2Π State Research Articles

Low-lying [formula omitted] electronic states of BiF: Perturbative versus variational approaches of spin–orbit coupling

The low-lying Ω states of bismuth monofluoride (BiF) below 50000 cm−1 have been theoretically studied using the multi-reference configuration interaction and the equation-of-motion coupled-cluster methods, where the spin–orbit coupling (SOC) effects are respectively considered perturbatively or variationally. Since the perturbative treatment of SOC is not a good approximation for the heavy atom Bi, the latter method exhibits higher accuracy and better agreements with the experimental spectroscopic constants. Our results show that the second 3Π state of BiF is due to the occupation on the Rydberg 7s-shell of Bi, which gives rise to the so-called “triplet C” state and its sub-states reported in the early literatures. With the help of our theoretical results, some experimentally assigned spectral bands with considerable confusion have also been clarified and reassigned.

On the effective vibrational temperature of the source using (2)3∏ - X3∏ system of GeC molecule

In this work, the experimental potential energy curves for (2)3Π and X3Π electronic states of GeC molecule have been constructed by using Rydberg-Klein-Rees (RKR) method. The radiative transition parameters viz., Franck-Condon (FC) factor, r-centroid, electronic transition moment, band strength, relative band strength, Einstein coefficients, radiative lifetime and oscillator strength for the (2)3Π−X3Π system of GeC molecule have been estimated for the experimentally observed vibrational levels from Rydberg-Klein-Rees (RKR) potential and the estimated values are tabulated. The estimated effective vibrational temperature found as 5628 K for the (2)3Π−X3Π system of GeC molecule. The radiative transition parameters and effective vibrational temperature are evident that the possible presence of GeC molecule in solar and sunspots atmosphere. Further, these parameters are employed in rationalizations of astrochemical and astrophysical observations.

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+)

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 – 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.

Accurate Ab Initio Investigation of Electronic and Radiative Properties, and Cross Sections for Charged Diatomic Systems FrLi+ and FrNa.

This paper presents an extensive ab initio investigation of the electronic properties and elastic collisions of charged diatomic systems FrLi+ and FrNa+. We employ an accurate ab initio approach using nonempirical pseudopotentials for Li+, Na+, and Fr+ cores. We calculate the potential energy curves of the ground state and low-lying excited states of 2Σ+, 2Π, and 2Δ symmetries, identifying and interpreting avoided crossings between higher 2Σ+ and 2Π states. The spectroscopic parameters, transition dipole moments, and vibrational energies associated with 1-32Σ+ states are calculated, along with the radiative lifetimes of the vibrational states trapped in the 22Σ+ state. Using accurate potential energy data, we evaluate partial and total cross sections across a wide range of energies. At low energies (<1 mK), the elastic cross section follows the Wigner law threshold comportment, while at high energies, it scales as E-1/3. To the best of our knowledge, no theoretical or experimental data have been collected on these charged diatomic systems until now. Hence, we proceeded to analyze our findings by comparing them with data acquired from comparable systems. The information pertaining to electronic structures, spectroscopic parameters, transition properties, and collision data provided in this work is expected to serve as a valuable guideline for future theoretical and experimental research on each considered system.

Potential Energy Curves of the Low-Lying Five 1Σ+ and 1Π States of a CH+ Molecule Based on the Free Complement - Local Schrödinger Equation Theory and the Chemical Formula Theory.

The potential energy curves (PECs) of the low-lying five 1Σ+ and 1Π states (X1Σ+, C1Σ+, 31Σ+, A1Π, and D1Π states) of a CH+ molecule, an important interstellar molecule, were calculated by the free complement (FC) - local Schrödinger equation (LSE) theory with the direct local sampling scheme. The FC wave functions were constructed based on the chemical formula theory (CFT), whose local characters correspond to the covalent dissociations: C+(2P°(s2p))) + H(2S) of the X1Σ+ and A1Π states and the ionic dissociations: C(1D(s2p2)) + H+ of the C1Σ+ and D1Π states. All the calculated PECs were obtained with satisfying the chemical accuracy, i.e., error less than 1 kcal/mol, as absolute total energy of the Schrödinger equation without any energy shift. The spectroscopic data calculated from the PECs agreed well with both experimental and other accurate theoretical references. We also analyzed the wave functions using the inverse overlap weights proposed by Gallup et al. with the CFT configurations. For the X1Σ+ and A1Π states, the covalent C+(sp2) and C+(p3) configurations played important roles for bond formation. In the small internuclear distances of the C1Σ+, D1Π, and 31Σ+ states, the covalent character was also dominant as a result of the electron charge transfer from C to H+. Thus, the present FC-LSE results not only are accurate but also can provide chemical understanding according to the CFT.

