Vibration-rotation Energy Research Articles

Vibration-rotation energy levels and corresponding eigenfunctions of 12CH4 up to the tetradecad

In this paper, we report the vibration-rotation energy levels of methane (12CH4) calculated using the latest version of the global effective Hamiltonian developed in Dijon [B. AMYAY et al.. J. Chem. Phys., 148, 134–306 (2018)]. 238,429 vibration-rotation energy levels are calculated rotationally up to J= 50 and vibrationally up to the Tetradecad ( ≈ 6200 cm−1). The corresponding wavefunctions mixings are also investigated in this work. The knowledge of both energy levels and wavefunctions mixings are essential for simulating high-resolution spectra of methane of astrophysical and atmospheric interests. An evidence of distinct regular and oscillatory contributions, is observed in the number of vibration-rotation levels of methane. This can be fully understood using the generating functions presented by Sadovskií and Zhilinskií [J. Chem. Phys. 103, 10–520 (1995)].

Marvel analysis of the measured high-resolution rovibrational spectra of H232S

44 325 measured and assigned transitions of H232S, the parent isotopologue of the hydrogen sulfide molecule, are collated from 33 publications into a single database and reviewed critically. Based on this information, rotation-vibration energy levels are determined for the ground electronic state using the Measured Active Rotational-Vibrational Energy Levels (Marvel) technique. The ortho and para principal components of the measured spectroscopic network of H232S are considered separately. The verified set of 25 293 ortho- and 18 778 para- H232S transitions determine 3969 ortho and 3467 para energy levels. The Marvel results are compared with alternative data compilations, including a theoretical variational linelist.

Study of the Water Vapor Absorption Spectrum in the Visible Spectral Region from 19480 to 20500 cm−1

The vibrational-rotational absorption spectrum of water vapor was recorded and analyzed in the visible spectral region from 19480 to 20500 cm−1. The measurements were carried out using an IFS-125M Fourier spectrometer with a resolution of 0.05 cm−1 at a pressure of 26.3 mbar, a temperature of (24 ± 1)°C, and optical path 24 m. We used a multipass White cell with a base length of 60 cm. A light-emitting diode was used as a radiation source. The signal-to-noise ratio was about 20000. The list of more than 420 lines has been compiled as a result of the analysis the spectrum, which includes line centers, intensities, and quantum vibrational-rotational numbers. More than 220 vibrational-rotational energy levels of 21 upper vibrational states have been determined from the experimental data.

Solutions of the Klein–Gordon equation with the improved Tietz potential energy model

We present the relativistic rotation–vibrational energy equation of a diatomic molecule which moves under the improved Tietz potential energy model in higher spatial dimensions. The nonrelativistic limits of the bound state solutions of the Klein–Gordon equation are the bound state solutions of the Schrodinger equation with the same potential energy function. Numerical analysis results show that there exists a critical point around which the solution behaviors bifurcate into two extreme cases. Below the critical point, the behavior of the relativistic vibrational energies for the ground electronic state of carbon monoxide in higher dimensions keeps similar to that of the three-dimensional system, while this symmetry phenomenon breaks and the Klein–Gordon equation has no stability solution upon the critical point.

Study of H216O and H218O absorption in the 16,460–17,200 cm−1 range using LED-based Fourier transform spectroscopy

The spectra of the Н216О and Н218О vapor have been recorded between 16,460 and 17,200 cm−1 by a Fourier transform spectrometer with spectral resolution of 0.05 cm−1 using high luminance LED light source and 60 cm multipath cell with a path length of 3480 cm. A high signal-to-noise ratio (S/N ≈ 5000) enable us to register the lines with intensities of 1.54 × 10−24 to 2.0 × 10−27 cm/molecule. More than 1300 lines were recorded in the spectrum of the natural abundance water vapor and over 1800 lines in the spectrum of the vapor enriched by 18O. 422 rotation-vibration energy levels of the H218O molecule have been assigned to twenty vibrational states. The majority of these energies was attributed to the (241), (321), (340), (420), (401), (500), and (123) states. 43 energy levels were tentatively assigned to the (043), (142), (302), (161), (260), and (062) states. Eleven energy levels were labeled as belonging to the (280), (081), (190), (0 10 0), (1 10 0), (0 11 0), and (0 12 0) states. The recorded spectra were compared with the simulations based on the HITRAN2016 database and variational lists.

