Dunham Parameters Research Articles

A comparative study of analytical representations of potential energy curves for CO in its ground electronic state

AbstractIn this work, a comparative study of four functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Hulburt‐Hirschfelder, followed by the Extended Rydberg potential function, ending with two of the most recent potentials presented in the literature for diatomic systems: the Araújo‐Ballester potential and the Improved Extended Lennard‐Jones potential. The chosen potentials have in common the fact that all their parameters are algebraically calculated, without any fitting procedure, and all of them have direct dependence on Dunham's parameters. The mathematical behavior of these functions for the short‐ and long‐range regions is discussed. As study case, the diatomic system in its ground electronic state was selected. To quantify the accuracy of the potential energy functions, the least‐squares Z‐test method, proposed by Murrell and Sorbie, is used. Furthermore, the main spectroscopic constants and vibrational energy levels are calculated and compared for all potentials.

High resolution spectroscopy of [formula omitted] transitions in 130Te2: Reference lines spanning the 443.2–451.4 nm region

Molecular tellurium (130Te2) has long been regarded as a promising candidate for a variety of spectroscopic applications, especially as a frequency reference. Absorption lines of 130Te2 were published extensively in the past few decades, however, the spectral resolution was not sufficiently high to be considered a precision spectroscopic reference. Here, a high resolution spectral atlas of 130Te2 Doppler-free saturated absorption transitions is reported, and used to assign multiple ro-vibrational bands in the B(Σu-3)0u+←X(Σu-3)0g+ electronic transition via the Dunham model, giving updated Dunham parameters and diatomic constants for the B(Σu-3)0u+ state at an unprecedented level of precision. Our findings reveal spectroscopic properties of 130Te2 that might eventually contribute to frequency reference in precision measurement such as the quest for non-zero electron’s Electric Dipole Moment (eEDM).

High-resolution FT-VIS emission spectroscopy of the [formula omitted] system of AlH

An extensive high-resolution visible wavelength emission spectrum of AlH, that covers eight bands of the A1Π−X1Σ+ system, has been observed with a Fourier-transform spectrometer for the first time. The 0−0,1,2 and 1−0,1,2,3,4 bands were recorded with an instrumental resolution of 0.03 cm−1. The best signal-to-noise ratio of 9000:1 was obtained for the strongest 0−0 band. In total, 259 ro-vibronic frequencies were measured with an absolute accuracy of about 0.0020 cm−1. The experimental data were fitted using the PGOPHER program written by Western (2017). Molecular constants were derived for the X1Σ+, ν=0−4 and A1Π, ν=0,1 levels. Also derived were rotational term values for the A1Π, ν=0,1 levels. The current data were combined with the previous ground state results of White et al. (1993) using the instruction called the constraints on parameters within PGOPHER. The Dunham parameters (Ykl) for the A1Π state of AlH were determined for the first time. A very small shifts of the A1Π, ν=0,J=17 and ν=1,J=5 levels have been observed and identified as result of the possible interaction between A1Π and 3Σ+ states.

High resolution spectroscopic measurement of 130Te2: Reference lines near 444.4 nm for eEDM experiment using PbF molecules

Molecular tellurium (Te2) offers a wide range of potential applications, including frequency reference. Spectroscopic results about the 130Te2 spectrum were previously reported, but few lines lie around the PbF transition of A (2Σ+) (υ′ = 0) ← X12Π1/2 (υ = 0) (∼444.4 nm) which is regarded as an eEDM (electron’s Electric Dipole Moment) sensitive transition. Here electronic transition lines for 130Te2 were determined using the Saturated Absorption Spectroscopy method, where the origin of the transition band was investigated for the B1 (3Σu-)0u+ (υ′ = 10) ← X1 (3Σg-)0g+ (υ = 5) transition. The Dunham model with high orders was utilized to assign these transition lines, while Dunham parameters of the excited state B1 (υ′ = 10) were updated to a new level. The Toptica TA-SHG Pro laser was then locked to a single absorption line using a P-I servo. Our results here not only provide the assigned atlas of Te2 spectrum near 444.4 nm, but also contribute to a stable and sensitive spectroscopic detection of PbF molecules toward the eEDM measurement, which is significant in understanding the fundamental physics beyond the Standard Model.

