Vibration-rotation Energy Levels Research Articles

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.

Ab initio potential energy surface and vibration-rotation energy levels of disilicon carbide, CSi2

The accurate potential energy surface of disilicon carbide, CSi2, in its ground electronic state X∼1A1 has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. The core-electron correlation, higher-order valence-electron correlation, scalar relativistic, and adiabatic effects were taken into account. The potential energy barrier to the linear SiCSi configuration was predicted to be 832cm−1. The vibration-rotation energy levels of the CSi2, 13CSi2, CSi29Si, and CSi30Si isotopologues were predicted using a variational approach. The experimental vibration-rotation energy levels of the main isotopologue were reproduced to high accuracy. In particular, long vibrational progressions in the highly anharmonic SiCSi bending mode ν2 originating from the ground vibrational state of CSi2 are reproduced to within about 2.4cm−1 on average, close to the experimental accuracy.

A benchmark study of Li2+, Li2−, LiH+ and LiH−: Quantum Monte-Carlo and coupled-cluster computations

For the first time, very accurate potential energy curves (PEC) have been computed by the all electron Diffusion Quantum Monte-Carlo (DMC) and CCSD(T) methods for the ground-state of the Li2+, Li2−, LiH+ and LiH− ions. In addition to the molecular moieties, Li+, Li−, H− ions have also been studied by the aforementioned methods. The employed trial wave functions for the DMC calculations are a multiplication of multi-configuration expansions which are prepared by the Complete Active Space Self-Consistent Field method (CASSCF) with the aug-cc-pVTZ and the aug-cc-pCVTZ basis sets and the Jastrow factor. The CCSD(T) computations with all electrons correlated, have been performed by the cc-pV5Z, aug-cc-pCVQZ and aug-cc-pV6Z basis sets. In addition, the correlation energies for all of the studied atomic and molecular species have been calculated. For the studied molecular species, the Hartree-Fock energies in the complete basis set limit (ECBS) have not been reported. In this work for each of the molecular systems, the most negative energy which has been computed by the cc-pV5Z or aug-cc-pCVQZ basis sets has been used. The obtained PECs by the DMC and CCSD(T) methods are used to calculate the vibration-rotation energy levels and spectroscopic constants.

Information system for molecular spectroscopy: 6—systematization of spectral data on deutero-substituted isotopologues of the hydrogen sulfide molecule

Properties of data published on the spectral line parameters for deutero-substituted isotopologues of the hydrogen sulfide molecule (HDS, HD34S, D2S, and D2 34S) are described. Most properties follow from the results of vacuum wavenumber quality analysis. Two applications used for the data quality analysis in W@DIS information system are described. The results of computer-based data quality analysis of vacuum wavenumbers are completed by the expert evaluation of the quality of the same data set. The rotation-vibrational transitions and energy levels of deutero-substituted isotopologues of the hydrogen sulfide molecule are imported into the database; their properties are collected in the knowledge base and available in the W@DIS information system (http://wadis.saga.iao.ru/).

Ab initio potential energy surface and vibration-rotation energy levels of sulfur dioxide.

An accurate potential energy surface of sulfur dioxide, SO2 , in its ground electronic state X∼ 1A1 has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. The results obtained with the conventional and explicitly correlated coupled-cluster methods are compared. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, and adiabatic effects in determining the structure and dynamics of the SO2 molecule is discussed. The vibration-rotation energy levels of the 32 SO2 and 34 SO2 isotopologues were predicted using a variational approach. It was shown that the inclusion of the aforementioned effects was mandatory to attain the "spectroscopic" accuracy. © 2017 Wiley Periodicals, Inc.