THz spectroscopy of [formula omitted]CH+, 13CH+, and [formula omitted]CD+: A combined Dunham analysis of Terahertz lines and [formula omitted] transitions

The THz rotational lines of CH+ and its isotopologues have been observed in the range of 0.9–2.6 THz with JPL frequency multiplication chains. They were analyzed together with the known A1Π-X1Σ+ band system data by using the Dunham formulation and the conventional vibration–rotation energy formula. The Λ-doubling in 1Π states was reexamined, and the doubling or shifts were found to be different for the e- and f-parity levels. In this investigation, the e- and f-parity states were treated as two separate states. The major molecular constants were determined accurately for these two states separately, and were compared with the values obtained previously.

Potential energy surface of triplet O4.

We present a global ground-state potential energy surface (PES) for the triplet spin state of O4 that is suitable for treating high-energy vibrational-rotational energy transfer and collision-induced dissociation in electronically adiabatic spin-conserving O2-O2 collisions. The surface is based on MS-CASPT2/maug-cc-pVTZ electronic structure calculations with scaled external correlation; the active space has 16 electrons in 12 orbitals. The global ground-state potential energy surface was fitted by a many-body approach with an accurate O-O pairwise interaction and a fit of the many-body interaction potential to 10 180 electronic structure data points. The many-body fit is based on permutationally invariant polynomials in terms of bond-order functions of the six interatomic distances; the bond-order functions are mixed exponential-Gaussian functions. The geometries calculated and used for the fit include geometry scans corresponding to dissociative and vibrationally excited diatom-diatom collisions of O2, scans corresponding to O3 interacting with O, additional geometries identified by running trajectories, and geometries along linear synchronous transit paths connecting randomly selected points. The global O4 PES includes subsurfaces describing the interaction of diatomic molecules with other diatomic molecules or interactions of triatomic molecules and an atom. The interaction of ozone with a ground-state oxygen atom occurs on the triplet O4 surface, and our surface includes high-energy points with O3-O geometries as well as O2-O2 geometries and O2-O-O geometries.

Ab initio potential energy surface and vibration-rotation energy levels of germanium dicarbide, GeC2.

The accurate ground-state potential energy surface of germanium dicarbide, GeC2 , has been determined from ab initio calculations using the coupled-cluster approach. The core-electron correlation, higher-order valence-electron correlation, and scalar relativistic effects were taken into account. The potential energy surface of GeC2 was shown to be extraordinarily flat near the T-shaped equilibrium configuration. The potential energy barrier to the linear CCGe configuration was predicted to be 1218 cm-1 . The vibration-rotation energy levels of some GeC2 isotopologues were calculated using a variational method. The vibrational bending mode ν3 was found to be highly anharmonic, with the fundamental wavenumber being only 58 cm-1 . Vibrational progressions due to this mode were predicted for the v1=1, v2=1, and v2=2 states of GeC2 . © 2018 Wiley Periodicals, Inc.

Rotational state modification and fast ortho-para conversion of H2 trapped within the highly anisotropic potential of Pd(210)

The rotational state and ortho-para conversion of ${\mathrm{H}}_{2}$ on a Pd(210) surface is investigated with rotational-state-selective temperature-programmed desorption (RS-TPD) and theoretical calculations. The isotope dependence of TPD shows a higher desorption energy for ${\mathrm{D}}_{2}$ than that for ${\mathrm{H}}_{2}$, which is ascribed to the rotational and zero-point vibrational energies. The RS-TPD data show that the desorption energy of ${\mathrm{H}}_{2}$($J=1$) ($J$: rotational quantum number) is higher than that of ${\mathrm{H}}_{2}$($J=0$). This is due to the orientationally anisotropic potential confining the adsorbed ${\mathrm{H}}_{2}$, which is in agreement with theoretical calculations. Furthermore, the ${\mathrm{H}}_{2}$ desorption intensity ratio in $J=1$ and $J=0$ indicates fast ortho-para conversion in the adsorption state, which we estimate to be of the order of 1 s.

High Accuracy ab Initio Calculations of Rotational-Vibrational Levels of the HCN/HNC System.

Highly accurate ab initio calculations of vibrational and rotational-vibrational energy levels of the HCN/HNC (hydrogen cyanide/hydrogen isocyanide) isomerising system are presented for several isotopologues. All-electron multireference configuration interaction (MRCI) electronic structure calculations were performed using basis sets up to aug-cc-pCV6Z on a grid of 1541 geometries. The ab initio energies were used to produce an analytical potential energy surface (PES) describing the two minima simultaneously. An adiabatic Born-Oppenheimer diagonal correction (BODC) correction surface as well as a relativistic correction surface were also calculated. These surfaces were used to compute vibrational and rotational-vibrational energy levels up to 25 000 cm-1 which reproduce the extensive set of experimentally known HCN/HNC levels with a root-mean-square deviation σ = 1.5 cm-1. We studied the effect of nonadiabatic effects by introducing opportune radial and angular corrections to the nuclear kinetic energy operator. Empirical determination of two nonadiabatic parameters results in observed energies up to 7000 cm-1 for four HCN isotopologues (HCN, DCN, H13CN, and HC15N) being reproduced with σ = 0.37 cm-1. The height of the isomerization barrier, the isomerization energy and the dissociation energy were computed using a number of models; our best results are 16 809.4, 5312.8, and 43 729 cm-1, respectively.

