Low-lying Doublet Research Articles

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

Static or dynamic pear shapes in radioactive nucleus 224Rn?

We report a comprehensive study on low-lying parity doublet states of 224Rn by mixing both quadrupole- and octupole-shaped configurations in multireference covariant density functional theory, in which broken symmetries in configurations are restored using projection techniques. The low-lying energy spectrum is reasonably reproduced when the shape fluctuations in both the quadrupole and octupole shapes are considered. Electric octupole transition strength in 224Rn is found to be B(E3;31-→01+)=43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B(E3; 3^-_1 \\rightarrow 0^+_1)=43$$\\end{document} W.u., comparable to that in 224Ra, whose data are 42(3) W.u.. Our results indicate that 224Rn shares similar low-energy structure with 224Ra despite the excitation energy of first 3-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3^-$$\\end{document} state of the former nucleus is higher than that of the latter. This study suggests 224Rn is a candidate for the search for permanent electric dipole moment.

A Discrete, Boron-Containing Triangular Triradical.

A neutral boron-containing triangular triradical based on a triptycene derivative has been designed and synthesized. Its structure, bonding and physical property have been studied by EPR spectroscopy, SQUID magnetometry and single crystal X-ray diffraction, as well as theoretical calculations. The triradical has a series of isosceles triangle conformations in the solution due to the Jahn-Teller distortion, leading to the splitting of the two low-lying doublet states. This factor together with negligible spin-orbit coupling (SOC) of composing light atoms quenches the spin frustration. The work represents a rare example of a neutral through-space triangular triradical.

High-Spin Blatter's Triradicals.

Robust organic triradicals with high-spin quartet ground states provide promising applications in molecular magnets, spintronics, etc. In this context, a triradical based on Blatter's radical has been synthesized recently, having two low-lying non-degenerate doublet states with a quartet ground state. The traditional broken-symmetry (BS)-DFT computed doublet-quartet energy gaps are reported to be somewhat overestimated in comparison to the experimentally observed values. In this work, we have employed different ab initio methods on this prototypical system to obtain more accurate doublet-quartet energy gaps for this triradical. The spin-constraint broken-symmetry (CBS)-DFT method has been used to reduce the overestimation of energy gaps from BS-DFT. To address the issues of spin-contamination and the multireference nature of low-spin states affecting the DFT methods, we have computed the energy gaps using appropriately state-averaged CASSCF and NEVPT2 computations. Using a series of active spaces, our calculations are shown to provide quite accurate values in concordance with the experimentally observed results. Furthermore, we have proposed and modeled another two triradicals based on Blatter's radical, which are of interest for experimental synthesis and characterization. Our computations show that all these triradicals also have a quartet ground state with a similar energy difference between the excited doublet states.

Spectroscopic Parameters of 15 Low-Lying Doublet and Quartet Λ-S States as Well as 36 Ω States of VO

Spectroscopic Parameters of 15 Low-Lying Doublet and Quartet Λ-S States as Well as 36 Ω States of VO

Photodynamics of the Molecular Ruby [Cr(ddpd)2]3.

The introduction of strong-field ligands can enable luminescence in first-row transition-metal complexes. In this way, earth-abundant near-infrared emitters can be obtained using early 3d metals. A prime example is the molecular ruby [Cr(ddpd)2]3+ (ddpd = N,N'-dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine) that can achieve high phosphorescence quantum yields at room temperature in aqueous solution. To understand these remarkable properties, here, we simulate its photodynamics in water using trajectory surface hopping on linear vibronic coupling potentials parametrized from multiconfigurational CASSCF/CASPT2 calculations. We find that after excitation to the second absorption band, a relaxation cascade through metal-centered states occurs. After an initial back-and-forth intersystem crossing with higher-lying doublet states, the complex relaxes through a manifold of quartet metal-centered states to the low-lying doublet metal-centered states which are responsible for the experimentally observed emission. These electronic processes are driven by an elongation of the Cr-ligand bond lengths as well as the twisting motion of the trans-coordinated pyridine units in the ddpd ligands. The low-lying doublet states are reached within 1-2 ps and are close in geometry to the doublet minima, thus explaining the high phosphorescence quantum yield of the molecular ruby [Cr(ddpd)2]3+.

