Rovibronic Energy Levels Research Articles

Predissociation dynamics of the hydroxyl radical (OH) based on a five-state spectroscopic model.

Multi-reference configuration interaction potential energy curves (PECs) and spin-orbit couplings for the X 2Π, A 2Σ+, 1 2Σ-, 1 4Σ-, and 1 4Π states of OH are computed and refined against empirical energy levels and transitions to produce a spectroscopic model. Predissociation lifetimes are determined by discretizing continuum states in the variational method nuclear motion calculation by restricting the calculation to a finite range of internuclear separations. Varying this range gives a series of avoided crossings between quasi-bound states associated with the A 2Σ+ and continuum states, from which predissociation lifetimes are extracted. 424 quasi-bound A 2Σ+ state rovibronic energy levels are analyzed, and 374 predissociation lifetimes are produced, offering good coverage of the predissociation region. Agreement with measured lifetimes is satisfactory, and a majority of computed results were within experimental uncertainty. A previously unreported A 2Σ+ state predissociation channel that goes via X 2Π is identified in the calculations. A Python package, binSLT, produced to calculate predissociation lifetimes, associated line broadening parameters, and lifetime uncertainties is made available. The PECs and other curves from this work will be used to produce a rovibronic ExoMol line list and temperature-dependent photodissociation cross sections for the hydroxyl radical.

ExoMol line lists – LII. Line lists for the methylidyne cation (CH+)

ABSTRACTComprehensive and accurate rovibronic line lists for the X 1Σ+ and A 1Π states of 12C1H+ and 13C1H+ which should be applicable up to temperatures of 5000 K are presented. Available empirical potential energy curves and high-level ab initio dipole and transition dipole moment curves are used with the program level to compute rovibronic energy levels and Einstein A coefficients. Λ-doubling is incorporated into the energy levels and A-coefficients involving the A 1Π state using an empirical method. For 12C1H+, line positions are improved by using both laboratory and astronomical observational spectra as input to the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. The 12C1H+ line list contains 1505 states and 34 194 transitions over the frequency range of 0–33 010 cm−1 (λ > 300 nm). Comparisons with observed astronomical and laboratory spectra give very good agreement. The PYT CH+ line lists and partition functions are available from the ExoMol database at www.exomol.com.

ExoMol line lists – LVI. The SO line list, MARVEL analysis of experimental transition data and refinement of the spectroscopic model

ABSTRACT A semi-empirical IR/Vis line list, SOLIS, for the sulphur monoxide molecule 32S16O is presented. SOLIS includes accurate empirical rovibrational energy levels, uncertainties, lifetimes, quantum number assignments, and transition probabilities in the form of Einstein A coefficients covering the $X\, {}^{3}\Sigma ^{-}$$, a\, {}^{1}\Delta , b\, {}^{1}\Sigma ^{+}, A\, {}^{3}\Pi , B\, {}^{3}\Sigma ^{-}, A^{\prime \prime }\, {}^{3}\Sigma ^{+}, A^{\prime }\, {}^{3}\Delta$, and $e\, {}^{1}\Pi$ systems and wavenumber range up to 43 303.5 cm−1 (≥230.93 nm) with J ≤ 69. SOLIS has been computed by solving the rovibronic Schrödinger equation for diatomics using the general purpose variational code Duo and starting from a published ab initio spectroscopic model of SO (including potential energy curves, coupling curves, (transition) dipole moment curves) which is refined to experimental data. To this end, a database of 50 106 experimental transitions, 48 972 being non-redundant, has been compiled through the analysis of 29 experimental sources, and a self-consistent network of 8558 rovibronic energy levels for the X, a, b, A, B, and C electronic states has been generated with the marvel algorithm covering rotational and vibrational quantum numbers J ≤ 69 and v ≤ 30 and energies up to 52 350.40 cm−1. No observed transitions connect to the $B\, {}^{3}\Sigma ^{-}$(v = 0) state which is required to model perturbations correctly, so we leave fitting the $B\, {}^3\Sigma ^-$ and $C\, {}^3\Pi$ state UV model to a future project. The SO line list is available at ExoMol from www.exomol.com.