Time-resolved Fourier transform infrared emission spectroscopy of CO ∆v = 1 and ∆v = 2 extended bands in the ground X1Σ+ state produced by formamide glow discharge

This paper presents an extension to our knowledge of ∆v = 1 and ∆v = 2 bands of carbon monoxide in the ground state, measured by Fourier transform infrared spectroscopy of glow discharge of formamide-nitrogen mixture. Lines in declared bands are measured up to v = 30 for ∆v = 1 and up to v = 24 for ∆v = 2 band, by use of both InSb and MCT detectors, which have not been measured in the laboratory before. Dunham parameters obtained by fitting our lines are presented as well as comparison to other authors. The paper also demonstrates the interesting impossibility of sufficient population of ∆v = 2 band of CO when only pure CO is used in the glow discharge, instead of formamide-based mixture. Additionally, we present a non-LTE model to describe the intensity pattern of the ∆v = 1 and the ∆v = 2 bands of 12C16O experimental spectra by simulating the corresponding non-LTE vibrational populations of CO.

Higher vibrational levels of the [formula omitted] state of dicarbon: New Mulliken bands

The Δv=+2 sequence of the Mulliken system of C2 is reported for the first time. Seven new levels of the D1Σu+ state of C2, v=5 through v=11, were found. The analysis reveals the rotational constants and origin of each band. The numbers are combined with the data reported for previously reported levels, v=0 through v=4, to generate updated Dunham parameters for the D1Σu+ state: ωe=1829.905(57) cm−1, ωexe=14.089(8) cm−1, ωeye=0 cm−1, ωeze=0.00124(3) cm−1, Be=1.83254(46) cm−1, αe=0.01909(18) cm−1and βe=-7.28(14)×10-5 cm−1. The determined equilibrium bond length Re=1.23804(28) Å. The fluorescence lifetimes of the new levels are also reported.

High-Resolution Rotational Spectrum, Dunham Coefficients, and Potential Energy Function of NaCl.

We report laboratory spectroscopy for the first time of the J = 1-0 and J = 2-1 lines of Na35Cl and Na37Cl in several vibrational states. The hyperfine structure has been resolved in both transitions for all vibrational levels, which permit us to predict with high accuracy the hyperfine splitting of the rotational transitions of the two isotopologues at higher frequencies. The new data have been merged with all previous works at microwave, millimeter, and infrared wavelengths and fitted to a series of mass-independent Dunham parameters and to a potential energy function. The obtained parameters have been used to compute a new dipole moment function, from which the dipole moment for infrared transitions up to Δv = 8 has been derived. Frequency and intensity predictions are provided for all rovibrational transitions up to J = 150 and v = 8, from which the ALMA data of evolved stars can be modeled and interpreted.

Study of infrared emission spectroscopy for the B(1)Δg-A(1)Πu and B'(1)Σg(+)-A(1)Πu systems of C2.

Thirteen bands for the B(1)Δg-A(1)Πu system and eleven bands for the B'(1)Σg(+)-A(1)Πu system of C2 were identified in the Fourier transform infrared emission spectra of hydrocarbon discharges. The B'(1)Σg(+)v = 4 and the B(1)Δg v = 6, 7, and 8 vibrational levels involved in nine bands were studied for the first time. A direct global analysis with Dunham parameters was carried out satisfactorily for the B(1)Δg-A(1)Πu system except for a small perturbation in the B(1)Δg v = 6 level. The calculated rovibrational term energies up to B(1)Δg v = 12 showed that the level crossing between the B(1)Δg and d(3)Πg states is responsible for many of the prominent perturbations in the Swan system observed previously. Nineteen forbidden transitions of the B(1)Δg-a(3)Πu transition were identified and the off-diagonal spin-orbit interaction constant AdB between d(3)Πg and B(1)Δg was derived as 8.3(1) cm(-1). For the B'(1)Σg(+)-A(1)Πu system, only individual band analyses for each vibrational level in the B'(1)Σg(+) state could be done satisfactorily and Dunham parameters obtained from these effective parameters showed that the anharmonic vibrational constant ωexe is anomalously small (nearly zero). Inspection of the RKR (Rydberg-Klein-Rees) potential curves for the B'(1)Σg(+) and X(1)Σg(+) states revealed that an avoided crossing or nearly avoided crossing may occur around 30,000 cm(-1), which is responsible for the anomalous molecular constants in these two states.

