Excited Vibrational States Research Articles

Optimizing hydroxyl airglow retrievals from long-slit astronomical spectroscopic observations

Abstract. Astronomical spectroscopic observations from ground-based telescopes contain background emission lines from the terrestrial atmosphere's airglow. In the near infrared, this background is composed mainly of emission from Meinel bands of hydroxyl (OH), which is produced in highly excited vibrational states by reduction of ozone near 90 km. This emission contains a wealth of information on the chemical and dynamical state of the Earth's atmosphere. However, observation strategies and data reduction processes are usually optimized to minimize the influence of these features on the astronomical spectrum. Here we discuss a measurement technique to optimize the extraction of the OH airglow signal itself from routine J-, H-, and K-band long-slit astronomical spectroscopic observations. As an example, we use data recorded from a point-source observation by the Nordic Optical Telescope's intermediate-resolution spectrograph, which has a spatial resolution of approximately 100 m at the airglow layer. Emission spectra from the OH vibrational manifold from v′ = 9 down to v′ = 3, with signal-to-noise ratios up to 280, have been extracted from 10.8 s integrations. Rotational temperatures representative of the background atmospheric temperature near 90 km, the mesosphere and lower thermosphere region, can be fitted to the OH rotational lines with an accuracy of around 0.7 K. Using this measurement and analysis technique, we derive a rotational temperature distribution with v′ that agrees with atmospheric model conditions and the preponderance of previous work. We discuss the derived rotational temperatures from the different vibrational bands and highlight the potential for both the archived and future observations, which are at unprecedented spatial and temporal resolutions, to contribute toward the resolution of long-standing problems in atmospheric physics.

Conformational Landscape and Torsion-Rotation-Vibration Effects in the Two Conformers of Methyl Vinyl Ketone, a Major Oxidation Product of Isoprene.

Methyl vinyl ketone is the second major oxidation product of isoprene, and as such an important volatile organic compound present in the troposphere. In the present study, quantum chemical calculations coupled to high-resolution millimeter-wave spectroscopy have been performed to characterize the ground and first excited vibrational states of the two stable conformers. Equilibrium structures, internal rotation barriers, and relative energies have been calculated at the MP2 and M062X levels of theory. Experimental molecular parameters have been obtained that model the rotational and torsional structures, including splitting patterns due to the internal rotation of the methyl group. For the most stable antiperiplanar (s-trans) conformer, the set of parameters obtained for the ground state should be useful to further model IR spectra up to room temperature. By combining theoretical and experimental data, we obtained a relative energy value of 164 ± 30 cm-1 in the gas phase between the more stable antiperiplanar and the less stable synperiplanar conformers. Moreover, we compared our system with related molecules for the variation in the barriers of methyl rotors in different molecular environments. In addition, the inverse sequence of A and E tunneling substates for the rotational lines of the first excited skeletal torsional state and Coriolis-type coupling with methyl torsion have been observed. For the less stable synperiplanar (cis) conformer, molecular parameters for the ground and first excited torsional states as well as of the first excited skeletal torsional state are presented.

Hydrogen bond network rearrangement dynamics in water clusters: Effects of intermolecular vibrational excitation on tunneling rates.

Theoretical studies of hydrogen bond network rearrangement (HBNR) dynamics in liquid water have indicated that librational motions initiate the hydrogen bond breaking/formation processes. We present the results of using a simple time evolution method to extract and compare the tunneling lifetimes for motions that break and reform the hydrogen bond for the water dimer, trimer, and pentamer from the experimentally measured tunneling splittings in the ground and excited intermolecular vibrational states. We find that the specific nature of the intermolecular vibrational excitation does not significantly influence the tunneling lifetime of the dimer, but that only excitations to a librational vibration affect the water trimer and pentamer lifetimes. The specific enhancement of bifurcation tunneling in larger clusters relative to the dimer also indicates that hydrogen bond cooperativity is a vital element of these dynamics.