Empirical rovibronic energy levels of C3

ABSTRACT The carbon trimer, C 3 also known as propadienediylidene, is a quasi-linear molecule with an unusual electronic structure and a very flat bending potential in its ground electronic state. C 3 is an important species in astrophysics and carbon plasmas. Observed transition wavenumbers within and between the X ~ 1 Σ g + and A ~ 1 Π u states of C 3 are extracted from 21 papers and then subjected to a Measured Active Rotational-Vibrational Energy Levels (MARVEL) analysis: a corrected list of 4940 transitions are inverted to yield 1887 empirical energy levels. Uncertainties for these levels are determined using a newly implemented bootstrap method. These levels will provide input for developing a full spectroscopic model for C 3 which can used to generate a line list for the X ~ 1 Σ g + and A ~ 1 Π u states.

ExoMol line lists – XLV. Rovibronic molecular line lists of calcium monohydride (CaH) and magnesium monohydride (MgH)

ABSTRACT New molecular line lists for calcium monohydride (40Ca1H) and magnesium monohydride (24Mg1H) and its minor isotopologues (25Mg1H and 26Mg1H) are presented. The rotation-vibration-electronic (rovibronic) line lists, named XAB, consider transitions involving the $X\, {}^{2}\Sigma ^{+}$, $A\, {}^{2}\Pi$, and $B/B^{\prime }\, {}^{2}\Sigma ^{+}$ electronic states in the 0–30 000 cm−1 region (wavelengths λ > 0.33 μm) and are suitable for temperatures up to 5000 K. A comprehensive analysis of the published spectroscopic literature on CaH and MgH is used to obtain new extensive data sets of accurate rovibronic energy levels with measurement uncertainties and consistent quantum number labelling. These data sets are used to produce new spectroscopic models for CaH and MgH, composed of newly empirically refined potential energy curves and couplings in/between the different electronic states (e.g. spin-orbit, electronic angular momentum, Born-Oppenheimer breakdown, spin-rotation, Λ-doubling), and previously published ab initio transition dipole moment curves. Along with Einstein A coefficients, state lifetimes and Landé g-factors are provided, the latter being particularly useful as CaH and MgH can be used to probe stellar magnetic fields. Computed energy levels have been replaced with the more accurate empirical values (if available) when post-processing the line lists, thus tailoring the line lists to high-resolution applications. The XAB line lists are available from the ExoMol database at www.exomol.com and the CDS astronomical database.

Analysis of measured high-resolution doublet rovibronic spectra and related line lists of 12CH and 16OH.

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a multitude of modelling efforts within multiple chemical, combustion, astrophysical, and atmospheric environments. Accurate empirical rovibronic energy levels, with associated uncertainties, are reported for the low-lying doublet electronic states of 12CH and 16OH, using the Measured Active Rotational-Vibrational Energy Levels (Marvel) algorithm. For 12CH, a total of 1521 empirical energy levels are determined in the primary spectroscopic network (SN) of the radical, corresponding to the following seven electronic states: X 2Π, A 2Δ, B 2Σ−, C2 Σ+, D 2Π, E 2Σ+, and F 2Σ+. The energy levels are derived from 6348 experimentally measured and validated transitions, collected from 29 sources. For 16OH, the lowest four doublet electronic states, X 2Π, A 2Σ+, B 2Σ+, and C 2Σ+, are considered, and a careful analysis and validation of 15 938 rovibronic transitions, collected from 45 sources, results in 1624 empirical rovibronic energy levels. The large set of spectroscopic data presented should facilitate the refinement of line lists for the 12CH and 16OH radicals. For both molecules hyperfine-resolved experimental transitions have also been considered, forming SNs independent from the primary SNs.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

Experimental energy levels of 12C14N through marvel analysis.

The cyano radical (CN) is a key molecule across many different factions of astronomy and chemistry. Accurate, empirical rovibronic energy levels with uncertainties are determined for eight doublet states of CN using the marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. 40 333 transitions were validated from 22 different published sources to generate 8083 spin-rovibronic energy levels. The empirical energy levels obtained from the marvel analysis are compared to current energy levels from the mollist line list. The mollist transition frequencies are updated with marvel energy level data which brings the frequencies obtained through experimental data up to 77.3percent from the original 11.3percent, with 92.6percent of the transitions with intensities over 10-23 cm molecule-1 at 1000K now known from experimental data. At 2000K, 100.0percent of the partition function is recovered using only marvel energy levels, while 98.2percent is still recovered at 5000K.