Absorption Line Oscillator Strengths for the C 2Π(0)-A 2Σ+(0) Band of Nitric Oxide

We have determined absorption oscillator strengths for rotational transitions of the C 2Π(0)-A 2Σ+(0) band of NO, which has been detected in the upper atmosphere of Venus. The molecular quantum defect orbital method has been used in the calculation of the electronic transition moment and the Rydberg–valence interaction between the C 2Π(v = 0) and the B 2Π (v = 7) states has been considered. Considerable deviations from normal intensity distribution of the rotational lines have been found at J ≤ 5.5. As far as we know, the present line f-values are reported here for the first time. These data may be useful in the interpretation of the observations obtained by the Visible and Infrared Thermal Imaging Spectrometer instrument on the Venus Express spacecraft.

The brightness of the CO Cameron bands in the martian discrete aurora: A study based on revised cross sections

We analyze the consequences of the new laboratory measurements of the emissions cross sections of the Cameron bands excited by electron impact on CO2 and CO in the Mars aurora. We use Monte Carlo simulations to investigate the importance of these changes and their dependence on the initial electron energy. The Mars Climate Database (MCD) is used as an input for the temperature and neutral density profiles. Auroral density profiles of O2+, CO2+ and electrons in the aurora are calculated for a range of precipitating electron energies. The total nadir brightness of the Cameron bands is reduced by a factor of 4.5 at 150 eV and 5.1 at 700 eV relative to calculations made with the previously recommended cross section. The relative contributions to the production of the Cameron bands by electron collisions with CO2 and CO are examined. It varies with the CO/CO2 density ratio near the emission peak that depends on the neutral model and season. Dissociative recombination of CO2+ ions provides a contribution between 10% and 45% at the altitude of maximum production of the a 3Π state. The efficiency of the nadir brightness of the Cameron bands is 2.5–3.6 kilorayleighs per incident electron energy flux of 1 mW m−2, with a small dependence on the initial electron energy. Model simulations predict that the intensity ratio of the Cameron bands to the CO2+ UV doublet (UVD) depends on the electron initial energy. It varies from 2.0 at 500 eV to 5.3 at 50 eV, for both Ls = 90° and 225°.

Dissociation dynamics of anionic carbon monoxide in dark states.

A resonant system consisting of an excess electron and a closed-shell atom or molecule, as a temporary negative ion, is usually in doublet-spin states that are analogous to bright states of photoexcitation of the neutral. However, anionic higher-spin states, noted as dark states, are scarcely accessed. Here, we report the dissociation dynamics of CO- in dark quartet resonant states that are formed by electron attachments to electronically excited CO (a3Π). Among the dissociations to O-(2P) + C(3P), O-(2P) + C(1D), and O-(2P) + C(1S), the latter two are spin-forbidden in the quartet-spin resonant states of CO-, while the first process is preferred in 4Σ- and 4Π states. The present finding sheds new light on anionic dark states.

Electron Detachments of NbSin–/0 (n = 1–3) Clusters from Density Matrix Renormalization Group-CASPT2 Calculations

The electronic states of NbSin-/0/+ (n = 1-3) clusters have been explored using the state-of-the-art DMRG-CASPT2 method with relatively large active spaces. The leading configurations, bond distances, vibrational frequencies, and relative energies of the low-lying states were identified. Electron detachment energies of the anionic cluster and ionization energies of the neutral clusters were reported at the DMRG-CASPT2 level. The ground states of the NbSin-/0/+ (n = 1-3) clusters were predicted as the 3Δ, 4Π, and 5Π states of the linear NbSi-/0/+, the 3A2, 4B1, and 3B1 states of cyclic NbSi2-/0/+, and the 1A', 2A', and 3A″ states of tetrahedral NbSi3-/0/+ isomers. The first feature in the photoelectron spectrum of NbSi- was attributed to the transitions from the anionic 3Δ ground state to the neutral 4Π, 4Δ, and 4Φ states, whereas the second feature was assigned to the transitions to the neutral 2Δ, 2Σ+, and 2Φ states. The first band in the photoelectron spectrum of NbSi3- was ascribed to the transition from the anionic 1A' ground state to the neutral 12A' and 12A″ states; the second band was attributed to the transitions to 22A', 22A″, and 32A' states; and the third band was assigned to the transition to 32A' states.

