Rovibronic Energy 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.

Fourier-transform spectroscopy and global deperturbation treatment of the A1Σu+ and b3Πu states of K2 in the entire bound energy range.

Rotationally resolved Fourier-transform spectra of laser-induced fluorescence A1Σu+∼b3Πu→X1Σg+ of K2 molecules were recorded and analyzed, yielding 4053 term values of the spin-orbit (SO) coupled A ∼ b complex of the 39K2 isotopologue with ∼0.01 cm-1 accuracy. Their compilation with 1739 term values from previously published sources allowed them to cover the energy range [9955, 17 436] cm-1 from the bottom of the lower-lying b3Πu state up to the vicinity of the atomic asymptote 4s2S12 + 4p2P12, with a rotational quantum number J ∈ [0, 149]. The experimental data were processed by a direct 6 × 6 coupled-channel (CC) deperturbation treatment, which accounted explicitly for both SO and electronic-rotational interactions between all six e-symmetry states: A1Σu+(0u+), b3Πu(0u+,1u,2u), c3Σu(1u), and B1Πu(1u). The initial parameters of the global deperturbation model have been estimated in the framework of abinitio electronic structure calculations applying multi-reference configuration-interaction and coupled-clusters methods. The interatomic potentials analytically defined for A and b states, as well as SO-splitting of the triplet b state and A ∼ b SO-coupling functions, have been particularly refined to fit the 5792 term values of the 39K2 isotopologue, whereas the rest parameters were fixed on their abinitio values. The resulting mass-invariant parameters of the 6 × 6 CC model reproduced the overall rovibronic term energies of the A ∼ b complex of 39K2 with accuracy, which is well within the experimental errors. The quality of the deperturbation analysis was independently confirmed by comparison with the present obtained 705 and 14 term values of respective 39K41K and 41K2 isotopologues, as well as by agreement between measured and predicted relative intensity distributions in long A ∼ b → X(vX) band progressions. This deperturbation analysis provided the refined dissociation energy Tdis = 17 474.569(5) cm-1 and the long-range coefficient C3Σ = 5.501(4) × 105 cm-1 Å3 relevant to the non-relativistic atomic limit 4s + 4p. The derived Tdis yielded the accurate well depth De = 4450.910(5) cm-1 for the ground X1Σg+ state, whereas the new C3Σ value yielded the improved estimates for atomic K(4p2P12;32) radiative lifetimes, τ12 = 26.67(3) and τ32 = 26.32(3) ns.

Verification labels for rovibronic quantum-state energy uncertainties

Transition wavenumbers contained in line-by-line rovibronic databases can be compromised by errors of various nature. When left undetected, these errors may result in incorrect quantum-state energies, potentially compromising a large number of derived spectroscopic data. Spectroscopic networks treat the complete set of line-by-line spectroscopic data as a large graph, and through a least-squares refinement the measured line positions are converted into empirical quantum-state energies. Spectroscopic networks also offer a highly useful framework to develop mathematical tools helping to identify possible errors and conflicts within the dataset. For example, wavenumber errors can be detected by checking for violations of the law of energy conservation. This paper describes a new graph-theory tool, which results in so-called verification labels for the quantum states. Verification labels help to express the vulnerability of a calculated empirical energy value and its uncertainty against possible wavenumber errors, providing complementary information to simple statistical uncertainties.

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules.

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

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

ABSTRACT Comprehensive 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 – LIV. Empirical line lists for AlH and AlD and experimental emission spectroscopy of AlD in A1Π (v = 0, 1, 2)

ABSTRACT New ExoMol line lists AloHa for aluminium hydride (AlH and AlD) are presented improving the previous line lists WYLLoT. The revision is motivated by the recent experimental measurements and astrophysical findings involving the highly excited rotational states of AlH in its A 1Π − X 1Σ+ system. A new high-resolution emission spectrum of 10 bands from the A 1Π − X 1Σ+ system of AlD, in the region 17 300–32 000 cm−1 was recorded with a Fourier transform spectrometer, which probes the predissociative A 1Π v = 2 state. The AlD new line positions are combined with all available experimental data on AlH and AlD to construct a comprehensive set of empirical rovibronic energies of AlH and AlD covering the X 1Σ+ and A 1Π electronic states using the MARVEL approach. We then refine the spectroscopic model WYLLoT to our experimentally derived energies using the nuclear-motion code Duo and use this fit to produce improved line lists for 27AlH, 27AlD, and 26AlH with a better coverage of the rotationally excited states of A 1Π in the predissociative energy region. The lifetimes of the predissociative states are estimated and are included in the line list using the new ExoMol data structure, alongside the temperature-dependent continuum contribution to the photoabsorption spectra of AlH. The new line lists are shown to reproduce the experimental spectra of both AlH and AlD well, and to describe the AlH absorption in the recently reported Proxima Cen spectrum, including the strong predissociative line broadening. The line lists are included into the ExoMol data base 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.