The influence of vibrations of polyatomic molecules on dipole moment and static dipole polarizability: theoretical study

Dipole moment and static dipole polarizability surfaces for 50 polyatomic molecules, that are important for material science, combustion, and atmospheric chemistry, are explored in the vicinity of their equilibrium nuclear configurations by using density functional theory. The effective values of dipole moment and static polarizability of these molecules in individual vibrational states are determined using the calculated data on the electric properties and potential energy surfaces. Special attention is paid to the effect of the zero-point vibrations on the electric properties. The simple approximation scheme, allowing low-cost estimation of the zero-point vibrational corrections to polarizability, applicable for wide range of polyatomic compounds, are developed on the basis of the obtained data. The influence of the excitation of vibrational states on the dipole moment and dipole polarizability of polyatomic molecules are discussed with respect to the possible change of some important properties of molecular gases, such as refractive index, diffusion coefficients, and rates of chemical reactions.

Experimental and theoretical investigations of H2O-Ar.

We have used continuous-wave cavity ring-down spectroscopy to record the spectrum of H2O-Ar in the 2OH excitation range of H2O. 24 sub-bands have been observed. Their rotational structure (Trot = 12 K) is analyzed and the lines are fitted separately for ortho and para species together with microwave and far infrared data from the literature, with a unitless standard deviation σ=0.98 and 1.31, respectively. Their vibrational analysis is supported by a theoretical input based on an intramolecular potential energy surface obtained through ab initio calculations and computation of the rotational energy of sub-states of the complex with the water monomer in excited vibrational states up to the first hexad. For the ground and (010) vibrational states, the theoretical results agree well with experimental energies and rotational constants in the literature. For the excited vibrational states of the first hexad, they guided the assignment of the observed sub-bands. The upper state vibrational predissociation lifetime is estimated to be 3 ns from observed spectral linewidths.

Millimeter-wave and Submillimeter-wave Spectra of Aminoacetonitrile in the Three Lowest Vibrational Excited States

Abstract It is important to study possible precursors of amino acids such as glycine to enable future searches in interstellar space. Aminoacetonitrile (NH2CH2CN) is one of the most feasible molecules for this purpose. This molecule was already detected toward Sgr B2(N). Aminoacetonitrile has a few low-lying vibrational excited states, and transitions within these states may be found in space. In this study, the pure-rotational transitions in the three lowest vibrational states in the 80–450 GHz range have been assigned and analyzed. It was found to be very important to include Coriolis coupling between the two lowest vibrational fundamentals, while the third one was unperturbed. The partition function was evaluated considering these new results.

Accurate sub-millimetre rest frequencies for HOCO+ and DOCO+ ions

HOCO$^+$ is a polar molecule that represents a useful proxy for its parent molecule CO$_2$, which is not directly observable in the cold interstellar medium. This cation has been detected towards several lines of sight, including massive star forming regions, protostars, and cold cores. Despite the obvious astrochemical relevance, protonated CO$_2$ and its deuterated variant, DOCO$^+$, still lack an accurate spectroscopic characterisation. The aim of this work is to extend the study of the ground-state pure rotational spectra of HOCO$^+$ and DOCO$^+$ well into the sub-millimetre region. Ground-state transitions have been recorded in the laboratory using a frequency-modulation absorption spectrometer equipped with a free-space glow-discharge cell. The ions were produced in a low-density, magnetically-confined plasma generated in a suitable gas mixture. The ground-state spectra of HOCO$^+$ and DOCO$^+$ have been investigated in the 213-967 GHz frequency range, with the detection of 94 new rotational transitions. Additionally, 46 line positions taken from the literature have been accurately remeasured. The newly-measured lines have significantly enlarged the available data sets for HOCO$^+$ and DOCO$^+$, thus enabling the determination of highly accurate rotational and centrifugal distortion parameters. Our analysis showed that all HOCO$^+$ lines with Ka $\geq$ 3 are perturbed by a ro-vibrational interaction that couples the ground state with the v$_ 5$ = 1 vibrationally-excited state. This resonance has been explicitly treated in the analysis in order to obtain molecular constants with clear physical meaning. The improved sets of spectroscopic parameters provide enhanced lists of very accurate, sub-millimetre rest-frequencies of HOCO$^+$ and DOCO$^+$ for astrophysical applications. These new data challenges a recent tentative identification of DOCO$^+$ toward a pre-stellar core.