Population of ground and lowest excited states of sulfur via the dissociative recombination of SH+ in the diffuse interstellar medium

ABSTRACT Our previous study on dissociative recombination of ground state SH+ through 2Π states of SH is extended by taking into account the contribution of 4Π states recently explored by quantum chemistry methods. Multichannel quantum defect theory is employed for the computation of cross sections and rate coefficients for dissociative recombination, but also for vibrational excitation. Furthermore, we produce the atomic yields resulting from recombination, quantifying the generation of sulfur atoms in their ground (3P) and lowest excited (1D) states, respectively.

Ultraviolet photoabsorption in the B 3Σ- − X 3Σ- and C 3Π − X 3Σ- band systems of SO sulphur isotopologues

High-resolution far-ultraviolet broadband Fourier-transform photoabsorption spectra of 32S16O, 33S16O, 34S16O, and 36S16O are recorded in a microwave discharge seeded with SO2. The and bands are observed or inferred in the –51,000 cm−1 (196 to 233 nm) spectral range. This is the first experimental detection of a level and of any of these observed bands in an S-substituted isotopologue. Additional measurements of provide a calibration of the SO column density. Measured band profiles are fitted to an effective-Hamiltonian model of coupled excited B 3Σ− and C 3Π states along with their predissociation linewidths and absorption band strengths. Electronic-state potential-energy curves and transition moments are deduced. The end result is a list of line frequencies, f-values, and dissociation widths describing the far-ultraviolet photodissociation spectrum of SO that is accurate enough for computing atmospheric photolytic isotope-fractionation. Linelists, and photoabsorption and photodissociation cross sections are available as supplementary data.

Photo-enhanced O−, H− and Br− ion production in caesium sputter negative ion source—no evidence for resonant ion pair production

It has been proposed that the negative ion yield of a caesium sputter ion source could be enhanced by promoting neutral caesium atoms to electronically excited 7p states supporting resonant ion pair production. We have tested this hypothesis by illuminating the cathode of a caesium sputter ion source with an adjustable wavelength laser and measuring its effect on the extracted beam currents of O−, H− and Br− anions. The laser exposure causes the beam currents to increase but the effect is independent of the wavelength in the range of 440–460 nm, which leads us to conclude that there is no evidence for resonant ion pair production. The photon-induced beam current enhancement scales with the applied laser power and, depending on the ion source conditions, can more than double the extracted beam current. We present a qualitative explanation for the observed effect. The model, based on photoelectron emission and subsequent increase of the caesium sputtering rate, thus liberating negative ions from the cathode, is supported by the data demonstrating that the caesium sputter ion source can produce Br− beams without thermal surface ionization as a source of Cs+ ions, i.e. in external laser-driven mode without heating the surface ionizer.

Intensities of KCs [formula omitted] band system up to dissociation threshold: an interplay between spin-orbit, hyperfine and rovibronic coupling effects

The relative intensity distribution in the rotationally resolved laser-induced fluorescence spectra belonging to the E(4)1Σ+→(a3Σ1+,X1Σ+) band systems of the KCs molecule was analyzed. The experimental intensities in doublet P,R progressions assigned to spin-allowed E→X and spin-forbidden E→a transitions up to their common ground dissociation limit were described in the framework of a coupled-channels (CC) deperturbation model applied for the interacting X1Σ+ and a3Σ+ states. The CC intensity simulation was based solely on fixed electronic structure parameters as functions of the internuclear distance R, namely: accurate empirical potential energy curves for all three states, ab initio estimates for matrix elements A(R) of the hyperfine structure (HFS), and transition dipole moments dEX(R) and dEa(R). A comparison between the measured intensities and their theoretical counterparts demonstrates a strong competition between different intramolecular interactions. A weak spin-orbit coupling of the upper E(4)1Σ+ state with the remote 3Π states is responsible for appearance of the E→a vibrational bands for the intermediate va-values. In turn, the HFS coupling between X1Σ+ and a3Σ+ states leads to peculiarities in E→(X,a) intensities, which are pronounced for high vX/a-values in the vicinity of K(42S)+Cs(62S) dissociation threshold. Both adiabatic ro-vibrational and non-adiabatic electronic-rotational interactions explain the abrupt deviation of some observed P/R intensity ratios from the expected Hönl-London factors.