Room temperature linelists for CO2 asymmetric isotopologues with ab initio computed intensities

The present paper reports room temperature line lists for six asymmetric isotopologues of carbon dioxide: 16O12C18O (628), 16O12C17O (627), 16O13C18O (638),16O13C17O (637), 17O12C18O (728) and 17O13C18O (738), covering the range 0–8000cm−1. Variational rotation-vibration wavefunctions and energy levels are computed using the DVR3D software suite and a high quality semi-empirical potential energy surface (PES), followed by computation of intensities using an ab initio dipole moment surface (DMS). A theoretical procedure for quantifying sensitivity of line intensities to minor distortions of the PES/DMS renders our theoretical model as critically evaluated. Several recent high quality measurements and theoretical approaches are discussed to provide a benchmark of our results against the most accurate available data. Indeed, the thesis of transferability of accuracy among different isotopologues with the use of mass-independent PES is supported by several examples. Thereby, we conclude that the majority of line intensities for strong bands are predicted with sub-percent accuracy. Accurate line positions are generated using an effective Hamiltonian, constructed from the latest experiments. This study completes the list of relevant isotopologues of carbon dioxide; these line lists are available to remote sensing studies and inclusion in databases.

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of 48Ti16O

Abstract Accurate, experimental rovibronic energy levels, with associated labels and uncertainties, are reported for 11 low-lying electronic states of the diatomic molecule, determined using the Marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. All levels are based on lines corresponding to critically reviewed and validated high-resolution experimental spectra taken from 24 literature sources. The transition data are in the 2–22,160 cm−1 region. Out of the 49,679 measured transitions, 43,885 are triplet–triplet, 5710 are singlet–singlet, and 84 are triplet–singlet transitions. A careful analysis of the resulting experimental spectroscopic network (SN) allows 48,590 transitions to be validated. The transitions determine 93 vibrational band origins of , including 71 triplet and 22 singlet ones. There are 276 (73) triplet–triplet (singlet–singlet) band-heads derived from Marvel experimental energies, 123(38) of which have never been assigned in low- or high-resolution experiments. The highest J value, where J stands for the total angular momentum, for which an energy level is validated is 163. The number of experimentally derived triplet and singlet rovibrational energy levels is 8682 and 1882, respectively. The lists of validated lines and levels for are deposited in the supporting information to this paper.

Investigations of the Rg-BrCl (Rg = He, Ne, Ar, Kr, Xe) binary van der Waals complexes: ab initio intermolecular potential energy surfaces, vibrational states and predicted pure rotational transition frequencies

The intermolecular potential energy surfaces (PESs) of the ground electronic state for the Rg-BrCl (Rg=He, Ne, Ar, Kr, Xe) van der Waals complexes have been constructed by using the coupled-cluster method in combination with the augmented quadruple-zeta correlation-consistent basis sets supplemented with an additional set of bond functions. The features of the anisotropic PESs for these complexes are remarkably similar, which are characterized by three minima and two saddle points between them. The global minimum corresponds to a collinear Rg-Br-Cl configuration. Two local minima, correlate with an anti-linear Rg-Cl-Br geometry and a nearly T-shaped structure, can also be located on each PES. The quantum bound state calculations enable us to investigate intermolecular vibrational states and rotational energy levels of the complexes. The transition frequencies are predicted and are fitted to obtain their corresponding spectroscopic constants. In general, the periodic trends are observed for this complex family. Comparisons with available experimental data for the collinear isomer of Ar-BrCl demonstrate reliability of our theoretical predictions, and our results for the other two isomers of Ar-BrCl as well as for other members of the complex family are also anticipated to be trustable. Except for the collinear isomer of Ar-BrCl, the data presented in this paper would be beneficial to improve our knowledge for these experimentally unknown species.

Ab initio potential energy surface and vibration-rotation energy levels of beryllium monohydroxide.

The accurate potential energy surface of beryllium monohydroxide, BeOH, in its ground electronic state X 2A' has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The higher-order electron correlation, scalar relativistic, and adiabatic effects were taken into account. The BeOH molecule was confirmed to be bent at equilibrium, with the BeOH angle of 141.2° and the barrier to linearity of 129 cm-1 . The vibration-rotation energy levels of the BeOH and BeOD isotopologues were predicted using a variational approach and compared with recent experimental data. The results can be useful in a further analysis of high-resolution vibration-rotation spectra of these interesting species. © 2016 Wiley Periodicals, Inc.

Small Molecules-Big Data.

