Dunham Coefficients Research Articles

Rotational spectrum and hyperfine structure of the 2Σ radicals BaF and BaCl

Microwave rotational spectra have been measured for BaF and BaCl. Precise Dunham coefficients Y ik and spin—rotation parameters γ ik are derived from this first rotational analysis for the BaCl molecule. Hyperfine structure has been measured for the isotopes 137Ba 19F and 137Ba 35Cl in which coupling of two nuclei has to be considered. Matrix elements for calculation of energy levels and relative intensities are given in the text. The measured hfs coupling constants are: b( 137Ba) = 2301(9) MHz, c( 137Ba) = 75(6) MHz, eqQ( 137Ba) = −117(12) MHz, and b( 19F) = 60(6) MHz. A comparison between these first gas phase measurements of metal hfs coupling constants in group II monohalides with previous matrix ESR data and hfs splitting factors A and B in the free B + ion yields information about polarization of closed Ba shells and 6s-6p-5d hybridization of the unpaired electron due to the field of the F − ion.

Laser Spectroscopy of Iodine Monofluoride Produced in Situ in a Molecular Beam Experiment

AbstractNascent IF molecules in various vibrational‐rotational manifolds of the electronic ground state have been prepared in a molecular beam experiment. High‐resolution laser spectroscopy has been applied to determine accurate band head positions and band origins of the B→X transition. Dunham coefficients have been calculated for the X1Σ+ and B3Π(O+) states. The hyperfine structure of the rotational lines has been observed.

Millimeter and submillimeter wave spectrum of CS 1Σ in high vibrational states: Isotopic dependence of Dunham coefficients

Rotational lines of CS were observed in an rf discharge in CS 2. Transitions belonging to different isotopic species were measured in excited vibrational states (up to v = 20) for different J values. These measurements led to a precise determination of some Dunham coefficients and of the Δ 01 mass scaling coefficients.

Rotational analysis of the A2Σ + → X2Π system of OT. Merged molecular constants for OT A2Σ +, v ≤ 4 and X2Π, v ≤ 3

The A 2Σ + → X 2Π band system of OT was observed for the first time. Fourteen bands with 0 ≤ v′ ≤ 4 and 0 ≤ v″ ≤ 3 were photographed at high resolution and rotationally assigned. Fitted values of 18 effective parameters of the model Hamiltonians used to describe individual vibrational levels of the two states are determined by least-squares from the data of each band. Multiple determinations of the parameters are merged to obtain single-valued estimates of the same parameters, as well as Dunham coefficients describing their vibrational dependence.

Hyperfine structure of the X 2Σ+ ground state of Ca 35Cl and Ca 37Cl by molecular-beam, laser-rf double resonance

The hyperfine structure of the X 2Σ+ state of Ca 35Cl and Ca 37Cl, unresolved in previous studies, has been investigated in detail by the molecular-beam, laser-rf, double-resonance technique. Results for the spin-rotation interaction and the dipole and quadrupole hfs constants are given in the form of Dunham coefficients so that the N\ and v\ dependence of each constant can be explicitly exhibited. The results, after dividing out the purely nuclear effects, fall between the corresponding values for CaF and CaBr, as expected.

Infrared spectrum of boron chloride (BCl)

The spectrum of the Δ v = 1 band of BCl was measured between 828 and 870 cm −1 with a tunable diode laser. The absorptions of the v = 1-0, 2-1, 3-2, and 4-3 transitions of BCl were observed in both a microwave discharge and a dc discharge through BCl 3. Spectra of 11B 35Cl, 11B 37Cl, 10B 35Cl, and 10B 37Cl were observed in natural abundance. A set of eight Dunham coefficients was determined by fitting the data for all observed isotopic species with the appropriate reduced mass factors. A BCl bond distance, r e = 0.1715283(31) nm, was determined which agrees with the value derived from the electronic spectrum of BCl. The band center for the v = 1-0 transition of 11B 35Cl is ν 0 = 829.4087(8) cm −1.

