Heterodyne measurements of 12C16O laser frequencies and improved Dunham coefficients

Earlier measurements of absolute frequencies of ¹²C¹⁶O laser lines by heterodyning with second harmonics of a ¹²C¹⁶O₂ laser have been extended to 15 more lines by use of the rare isotopes ¹²C¹⁸O₂ and ¹³C¹⁶O₂. Interband difference frequencies for 20 pairs of ¹²C¹⁶O lines have also been measured by beat frequency techniques. These data together with 1438 other previously reported frequency measurements in the microwave and infrared regions have been analyzed to determine coefficients of a Dunham series $\text{E}{}_{\mathrm{vJ}}\text{=}\text{Σ}{}_{\mathrm{m,n}}\text{Y}{}_{\mathrm{mn}}\text{(v +}\text{1}\text{2}\text{)}{}^{\mathrm{m}}\text{[J(J + 1)]}{}^{\mathrm{n}}$ for the CO electronic ground state. Transition frequencies predicted from the derived coefficients are substantially more accurate than earlier tabulations, having estimated uncertainties of the order of 2 MHz in the strongest laser bands. The coefficient Y₃₁ has been determined for the first time.     

Infrared emission of 12C16O, 13C16O,and 12C18O

The combination of a new high-resolution grating spectrometer and a spontaneous emission source has made it possible to measure precisely the 1 → 0, 2 → 1, and 2 → 0 transitions of ¹²C¹⁶O relative to the accurately known ¹²C¹⁶O laser lines which have been referred to pure frequency standards by Eng et al. The 1 → 0 and 2 → 0 band centers agree to within 0.0002 cm^?1 with those measured relative to wavelength standards by Fourier transform spectroscopy (FTS). From a weighted simultaneous fit to the FTS-absorption, FTS-flame, our grating-emission, and microwave results, a set of calculated line positions was obtained for the 1 → 0, 2 → 1, and 2 → 0 transitions of ¹²C¹⁶O. The absolute accuracy of these line positions is believed to be ±0.0005 cm^?1 and we propose that the lines can be used as secondary wavenumber standards in the infrared.The spontaneous emission sequences v′ → (v′ ? 1) were measured for ¹²C¹⁶O up to v′ = 20, for ¹³C¹⁶O up to v′ = 11 (using a ¹³C-enriched sample), and for ¹²C¹⁸O up to v′ = 4 (in natural abundance). Internally consistent sets of Dunham coefficients were calculated from the best available data for the molecules of ¹²C¹⁶O, ¹³C¹⁶O, and ¹²C¹⁸O.     

Dunham coefficients for seven isotopic species of CO

An extensive work on vibration-rotation spectra in the fundamental ¹Σ⁺ electronic state of CO is reported. More than 30 000 Doppler-limited measurements corresponding to about 8500 transitions of 255 bands of ¹²C¹⁶O, ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O, most of them observed for the first time, have been obtained with a high information Fourier transform interferometer on the sequences Δv = 1, 2, and 3. The highest v and J values are 41 and 93, respectively. Experimental vibrational levels are then well observed up to three fourths of the dissociation energy limit. These accurate infrared wavenumbers, with an additional selected set of all previous measurements, have been simultaneously fitted to the Dunham expression in a weighted nonlinear least-squares calculation covering seven different isotopic species. It significantly improves both the number of parameters (U and Δ) obtained by the best previous work (35 instead of 23) and their corresponding standard deviations. The rms of the fit is equal to 13 × 10^?6 cm^?1 (390 KHz). Calculated wavenumbers from the 35 reduced Dunham and mass-scaling coefficients can then be used as secondary standards, even for transitions involving high v and J values of the various isotopic species. These new parameters should be a convenient and useful tool for several purposes, such as assignment of infrared laser lines and identification of microwave and infrared transitions in astronomical spectra. The Dunham coefficients Y are also reported for ¹²C¹⁶O, ¹²C¹⁷O, ¹²C¹⁸O, ¹³C¹⁶O, ¹³C¹⁷O, ¹³C¹⁸O, and ¹⁴C¹⁶O. These experimentally determined accurate Y should also be useful for further examination of the potential energy and dipole moment formulations.     

