Centrifugal Constants Research Articles

Nitrogen and Deuterium Hyperfine Structure in the Rotational Spectrum of Morpholine

Abstract We reinvestigated the rotational spectra of morpholine and N-deutero morpholine with the higher precision of microwave Fourier transform spectroscopy. The rotational, centrifugal, and nitrogen quadrupole coupling constants were improved and the deuterium quadrupole coupling constants determined.

On the determination of spectroscopic constants as functions of intramolecular parameters

The symmetrised form of the operator Van Vleck perturbation theory is considered (the irreducible tensorial set theory is used as the mathematical basis of this consideration). General formulae which define spectroscopic rotational, centrifugal and resonance constants of molecules as functions of reduced matrix elements of vibrational operators are obtained. Algorithms for the ES-1055 computer have been derived on the basis of the formulae obtained, and a system of analytical calculations using the language 'REDUCE' has been created. The dyad and pentad of the CH4-type molecule are considered for illustration. Formulae are obtained which connect spectroscopic and intramolecular constants not only for isolated but also for interacting vibrational states.

Rotational spectrum, H, 19F spin–spin and D–nuclear quadrupole coupling constants, and molecular geometry of the sulphur dioxide–hydrogen fluoride dimer

The ground state rotational spectra of three isotopic species 32SO2⋅⋅⋅HF, 32SO2⋅⋅⋅DF, and 34SO2⋅⋅⋅HF of a dimer formed between sulphur dioxide and hydrogen fluoride have been detected and measured using a pulsed-nozzle, Fourier-transform microwave spectrometer. An analysis of observed nuclear hyperfine structure leads to the H, 19F nuclear spin–nuclear spin coupling constants DHFaa =−190(2) kHz and (DHFbb−DHFcc) =−57(4) kHz for 32SO2⋅⋅⋅HF, and to the D-nuclear quadrupole coupling constants χaa =227(3) kHz and (χbb−χcc) =68(13) kHz for 32SO2⋅⋅⋅DF. Rotational and centrifugal constants have been determined for all three isotopic species, with the following values for 32SO2⋅⋅⋅HF: A0=16 502.775(4) MHz, B0=2100.308(1) MHz, C0=1853.642(1) MHz, ΔJ =18.31(2) kHz, ΔJK =−521.78(4) kHz, and δJ =4.37(3) kHz. The rotational constants for the three isotopic species are interpreted in terms of a planar geometry in which hydrogen fluoride forms a cis hydrogen bond to one of the oxygen atoms of SO2. Assuming a linear hydrogen bond and unchanged subunit geometries, it is found that r(O⋅⋅⋅F)=2.818(8) Å and θ=215.1° where θ is the S=O⋅⋅⋅H bond angle. The nuclear hyperfine coupling constants are shown to be consistent with this arrangement.

The submillimeter rotational spectrum of CD3Cl

Advances in radio astronomy and quantum electronics have led to research on submillimeter spectra for polyatomic molecules, particularly ones of symmetrical top type, and there is now realistic scope for determining the exact structure on the basis of rotational and centrifugal parameter of any order. A direct impetus to this study was provided by the observation of submillimeter lasing by Cd/sub 3/Cl, which occurs on transitions in the excited vibrational states v/sub 2/ and v/sub 5/, but a quantitative description of the lasing is much assisted by an exact calculation on the ground-state rotational spectum. Rotation and centrifugal constants are given which provide a reliable basis for accurate calculation of the submillimeter rotational spectrum of CD/sub 3/Cl and provide valuable information on the geometry and force field.

Joint use of electron-diffraction and spectroscopic data in research on the structure and potential functions of SeO2 and ClO2

Use is made of the harmonic-potential constants and parameters in linearized and curvilinear internal coordinates in an analysis of the data on electron scattering intensities, vibration frequencies, Coriolis constants, and rotational centrifugal constants for SeO/sub 2/ and ClO/sub 2/, including data for isotopic molecules. In addition, the spectral anharmonicity constants have also been used for ClO/sub 2/ in a simplified anharmonic analysis. It is shown that the results for the equilibrium internuclear distances and the force constants have less error than those determined in each measurement separately, with the harmonic approximation in curvilinear coordinates more accurately describing the data set than the analogous approximation in linearized coordinates.

A rotational analysis of the [formula omitted] electronic origin band of NCNO near 882 nm

The origin band near 882 nm in the A ̃ 1A″- X ̃ 1A′ system of NCNO has been recorded using a Fourier transform spectrometer. The rotational structure has been analyzed in detail, and requires high-order terms in the rotational Hamiltonian to account for the gross centrifugal distortion. The rotational and centrifugal constants are used in a discussion of the possible excited state geometry and force field.