The low-lying electronic states of VO4 and VO4 –: a computational study

Vanadium tetraoxide (VO4) has several isomers, and VO2(η2-O2) is the most stable one. The low-lying doublet states of VO2(η2-O2) and low-lying singlet states of VO2(η2-O2)− were studied using the SAC-CI theory. The electron detachment energies from the ground electronic state of VO2(η2-O2)− to the low-lying doublet states of VO2(η2-O2) were obtained. These electron detachment energies can be compared with the previous experimental photoelectron spectrum of VO4 −, and possible candidate states for the unassigned bands were found. The ground electronic states of VO2(η2-O2)/VO2(η2-O2)− and seven doublet excited states of VO2(η2-O2) were optimised. The vertical excitation spectra of VO2(η2-O2) and VO2(η2-O2)− were calculated. The lowest doublet/quartet states of VO4 and lowest singlet/triplet states of VO4 – were also computed at the BP86/aug-cc-pVTZ level. Highlights VO2(η2-O2) is the most stable isomer of VO4. The low-lying electronic states of VO2(η2-O2) and VO2(η2-O2)− were calculated using the SAC-CI theory. The unassigned bands in previous photoelectron spectrum of VO4 – were assigned, and the main structures of this spectrum can be described by the electron detachments from VO2(η2-O2)− to the low-lying doublet states of VO2(η2-O2). The computational results presented in this study were useful for the spectroscopic studies of VO4/VO4 –. Knowledge obtained in this study would be also helpful in understanding the electronic structures of MO4/MO4 – (M = Metal).

Why Are MgC3H Isomers Missing in the Interstellar Medium?

Considering the recent findings of linear doublet (2Σ+) MgCnH isomers (n = 2, 4, and 6) in the evolved carbon star IRC+10216, various structural isomers of MgC3H and MgC3H+ are theoretically investigated here. For MgC3H, 11 doublet and 8 quartet stationary points ranging from 0.0 to 71.8 and 0.0 to 110.1 kcal mol–1, respectively, have been identified initially at the UωB97XD/6-311++G(2d,2p) level. To get accurate relative energies, further energy evaluations are carried out for all isomers with coupled cluster methods and thermochemical modules such as G3//B3LYP, G4MP2, and CBS-QB3 methods. Unlike the even series, where the global minima are linear molecules with a Mg atom at one end, in the case of MgC3H, the global minimum geometry turns out to be a cyclic isomer, 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1, C2v, 2A1). In addition, five low-lying isomers, magnesium-substituted cyclopropenylidene (2, Cs, 2A′), 1-magnesabut-2,3-dien-1-yl-4-ylidene (3, Cs, 2A″), 1-magnesabut-2-yn-1-yl-4-ylidene (4, Cs, 2A″), 2λ3-magnesabicyclo[1.1.0]but-1,3-diyl-4-ylidene (5, C2v;, 2A1), and 1-magnesabut-2,3-dien-2-yl-4-ylidene (6, C∞v, 2Σ+), were also identified. The doublet linear isomer of MgC3H, 1-magnesabutatrienyl (10, C∞v, 2Σ+) turns out to be a minimum but lies 54.1 kcal mol–1 above 1 at the ROCCSD(T)/cc-pVTZ level. The quartet (4Σ+) electronic state of 10 was also found to be a minimum, but it lies 8.0 kcal mol–1 above 1 at the same level. Among quartets, isomer 10 is the most stable molecule. The next quartet electronic state (of isomer 11) is 34.4 kcal mol–1 above 10, and all other quartet electronic states of other isomers are not energetically close to low-lying doublet isomers 2 to 6. Overall, the chemical space of MgC3H contains more cyclic isomers (1, 2, and 3) on the low-energy side unlike their even-numbered MgCnH counterparts (n = 2, 4, and 6). Though the quartet electronic state of 10 is linear, it is not the global minimum geometry on the MgC3H potential energy surface. Isomerization pathways among the low-lying isomers (doublets of 1–4 and a quartet of 10) reveal that these molecules are kinetically stable. For the cation, MgC3H+, the cyclic isomers (1+, 2+, and 3+) are on the low-energy side. The singlet linear isomer, 10+, is a fourth-order saddle point. The low-lying cations are quite polar, with dipole moment values of >7.00 D. The current theoretical data would be helpful to both laboratory astrophysicists and radioastronomers for further studies on the MgC3H0/+ isomers.