Critical evaluation of measured rotational–vibrational transitions of four sulphur isotopologues of S16O2

A critical evaluation and validation of the complete set of previously published experimental rotational–vibrational line positions is reported for the four stable sulphur isotopologues of the semirigid SO2 molecule – i.e., 32S16O2, 33S16O2, 34S16O2, and 36S16O2. The experimentally measured, assigned, and labeled transitions are collated from 43 sources. The 32S16O2, 33S16O2, 34S16O2, and 36S16O2 datasets contain 40,269, 15,628, 31,080, and 31 lines, respectively. Of the datasets collated, only the extremely limited 36S16O2 dataset is not subjected to a detailed analysis. As part of a detailed analysis of the experimental spectroscopic networks corresponding to the ground electronic states of the 32S16O2, 33S16O2, and 34S16O2 isotopologues, the MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the rovibrational energy levels. The rovibrational levels and their vibrational parent and asymmetric-top quantum numbers are compared to ones obtained from accurate variational nuclear-motion computations as well as to results of carefully designed effective Hamiltonian models. The rovibrational energy levels of the three isotopologues having the same labels are also compared against each other to ensure self-consistency. This careful, multifaceted analysis gives rise to 15,130, 5852, and 10,893 validated rovibrational energy levels, with a typical accuracy of a few 0.0001 cm−1, for 32S16O2, 33S16O2, and 34S16O2, respectively. The extensive list of validated experimental lines and empirical (MARVEL) energy levels of the S16O2 isotopologues studied are deposited in the Supplementary Material of this article, as well as in the distributed information system ReSpecTh (http://respecth.hu).

Channel branching ratios in CH2CN- photodetachment: Rotational structure and vibrational energy redistribution in autodetachment.

We report photoelectron spectra of CH2CN-, recorded at photon energies between 13 460 and 15 384 cm-1, which show rapid intensity variations in particular detachment channels. The branching ratios for various spectral features reveal rotational structure associated with autodetachment from an intermediate anion state. Calculations using equation-of-motion coupled-cluster method with single and double excitations reveal the presence of two dipole-bound excited anion states (a singlet and a triplet). The computed oscillator strength for the transition to the singlet dipole-bound state provides an estimate of the autodetachment channel contribution to the total photoelectron yield. Analysis of the different spectral features allows identification of the dipole-bound and neutral vibrational levels involved in the autodetachment processes. For the most part, the autodetachment channels are consistent with the vibrational propensity rule and normal mode expectation. However, examination of the rotational structure shows that autodetachment from the ν3 (v = 1 and v = 2) levels of the dipole-bound state displays behavior counter to the normal mode expectation with the final state vibrational level belonging to a different mode.

The 1943 K emission spectrum of H216O between 6600 and 7050 cm[formula omitted

An emission spectrum of H216O has been recorded, with Doppler-limited resolution, at 1943 K using Hot Gas Molecular Emission (HOTGAME) spectroscopy. The wavenumber range covered is 6600 to 7050 cm−1. This work reports the analysis and subsequent assignment of close to 3700 H216O transitions out of a total of more than 6700 measured peaks. The analysis is based on the Measured Active Rotational-Vibrational Energy Levels (MARVEL) energy levels of H216O determined in 2013 and emission line intensities obtained from accurate variational nuclear-motion computations. The analysis of the spectrum yields about 1300 transitions not measured previously and 23 experimentally previously unidentified rovibrational energy levels. The accuracy of the line positions and intensities used in the analysis was improved with the spectrum deconvolution software SyMath via creating a peak list corresponding to the dense emission spectrum. The extensive list of labeled transitions and the new experimental energy levels obtained are deposited in the Supplementary Material of this article as well as in the ReSpecTh (http://www.respecth.hu) information system.

Calculating vibration-rotation spectrum intensities of laser-induced fluorescence for the B1Π – Χ1Σ+ electronic transition in a LiCs molecule

The purpose of this study was to calculate the intensities of the vibration-rotation spectrum of laser-induced fluorescence for the B1Π – Χ1Σ+ electronic transition in a LiCs molecule. We find vibration-rotation energies and wave functions as a result of numerically solving the radial wave equation based on potential energy curves plotted in the present work for the ground and excited states. We compare calculated and experimental intensities.