Hidden role of intermolecular proton transfer in the anomalously diffuse vibrational spectrum of a trapped hydronium ion

We report the vibrational spectra of the hydronium and methyl-ammonium ions captured in the C3v binding pocket of the 18-crown-6 ether ionophore. Although the NH stretching bands of the CH3NH3+ ion are consistent with harmonic expectations, the OH stretching bands of H3O+ are surprisingly broad, appearing as a diffuse background absorption with little intensity modulation over 800 cm-1 with an onset ∼400 cm-1 below the harmonic prediction. This structure persists even when only a single OH group is present in the HD2O+ isotopologue, while the OD stretching region displays a regular progression involving a soft mode at about 85 cm-1 These results are rationalized in a vibrationally adiabatic (VA) model in which the motion of the H3O+ ion in the crown pocket is strongly coupled with its OH stretches. In this picture, H3O+ resides in the center of the crown in the vibrational zero-point level, while the minima in the VA potentials associated with the excited OH vibrational states are shifted away from the symmetrical configuration displayed by the ground state. Infrared excitation between these strongly H/D isotope-dependent VA potentials then accounts for most of the broadening in the OH stretching manifold. Specifically, low-frequency motions involving concerted motions of the crown scaffold and the H3O+ ion are driven by a Franck-Condon-like mechanism. In essence, vibrational spectroscopy of these systems can be viewed from the perspective of photochemical interconversion between transient, isomeric forms of the complexes corresponding to the initial stage of intermolecular proton transfer.

Study of highly excited ro-vibrational states of S18O2 from “hot” transitions: The bands ν1+ν2+ν3−ν2, 2ν1+ν2−ν2, and 2ν2+ν3−ν2

Transitions belonging to the three “hot” bands of the S18O2 molecule, ν1+ν2+ν3−ν2 (621 transitions with the values of quantum numbers Jmax=49 and Kamax=14), 2ν1+ν2−ν2 (332 transitions with Jmax=42 and Kamax=12) and 2ν2+ν3−ν2 (15 transitions with Jmax=14 and Ka=8 and 9), were assigned in the spectral 2100–2700cm−1 region. This enabled for the first time to get high accurate values of 388, 185 and 13 ro-vibrational energies for the highly excited vibrational states (111), (210) and (021), respectively. A weighted fit analysis using the obtained ro-vibrational energies allowed us to generate a set of 20 fitted parameters which reproduce the initial 586 energy values (about 970 assigned experimental transitions) with the drms deviations of 1.9×10−4cm−1, 2.8×10−4cm−1 and 2.5×10−4cm−1 for the states (111), (210) and (021).

Relativistic Dirac analyses of polarized proton scatterings to the 2+ gamma vibrational band in 24Mg and 26Mg

Relativistic Dirac analyses are performed phenomenologically for the high-lying excited states that belong to the 2+ gamma vibrational band at the 800 MeV polarized proton inelastic scatterings from the s-d shell nuclei, 24Mg and 26Mg. Optical potential model is used and scalar and time-like vector potentials are considered as direct potentials. First-order vibrational collective models are used to obtain the transition optical potentials to accommodate the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically to reproduce the differential cross section and analyzing power data by varying the optical potential and deformation parameters. It is found that the relativistic Dirac coupled channel calculation could describe the high-lying excited states of the 2+ gamma vibrational band at the 800 MeV polarized proton inelastic scatterings from s-d shell nuclei 24Mg and 26Mg reasonably well, showing mostly better agreement with the experimental data compared to the results obtained from the nonrelativistic calculations. Calculated deformation parameters for the excited states are analyzed and compared with those of nonrelativistic calculations.

Diabatic models with transferrable parameters for generalized chemical reactions

Diabatic models applied to adiabatic electron-transfer theory yield many equations involving just a few parameters that connect ground-state geometries and vibration frequencies to excited-state transition energies and vibration frequencies to the rate constants for electron-transfer reactions, utilizing properties of the conical-intersection seam linking the ground and excited states through the Pseudo Jahn-Teller effect. We review how such simplicity in basic understanding can also be obtained for general chemical reactions. The key feature that must be recognized is that electron-transfer (or hole transfer) processes typically involve one electron (hole) moving between two orbitals, whereas general reactions typically involve two electrons or even four electrons for processes in aromatic molecules. Each additional moving electron leads to new high-energy but interrelated conical-intersection seams that distort the shape of the critical lowest-energy seam. Recognizing this feature shows how conical-intersection descriptors can be transferred between systems, and how general chemical reactions can be compared using the same set of simple parameters. Mathematical relationships are presented depicting how different conical-intersection seams relate to each other, showing that complex problems can be reduced into an effective interaction between the ground-state and a critical excited state to provide the first semi-quantitative implementation of Shaik’s “twin state” concept. Applications are made (i) demonstrating why the chemistry of the first-row elements is qualitatively so different to that of the second and later rows, (ii) deducing the bond-length alternation in hypothetical cyclohexatriene from the observed UV spectroscopy of benzene, (iii) demonstrating that commonly used procedures for modelling surface hopping based on inclusion of only the first-derivative correction to the Born-Oppenheimer approximation are valid in no region of the chemical parameter space, and (iv), demonstrating the types of chemical reactions that may be suitable for exploitation as a chemical qubit in some quantum information processor.