Global Multi-isotopologue fit of measured rotation and vibration–rotation line positions of CO in X1Σ+ state and new set of mass-independent Dunham coefficients

A set of mass-independent U_mj and Δ_mj parameters globally describing vibration–rotation energy levels of the CO molecule in the X¹Σ⁺ ground electronic state was fitted to more than 19,000 transitions of ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹²C¹⁸O, and ¹³C¹⁸O isotopologues collected from the literature. The maximal values of the vibrational V and the rotational J quantum numbers included in the fit was 41 and 128, respectively. The weighted standard deviation of the fit is .66. Fitted parameters were used for calculation of Dunham coefficients Y_mj for nine isotopologues ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹⁴C¹⁷O, ¹²C¹⁸O, ¹³C¹⁸O, and ¹⁴C¹⁸O. Calculated transition frequencies based on the fitted parameters were compared with previously reported. A critical analysis of the CO HITRAN and HITEMP data is also presented.     

Determination of laser line frequencies and vibrational-rotational constants of the 12C18O2, 13C16O2, and 13C18O2 isotopes from measurements of CW beat frequencies with fast HgCdTe photodiodes and microwave frequency counters

The frequencies of ¹²C¹⁸O₂, ¹³C¹⁶O₂, and ¹³C¹⁸O₂ isotope lasers have been measured to better than 3 MHz (0.0001 cm^?1) by comparing with a ¹²C¹⁶O₂ reference laser. Heterodyne techniques were used to generate 139 difference frequencies in a liquid nitrogen cooled HgCdTe photodiode. Microwave frequency counter measurements of the difference frequencies were then used to calculate new values for the band centers and rotational constants of the rare isotopes. Procedures to achieve further improvements are discussed.     

The 5v 3 bands of 18O enriched ozone: line positions of 16O16O18O, 16O18O16O, 16O18O18O and 18O16O18O

The four 5v ₃ bands of ¹⁸O enriched ozone have been observed and analysed for the first time. Two species (¹⁶O¹⁸O¹⁶O and ¹⁸O¹⁶O¹⁸O) belong to the C_2v symmetry group and two other (¹⁸O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O) to the C_s symmetry group. They have been recorded at a resolution of 0.008 cm^?1 with a pathlength of 32.16 m. Despite the very weak absorptions observed, almost 250 energy levels have been derived for each of the 4 species, with J ? 35 and K _a ? 13, and suitable sets of Hamiltonian parameters have been determined. For 3 species it has been necessary to account for the resonance between the (005) and (311) states to correctly reproduce the spectra observed. These resonances, anharmonic for C_2v, and hybrid (both anhar-monic and Coriolis) for C_s symmetry confirm the accidentally extremely strong coupling between the (005) and (311) states for ¹⁶O₃, due in that case to the very close distance between unperturbed energy levels. This work also confirms the excellent prediction of band centres of these four species derived from the recently determined isotopically invariant molecular potential function.     

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 and for each atom i. The resultant formula for Y_kl is Y_kl=μ_c^−(k+2l)/2U_kl{1+m_eΔ_kl^a/M_a+m_eΔ_kl^b/M_b+O(m_e²/M_i²)}, 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_klΔ_klⁱ are related to the functions and and to the Dunham corrections. Recent data for the CO molecule are discussed, and it is suggested that some large Δ_klⁱ values are associated with accidentally small U_kl values, since the size of U_klΔ_klⁱ is not directly related to that of U_kl.     

Microwave spectra of carbonyl sulfide: Measurements of ground state and vibrationally excited 16O13C32S, 18O12C32S,and other isotopic species

Microwave measurements have been made on isotopically enriched samples of ¹³C-carbonyl sulfide and ¹⁸O-carbonyl sulfide. Centrifugal distortion constants and l-type doubling constants have been determined for these isotopically substituted molecules. Rotational constants have been measured for all vibrational states below 2150 cm^?1 and B_e values have been determined. The equilibrium bond distances calculated from different pairs of isotopes are compared and a substitution equilibrium structure is given. Some new measurements are also reported for the isotopic species ¹⁸O¹³C³²S, ¹⁸O¹³C³⁴S, ¹⁸O¹²C³⁴S, and ¹⁶O¹³C³⁴S.     

Infrared-microwave two-photon spectroscopy with13C16O2 and12C18O2 lasers of the ν2-band of ammonia

A tunable microwave frequency was added to, or subtracted from fixed frequency¹³C¹⁶O₂ and¹²C¹⁸O₂ laser lines using the nonlinearity of molecular absorptions. In this way the frequency of 30 transitions of the ν₂-band of ammonia were measured with an accuracy of ±0.0005 cm⁻¹. A further four transitions were measured with an accuracy of ±0.0001 cm⁻¹ by saturating the two-photon transition and observing the Lamb dip. For laser lines up to 11 GHz off-resonant with in frared transitions Doppler-limited signals were observed with microwave power densities of only 10 mW/cm² using a wide-band intracavity cell.     