High-resolution Fourier transform study of the perpendicular band ν11 of allene at 353 cm −1

The ν 11 perpendicular band of the allene (propadiene) molecule was measured in the region 310–390 cm −1 on a high-resolution Fourier transform instrument. A total of 1880 lines was assigned to 22 subbands with KΔ K values between −10 and +12. Subband constants which reproduce the observed line positions with standard deviations of 0.0005-0.0008 cm −1 are tabulated. The strong effects of the two types of l-type interactions allowed for this molecule are included in the Hamiltonian matrix used for the treatment of the spectrum and for the least-squares adjustment of the spectroscopic constants for the ν 11 state. A table of the rovibrational energy levels of the ν 11 state is given to facilitate analysis of the various hot bands observed throughout the spectrum of allene. Improved estimates are obtained for the elusive rotational constant, A 0, and for the centrifugal constant, D K 0, by combining published Raman data for the ν 11 band with the new accurate infrared measurements.

Nitrous acid: vibrational frequency shifts due to15N substitution, and the harmonic force field

Vibration rotation spectra of HO15 NO and DO15 NO have been measured at a resolution of 0·04 cm-1 to determine the isotopic shifts in the vibrational band origins. These have been used together with recently determined data on the vibrational band origins, Coriolis constants, and centrifugal distorition constants, to determine the harmonic force field of both cis and trans nitrous acid in least squares refinement calculations. The results are discussed in relation to recent ab initio calculations, the inertia defects, and the torsional potential function.

Description of the absorption spectrum of iodine recorded by means of Fourier Transform Spectroscopy : the (B-X) system

An in extenso analysis of the (B-X) I2 iodine absorption spectrum recorded by means of Fourier Transform Spectroscopy is presented. It is shown that the 100 000 recorded transitions covering the 11 000-20 040 cm-1 range and published in several Atlases may be recalculated by means of only 46 constants : 45 are Dunham coefficients describing the vibrational and rotational constants of both X state (up to v = 19) and B state (up to v' = 80, situated only at 1.6 cm-1 from the dissociation limit of the B state), and one empirical scaling factor which takes account of neglected centrifugal constants higher than Mv. The overall standard error between computed and measured wavenumbers is equal to 0.002 cm -1 in agreement with the differences of numerous independent absolute wavenumbers and the computed ones.

Analysis of the ν1 and ν3 absorption bands of 32S 16O 2

The spectrum of 32S 16O 2 between 1055 and 2000 cm −1 has been investigated under high resolution with a Fourier transform interferometer. Two fundamental bands have been analyzed; the A-type band ν 3 and the B-type band ν 1. A careful analysis of these bands has led to the availability of an extended and more precise set of rotational levels belonging to the vibrational states (000), (100) and (001). From this set of improved vibrational energies, rotational and centrifugal constants for the states (000), (100), and (001) have been obtained.

Study of thev2infrared band of GeH4:Q-branch

The results of recording of the diode-laser spectrum of GeH4, having a natural distribution of isotopes, within the range 932·4-937·5 cm-1 are presented. Taking into account the Coriolis interaction between (0100) and (0001) vibrational states, the rotational and centrifugal constants are obtained.

Higher-order vibration-rotation energies of the X 3 molecule

Higher-order vibration-rotation perturbation calculations are presented for the X 3 molecular model, employing a sequential contact transformation procedure. The calculations are simpler than for a general molecule because the principal Coriolis interaction is diagonal in the quantum numbers ( V 1, V 2). Most of the terms of the effective Hamiltonian that depend on quartic or lower potential constants are evaluated, including the vibrational dependence of the quartic centrifugal and Coriolis constants. The inertial and centrifugal planarity defects are proportional to ( V 2 + 1). To a good approximation, the energies are diagonal in the quantum number G = | k − l 2| and are given by a secular equation of dimension ( V 2 + 1) or lower. Explicit rotational energy level formulas are given for the vibrational states with any value of V 1 and with V 2 = 0 or 1.

On some new aspects in the conventional theory of vibration-rotation states of molecules

An approach which enables consideration of the problem of determining the energy spectrum of molecules containing vibrations of large amplitude within the framework of the standard Nielsen theory without the use of the Hougen-Bunker-Johns model is presented. The use of the H 2O molecule as an example has shown that such an approach allows the behavior of rotational and centrifugal constants of (0 v0) states with the increasing quantum number v to be described not only qualitatively but also quantitatively.