The rotational spectra, potential function, Born–Oppenheimer breakdown, and hyperfine structure of GeSe and GeTe

The pure rotational spectra of 18 and 21 isotopic species of GeSe and GeTe have been measured in the frequency range 5-24 GHz using a Fabry-Pérot-type resonator pulsed-jet Fourier-transform microwave spectrometer. Gaseous samples of both chalcogenides were prepared by a combined dc discharge/laser ablation technique and stabilized in supersonic jets of Ne. Global multi-isotopologue analyses of the derived rotational data, together with literature high-resolution infrared data, produced very precise Dunham parameters, as well as rotational constant Born-Oppenheimer breakdown (BOB) coefficients (δ(01)) for Ge, Se, and Te. A direct fit of the same datasets to an appropriate radial Hamiltonian yielded analytic potential-energy functions and BOB radial functions for the X(1)Σ(+) electronic state of both GeSe and GeTe. Additionally, the electric quadrupole and magnetic hyperfine interactions produced by the nuclei (73)Ge, (77)Se, and (125)Te were observed, yielding much improved quadrupole coupling constants and first determinations of the spin-rotation parameters.

Rotational spectra of 34S- and 33S-containing isotopologues of laser ablation generated tin monosulfide

Abstract Using a newly constructed source, tin monosulfide is produced by the reaction between carbonyl sulfide and the products resulting from the ablation of tin metal by the pulsed output of a frequency-doubled Nd:YAG laser ( λ = 532 nm). Entrained in argon carrier gas, SnS is introduced into the cavity of a Balle–Flygare Fourier transform microwave spectrometer that has a frequency range encompassing the two lowest rotational transitions ( J = 1 − 0 and 2 − 1) for this molecule. Except for 115 Sn 34 S, spectra are obtained in natural abundance for all 34 S-containing isotopologues with naturally occurring tin isotopes. Additionally, spectra were obtained for the rare isotopologues, 115 Sn 32 S and 120 Sn 33 S. Resolution of the hyperfine structure in the latter species allows a more precise determination of its 33 S nuclear quadrupole coupling constant. Spectra for all species containing 34 S are analyzed in terms of mass-independent Dunham parameters and are combined with all available isotopologues to determine Born–Oppenheimer breakdown terms for both tin and sulfur.

Frequency measurement of pure rotational transitions of OD −

Frequencies of pure rotational transitions of OD − have been measured in the 1–5 THz region using a high-precision tunable far-infrared spectrometer based on difference frequency of two CO 2 lasers. The measured frequencies were analyzed together with the data in the infrared and the sub-millimeter region to refine the rotational parameters. Isotopically invariant Dunham parameters were also obtained.

Rotational spectra, potential function, Born–Oppenheimer breakdown and magnetic shielding of SiSe and SiTe

The pure rotational spectra of 18 isotopic species of SiSe (8) and SiTe (10) have been measured in their X 1Σ + electronic state with a pulsed-jet resonator Fourier transform microwave spectrometer. The molecules were prepared by a combined DC discharge/laser ablation technique and stabilised in a supersonic jet of Ar. Global multi-isotopologue analyses yielded spectroscopic Dunham parameters Y 01, Y 11, Y 21, Y 31 and Y 02 for both species, as well as effective Born–Oppenheimer breakdown (BOB) coefficients δ 01 for Si, Se and Te. A direct fit of the same data sets to an appropriate radial Hamiltonian yielded analytic potential energy functions and BOB radial functions for the X 1Σ + electronic state of both SiSe and SiTe. Additionally, the magnetic hyperfine interactions produced by the uneven mass number A nuclei 29Si, 77Se and 125Te were observed, yielding first determinations of the corresponding nuclear spin–rotation coupling constants.