The infrared spectra of 12C32S, 12C34S, 13C32S,and 12C33S

Using a tunable diode laser spectrometer, the infrared absorption spectra of four isotopic species of carbon monosulfide have been observed in the positive column of a dc discharge of CS₂ and Ar. The wavenumbers of 115 vibration-rotation transitions between 1180.5 and 1266.1 cm^?1 have been measured. These lines were assigned to the 1-0, 2-1, 3-2, and 4-3 bands of ¹²C³²S, the 1-0 and 2-1 bands of ¹²C³⁴S and ¹³C³²S, and the 1-0 band of ¹²C³³S. These new data have been combined with the previous infrared and microwave results to determine Dunham coefficients (Y_ij), the Dunham potential expansion constants (a₀,a₁,a₂,a₃, and a₄), and the classical turning points by the RKR method.     

A precise study of the rotational spectrum of formaldehyde H212C16O,H213C16O,H212C18O,H213C18O

The rotational spectra of formaldehyde, H₂¹²C¹⁶O and its isotopic species H₂¹³C¹⁶O, H₂¹²C¹⁸O, and H₂¹³C¹⁸O have been investigated in the ground vibrational state in the frequency region between 8 and 460 GHz. For most cases in which measurements of the a-type R- and Q-branch transitions already existed the accuracy of the line position has been improved to about 10 kHz. For H₂¹²C¹⁶O and H₂¹³C¹⁶O a large number of ΔK_a = ±2 transitions were measured with similar accuracy. These new data when combined with all other available data and appropriate weightings lead to a set of ground state parameters which for the first time are compatible with infrared and ultraviolet data. The rotational constants (and 3σ standard deviations) obtained using Watson's A-reduced Hamiltonian are:

     

12.

Die Energiespektren der Photoprotonen aus C13 und O18     

R. Kosiek  K. Schlüpmann  H. W. Siebert  R. Wendling 《Zeitschrift für Physik A Hadrons and Nuclei》1964,179(1):9-15

The energy spectra of photoprotons from C¹³ and O¹⁸ were investigated with 31,5 MeV bremsstrahlung from the Heidelberg betatron using a CsI(Tl)-spectrometer. The spectra are compared to those of C¹² and O¹⁶. Yield values and cross sections are given.     

13.

Dunham energy parameters of isotopic carbon monoxide,hydrogen halide,and hydroxyl radical molecules     

J.F. Ogilvie 《Journal of Molecular Spectroscopy》1978,69(2):169-172

Dunham potential energy coefficients a₁-a₆ for ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, H⁸¹Br, HI, and OH have been calculated, including error limits, from published experimental spectroscopic data. There is no indication of deviation from Born-Oppenheimer behavior for a₁-a₆ of the carbon monoxide molecules, and the mass-independent internuclear separation R_e and force constants k_e and a₀ have also been calculated.     

14.

Analysis of the Fourier transform spectra of 12C17O2 and 12C17O18O: The ν2 (15 μm) region     

M.J. Reisfeld  H. Flicker  M. Goldblatt 《Journal of Molecular Spectroscopy》1980,82(2):411-417

The vibration-rotation spectra of the ν₂ fundamental of ¹²C¹⁷O₂ and ¹²C¹⁷O¹⁸O have been obtained by Fourier transform spectroscopy at 0.05 cm^?1 resolution. The data were fitted by a least-squares routine to obtain a number of the molecular constants. The band center for ¹²C¹⁷O₂ lies at 662.0716 cm^?1 while that for ¹²C¹⁷O¹⁸O is at 659.7057 cm^?1. The difference bands ν₁ - ν₂ have also been observed for the two molecular species.     

15.

Laser Stark measurements on OCS including the observation of zero-field-forbidden ΔJ = 0, ±2 transitions     

Arthur G. Maki  Samuel M. Freund 《Journal of Molecular Spectroscopy》1976,62(1):90-98

Laser Stark measurements have been made on the 02⁰000⁰0 and 03¹001¹0 vibrational transitions of ¹⁶O¹²C³²S, ¹⁶O¹²C³⁴S, and ¹⁸O¹²C³²S, and on the 03¹001¹0 transition of ¹⁶O¹³C³²S, using a CO₂ laser. In addition to providing dipole moment information for excited vibrational states, these measurements give vibrational band centers accurate to several megahertz. To aid in optical pumping experiments, several near coincidences between CO₂ laser transitions and OCS absorption lines are discussed. Electric-field-allowed ΔJ = 0 transitions are observed for the 2ν₂ band of ¹⁶O¹²C³²S and ¹⁶O¹²C³⁴S, as well as ΔJ = 2 transitions for the same band of ¹⁸O¹²C³²S.     