Self-consistent time dependent vibrational and free electron kinetics for CO2 dissociation and ionization in cold plasmas

A self-consistent time dependent model, based on the coupling between the Boltzmann equation for free electrons, the non equilibrium vibrational kinetics for the asymmetric mode of CO2 and simplified global models for the dissociation and ionization plasma chemistry, has been applied to conditions which can be met under pulsed microwave (MW), dielectric barrier discharge (DBD) and nanosecond pulsed discharges (NPD). Under MW discharge type conditions, the selected pulse duration generates large concentration of vibrational excited states, which affects the electron energy distribution function (eedf) through the superelastic vibrational collisions. Moreover, in discharge conditions, plateaux appear in the vibrational distribution function (vdf) through the vibrational–vibrational up pumping mechanism, persisting also in the post discharge. In post discharge conditions, also the eedf is characterized by plateaux due to the superelastic collisions between cold electrons and the CO2 electronic state at 10.5 eV. The plateau in vdf increases the dissociation of pure vibrational mechanism (PVM), which can become competitive with the dissociation mechanism induced by electron molecule collisions. The PVM rates increase with the decrease of gas temperature, generating a non-Arrhenius behaviour. The situation completely changes under DBD and NPD type conditions characterized by shorter pulse duration and higher applied E/N values. Under discharge conditions, both vdf and eedf plateaux disappear, reappering in the afterglow.

Search for long-living topological solutions of the nonlinear ϕ4 field theory

We look for long-living topological solutions of classical nonlinear $(1+1)-$ dimensional $\varphi^4$ field theory. To that effect we use the well-known cut-and-match method. In this framework, new long-living states are obtained in both topological sectors. In particular, in one case a highly excited state of a kink is found. We discover several ways of energy reset. In addition to the expected emission wave packets (with small amplitude), for some selected initial conditions the production of kink-antikink pairs results in a large energy reset. Also, the topological number of a kink in the central region changes in the contrast of saving full topological number. At lower excitation energies there is a long-living excited vibrational state of the kink; this phenomenon is the final stage of all considered initial states. Over time this excited state of the kink changes to a well-known linearized solution - a discrete kink excitation mode. This method yields a qualitatively new way to describe the large-amplitude bion, which was detected earlier in the kink-scattering processes in the nontopological sector.

Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction.

On the elementary level, electronic current consists of individual electron tunnelling events that are separated by random time intervals. The waiting time distribution is a probability to observe the electron transfer in the detector electrode at time t+τ given that an electron was detected in the same electrode at an earlier time t. We study waiting time distribution for quantum transport in a vibrating molecular junction. By treating the electron-vibration interaction exactly and molecule-electrode coupling perturbatively, we obtain the master equation and compute the distribution of waiting times for electron transport. The details of waiting time distributions are used to elucidate microscopic mechanism of electron transport and the role of electron-vibration interactions. We find that as nonequilibrium develops in the molecular junction, the skewness and dispersion of the waiting time distribution experience stepwise drops with the increase of the electric current. These steps are associated with the excitations of vibrational states by tunnelling electrons. In the strong electron-vibration coupling regime, the dispersion decrease dominates over all other changes in the waiting time distribution as the molecular junction departs far away from the equilibrium.