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of the Calcium Monohydroxide Radical (CaOH)

The calcium monohydroxide radical (CaOH) is an important astrophysical molecule relevant to cool stars and rocky exoplanets, amongst other astronomical environments. Here, we present a consistent set of highly accurate rovibronic (rotation-vibration-electronic) energy levels for the five lowest electronic states ($\tilde{X}\,^2\Sigma^+$, $\tilde{A}\,^2\Pi$, $\tilde{B}\,^2\Sigma^+$, $\tilde{C}\,^2\Delta$, $\tilde{D}\,^2\Sigma^+$) of CaOH. A comprehensive analysis of the published spectroscopic literature on this system has allowed 1955 energy levels to be determined from 3204 rovibronic experimental transitions, all with unique quantum number labelling and measurement uncertainties. The dataset covers rotational excitation up to $J=62.5$ for molecular states below 29\,000~cm$^{-1}$. The analysis was performed using the MARVEL algorithm, which is a robust procedure based on the theory of spectroscopic networks. The dataset provided will significantly aid future interstellar, circumstellar and atmospheric detections of CaOH, as well as assisting in the design of efficient laser cooling schemes in ultracold molecule research and precision tests of fundamental physics.

MARVEL analysis of the measured high-resolution spectra of [formula omitted]NH

Rovibronic energy levels are determined for four low-lying electronic states (X3Σ-, A3Π, a1Δ, and c1Π) of the imidogen free radical (14NH) using the Marvel (Measured Active Rotational-Vibrational Energy Levels) technique. Compilation of transitions from both laboratory measurements and solar spectra, found in 18 publications, yields a dataset of 3002 rovibronic transitions forming elements of a measured spectroscopic network (SN). At the end of the MARVEL procedure, the majority of the transitions form a single, self-consistent SN component of 2954 rovibronic transitions and 1058 energy levels, 542, 403, and 58 for the X3Σ-, A3Π, and c1Π electronic states, respectively. The a1Δ electronic state is characterized by 55 Λ-doublet levels, counting each level only once. Electronic structure computations show that unusually the CCSD(T) method does not accurately predict the a1Δ excitation energy even at the complete basis set limit.

MARVEL Analysis of the Measured High-Resolution Rovibronic Spectra and Definitive Ideal-Gas Thermochemistry of the 16O2 Molecule

Accurate, empirical rovibronic energy levels, with associated uncertainties, are determined for the lowest seven electronic states of the 16O2 molecule using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm. After careful analysis and validation of 30 671 rovibronic transitions (including 24 376 measured and 6295 artificial transitions), collected from 91 publications, 4279 empirical rovibronic energy levels are determined. The highly accurate empirical (MARVEL) energy database is then augmented with rovibronic energies obtained from accurate effective Hamiltonians for the lowest six electronic states, establishing a hybrid database containing 15 946 rovibronic energy levels. Based on this hybrid database, complete up to the first dissociation limit, 41 260 cm−1, an accurate temperature-dependent ideal-gas partition function, Qint(T), and some related thermochemical functions [isobaric heat capacity, Cpo(T), entropy, So(T), and (absolute) enthalpy, Ho(T)] are derived for 16O2 employing the direct-summation technique. All thermochemical functions are reported, in 1 K increments up to 5000 K, in the supplementary material to this paper.

Marvel Analysis of the Measured High-resolution Rovibronic Spectra of 90Zr16O

Abstract Zirconium oxide (ZrO) is an important astrophysical molecule that defines the S-star classification class for cool giant stars. Accurate, empirical rovibronic energy levels, with associated labels and uncertainties, are reported for nine low-lying electronic states of the diatomic molecule. These 8088 empirical energy levels are determined using the Measured Active Rotational-Vibrational Energy Levels algorithm with 23,317 input assigned transition frequencies, 22,549 of which were validated during this study. A temperature-dependent partition function is presented alongside updated spectroscopic constants for the nine low-lying electronic states.

Synthetic spectra of BeH, BeD and BeT for emission modeling in JET plasmas

A theoretical model for isotopologues of beryllium monohydride, BeH, BeD and BeT, A to X visible and X to X infrared rovibronic spectra is presented. The MARVEL procedure is used to compute empirical rovibronic energy levels for BeH, BeD and BeT, using experimental transition data for the X , A , and C states. The energy levels from these calculations are then used in the program Duo to produce a potential energy curve for the ground state, X , and to fit an improved potential energy curve for the first excited state, A , including a spin–orbit coupling term, a Λ-doubling state to state (A–X states) coupling term, and Born–Oppenheimer breakdown terms for both curves. These, along with a previously computed ab initio dipole curve for the X and A states are used to generate vibrational-rotational wavefunctions, transition energies and A-values. From the transition energies and Einstein coefficients, accurate assigned synthetic spectra for BeH and its isotopologues are obtained at given rotational and vibrational temperatures. The BeH spectrum is compared with a high resolution hollow-cathode lamp spectrum and the BeD spectrum with high resolution spectra from JET giving effective vibrational and rotational temperatures. Full A–X and X–X line lists are given for BeH, BeD and BeT and provided as supplementary data on the ExoMol website.