Pure rotational spectra of PbSe and PbTe: potential function, Born–Oppenheimer breakdown, field shift effect and magnetic shielding

The pure rotational spectra of 41 isotopic species of PbSe and PbTe have been measured in their X 1Sigma+ electronic state with a resonator pulsed-jet Fourier transform microwave spectrometer. The molecules were prepared by laser ablation of suitable target rods and stabilised in supersonic jets of noble gas. Global multi-isotopologue analyses yielded spectroscopic Dunham parameters Y01, Y11, Y21, Y31, Y02, and Y12 for both species, as well as effective Born-Oppenheimer breakdown (BOB) coefficients delta01 for Pb, Se and Te. Unusual large values of the BOB parameters for Pb have been rationalized in terms of finite nuclear size (field shift) effect. A direct fit of the same data sets to an appropriate radial Hamiltonian yielded analytic potential energy functions and BOB radial functions for the X 1Sigma+ electronic state of both PbSe and PbTe. Additionally, the magnetic hyperfine interactions produced by the uneven mass number A nuclei 207Pb, 77Se, 123Te, and 125Te were observed, yielding first determinations of the corresponding nuclear spin-rotation coupling constants.

The rotational spectra, potential function, Born-Oppenheimer breakdown, and magnetic shielding of SnSe and SnTe

The pure rotational spectra of 27 isotopic species of SnSe and SnTe have been measured in the frequency range of 5-24 GHz using a Fabry-Perot-type resonator pulsed-jet Fourier-transform microwave spectrometer. Gaseous samples of both chalcogenides were prepared by laser ablation of suitable target rods and were stabilized in supersonic jets of Ar. Global multi-isotopolog analyses of all available high-resolution data produced spectroscopic Dunham parameters Y01, Y11, Y21, Y31, Y02, and Y12 for both species, as well as Born-Oppenheimer breakdown (BOB) coefficients delta01 for Sn, Se, and Te. A direct fit of the same data sets to an appropriate radial Hamiltonian yielded analytic potential energy functions and BOB radial functions for the X 1Sigma+ electronic state of both SnSe and SnTe. Additionally, the magnetic hyperfine interaction produced by the dipolar nuclei 119Sn, 117Sn, 77Se, and 125Te was observed, yielding first determinations of the corresponding spin-rotation coupling constants.

Direct observation of the D′ 2 g( 3P2)– A′ 3Π(2 u) system for Cl 2 by laser induced fluorescence spectroscopy: Determination of the absolute position of the A′ state

In a discharged supersonic jet of Cl 2, transitions of the D′ 2 g ( 3 P 2)– A′ 3Π(2 u ) system for 35Cl 2 were observed directly by laser induced fluorescence spectroscopy. By a discharge in Cl 2, the Cl 2 molecules were populated into the A′ state, which is a metastable and optically forbidden state, from the X 1 Σ g + ( 0 g + ) state. An ultraviolet laser radiation excites the molecules to the D′ ion-pair state. A set of Dunham parameters for the A′ state is determined from a global least-squares fitting for 59 vibronic bands with v″ = 0–7. In the fitting, the previously reported data, T( v) and B( v) for the v = 14 and 15 bands of the A′ state [T. Ishiwata, A. Ishiguro, K. Obi, J. Mol. Spectrosc. 147 (1991) 300–320], were included. Y 00 = 57295.723(5) cm −1 of the D′ state [J.-H. Si, T. Ishiwata, K. Obi, J. Mol. Spectrosc. 147 (1991) 334–345] was also included in the global fitting in order to determine the absolute position of the A′ state. The determined parameters of the A′ state are Y 00 = 17171.506(14), Y 10 = 255.915(85), Y 20 = −4.465(70), Y 30 = −8.7(23) × 10 −2, Y 40 = 6.3(35) × 10 −3, Y 50 = −4.9(26) × 10 −4, Y 60 = 1.43(69) × 10 −5, Y 01 = 0.16282(15), Y 11 = −2.363(68) × 10 −3, Y 21 = −5.01(93) × 10 −5, and Y 31 = −3.01(36) × 10 −6 (in cm −1 and one standard deviations of the fit in parentheses). The absolute position of the A′ state is determined with good accuracy.