Fundamental Vibration-Rotation Bands and Molecular Constants for the ArH+ Ground State (1Σ+)

Five vibration-rotation bands of the ground state X1Σ+ of ArH+ have been observed in the infrared emission spectrum of a carbon hollow cathode lamp, using the McMath solar Fourier transform spectrometer at KPNO. The leading Dunham coefficients are found to be (in cm-1): Y10 = 2710.9191, Y20 = -61.630 75, Y30 = 0.502 654, Y40 = -0.001 091 7; Y01 = 10.461 276, Y11 = -0.378 782, Y21 = 0.003 017 3; Y02 = -6.230 × 10-4, Y12 = 0.082 97 × 10-4; Y03 = 1.584 × 10-8, Y13 = -0.0459 × 10-8; Y04 ∼ -0.64 × 10-12.

Measurement of the LiD (A–X) transition moment from laser-excited fluorescence and test of the R-centroid approximation

Improved Dunham coefficients of the X 1Σ+ and A 1Σ+ states of LiD were derived, based on the observation of vibrational levels up to v″ = 26, corresponding to 96% of the ground state dissociation energy. From accurate intensity measurements over long fluorescence progressions, the electronic transition moment M was obtained as a function of the internuclear distance R. The dependence M(R) has an unusual S shape. The R-centroid method was found to be valid even in this case.

Microwave optical double resonance of X 1Σ+ of NaK

A microwave optical double resonance (MODR) study of the ground state X 1Σ+ is NaK is reported. The ν″ = 0 J = 7→8 and J = 8←9, and ν″4 J = 5←6 rotational transitions were observed as changes in the laser induced photoluminescence intensity with the Ar+ laser coincidences (12–0) band P(8) (4765 Å) and (’–4) band Q(5) (4965 Å), respectively, of the D 1Π–X 1Σ+ system of NaK. The improvement in sensitivity of the MODR technique over traditional microwave spectroscopy is discussed. Improved Dunham coefficients for the X 1Σ+ state are obtained by a weighted merged fit of the previous optical data with the three transitions obtained in the present work.

Predissociation spectroscopy of O+2: a 4Πu (v′′=6–11)→b 4Σ−g (v′=5–9)

Moderate-resolution spectra (Δλ=0.25 Å) have been obtained for the (5,6), (5,7), (6,7), (6,8), (7,8) (7,9), (8,9), (8,10), and (9,11) bands of the transition O+2 (a 4Πu→b 4Σ−g), where the upper b state levels are all predissociated. The study was made by observing the resulting O+ photofragments using a coaxial beams photofragment spectrometer. The results are used to obtain values of the vibrational band origins and term values. The remaining molecular constants are, within the resolution of this work, consistent with calculations based on previously determined Dunham coefficients.

Infrared bands of HCl and DCl by Fourier transform spectroscopy: Dunham coefficients for HCl, DCl, and TCl

Fourier absorption spectra of HCl and DCl are recorded simultaneously in the spectral range [2840 cm −1–8450 cm −1]. A U ij reduced Dunham coefficient set is deduced by fitting all the available data and then used together with four mass-scaling parameters to predict the TCl Y ij Dunham coefficients.

Polarization labelling spectroscopy of the A 1Σ +u band of Na 2

A result of the polarization labelling spectroscopy of the A 1Σ + u band of sodium dimer for the high vibrational quantum number υ'>20 is reported. The frequency difference δ v= v obs- v cal is found to decrease from 2 to -3 cm -1 as the rotational levels (υ'=27−30), where v cal is the calculated transition frequency using the Dunham coefficients of Demtröder and Stock for the X 1Σ + g band and of Kusch and Hessel for the A 1Σ + u band.

Millimeter wave measurements of the rotational spectra of ClF, BrF, BrCl, ICl, and IBr

The rotational spectra of all twelve stable isotopic species of ClF, BrF, BrCl, ICl, and IBr were observed and measured in the millimeter wave region by means of a sensitive microwave spectrometer. Transitions were detected over a wide range of frequencies for molecules in both the ground vibrational state and several excited states. The rotational spectrum of each molecule was split by the nuclear quadrupole interaction. Altogether, 250 new lines were measured. These correspond to 136 pure rotational transitions. Values of the Dunham coefficients Y01, Y11, Y21, Y31, Y02, Y12, and Y03 were obtained from a computer analysis of the measured frequencies. From these coefficients a number of equilibrium constants were derived to significantly greater accuracy than in previous work. In particular, the equilibrium distance, re, was found to two or three more significant figures.