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.

The low-lying electronic states of YO2− and YO2: A computational study

• The vertical excitation spectra of YO 2 – and YO 2 were calculated. • Several bound anionic states of YO 2 – were found. • Electron detachment energies to low-lying doublet states of YO 2 were obtained. The low-lying electronic states of YO 2 − and YO 2 were studied using the SAC-CI theory. The vertical excitation spectra of YO 2 − and YO 2 were calculated. For YO 2 − , the X 1 A 1 state, five valence-bound singlet–triplet pair states (2 1 A 1 /1 3 A 1 , 1 1 A 2 /1 3 A 2 , 1 1 B 1 /1 3 B 1 , 1 1 B 2 /1 3 B 2 , and 2 1 B 2 /2 3 B 2 ), and one dipole-bound singlet–triplet pair states ( 1 B 2 (DB)/ 3 B 2 (DB)) were investigated. For YO 2 , the X 2 B 2 , 1 2 A 1 /2 2 A', 2 2 A 1 , 1 2 A 2 , 1 2 B 1 /1 2 A“, and 2 2 B 2 states were studied. The geometries of these anionic and neutral states were optimized. The adiabatic electron detachment energies from the anionic states to the neutral states can be obtained from these computed results. The vertical electron detachment energies from the X 1 A 1 state of YO 2 − to the low-lying doublet states of YO 2 were calculated and compared with previous experimental photoelectron spectra. Density functional theories (B3LYP, BPW91, and BP86) were also employed to compute the low-lying electronic states of YO 2 – and YO 2 for comparison.

A computational study of the non-adiabatic coupling among low-lying doublet states of the CN radical

First principle electronic structure calculations on low-lying doublet states of the CN radical have been performed using the multi-reference configuration interaction method and large all-electron basis sets. Beside the adiabatic interatomic potentials, the non-adiabatic spin-orbit and L-uncoupling electronic matrix elements were evaluated for the mutually perturbed (2)B2Σ+∼(1–4)2Π and (1)A2Π∼(1–3)2Σ+, (1)2Σ−, (1,2)2Δ pairs of states. The radial coupling matrix element was calculated between the X2Σ+ and B2Σ+ states. The reliability of the derived A∼X and A∼B matrix elements was confirmed by comparison with their empirical counterparts. Both local and regular perturbations in the A∼B∼X complex were found to depend mostly on spin-orbit and electronic-rotational interactions between the lowest A2Π, and B2Σ+ states. Excited states, in all their diversity, have little effect on the fine structure of the A∼B complex, except for the qA Λ-doubling function. The ab initio coupling functions can be crucial to providing a global deperturbation treatment for the A, B and X states on a spectroscopic level of accuracy.

Radiative association of atomic and ionic nitrogen

ABSTRACT Radiative association for the formation of molecular nitrogen cation ${\rm{N}}_2^ + $ during the collision of an N(4Su) atom and an N+(3Pg) ion is investigated. The corresponding cross-sections and rate coefficients are computed by the quantum mechanical method based on ab initio potential energy curves and transition dipole moments, which are obtained by the internally contracted multireference configuration interaction method with the Davidson correction and aug-cc-pCV5Z-DK basis set. A number of low-lying doublet, quartet, and sextet states correlating to the N(4Su) + N+(3Pg) dissociation limit are considered. Hence, we investigate a number of dipole-allowed transitions and determine their contributions to the radiative association. The results show that transitions originating in the f4Πu, D2Πg, ${{\rm{B}}^2}\Sigma _{\rm{u}}^ + $, ${{\rm{1}}^4}\Sigma _{\rm{g}}^{\rm{ + }}$, and ${{\rm{1}}^6}\Sigma _{\rm{u}}^{\rm{ + }}$states are the main contributors for the radiative association process. The calculated rate coefficients are valid for temperatures from 100 to 10 000 K and fitted to the analytical function suitable for astrochemical reaction applications.