Electronic spectroscopy of the [formula omitted] system of CDCl

We report fluorescence excitation and single vibronic level emission spectra of the A ˜ 1 A ″ ↔ X ˜ 1 A ′ system of CDCl in the 500–740 nm region, measured under jet-cooled conditions using a pulsed discharge source. A total of 29 cold bands involving the pure bending levels 2 0 n ( n = 2–11), C–D stretching fundamental ( 1 0 1 ), and combination bands 2 0 n 3 0 1 ( n = 2–10), 2 0 n 3 0 2 ( n = 9), 1 0 1 2 0 n ( n = 2–8), and 1 0 1 2 0 n 3 0 1 ( n = 7) were observed; most of these are reported here for the first time. Rotational analysis typically yielded band origins and rotational constants for both isotopomers (CD 35Cl, CD 37Cl). The derived A ˜ 1 A ″ vibrational intervals are combined with previous studies at lower energy to determine excited state barriers to linearity for the 2 n , 2 n 3 1, and 1 12 n progressions. The A ˜ 1 A ″ state C–D stretching frequency (2229.6 cm −1) is determined here for the first time, in excellent agreement with ab initio theory. Following our observation of new bands in this system, we obtained single vibronic level (SVL) emission spectra which probe the vibrational structure of the X ˜ 1 A ′ state up to ∼8000 cm −1 above the vibrationless level. The total number of X ˜ 1 A ′ and a ˜ 3 A ″ levels observed is more than twice that previously reported, and a complete set of Dunham parameters was determined for the X ˜ 1 A ′ state of CD 35Cl and CD 37Cl. Comparisons with previous experimental and recent high level ab initio studies are reported. Our results shed new light on the vibrational structure of the X ˜ 1 A ′ , A ˜ 1 A ″ , and a ˜ 3 A ″ states of CDCl, and, more generally, spin–orbit coupling in the monohalocarbenes.

The pure rotational spectrum of TeSe: Rotational parameters, Born–Oppenheimer breakdown corrections, and hyperfine constants

The characterization of tellurium selenide in its electronic ground state (X0 + ∑ − ) was possible by using LASER-ablation to isolate the diatomic in a pulsed molecular beam and by applying Fourier transform microwave spectroscopy to obtain the pure rotational spectrum. Employing a global multi-isotopologue analysis to transitions of 43 isotopologues of TeSe in seven vibrational states spectroscopic Dunham parameters Y ℓ , m , Born–Oppenheimer breakdown coefficients δ ℓ , m , the equilibrium bond lengths r e, as well as the vibration parameters ω e and ω e x e were obtained for all analysed isotopologues. For low vibrational states, the Morse-potential function describes the TeSe-potential very well and provides an estimate of the maximum dissociation energy for this semi-metal compound. In addition, the isotopologue independent molecular constants U ℓ , m and the corresponding Born–Oppenheimer breakdown coefficients Δ ℓ , m were determined. Quite large coefficients Δ 0 , 1 Te and Δ 0 , 1 Se were necessary for Watson's reference isotopologue independent analysis. This is rationalized by the interaction between the two sublevels of the electronic 3Σ-state. Also the magnetic spin–rotation coupling constants that were achieved for some of the isotopologues reflect this electronic ground state. Field shift effects are found to be negligible.