Quantum mechanics builds large-scale graphs (networks): the vertices are the discrete energy levels the quantum system possesses, and the edges are the (quantum-mechanically allowed) transitions. Parts of the complete quantum mechanical networks can be probed experimentally via high-resolution, energy-resolved spectroscopic techniques. The complete rovibronic line list information for a given molecule can only be obtained through sophisticated quantum-chemical computations. Experiments as well as computations yield what we call spectroscopic networks (SN). First-principles SNs of even small, three to five atomic molecules can be huge, qualifying for the big data description. Besides helping to interpret high-resolution spectra, the network-theoretical view offers several ideas for improving the accuracy and robustness of the increasingly important information systems containing line-by-line spectroscopic data. For example, the smallest number of measurements necessary to perform to obtain the complete list of energy levels is given by the minimum-weight spanning tree of the SN and network clustering studies may call attention to "weakest links" of a spectroscopic database. A present-day application of spectroscopic networks is within the MARVEL (Measured Active Rotational-Vibrational Energy Levels) approach, whereby the transitions information on a measured SN is turned into experimental energy levels via a weighted linear least-squares refinement. MARVEL has been used successfully for 15 molecules and allowed to validate most of the transitions measured and come up with energy levels with well-defined and realistic uncertainties. Accurate knowledge of the energy levels with computed transition intensities allows the realistic prediction of spectra under many different circumstances, e.g., for widely different temperatures. Detailed knowledge of the energy level structure of a molecule coming from a MARVEL analysis is important for a considerable number of modeling efforts in chemistry, physics, and engineering.

Calculation of rotation-vibration energy levels of the ammonia molecule based on an ab initio potential energy surface

An ab initio potential energy surface (PES) for gas-phase ammonia NH3 has been computed using the methodology pioneered for water (Polyansky et al., 2013). Multireference configuration interaction calculations are performed at about 50000 points using the aug-cc-pCVQZ and aug-cc-pCV5Z basis sets and basis set extrapolation. Relativistic and adiabatic surfaces are also computed. The points are fitted to a suitable analytical form, producing the most accurate ab initio PES for this molecule available. The rotation-vibration energy levels are computed using nuclear motion program TROVE in both linearised and curvilinear coordinates. Better convergence is obtained using curvilinear coordinates. Our results are used to assign the visible spectrum of 14NH3 recorded by Coy and Lehmann (1986). Rotation-vibration energy levels for the isotopologues NH2D, NHD2, ND3 and 15NH3 are also given. An ab initio value for the dissociation energy D0 of 14NH3 is also presented.

Ab initio potential energy surface and vibration-rotation energy levels of silicon dicarbide, SiC2.

The accurate ground-state potential energy surface of silicon dicarbide, SiC2 , has been determined from ab initio calculations using the coupled-cluster approach. Results obtained with the conventional and explicitly correlated coupled-cluster methods were compared. The core-electron correlation, higher-order valence-electron correlation, and scalar relativistic effects were taken into account. The potential energy barrier to the linear SiCC configuration was predicted to be 1782 cm(-1) . The vibration-rotation energy levels of the SiC2 , (29) SiC2 , (30) SiC2 , and SiC(13) C isotopologues were calculated using a variational method. The experimental vibration-rotation energy levels of the main isotopologue were reproduced to high accuracy. In particular, the experimental energy levels of the highly anharmonic vibrational ν3 mode of SiC2 were reproduced to within 6.7 cm(-1) , up to as high as the v3 = 16 state.

EXPERIMENTAL ENERGY LEVELS AND PARTITION FUNCTION OF THE 12C2 MOLECULE

ABSTRACT The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the state, corresponding to the J = 2 total angular momentum quantum number and the F 1 spin-multiplet component, is 603.817(5) cm−1. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4000 K.