Theoretical study of the low-lying doublet and quartet electronic states of 7Li16O molecule including spin-orbit coupling effect and a new limit to the adiabatic ionization energy

Abstract The potential energy curves of 7Li16O molecule for energies below 50,000 cm−1 have been investigated. All doublet and quartet electronic states considered here are studied at the CASSCF/icMRCI(Q) level of theory associated with the aug-cc-pV5Z basis set. Within this range of energies, analytical representations are proposed. To evaluate the accuracy of these functional forms, a novel set of spectroscopic parameters have been derived. Transition probability parameters as the Franck–Condon factors and Einstein A coefficients of certain vibronic emissions from the A 2 Σ + - X 2 Π , 2 2 Π - X 2 Π , and 2 2 Π - A 2 Σ + band systems are reported. It was found that rotationless radiative lifetimes of the order of milliseconds are determined for A-X and C-X bands. Overall, our results transition probabilities suggest that these vibronic emissions are weak and, therefore, difficult to measure in spectroscopy experiments. Additionally, we obtained an adiabatic ionization energy value of 68,002 cm−1.

Multipolar magnetism in d -orbital systems: Crystal field levels, octupolar order, and orbital loop currents

Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J\!=\!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($\mu$SR) experiments on cubic $5d^2$ osmate double perovskites Ba$_2$ZnOsO$_6$, Ba$_2$CaOsO$_6$, and Ba$_2$MgOsO$_6$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J\!=\!2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate Ba$_2$YReO$_6$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.

Multireference study of ionic/covalent electronic states of MF (M=Be, Mg and Ca).

Ultracold environments composed by atoms or molecules offer an opportunity to study chemical reactions at the quantum-state level, for simulation of solid-state systems, as qubits in quantum computing, and for test fundamental symmetries. Those ultracold conditions formed by molecules can be obtained from cryogenic buffer gas, via supersonic expansion, followed by deceleration or from the laser cooling process. Diatomic alkaline earth monofluoride molecules have been shown as great candidates for the laser cooling process. In this sense, the present work focuses on the characterization of the low-lying doublet electronic states correlated to the first dissociation channel of the alkaline earth monofluorides diatomic molecules MF (M=Be, Mg and Ca). The developed state-of-the-art methodology was based on a qualitative analysis of the diatomic electronic structure, employing a hypothetical potential energy curve or by a simple molecular orbital diagram combined with bond order analysis. The potential energy curves, excitation and dissociation energies, and various sets of spectroscopic parameters were calculated by the MRCI/cc-pV5Z methodology. Transition probabilities for emission and radiative lifetimes among the characterized electronic states were also calculated for the (A)2Π⟶(X)2Σ+ electronic transition. Comparing the spectroscopy properties, we were able to indicate the CaF molecule as the best candidate molecule for laser cooling devices among the studied molecules.

A Barrierless Pathway Accessing the C9H9 and C9H8 Potential Energy Surfaces via the Elementary Reaction of Benzene with 1-Propynyl

The crossed molecular beams reactions of the 1-propynyl radical (CH3CC; X2A1) with benzene (C6H6; X1A1g) and D6-benzene (C6D6; X1A1g) were conducted to explore the formation of C9H8 isomers under single-collision conditions. The underlying reaction mechanisms were unravelled through the combination of the experimental data with electronic structure and statistical RRKM calculations. These data suggest the formation of 1-phenyl-1-propyne (C6H5CCCH3) via the barrierless addition of 1-propynyl to benzene forming a low-lying doublet C9H9 intermediate that dissociates by hydrogen atom emission via a tight transition state. In accordance with our experiments, RRKM calculations predict that the thermodynamically most stable isomer – the polycyclic aromatic hydrocarbon (PAH) indene – is not formed via this reaction. With all barriers lying below the energy of the reactants, this reaction is viable in the cold interstellar medium where several methyl-substituted molecules have been detected. Its underlying mechanism therefore advances our understanding of how methyl-substituted hydrocarbons can be formed under extreme conditions such as those found in the molecular cloud TMC-1. Implications for the chemistry of the 1-propynyl radical in astrophysical environments are also discussed.