Probing spin–orbit mixing and the singlet–triplet gap in dichloromethylene via Ka-sorted emission spectra

The magnitude of the singlet-triplet gap in dichloromethylene (CCl(2)) has been a point of controversy in the recent literature. In this study, we report single vibronic level emission spectra of the A(1)B(1)-->X[combining tilde](1)A(1) system of the carbene C(35)Cl(2), which probes the vibrational structure of the X[combining tilde](1)A(1) state up to approximately 10,000 cm(-1) above the vibrationless level. By the careful selection of bands where complete isotope and K(a)' selectivity in excitation was possible, we measured K(a)'-sorted emission spectra in order to test the previously established hypothesis [M.-L. Liu, C.-L. Lee, A. Bezant, G. Tarczay, R. J. Clark, T. A. Miller and B.-C. Chang, Phys. Chem. Chem. Phys., 2003, 5, 1352] that unassigned lines lying above approximately 5,000 cm(-1) belong to levels of the ã(3)B(1) state. The K(a)'-sorting method discriminates between singlet and triplet levels via the (A''-B[combining macron]'') rotational constant, which is significantly larger for pure triplet levels due to the larger equilibrium bond angle. In the region between 3,500 and 9,000 cm(-1) above the vibrationless level of the X[combining tilde](1)A(1) state, we find only a very modest increase in (A''-B[combining macron]''), and approximately 86% of the lines observed between 5,000 and 9,000 cm(-1) can be assigned to X[combining tilde](1)A(1) levels within 3 standard deviations of our Dunham expansion fit, which included more than 140 levels in total. A nearly complete set of Dunham parameters was determined for the C(35)Cl(2) isotopomer, and the X[combining tilde](1)A(1) state term energies up to 4,000 cm(-1) are in excellent agreement with recent variational calculations of Tarczay, et al. [G. Tarczay, T. A. Miller, G, Czakó and A. G. Császár, Phys. Chem. Chem. Phys., 2005, 7, 2881]. Finally, the implication of our results for the singlet-triplet gap in dichloromethylene is discussed.

Pure rotational spectroscopy of potassium chloride, KCl, up to 930 GHz and isotopically invariant analysis of KCl and NaCl

The pure rotational spectra of five isotopomers of KCl, i.e. 39K 35Cl, 39K 37Cl, 41K 35Cl, 41K 37Cl and 40K 35Cl have been recorded with the Cologne terahertz high-resolution spectrometer. A total of 295 new rotational lines have been measured in the frequency region between 170 and 930 GHz. For the isotopomers 39K 35Cl and 39K 37Cl 107 and 82, respectively, rotational transitions were assigned from the vibrational ground state up to the seventh excited vibrational ( ν≤7) state while the highest J quantum number was 127 (129). 104 lines were measured for the less abundant isotopomers of 41K 35Cl and 41K 37Cl with J≤128, ν≤6 and J≤131, ν≤5, respectively. Two lines were assigned to 40K 35Cl, which has an abundance of 0.01% relative to 39K 35Cl. The newly measured lines were fitted together with the previously published microwave and millimeter wave transitions to obtain an improved set of molecular parameters for the studied isotopomers. Besides this analysis, the isotopically invariant Dunham parameters U ij with the Born–Oppenheimer corrections for U 01 have been determined for the potassium as well as sodium chloride. The NaCl experimental data have been taken from our recent submm high-resolution study, where both isotopomers of NaCl were measured. The improved isotopically invariant parameters allow precise frequency predictions for the six KCl and two NaCl isotopomers ( 39K 35Cl, 39K 37Cl, 41K 35Cl, 41K 37Cl, 40K 35Cl, 40K 37Cl, 23Na 35Cl and 23Na 37Cl) to be made far into the terahertz region.

Isotopically invariant dunham parameters and the potential function of the HCl molecule

The isotopically invariant Dunham parameters U mj , Δ mj H and Δ mj Cl were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U m0 and U m1 values. The contributions to the vibrational terms of H35Cl caused by violation of the Born-Oppenheimer approximation were calculated.