-Condon analysis procedure, fairly reliable geometries of the ground state X~2B1 of the negative ion SeO2‾ are obtained.

Heavy quark radiation in the quark\u2013gluon plasma in the Moliere theory: angular distribution of the radiation

We study the effects of adding the Coulomb interactions to the harmonic oscillator (HO) approximation of the heavy parton propagating through the quark–gluon plasma (the extension to QCD of the Molliere theory). We explicitly find the expression for the transverse momentum distribution of the gluon radiation of the heavy quark propagating in the quark gluon plasma in the framework of the Moliere theory, taking into account the BDMPSZ radiation in the HO approximation, and the Coulomb logarithms described by the additional logarithmic terms in the effective potential. We show that these Coulomb logarithms significantly influence the HO distribution, derived in the BDMPSZ works, especially for the small transverse momenta, filling the dead cone, and reducing the dead cone suppression of the heavy quark radiation (dead cone effect). In addition we study the effect of the phase space constraints on the heavy quark energy loss, and argue that taking into account of both the phase space constraints and of the Coulomb gluons reduces the dependence of the heavy quark energy loss on its mass in the HO approximation.

Photoluminescence spectra of point defects in semiconductors: Validation of first-principles calculations

Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid-state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide information on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first principles calculations, including the use of the Franck-Condon principle and the displaced harmonic oscillator approximation. We focus on prototypical examples of solid-state qubits, the divacancy centers in SiC and the nitrogen-vacancy in diamond, and we report computed photoluminescence spectra as a function of temperature that are in very good agreement with the measured ones. As expected we find that the use of hybrid functionals leads to more accurate results than semilocal functionals. Interestingly our calculations show that constrained density functional theory (CDFT) and time-dependent hybrid DFT perform equally well in describing the excited state potential energy surface of triplet states; our findings indicate that CDFT, a relatively cheap computational approach, is sufficiently accurate for the calculations of photoluminescence spectra of the defects studied here. Finally, we find that only by correcting for finite-size effects and extrapolating to the dilute limit, one can obtain a good agreement between theory and experiment. Our results provide a detailed validation protocol of first principles calculations of photoluminescence spectra, necessary both for the interpretation of experiments and for robust predictions of the electronic properties of point defects in semiconductors.

Electronic spectroscopy of the A1̃2A′′/A2̃2A′−X̃2A′ transitions of jet-cooled calcium ethoxide radicals: Vibronic structure of alkaline earth monoalkoxide radicals of C s symmetry

Laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down spectra of the A1̃2A''/A2̃2A'-X̃2A' electronic transition of the calcium ethoxide (CaOC2H5) radical have been obtained under jet-cooled conditions. An essentially constant Ã2-Ã1 energy separation for different vibronic levels is observed in the LIF spectrum, which is attributed to both the spin-orbit (SO) interaction and non-relativistic effects. Electronic transition energies, vibrational frequencies, and spin-vibrational eigenfunctions calculated using the coupled-cluster method, along with results from previous complete active space self-consistent field calculations, have been used to predict the vibronic energy level structure and simulate the recorded LIF/DF spectra. Although the vibrational frequencies and Franck-Condon (FC) factors calculated under the Born-Oppenheimer approximation and the harmonic oscillator approximation reproduce the dominant spectral features well, the inclusion of the pseudo-Jahn-Teller (pJT) and SO interactions, especially those between the A1̃2A″/A2̃2A' and the B̃2A' states, induces additional vibronic transitions and significantly improves the accuracy of the spectral simulations. Notably, the spin-vibronic interactions couple vibronic levels and alter transition intensities. The calculated FC matrix for the A1̃2A''/A2̃2A'-X̃2A' transition contains a number of off-diagonal matrix elements that connect the vibrational ground levels to the levels of the ν8 (CO stretch), ν11 (OCC bending), ν12 (CaO stretch), ν13 (in-plane CaOC bending), and ν21 (out-of-plane CaOC bending) modes, which are used for vibrational assignments. Transitions to the ν21(a″) levels are allowed due to the pJT effect. Furthermore, when LIF transitions to the Ã-state levels of the CaOC-bending modes, ν13 and ν21, are pumped, A1̃2A''/A2̃2A'→X̃2A' transitions to the combination levels of these two modes with the ν8, ν11, and ν12 modes are also observed in the DF spectra due to the Duschinsky mixing. Implications of the present spectroscopic investigation to laser cooling of asymmetric-top molecules are discussed.

Non-equilibrium dissociation and relaxation behind the shock wave within two-temperature approach

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the equations for a dissociating diatomic gas have been derived assuming two-temperature (translational-rotational + vibrational) approximation. Corresponding expressions for the reaction and relaxation rates, determined by the quasi-stationary vibrational distributions, have been obtained under assumption of dissociation from the highest vibrational level. Cut-off harmonic oscillator approximation for the diatomic molecules is assumed. It is shown that all reaction rates are the complex functions of the species densities. Analysis of a flow behind a shock wave is performed in a wide range of the flow parameters. It is shown that under strong non-equilibrium condition the dissociation rate is determined not by the dissociation probability, but by the vibration probability, since the excitation of highest vibrational levels is the bottleneck of dissociation process. This means that the procedure of obtaining the data on dissociation rates needs the accurate revision.