A comparative study of the vibrational spectra of HCN in exact vibron model and in mean field approximation

The aim of this work is to study the highly excited vibrational states of hydrogen cyanide HCN in the exact vibron model and with mean field approximation in the vibron model. Considering the U(4) ⊗ U(4) spectrum-generating algebra for linear triatomic molecules, the standard Hamiltonian is constructed using the linear and quadratic combination of Casimir operators. For higher order corrections, the quadratic contributions of Casimir operators are used to construct the Hamiltonian. Using this Hamiltonian the higher excited vibrational levels of HCN are calculated in the local mode approximation. The energy levels are observed as a function of vibron number N. The best fit is obtained for N = 184 (N1 = 139, N2 = 45) with root mean square (r.m.s.) deviation 5.598 cm−1. The intermodal coupling within the same polyad is studied and addressed properly by introducing Majorana operator. The r.m.s. deviation is then reduced to 4.755 cm−1. The modification is negligible, which indicates the local nature of HCN. In this work, 35 experimental levels are taken for fit, out of which only two sets of levels are accidentally degenerate. The Fermi resonances of the accidentally degenerate levels are studied using the Fermi operator and r.m.s. deviation becomes 4.835. The coefficient of Majorana and Fermi coupling for different levels are obtained by diagonalzing the Majorana and Fermi matrices for each polyad. The Majorana and Fermi matrices for each polyad are diagonalized with the MATRIX CALCULATOR program. The algebraic parameters are evaluated by a least square fit against the experimental data using MATLAB R2015a. Using this model, a set of energy levels is predicted up to 30 000 cm−1, with very good accuracy. HCN is chosen for this study, because, its vibrational states can be fairly described without any modification due to Fermi resonance. The fundamental vibrational levels of HCN are again calculated, using mean field approximation and compared to those obtained using the vibron model. A good agreement is observed.

The high overtone and combination levels of SF6 revisited at Doppler-limited resolution: A global effective rovibrational model for highly excited vibrational states

Sulfur hexafluoride is an important prototypal molecule for modeling highly excited vibrational energy flow and multi quanta absorption processes in hexafluoride molecules of technological importance. It is also a strong greenhouse gas of anthropogenic origin. This heavy species, however, features many hot bands at room temperature (at which only 30% of the molecules lie in the ground vibrational state), especially those originating from the lowest, v6=1 vibrational state. Using a cryogenic long path cell with variable optical path length and temperatures regulated between 120 and 163K, coupled to Synchrotron Radiation and a high resolution interferometer, Doppler-limited spectra of the 2ν1+ν3, ν1+ν2+ν3, ν1+ν3, ν2+ν3, 3ν3, ν2+3ν3 and ν1+3ν3 from 2000 to 4000cm-1 near-infrared region has been recorded. Low temperature was used to limit the presence of hot bands. The spectrum has been analyzed thanks to the XTDS software package. Combining with previously observed weak difference bands in the far infrared region involving the v1, v2, v3=1 states, we are thus able to use the tensorial model to build a global fit of spectroscopic parameters for v1=1,2, v2=1, v3=1,2,3. The model constitutes a consistent set of molecular parameters and enable spectral rovibrational simulation for all multi-quanta transitions involving v1, v2 and v3 up to v1−3=3. Tests simulation on rovibrational transitions not yet rovibrationally assigned are presented and compared to new experimental data.

Dynamic Features of the Highly Excited Vibrational States of the HOCl Non-Integrable System Based on the Dynamic Potential and Lyapunov Exponent Approaches.

In this article the dynamic features of the highly excited vibrational states of the hypochlorous acid (HOCl) non-integrable system are studied using the dynamic potential and Lyapunov exponent approaches. On the condition that the 3:1 resonance between the H–O stretching and H–O–Cl bending modes accompany the 2:1 Fermi resonance between the O–Cl stretching and H–O–Cl bending modes, it is found that the dynamic potentials of the highly excited vibrational states vary regularly with different Polyad numbers (P numbers). As the P number increases, the dynamic potentials of the H–O stretching mode remain the same, but those of the H–O–Cl bending mode gradually become complex. In order to investigate the chaotic and stable features of the highly excited vibrational states of the HOCl non-integrable system, the Lyapunov exponents of different energy levels lying in the dynamic potentials of the H–O–Cl bending mode (P = 4 and 5) are calculated. It is shown that the Lyapunov exponents of the energy levels staying in the junction of Morse potential and inverse Morse potential are relative large, which indicates the degrees of chaos for these energy levels is relatively high, but the stabilities of the corresponding states are good. These results could be interpreted as the intramolecular vibrational relaxation (IVR) acting strongly via the HOCl bending motion and causing energy transfers among different modes. Based on the previous studies, these conclusions seem to be generally valid to some extent for non-integrable triatomic molecules.