Transition Energies and Line Oscillator Strengths of the C 2Π(0)-X 2Π(0–6) Absorption Bands of Nitric Oxide. A Theoretical Study

Theoretical absorption oscillator strengths and wavelengths for rotational transitions of the C 2Π(v′ = 0)-X 2Π(v″) bands with v″ = 0–6 of nitric oxide are reported. The Molecular Quantum Defect Orbital method has been used in the calculations and the known interaction between the C 2Π(v = 0) Rydberg and the B 2Π (v = 7) valence states has been dealt with through an appropriate rovibronic energy matrix. We hope that the reported data may be useful in the analysis of the observed ultraviolet nightglow emission from nitric oxide in the upper atmospheres of Earth, Venus, and Mars.

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 Study of the Rotational Structure of the c4′1Σu + (6)–X1Σg +(0–9) Absorption Bands of N2

Abstract We have theoretically determined the absorption oscillator strengths and wavenumbers for rotationally resolved transitions of the c4′1Σu + (6)-X1Σg +(0–9) bands of N2, which are relevant to analyze the spectra of planetary atmospheres. The Molecular Quantum Defect Orbital method has been used in our calculations. The interaction between the c4′1Σu + (6) Rydberg state and the b′1Σu + valence states has been considered using an adequate rovibronic energy matrix. In addition, we have calculated the lifetimes of the rotational levels of the c4′1Σu + (6) state. We hope that the reported data, most of them for the first time, can be useful in the interpretation of planetary atmospheres where N2 is present.

The collaboration Wolniewicz–Dressler 1976–1994

Lutoslaw Wolniewicz has spent two or three months each summer from 1976 to 1994 as guest of Kurt Dressler in Zurich to use the Computer Centre of the ETH for ab-initio calculations of rovibronic energies and transition moments in the hydrogen molecule.

Spectroscopy on the AΠ1←XΣ+1 transition of buffer-gas-cooled AlCl

Aluminum monochloride (AlCl) has been proposed as an excellent candidate for laser cooling. Here we present absorption spectroscopy measurements on the $A^1\Pi \leftarrow X^1\Sigma^+$ transition in AlCl inside a cryogenic helium buffer-gas beam cell. The high resolution absorption data enables a rigorous, quantitative comparison with our high-level ab initio calculations of the electronic and rovibronic energies, providing a comprehensive picture of the AlCl quantum structure. The combination of high resolution spectral data and theory permits the evaluation of spectroscopic constants and associated properties, like equilibrium bond length, with an order of magnitude higher precision. Based on the measured molecular equilibrium constants of the $A^1\Pi$ state, we estimate a Franck-Condon factor of the $A^1\Pi \leftarrow X^1\Sigma^+$ of 99.88%, which confirms that AlCl is amenable to laser cooling.

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.

Line Oscillator Strengths for the c4′ 1Σu +(4)–X1Σg +(0–7) Absorption Bands of N2

Abstract Theoretical absorption oscillator strengths for rotational lines of the c 4 ′ 1 Σ u + ( 4 ) – X 1 Σ g + (0–7) bands of N2, which are relevant to analyze the spectra of the atmospheres of the Earth, Titan, and Mars, are reported. The known interaction between the c 4 ′ 1 Σ u + ( 4 ) and c 3 1 Π u + ( 4 ) Rydberg states and the b ′ 1 Σ u + ( 13 ) valence state has been dealt with through an appropriate rovibronic energy matrix. Deviations in the intensity distribution of the rotational lines from considerations based on Hönl–London factors have been found for each of the studied bands. Emission branching ratios for the above bands and lifetimes of the rotational levels of the v = 4 level of the c 4 ′ 1 Σ u + state are also reported.

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.