Radiative Association of Atomic and Ionic Carbon

Abstract We present calculated cross sections and rate coefficients for the formation of the dicarbon cation ( ) by the radiative association process in collisions of a atom and a ion. Molecular structure calculations for a number of low-lying doublet and quartet states of are used to obtain the potential energy surfaces and transition dipole moments coupling the states of interest, substantially increasing the available molecular data for . Using a quantum-mechanical method, we explore a number of allowed transitions and determine those contributing to the radiative association process. The calculations extend the available data for this process down to the temperature of 100 K, where the rate coefficient is found to be about . We provide analytical fits suitable for incorporation into astrochemical reaction databases.

The low-lying electronic states of HfO2− and HfO2: A symmetry adapted cluster–configuration interaction (SAC-CI) study

The low-lying doublet states of the HfO2− anion and low-lying triplet excited states of the HfO2 molecule were studied using the SAC-CI method. The vertical excitation spectrum of HfO2− was calculated. Four valence-bound states (X2A1, 12B1, 22A1, and 12B2(II)) and one dipole-bound state (2A1(DB)) of HfO2− were found. The vertical electron detachment energies (VDEs) from the ground electronic state of HfO2− to the triplet excited states of HfO2 were obtained. These VDEs were compared with previous photoelectron spectra of HfO2−, and possible candidate states for the unassigned bands were found. The equilibrium geometries of the valence-bound states of HfO2− and some selected triplet excited states of HfO2 were optimized. The adiabatic relative energies of these electronic states were obtained. Density functional theory (BPW91) was also applied to compute some electronic states of HfO2− and HfO2 for comparison.

Electronic structure with dipole moment calculations of the high-lying electronic states of BeH, MgH and SrH molecules

By using the complete active space self consistent field (CASSCF) with multi-reference configuration interaction MRCI + Q method including single and double excitations with Davidson correction, the 26, 27 and 25 low-lying doublet and quartet electronic states in the representation 2s+1Λ(+/−) (without spin orbit interaction) of the molecules BeH, MgH and SrH have been investigated. The potential energy curves, the internuclear distance Re, the harmonic frequency ωe, the permanent dipole moment μ, the rotational constant Be and the electronic transition energy with respect to the ground state Te are calculated. Using the canonical approach the eigenvalue Ev, the rotational constant Bv and the abscissas of the turning points Rmin and Rmax have been calculated for the investigated electronic states. The comparison between the values of the present work and those available in the literature for several electronic states shows very good agreement.

Detection of Indistinct Fe-N Stretching Bands in Iron(V) Nitrides by Photodissociation Spectroscopy.

We report for the first time infrared spectra of three non-heme pseudo-octahedral iron(V) nitride complexes with assigned Fe-N stretching vibrations. The intensities of the Fe-N bands in two of the complexes are extremely weak. Their detection was enabled by the high resolution and sensitivity of the experiments performed at 3 K for isolated complexes in the gas phase. Multireference CASPT2 calculations revealed that the Fe-N bond in the ground doublet state is influenced by two low-lying excited doublet states. In particular, configuration interaction between the ground and the second excited state leads to avoided crossing of their potential energy surfaces along the Fe-N coordinate, which thus affects the ground-state Fe-N stretching frequency and intensity. Therefore, DFT calculated Fe-N stretching frequency strongly depends on the amount of Hartree-Fock exchange potential. As a result, by tuning the amount of Hartree-Fock exchange potential in the B3LYP functional, it was possible to obtain theoretical spectra perfectly consistent with the experimental data. The theory shows that the intensity of the Fe-N stretching vibration can almost vanish due to strong coupling with other stretching modes of the ligands.