Vibrational autoionization of state-selective jet-cooled methanethiol (CH3SH) investigated with infrared + vacuum-ultraviolet photoionization.

Vibrational autoionization of Rydberg states provides key information about nonadiabatic processes above an ionization threshold. We employed time-of-flight mass detection of CH3SH+ to record vibrational-state selective photo-ionization efficiency (PIE) spectra of jet-cooled methanethiol (CH3SH) on exciting CH3SH to a specific vibrationally excited state with an infrared (IR) laser, followed by excitation with a tunable laser in the vacuum-ultraviolet (VUV) region for ionization. Autoionizing Rydberg states assigned to the ns, np, nd and nf series are identified. When IR light at 2601 (ν3, SH stretching mode) and 2948 cm-1 (ν2, CH3 symmetric stretching mode) was employed, the Rydberg series converged to the respective vibrationally excited (ν3 and ν2) states of CH3SH+. When IR light at 3014 cm-1 (overlapped ν1/ν9, CH3 antisymmetric stretching and CH2 antisymmetric stretching modes) was employed, Rydberg series converging to two vibrationally excited states (ν1 and ν9) of CH3SH+ were observed. When IR light at 2867 cm-1 (2ν10, overtone of CH3 deformation mode) and 2892 cm-1 (2ν4, overtone of CH2 scissoring mode) was employed, both Δν = -1 and Δν = -2 ionization transitions were observed; there is evidence for direct ionization from the initial state into the CH3SH+ (ν4+ = 1) continuum. In all observed IR-VUV-PIE spectra, the ns and nd series show intensity greater than the other Rydberg series, which is consistent with the fact that the highest-occupied molecular orbital of CH3SH is a p-like lone pair orbital on the S atom. The quantum yields for autoionization of various vibrational excited states are discussed. Values of ν1 = 3035, ν2 = 2884, ν3 = 2514, and ν9 = 2936 cm-1 for CH3SH+ derived from the converged limits agree satisfactorily with values observed for Ar-tagged CH3SH+ at 3026, 2879, 2502, and 2933 cm-1.

Photoluminescence from vibrational excited-states for organic molecules adsorbed on Si nanoparticles

Herein, Si nanoparticles have been fabricated from Si swarf using a bead milling method. The adsorption of 9,10-dimethylanthracene (DMA) on Si nanoparticles enhances the photoluminescence (PL) intensity by ∼60 000 times that of DMA in hexane. The PL spectra possess peaked structures due to the vibronic transition of DMA. For the excitation energies higher than 4.0 eV, vibronic bands with energies higher than the (0, 0) band were observed and attributed to PL from the vibrational excited-states. The excitation spectra showed that incident light was absorbed by both DMA and the Si nanoparticles. The lifetime of the photo-generated electron-hole pairs in the Si nanoparticles was much longer than the DMA PL lifetime; this indicated that either a hole or an electron transferred to DMA first, followed by an opposite charge transfer. In the cases where a hole is first transferred to DMA, an electronic ground-state is stabilized via solvation. When an electron is captured by the potential of the electronic excited-state, transitions from the vibrational excited-states proceed due to the high transition probability, generating PL bands with energies higher than the (0, 0) band. In the cases where an electron is first transferred to DMA, internal relaxation to the vibrational ground-state occurs, and the potential of the electronic excited-state is lowered via solvation.

High resolution study of the rotational structure of doubly excited vibrational states of 32S16O18O: The first analysis of the 2ν1, [formula omitted], and 2ν3 bands

The high resolution infrared spectra of the 32S16O18O molecule were recorded with a Bruker IFS 120 HR Fourier transform interferometer for the first time in the region of 1800–2800cm−1 where the bands 2ν1, ν1+ν3, and 2ν3 are located. About 3970, 2960 and 3450 transitions were assigned in the experimental spectra with the maximum values of quantum numbers Jmax./Kamax. equal to 59/20, 68/25, and 43/18 to the bands 2ν1, ν1+ν3, and 2ν3, respectively. The subsequent weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes into account the resonance interactions between the studied vibrational states. As the result, a set of 39 fitted parameters was obtained which reproduces the initial 3213 ro-vibrational energy values obtained from the assigned transitions with the drms=2.4×10−4cm−1.