16.

Infrared diode laser spectroscopy of N212C18O2     

Toichi Konno  Shinya Yamaguchi  Yasushi Ozaki 《Journal of Molecular Spectroscopy》2011,270(1):66-69

The high-resolution infrared spectrum of N₂¹²C¹⁸O₂ has been observed in the ν₃ band (2314 cm^?1) region of ¹²C¹⁸O₂ with diode laser absorption spectroscopy of pulsed molecular beam. The geometry of N₂¹²C¹⁸O₂ is similar to N₂¹²C¹⁶O₂, a T-shaped structure with the nitrogen molecular axis pointing towards the carbon atom. The geometrical parameters of the T-shaped ground-state structure are determined as R_NcmC = 3.7285(5) Å and (90?Θ_NcmCO) = 6.85(3)°. The vibrational band origin of N₂¹²C¹⁸O₂ corresponding to the ν₃ mode of ¹²C¹⁸O₂ shows a shift of 0.52499(10) cm^?1 with respect to that of ¹²C¹⁸O₂.     

17.

Spectral measurements of high-temperature isotopic carbon dioxide in the 4.5- and 2.8-μm regions     

《Journal of Molecular Spectroscopy》1986,116(2):351-363

High-resolution measurements have been made using the AFGL 2-m path difference Fourier transform spectrometer on isotopically enriched samples of carbon dioxide. Two regions were investigated: 2140–2320 and 3470–3770 cm⁻¹. The samples were observed in absorption at temperatures up to 800 K. Observed line positions to high rotational levels were obtained for 15 parallel bands with Δv₃ = 1 for the isotopic variants ¹³C¹⁶O₂, ¹³C¹⁶O¹⁸O, and ¹³C¹⁶O¹⁷O in the 4.5-μm region and for 23 bands of the type Δv₁ = 1, Δv₃ = 1 for the species ¹²C¹⁶O₂, ¹²C¹⁶O¹⁸O, and ¹²C¹⁸O₂ in the 2.8-μm region.     

18.

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

G. Guelachvili  P. Niay  P. Bernage 《Journal of Molecular Spectroscopy》1981,85(2):271-281

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.     

19.

Interpretation of the ¹³C¹⁶O₂ spectrum at 4.4 μm     

Agostino Baldacci  Louise Linden  V. Malathy Devi  K. Narahari Rao  B. Fridovich 《Journal of Molecular Spectroscopy》1978,72(1):135-142

The overlapping structure observed in the region of the ν₃ fundamental of ¹³C¹⁶O₂ at 4.4 μm has been assigned to several transitions belonging to not only the 13-C variety of carbon dioxide (¹³C¹⁶O₂) but also to ¹³C¹⁶O¹⁷O and ¹³C¹⁶O¹⁸O species occurring in the sample. Molecular constants have been evaluated for the assigned transitions.     

20.

Microwave spectra of the ground vibrational state of formaldehyde substituted with 17O and 18O     

Danny T. Davies  Richard J. Richards  M.C.L. Gerry 《Journal of Molecular Spectroscopy》1980,80(2):307-319

Pure rotational transitions in the ground vibrational state have been measured for H₂¹²C¹⁸O, H₂¹²C¹⁷O, H₂¹³C¹⁸O, and H₂¹³C¹⁷O in the frequency region 8–75 GHz. These have included both Q- and R-branch transitions, and have permitted accurate evaluation of rotational constants and several quartic centrifugal distortion constants for each species. These in turn have permitted the prediction of several transitions of possible use in radioastronomy.     

	H212C16O	H213C16O	H212C18O	H213C18O
A/MHz	281 970.572 (24)	281 993.258(135)	281 961.94 (39)	281 985.00 (93)
B/MHz	38 836.0456(13)	37 811.0887(25)	36 904.1693(66)	35 859.256(10)
C/MHz	34 002.2034(12)	33 213.9790(25)	32 511.5311(63)	31 697.868(10)

Die Energiespektren der Photoprotonen aus C13 und O18

The energy spectra of photoprotons from C¹³ and O¹⁸ were investigated with 31,5 MeV bremsstrahlung from the Heidelberg betatron using a CsI(Tl)-spectrometer. The spectra are compared to those of C¹² and O¹⁶. Yield values and cross sections are given.     