Enhanced sensitivity to a possible variation of the proton-to-electron mass ratio in ammonia

Numerous accidental near-degeneracies exist between the $2\nu_2$ and $\nu_4$ rotation-vibration energy levels of ammonia. Transitions between these two states possess significantly enhanced sensitivity to a possible variation of the proton-to-electron mass ratio $\mu$. Using a robust variational approach to determine the mass sensitivity of the energy levels along with accurate experimental values for the energies, sensitivity coefficients have been calculated for over 350 microwave, submillimetre and far infrared transitions up to $J\!=\!15$ for $^{14}$NH$_3$. The sensitivities are the largest found in ammonia to date. One particular transition, although extremely weak, has a sensitivity of $T=-16,738$ and illustrates the huge enhancement that can occur between close-lying energy levels. More promising however are a set of previously measured transitions with $T=-32$ to $28$. Given the astrophysical importance of ammonia, the sensitivities presented here confirm that $^{14}$NH$_3$ can be used exclusively to constrain a spatial or temporal variation of $\mu$. Thus, certain systematic errors which affect the ammonia method can be eliminated. For all transitions analyzed we provide frequency data and Einstein A coefficients to guide future laboratory and astronomical observations.

Simulation of the vibrational-rotational energy levels of D2 18O, HD18O, D2 17O, and HD17O molecules by the effective Hamiltonian approach

The vibrational-rotational energy levels of the first and second triads and the first and second hexads of the D218O, HD18O, D217O, and HD17O molecules are simulated on the basis of the Watson-type Hamiltonian and the rotation operator written in terms of the Pade–Borel approximants. Rotational, centrifugal distortion, and resonance constants and mixing coefficients of the resulting wave functions are found by the least squares method. The resonance interactions are analyzed. The predictive capability of the effective Hamiltonian parameters found is examined for the long extrapolated rotational quantum numbers.

TheoReTS – An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces

Knowledge of intensities of rovibrational transitions of various molecules and theirs isotopic species in wide spectral and temperature ranges is essential for the modeling of optical properties of planetary atmospheres, brown dwarfs and for other astrophysical applications. TheoReTS (“Theoretical Reims–Tomsk Spectral data”) is an Internet accessible information system devoted to ab initio based rotationally resolved spectra predictions for some relevant molecular species. All data were generated from potential energy and dipole moment surfaces computed via high-level electronic structure calculations using variational methods for vibration–rotation energy levels and transitions. When available, empirical corrections to band centers were applied, all line intensities remaining purely ab initio. The current TheoReTS implementation contains information on four-to-six atomic molecules, including phosphine, methane, ethylene, silane, methyl-fluoride, and their isotopic species 13CH4, 12CH3D, 12CH2D2, 12CD4, 13C2H4,…. Predicted hot methane line lists up to T=2000K are included. The information system provides the associated software for spectra simulation including absorption coefficient, absorption and emission cross-sections, transmittance and radiance. The simulations allow Lorentz, Gauss and Voight line shapes. Rectangular, triangular, Lorentzian, Gaussian, sinc and sinc squared apparatus function can be used with user-defined specifications for broadening parameters and spectral resolution. All information is organized as a relational database with the user-friendly graphical interface according to Model-View-Controller architectural tools. The full-featured web application is written on PHP using Yii framework and C++ software modules. In case of very large high-temperature line lists, a data compression is implemented for fast interactive spectra simulations of a quasi-continual absorption due to big line density. Applications for the TheoReTS may include: education/training in molecular absorption/emission, radiative and non-LTE processes, spectroscopic applications, opacity calculations for planetary and astrophysical applications. The system is freely accessible via internet on the two mirror sites: in Reims, France (http://theorets.univ-reims.fr) and in Tomsk, Russia (http://theorets.tsu.ru).