The isotope dependence of diatomic Dunham coefficients

The isotope dependence of the Dunham vibration-rotation coefficients Y kl of a diatomic molecule is studied. Rovibronic interactions between different electronic states are taken into account by transformation to an effective vibration-rotation Hamiltonian for each electronic state. This contains modified vibrational and rotational reduced masses as well as the adiabatic correction to the potential energy. The effects of these contributions on the vibration-rotation energies are expressed in terms of two functions R ̃ i(r) and S ̃ i(r) for each atom i. The resultant formula for Y kl is Y kl=μ c −(k+2l) 2 U kl{1+ m eΔ kl a M a + m eΔ kl b M b +O( m e 2 M i 2 )} , where U kl , Δ kl a , and Δ kl b are isotopically invariant, M a and M b are the atomic masses, and μ c = M aM b (M a + M b − Cm e ) is the atomic reduced mass, modified by the molecular charge number C for charged species. The U kl with l ≥ 2 can be calculated from those with l = 0 and 1. The corrections U kl Δ kl i are related to the functions R ̃ i(r) and S ̃ i(r) and to the Dunham corrections. Recent data for the CO molecule are discussed, and it is suggested that some large Δ kl i values are associated with accidentally small U kl values, since the size of U kl Δ kl i is not directly related to that of U kl .

Analysis of perturbations in the A2Π- X2Σ + “Red” system of CN

Deperturbed vibration-rotation constants of the A 2Π( v′ = 0 to 12) and X 2Σ +( v″ = 0 to 8) states of CN are obtained. Specroscopic data from several sources are combined using a weighted, nonlinear least-squares fitting routine. The diagonalized effective Hamiltonian matrix contains as many as two 2Π and four 2Σ + mutually interacting vibronic levels. Perturbations of A 2Π by both X 2Σ + and B 2Σ + are treated simultaneously. The deperturbed constants and interaction matrix elements obtained provide a significantly more accurate representation of all perturbed and unperturbed observed lines than the previously reported values. The electronic factors of the spin-orbit and rotation-electronic perturbation matrix elements for the A ∼ X and A ∼ B interactions are determined and several previously unreported perturbations are detected and analyzed. Merged constants and Dunham coefficients are calculated; a detailed statistical treatment of the parameters and error estimates has also been carried out.

High-resolution photofragment spectroscopy of the O 2+b4Σ g− ( v′ = 3, 4, 5) ← a4Π u ( v′ = 3, 4, 5) First Negative system using coaxial dye-laser and velocity-tuned ion beams

A new photofragment spectrometer employing coaxial tunable single-mode laser and velocity-tuned fast-ion beams has been used to measure transition energies in the O 2 + b 4Σ g − ← a 4Π u First Negative system to an accuracy and precision that are an order of magnitude better than was previously possible in Doppler-limited emission spectroscopy. The technique consists of velocity-tuning a beam of metastable O 2 + a 4Π u ions such that a set of First Negative rotational transitions can be sequentially brought into resonance with the laser wavelength. The subsequent absorption transitions promote the ions to predissociating levels of the b 4Σ g − state and observation of the O + photofragments is the signal that denotes that each absorption transition has occurred. Repetition of the velocity tuning at different dye-laser frequencies provides a scan of the First Negative spectrum for predissociating upper-state vibrational levels, which are inaccessible to emission spectroscopy. The O + photofragment ions have a kinetic energy that depends on the height of the predissociating rotational level above the separatedatom limit. The present apparatus incorporates a photofragment energy analyzer that can often be used to separately record the wavenumbers of transitions to different upper-state rotational levels, but whose wavenumbers could not otherwise be resolved. A set of 359 wavenumbers involving the (4,4), (4,5), (5,5), and (3,3) bands were recorded with an estimated accuracy of ±0.0032 cm −1 and a precision of 0.0028 cm −1, the latter being estimated precisely with a statistical technique. These data were fitted to 4Σ and 4Π Hamiltonians used in recent studies of the First Negative emission spectrum to determine molecular constants for the v′ = 4, 5 and v″ = 4, 5 levels. The former represent an extension of the b 4Σ g − state to new levels and the latter represent substantial improvements over the constants that were available from previous moderate-resolution emission studies. These photofragment molecular constants were merged with those from the previous emission studies to yield a new consistent set of molecular constants and Dunham coefficients for the O 2 + b 4Σ g − and a 4Π u states. In the fit to the photofragment bands, it was found that the Hamiltonians, which were sufficient for the emission data, are inadequate to describe these states within the precision of the present measurements.