Relativistic spinless rotation-vibrational energies of carbon monoxide

We solve the Klein-Gordon equation with the simplified Poschl-Teller potential model by employing the shape invariance technique, and present the relativistic spinless rotation-vibrational energy equation for diatomic molecules with nuclear spin of zero. It is found that the relativistic effects subject to the relative motion of the ions increase slightly the spinless vibrational energies of the ground electronic state of the carbon monoxide molecule in comparison to the nonrelativistic results. We observe that the variation of the relativistic spinless rotation-vibrational energies with respect to the vibrational quantum number in larger rotational quantum numbers holds similar to that with rotational quantum number of zero.

Determining the Parameters of the Ground Vibrational State of the 28SiH4 Molecule

For high-precision determination of the rotational-vibrational energies of the ground vibrational state of the SiH4 molecule, high-resolution rotational-vibrational spectrum of this molecule in the range 600–1200 cm–1 in which bands of the ν2/ ν4 dyad are located is analyzed. As a result, rotational and centrifugal distortion parameters of the ground vibrational state with a root-mean-square deviation of 2·10–4 cm–1 are obtained.

MARVEL analysis of the measured high-resolution rovibrational spectra of C2H2

Rotation-vibration energy levels are determined for the electronic ground state of the acetylene molecule, 12C2H2, using the Measured Active Rotational-Vibrational Energy Levels (Marvel) technique. 37,813 measured transitions from 61 publications are considered. The distinct components of the spectroscopic network linking ortho and para states of the molecule are considered separately. The 20,717 ortho and 17,096 para transitions measured experimentally are used to determine 6013 ortho and 5200 para energy levels. The Marvel results are compared with alternative compilations based on the use of effective Hamiltonians.

Study of HDO absorption in the 11,200–12,400 cm−1 range using LED-based Fourier transform spectroscopy

A high resolution Fourier transform spectrum of mono-deuterated water vapor was studied between 11,200 and 12,400 cm−1 using a Fourier transform spectrometer with the spectral resolution of 0.05 cm−1, coupled to a multi-pass White-type cell that provided an optical path length of 24 m. A light-emitting diode was used as the radiation source to obtain a measurement signal-to-noise ratio of about 104. The rotational-vibrational assignment of more than 1560 lines was carried out using the VTT variational line list. The parameters of the spectral lines (line centers, intensities and half-widths) were determined by least-squares fitting of the Voigt contour parameters to the experimental data. A total of 584 rotational–vibrational energy levels with maximum rotational quantum numbers of J = 16 and Ka = 9 were determined. For the first time, 64 new energy levels belonging to the nine vibrational states: (032), (112), (301), (141), (410), (221), (330), (061) and (170) were derived from the experiment.

Potential energy surfaces of quintet and singlet O4.

We present global ground-state potential energy surfaces for the quintet and singlet spin states of the O4 system that are suitable for treating high-energy vibrational-rotational energy transfer and collision-induced dissociation in electronically adiabatic, spin-conserving O2-O2 collisions. The surfaces are based on MS-CASPT2/maug-cc-pVTZ electronic structure calculations with scaled external correlation. The active space has 16 electrons in 12 orbitals. The calculations cover nine kinds of geometrical arrangements corresponding to dissociative diatom-diatom collisions of O2, geometries corresponding to O3-O, geometries identified by running trajectories, and geometries along linear synchronous transit paths. The global ground-state potential energy surfaces were obtained by a many-body approach with an accurate O-O pairwise interaction and a fit of the many-body interaction to 12 684 electronic structure data points for the singlet and 10 543 electronic structure data points for the quintet. The many-body fit is based on permutationally invariant polynomials in terms of bond-order functions of the six interatomic distances; the bond-order functions are mixed exponential-Gaussian functions.

Relativistic rotation-vibrational energies for the 107Ag 109Ag isotope

We present the relativistic rotation-vibrational energy equation of a diatomic molecule which moves under the Morse potential model. In the nonrelativistic limit, the relativistic energy equation turns to the nonrelativistic rotation-vibrational energy expression of the diatomic molecule. We observe that the relativistic effects subject to the relative motion of the ions yield a little increase in the vibrational energies for the B-11 $\Pi_{\rm u}$ state of the 107Ag 109Ag isotope, and this result is consistent with that obtained by considering the relativistic effects subject to the electronic motion in the literature. It is observed that the behavior of the relativistic rotation-vibrational energies in larger rotational quantum numbers remains similar to that with zero rotational quantum number.