Outer-valence ionization of nitrous oxide: A high-resolution electron momentum spectroscopy investigation

We report a detailed study on the outer-valence ionization of nitrous oxide (N2O) by a high-resolution (e, 2e) spectrometer employing asymmetric non-coplanar kinematics at an impact energy of 2500 eV. Binding energy spectrum in the energy region of 11–30 eV is obtained. Benefiting from the high energy resolution of 0.55 eV, four main peaks and six satellite structures are clearly identified in this region. The measured electron momentum profiles are compared with the theoretical calculations. Renner-Teller-effect induced geometry distortion is used to qualitatively interpret the observed discrepancy at low momentum between experiment and theory for B2Π state. The assignments and the pole strengths for these ionization states are determined by comparing the shape and the intensity of the experimental electron momentum profiles with those of the theoretical ones. In particular, two low-lying satellites at 21.0 eV and 27.1 eV are confirmed for the first time and attributed to the 2Π and 2Σ shake-up states. The present results show the evidence of strong electron correlation effects in the final states for the outer-valence ionization of N2O.

ExoMol molecular line lists – XLIII. Rovibronic transitions corresponding to the close-lying X 2Π and A 2Σ+ states of NaO

ABSTRACT The sodium monoxide radical (NaO) is observed in night-glow in the Earth’s mesosphere and likely has astronomical importance. This study concerns the optical transitions within the ground X 2Π state and to the very low-lying (Te ≈ 2000 cm−1) excited A 2Σ+ state. A line list consisting of rovibronic term values, allowed electric dipole transitions, Einstein coefficients, and partition functions for varying temperature are produced using a variational solution of the coupled-channel Schrödinger equations using the program duo. multi-reference configuration interaction (MRCI) ab initio calculations characterizing the potential energy curves of the two states, spin-orbit and L-uncoupling non-adiabatic matrix elements, as well as permanent and transition dipole moments were integral in the formation of the final deperturbation model. Ab initio potential energy curves are represented in the analytical Extended Morse Oscillator form and refined, along with the spin-orbit and L-uncoupling functions, by least-squares fitting to the available spectroscopic data. The input experimental data consisted of pure rotational transitions within the fine-structure components of the X 2Π state for v″ ∈ [0, 3] vibrational levels as well as the rovibronic A 2Σ+(v′ = 0) ← X 2Π(v″ = 0) transitions, both with limited coverage over rotational excitation. The lack of data detailing the vibrational structure of the X and A states points to the need for further experimental study of higher excited levels, which would provide a more robust spectroscopic model. The NaO NaOUCMe line list is available via www.exomol.com and the CDS data base.

Threshold photoelectron spectroscopy of iminoborane, HBNH.

We report the mass-selected threshold photoelectron spectrum (ms-TPES) of iminoborane (HBNH), generated by pyrolysis of borazine. The adiabatic ionization energy (IE) of the X+ 2Π ← X 1Σ+ transition was determined to be 11.31 ± 0.02 eV and the wavenumber of the B-N stretching vibration in the cation was measured to be 1550 cm-1. The Renner-Teller splitting in the X+ 2Π state gives rise to two sets of vibrational progressions, separated by 70 meV.

Characterization of the lowest electronically excited-state ro-vibrational level of 23Na87Rb

Starting from an ultracold sample of ground-state 23Na87Rb molecules, we investigate the lowest ro-vibrational level of the b 3Π state with high resolution laser spectroscopy. This electronic spin-forbidden X 1Σ+ ↔ b 3Π transition features a nearly diagonal Franck–Condon factor and has been proposed useful for probing and manipulating the ultracold molecular gas. We measure the transition strength directly by probing the ac Stark shift induced by near resonance light and determine the total excited-state spontaneous emission rate by observing the loss of molecules. From the extracted branching ratio and the theoretical modeling, we find that the leakage to the continuum of the a 3Σ+ state plays the dominant role in the total transition linewidth. Based on these results, we show that it is feasible to create optical trapping potentials for maximizing the rotational coherence with laser light tuned close to this transition.

Photoionisation of the CH radical using the B-spline R-matrix method

Aims. The primary motivation for this paper is to provide accurate data for the photoionisation of the CH radical, including the absolute total photoionisation cross-section, partial cross-sections, and photoelectron angular distribution. In addition, the near threshold features in the photoionisation curve (which are absent in previous studies) are produced with high precision. Methods. A multichannel wavefunction based on the R-matrix approach, which uses the configuration interaction (CI) method to describe electronic correlation, is carried out in the present calculations. A set of B-spline orbitals is employed to represent the accurate continuum. The distinctive feature of the present calculations allows us to generate a more accurate description of the bound and continuum states than those employed before. Results. Total photoionisation cross-sections from the ground state of CH radicals and partial cross-sections corresponding to 1π, 3σ, and 2σ states of CH+ ions are presented for photon energies ranging from threshold to 80 eV. Extensive resonance structures, which are absent in previous studies, are observed for the first time near the ionisation threshold. The cross-section dataset obtained from the present calculations is expected to be sufficiently accurate and comprehensive for most current modelling applications involving the photon and CH radical scattering system.