On spectra of spectra

Spectroscopic networks (SNs), where the vertices are discrete, rovibronic energy levels and the edges are transitions among the levels allowed by quantum mechanics, serve as useful models helping to understand high-resolution spectra of molecular systems. The experimental SNs of the $$^{12}\hbox {C}_{2}, \hbox {H}_{3}^{+}$$ , $$\hbox {H}_{2}\hbox {D}^{+}$$ , $$\hbox {HD}_{2}^{+}$$ , $$^{14}\hbox {NH}_{3}$$ , and $$\hbox {H}_{2}{}^{16}\hbox {O}$$ molecules, containing a single copy of the known measured and assigned transitions, are investigated via the corresponding network representation matrices, including the Ritz matrix $${\varvec{X}}$$ , the adjacency matrix $${\varvec{A}}$$ , the combinatorial Laplacian matrix $${\varvec{L}}^{\mathrm{C}}$$ , and the normalized Laplacian matrix $${\varvec{L}}^{\mathrm{N}}$$ . Using elements of graph (network) theory and the eigenvalue spectra of the matrices mentioned, several interesting results relevant for high-resolution molecular spectroscopy are revealed about the structure of the investigated SNs. For example, as long as the parity selection rule of molecular rovibrational transitions is not violated, the experimental SNs investigated not only contain, with the exception of $$^{12}\hbox {C}_{2}$$ , two principal components but they are all bipartite networks, as proven by the symmetry of the eigenvalue spectrum of $${\varvec{A}}$$ about the origin. Furthermore, the PageRank ordering system is introduced to molecular spectroscopy to identify the most important vertices of SNs. The rankings provided by the degree of the levels and by PageRank may differ significantly; it appears that PageRank provides the more useful ranking. The connectors of relatively dense clusters of the SNs are identified and analysed via spectral clustering techniques based on $${\varvec{L}}^{\mathrm{C}}$$ and $${\varvec{L}}^{\mathrm{N}}$$ . The identification of connectors becomes especially important when judging the true accuracy of the experimental rovibrational energy levels obtained through the Measured Active Rotational-Vibrational Energy Levels (MARVEL) approach, built with the help of the Ritz matrix $${\varvec{X}}$$ .

Promoting and inhibiting tunneling via nuclear motions.

Accurate, experimental rotational-vibrational energy levels determined via the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm and published recently for the symmetric-top (14)NH3 molecule in J. Quant. Spectrosc. Radiat. Transfer, 2015, 116, 117-130 are analyzed to unravel the promoting and inhibiting effects of vibrations and rotations on the tunneling splittings of the corresponding symmetric (s) and antisymmetric (a) rovibrational energy level pairs. The experimental transition data useful from the point of view of the present analysis cover the range 0.7-7000 cm(-1), sufficiently detailed rovibrational energy sets worth analyzing are available for 20 vibrational bands. The highest J value, where J stands for the rotational quantum number, within the experimental dataset employed is 30. Coupling of the "umbrella" motion of (14)NH3 with other vibrational degrees of freedom has only a minor effect on the a-s tunneling splitting characterizing the ground vibrational state, 0.79436(70) cm(-1). In the majority of the cases rotation around the C3 axis increases, while rotation around the two perpendicular axes decreases the tunneling splittings. For example, for the pair of vibrational ground states, 0(+) and 0(-), the tunneling splitting basically disappears at around J = 25 for the (J,K) = (J,1) states, where K = |k| is the usual quantum number characterizing the projection of the rotational angular momentum on the principal axis. The tunneling splittings, defined as energy differences E(a) - E(s) of corresponding energy level pairs, as a function of J and K show a very regular behavior for the ground state (GS) and the nν2 bands. For the other bands investigated exceptions from a regular behavior do occur, especially for bands characterized by degenerate vibrations, and occasionally the data available are not sufficient to arrive at definitive conclusions. The most irregular behavior is observed for rotational states characterized by the k - l = 3n rule (l is the vibrational angular momentum quantum number), with n = 0, 1, 2,… High-quality, variationally computed rovibrational data support all the conclusions of this study based on experimental energy levels.

Deformed Heisenberg Algebra with a minimal length: Application to some molecular potentials

We review the essentials of the formalism of quantum mechanics based on a deformed Heisenbeg algebra, leading to the existence of a minimal length scale. We compute in this context, the energy spectra of the pseudoharmonic oscillator and Kratzer potentials by using a perturbative approach. We derive the molecular constants, which characterize the vibration-rotation energy levels of diatomic molecules, and investigate the effect of the minimal length on each of these parameters for both potentials. We confront our result to experimental data for the hydrogen molecule to estimate an order of magnitude of this fundamental scale in molecular physics.