ChemInform Abstract: MICROWAVE STUDY OF VIBRATION‐ROTATION SPECTRUM OF CARBON SUBOXIDE C3O2 IN THE 300 TO 1000 GHZ FREQUENCY RANGE

Abstract The submillimeter wave spectrum of the C3O2 molecule was investigated within the 300- to 1000-GHz range. The measured frequencies include 256 lines belonging to the ground vibrational state and to four excited vibrational states of ν7. Rotational and centrifugal constants and constants of “l” splitting for the ground and excited states ν71, 2ν72, 3ν73, 4ν74 as well as frequencies of purely vibrational transitions ν71 ← 0; 2ν72 ← ν71; 3ν73 ← 2ν72; 4ν74 ← 3ν73 together with their correlation matrix were determined.

ChemInform Abstract: ROTATION‐VIBRATION SPECTRA OF DEUTERATED WATER VAPOR IN THE 9160‐9390‐CM‐1 REGION

Abstract The absorption spectrum of mixtures of H 2 O, HDO and D 2 O has been recorded in the region 9161.5 to 9392.5 cm −1 with an absorption sensitivity of 10 −7 cm −1 and a line-center determination accuracy of 0.08 cm −1 . An attempt to identify the absorption bands of the spectrum obtained experimentally was undertaken. The justification for attributing the observed lines to the HDO bands (3 ν 1 + ν 2 ), ( ν 1 + 2 ν 2 + ν 3 ) and D 2 O bands ( ν 2 + 3 ν 3 ), ( ν 1 + ν 2 + 2 ν 3 ) is given. In this study the bands centers have been found and the molecular rotational and centrifugal constants have been determined as well.

On a method for determining the rotational and centrifugal constants for asymmetric top molecules

On a method for determining the rotational and centrifugal constants for asymmetric top molecules

Revised molecular constants for the E 1Σ state of the diatomic CuI molecule

A least-squares computer program has been used to fit the observed rotational line positions of the E 1Σ-X 1Σ band system of the Cul molecule. Molecular constants of the E state have been revised and higher vibrational terms in the rotational and centrifugal constants have been obtained.

V2-dependence of centrifugal constants of H2O molecules in the Morse oscillator model

It is shown in this paper that the centrifugal constantsC l (t) calculated in the Morse, oscillator model for the sequence $$H_z^{(t)} = \sum\limits_{1 \geqslant 0} {C_l^{(t)} j_z^{2l + 2} } $$ from the operator H red (t) , which is used in processing the rotational levels of the H2O molecule, are linked by recurrence relations, which enables H z (t) −H z (O) to be given in closed form.

The [formula omitted] band system of acetylene : Analysis of long-wavelength bands, and vibration-rotation constants for the levels nν″ 4 ( n = 0–4), nν′ 3 ( n = 0–3), and ν′ 2 + nν′ 3 ( n = 0–2)

The A ̃ - X ̃ band system of acetylene with origin near 2400 Å was photographed in absorption with higher resolution than in previous studies. A detailed rotational analysis of bands in the 2470–2150-Å region, involving the levels nν″ 4 ( n = 0–4) of the X ̃ 1 Σ g +(D ∞h) state and nν′ 3 ( n = 0–3) and ν′ 2 + nν′ 3 ( n = 0–2) of the A ̃ 1A u(C 2h) state, is presented. Some of the previous assignments are modified. Both the principal subbands with Δ K = ± 1 and the satellite subbands with Δ K = 0, ±2 (due to axis-switching) and Δ K = ±3 (due to axis-switching, asymmetry, and l resonance) are included in a comprehensive least-squares fit. Rotational levels of all the l components of the levels of ν″ 4 are observed, and are consistent with the theory of l doubling and l resonance of a linear molecule. The rotational structures of the vibrational levels of the nonlinear A ̃ state are fitted with asymmetric top rotational constants A v, B v, C v and principal centrifugal constants D v J , D v JK , D v K . A small perturbation of ν′ 2 + ν′ 3, together with the inertial defect Δ′ v, are discussed in terms of the unobserved vibrational frequencies of the A ̃ state.

Doppler-limited dye laser excitation spectroscopy of the CCN radical

The cw dye laser excitation spectrum of the A ̃ 2 Δ(000) ← X ̃ 2 Π(000) vibronic transition of the CCN radical was observed between 21 205 and 21 335 cm −1 with the Doppler-limited resolution, 0.04 cm −1. The CCN radical was produced by reaction of microwave discharged CF 4 with CH 3CN. The observed spectrum was analyzed to determine rotational and centrifugal constants and effective spin-orbit and spin-rotation coupling constants for both the A ̃ 2 Δ(000) and the X ̃ 2 Π(000) states, and also the Λ-type doubling constants for the X ̃ 2 Π(000) state. The constants determined reproduce the observed spectrum with an average deviation of 0.0027 cm −1, and are considered to be precise enough for predicting the ground-state microwave transition frequencies. No evidence was found for perturbation in either the A ̃ 2 Δ(000) or the X ̃ 2 Π(000) state.