Renner-Teller effects in the photoelectron spectra of CNC, CCN, and HCCN.

The line intensity of photoelectron spectra when either the neutral or cationic species display a Renner-Teller coupling is derived and applied to the modeling of the photoelectron spectra of CNC, CCN, and HCCN. The rovibronic energy levels of these three radicals and of their cations are investigated starting from ab initio results. A model treating simultaneously the bending mode and the overall rotation is developed to deal with the quasilinearity problem in CNC+, CCN+, and HCCN and accounts for the large amplitude nature of their bending mode. This model is extended to treat the Renner-Teller coupling in CNC, CCN, and HCCN+. Based on the derived photoelectron line intensity, the photoelectron spectra of all three molecules are calculated and compared to the experimental ones.

A stimulated emission study of the ground state bending levels of BH2 through the barrier to linearity and ab initio calculations of near-spectroscopic accuracy.

The ground state bending levels of 11BH2 have been studied experimentally using a combination of low-resolution emission spectroscopy and high-resolution stimulated emission pumping (SEP) measurements. The data encompass the energy range below, through, and above the calculated position of the barrier to linearity. For the bending levels (0,3,0) and above, the data show substantial K-reordering, with the Ka″ = 1 levels falling well below those with Ka″ = 0. A comparison of the high-resolution rotationally resolved SEP data to our own very high level ab initio calculations of the rovibronic energy levels shows agreement approaching near-spectroscopic accuracy (a few cm-1). The data reported in this work provide very stringent tests for future theoretical treatments of this prototypical seven-electron free radical.

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.

An experimental and theoretical study of the Ã(2)A(″)Π-X̃(2)A(') band system of the jet-cooled HBBr/DBBr free radical.

The electronic spectra of the HBBr and DBBr free radicals have been studied in depth. These species were prepared in a pulsed electric discharge jet using a precursor mixture of BBr3 vapor and H2 or D2 in high pressure argon. Transitions to the electronic excited state of the jet-cooled radicals were probed with laser-induced fluorescence and the ground state energy levels were measured from the single vibronic level emission spectra. HBBr has an extensive band system in the red which involves a linear-bent transition between the two Renner-Teller components of what would be a (2)Π state at linearity. We have used high level ab initio theory to calculate potential energy surfaces for the bent (2)A' ground state and the linear Ã(2)A(″)Π excited state and we have determined the ro-vibronic energy levels variationally, including spin orbit effects. The correspondence between the computed and experimentally observed transition frequencies, upper state level symmetries, and H and B isotope shifts was used to make reliable assignments. We have shown that the ground state barriers to linearity, which range from 10 000 cm(-1) in HBF to 2700 cm(-1) in BH2, are inversely related to the energy of the first excited (2)Σ ((2)A') electronic state. This suggests that a vibronic coupling mechanism is responsible for the nonlinear equilibrium geometries of the ground states of the HBX free radicals.

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.

An ab initio study of SbH2 and BiH2: The Renner effect, spin–orbit coupling, local mode vibrations and rovibronic energy level clustering in SbH2

We present the results of ab initio calculations for the lower electronic states of the Group 15 (pnictogen) dihydrides, SbH2 and BiH2. For each of these molecules the two lowest electronic states become degenerate at linearity and are therefore subject to the Renner effect. Spin–orbit coupling is also strong in these two heavy-element containing molecules. For the lowest two electronic states of SbH2, we construct the three dimensional potential energy surfaces and corresponding dipole moment and transition moment surfaces by multi-reference configuration interaction techniques. Including both the Renner effect and spin–orbit coupling, we calculate term values and simulate the rovibrational and rovibronic spectra of SbH2. Excellent agreement is obtained with the results of matrix isolation infrared spectroscopic studies and with gas phase electronic spectroscopic studies in absorption. For the heavier dihydride BiH2 we calculate bending potential curves and the spin–orbit coupling constant for comparison. For SbH2 we further study the local mode vibrational behavior and the formation of rovibronic energy level clusters in high angular momentum states.

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 $${\varvec{X}}$$ .