Microwave spectroscopy in an RF plasma: highly excited vibrational states of CS (ν ⩽ 14)

A microwave spectrometer is described where excited species are observed inside a plasma excited by an rf discharge. The J = 0 → 1 transition of CS is measured over a wide range of vibrational states for different isotopic substitutions in natural abundance: 12C 32S (ν ⩽ 14), 12C 34S (ν ⩽ 5), and 13C 32S (ν </ 3). Some new Dunham coefficients are determined.

Improved laser frequencies and Dunham coefficients for isotopically substituted carbon monoxide

New measurements of carbon monoxide laser frequencies in the 5.3 to 7.2 μm region have been made using the techniques of infrared grating spectroscopy and heterodyne beat frequency detection. The observations concentrated on the rarer isotopic species 13C16O, 12C18O, and 13C18O, and on the lower frequency region of CO laser oscillation, where less data have previously been available. The new results have been combined with a large amount of previous data in a simultaneous least-squares fit involving all known isotopic species of CO. The resulting parameters are a set of 'reduced' Dunham coefficients and a set of mass-scaling factors which describe how their isotopic variation differs from the simple mass-dependence normally assumed. Laser frequencies calculated from the new Dunham coefficients are improved from those previously available, especially in the relative accuracy of each isotope compared to the others, and they should prove useful in spectroscopic applications of the CO laser. Comprehensive tables of Dunham coefficients for all CO isotopes and of calculated laser frequencies for 12C16O,13C16O, 12C18O, and 13C18O are given in the paper and in an Appendix.

Absolute wavenumbers and molecular constants of the fundamental bands of 12C 16O, 12C 17O, 12C 18O, 13C 16O, 13C 17O, 13C 18O and of the 2-1 bands of 12C 16O and 13C 16O, around 5μm, by Fourier spectroscopy under vacuum

This paper is part of a more general work undertaken on the determination of Dunham coefficients for all the isotopic species of CO. The absolute wavenumbers of 466 CO lines obtained from absorption spectra of six different isotopic forms in the 5 μm region are reported with an accuracy of the order of 3 MHz or less for about 300 lines. Absolutely measured within 9 MHz, 43 lines of 13C 17O (a molecule whose spectrum has not been observed in the infrared before) are given together with 59 wavenumbers measured within 3.2 MHz of 12C 17O, also reported for the first time. The wavenumbers extend from 1939 to 2271 cm −1. More than 50 accurate molecular constants are available allowing precise determination of pure rotational transitions. These metrologic data should be helpful both for microwave or infrared identification in astronomy, for instance, and for more specific molecular purposes. The high self-consistency of these Fourier results measured versus the Krypton line, and their consistency with all the other accurate measurements suggest that the reported values be adopted as secondary standards.

New analysis of the C 2 Ballik-Ramsay system from flame emission spectra

The C 2 b 3Σ g − → a 3Π u Ballik-Ramsay system has been studied through emission flame spectra recorded with a Fourier transform interferometer. The 14 bands 0-0, 1-0, 1-1, 2-0, 2-1, 3-0, 3-1, 3-2, 4-1, 4-2, 5-2, 5-3, 6-3, and 7-4 were identified in the 4850- 9900-cm −1 spectral range. They have been reduced to molecular constants using an iterative, nonlinear, least-squares method. Rotational perturbations, observed in the b 3Σ g − v = 0, 1, 2, 5, and 6 levels, have been reduced. Dunham coefficients are obtained for both the b 3Σ g − and a 3Π u states.