Dunham energy parameters of isotopic carbon monoxide,hydrogen halide,and hydroxyl radical molecules

Dunham potential energy coefficients a₁-a₆ for ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, H⁸¹Br, HI, and OH have been calculated, including error limits, from published experimental spectroscopic data. There is no indication of deviation from Born-Oppenheimer behavior for a₁-a₆ of the carbon monoxide molecules, and the mass-independent internuclear separation R_e and force constants k_e and a₀ have also been calculated.     

Analysis of the Fourier transform spectra of 12C17O2 and 12C17O18O: The ν2 (15 μm) region

The vibration-rotation spectra of the ν₂ fundamental of ¹²C¹⁷O₂ and ¹²C¹⁷O¹⁸O have been obtained by Fourier transform spectroscopy at 0.05 cm^?1 resolution. The data were fitted by a least-squares routine to obtain a number of the molecular constants. The band center for ¹²C¹⁷O₂ lies at 662.0716 cm^?1 while that for ¹²C¹⁷O¹⁸O is at 659.7057 cm^?1. The difference bands ν₁ - ν₂ have also been observed for the two molecular species.     

Laser Stark measurements on OCS including the observation of zero-field-forbidden ΔJ = 0, ±2 transitions

Laser Stark measurements have been made on the 02⁰000⁰0 and 03¹001¹0 vibrational transitions of ¹⁶O¹²C³²S, ¹⁶O¹²C³⁴S, and ¹⁸O¹²C³²S, and on the 03¹001¹0 transition of ¹⁶O¹³C³²S, using a CO₂ laser. In addition to providing dipole moment information for excited vibrational states, these measurements give vibrational band centers accurate to several megahertz. To aid in optical pumping experiments, several near coincidences between CO₂ laser transitions and OCS absorption lines are discussed. Electric-field-allowed ΔJ = 0 transitions are observed for the 2ν₂ band of ¹⁶O¹²C³²S and ¹⁶O¹²C³⁴S, as well as ΔJ = 2 transitions for the same band of ¹⁸O¹²C³²S.     

Infrared diode laser spectroscopy of N212C18O2

The high-resolution infrared spectrum of N₂¹²C¹⁸O₂ has been observed in the ν₃ band (2314 cm^?1) region of ¹²C¹⁸O₂ with diode laser absorption spectroscopy of pulsed molecular beam. The geometry of N₂¹²C¹⁸O₂ is similar to N₂¹²C¹⁶O₂, a T-shaped structure with the nitrogen molecular axis pointing towards the carbon atom. The geometrical parameters of the T-shaped ground-state structure are determined as R_NcmC = 3.7285(5) Å and (90?Θ_NcmCO) = 6.85(3)°. The vibrational band origin of N₂¹²C¹⁸O₂ corresponding to the ν₃ mode of ¹²C¹⁸O₂ shows a shift of 0.52499(10) cm^?1 with respect to that of ¹²C¹⁸O₂.     

Spectral measurements of high-temperature isotopic carbon dioxide in the 4.5- and 2.8-μm regions

High-resolution measurements have been made using the AFGL 2-m path difference Fourier transform spectrometer on isotopically enriched samples of carbon dioxide. Two regions were investigated: 2140–2320 and 3470–3770 cm⁻¹. The samples were observed in absorption at temperatures up to 800 K. Observed line positions to high rotational levels were obtained for 15 parallel bands with Δv₃ = 1 for the isotopic variants ¹³C¹⁶O₂, ¹³C¹⁶O¹⁸O, and ¹³C¹⁶O¹⁷O in the 4.5-μm region and for 23 bands of the type Δv₁ = 1, Δv₃ = 1 for the species ¹²C¹⁶O₂, ¹²C¹⁶O¹⁸O, and ¹²C¹⁸O₂ in the 2.8-μm region.     

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.     

Interpretation of the 13C16O2 spectrum at 4.4 μm

The overlapping structure observed in the region of the ν₃ fundamental of ¹³C¹⁶O₂ at 4.4 μm has been assigned to several transitions belonging to not only the 13-C variety of carbon dioxide (¹³C¹⁶O₂) but also to ¹³C¹⁶O¹⁷O and ¹³C¹⁶O¹⁸O species occurring in the sample. Molecular constants have been evaluated for the assigned transitions.     

Microwave spectra of the ground vibrational state of formaldehyde substituted with 17O and 18O

Pure rotational transitions in the ground vibrational state have been measured for H₂¹²C¹⁸O, H₂¹²C¹⁷O, H₂¹³C¹⁸O, and H₂¹³C¹⁷O in the frequency region 8–75 GHz. These have included both Q- and R-branch transitions, and have permitted accurate evaluation of rotational constants and several quartic centrifugal distortion constants for each species. These in turn have permitted the prediction of several transitions of possible use in radioastronomy.