Fine structure and centrifugal distortion in the electronic and microwave spectra of O2 and SO

The fine structure theory of ³Σ states in diatomic molecules is re-examined with particular emphasis on centrifugal distortion in the triplet splitting parameters. The theoretical results are compared with optical and microwave data for the ³Σ ground states of O₂ and SO. Excellent agreement is found between theoretical predictions and experimental results concerning the centrifugal distortion in the spin-spin splitting for both O₂ and SO. However, in contrast to ab initio calculations this agreement indicates that the second-order contribution to the spin-spin splitting is of minor importance. The theoretical value of the centrifugal distortion in the spin-rotation coupling constant is about twice the experimental one for O₂. It is pointed out that a slight transition towards coupling case (c) yields a reasonable explanation for this discrepancy.     

Microwave spectra and centrifugal distortion constants of oxetane

The microwave spectra of oxetane (trimethylene oxide) and its three symmetrically deuterated isotopic species have been observed on a Hewlett-Packard microwave spectrometer from 26.5 to 40 GHz. For the parent species, the β-d₂ and the αα′-d₄ species, about 300 lines have been assigned for each molecule, and for the d₆ species more than 600 lines have been assigned. The assignments range from v = 0 to v = 5 in the puckering vibration; although they are mostly Q transitions, either 3 or 4 R transitions have been observed for each vibrational state.The spectra have been interpreted using an effective rotational hamiltonian for each vibrational state, including five quartic distortion constants according to Watson's formulation, and a variable number of sextic distortion constants; in general, the lines are fitted to about ± 10 kHz. The distortion constants show an anomalous zig-zag dependence on the puckering vibrational quantum number, similar to that first observed for the rotational constants by Gwinn and coworkers. This is interpreted according to a simple modification of the standard theory of centrifugal distortion, involving the double minimum potential function in the puckering coordinate.     

An investigation of centrifugal distortion in the microwave spectrum of formamide

Measurements of the microwave spectrum of formamide have been extended in order to account accurately for the effects of centrifugal distortion. A total of 22 new transitions involving J ≤ 29 have been measured for ¹⁴NH₂¹²CH¹⁶O in the ground vibrational state. Combined with previous observations, these transitions have been fit to a model containing five quartic distortion terms and seven sextic terms with a rms deviation of 64 kHz. A large number of resolved quadrupole shifts were fit with an rms deviation of 42 kHz. The remainder of the spectrum for J ≤ 30 has been calculated with standard deviations less then 3 MHz. Correct weighting of the observed transitions has been found to be important.     

Radiative electron-attachment spectra of O3 and SO2

Several aspects of radiative electron-attachment processes are discussed and the corresponding photon energy spectra computed for O₃ and SO₂. In both cases the vibrational stretching mode is significantly excited. The calculated electron attachment spectrum of SO₂ is compared with the laser photo-detachment spectrum of SO₂ ^-. The computed electron affinities and changes in geometry between natural and negative ion are in good agreement with the experimental data.     

Molecular structure and centrifugal distortion constants of isocyanic acid from the microwave,millimeter wave,and far-infrared spectra

The pure rotational spectra of HNCO and DNCO were measured in the far-infrared region from 80 to 350 cm^?1 by a Fourier transform spectrometer with a resolution of 0.1 cm^?1. The ^rR_K branches were measured and assigned for HNCO from K = 1 to 6, and for DNCO from K = 3 to 8. The measured transition wavenumbers were analyzed together with the microwave and millimeter wave data reported by Hocking, Gerry, and Winnewisser [Can. J. Phys.53, 1869–1901 (1975)] and with the far-infrared data of Krakow, Lord, and Neely [J. Mol. Spectrosc.27, 148–176 (1968)] in the low-wavenumber region. The microwave and millimeter wave data of H¹⁵NCO, HN¹³CO, and HNC¹⁸O reported by Hocking et al. were reanalyzed assuming several centrifugal distortion constants to be identical with those of the normal species. The molecular structure of HNCO was reevaluated using a modified substitution method from the rotational constants obtained in this work. The molecule has a bent structure in a trans configuration with $\text{r}\text{(NH) = 0.995}\text{A}\text{?}$, $\text{r}\text{(NC) = 1.314}\text{A}\text{?}$, $\text{r}\text{(CO) = 1.668}\text{A}\text{?}$, ∠HNC = 123.9°, and ∠NCO = 172.6°.     

The microwave spectrum and centrifugal distortion constants of propiolic acid

The microwave spectra of propiolic acid and propiolic acid-d have been measured up to J = 30. These have enabled accurate evaluation of the rotational and centrifugal distortion constants for each species. The measured frequencies are presented, along with some predictions of transitions unmeasured in the present work, but of potential use in radioastronomy.     

The microwave spectrum and centrifugal distortion constants of vinyl fluoride

The rotational spectrum of vinyl fluoride up to J = 40 has been assigned and measured in the frequency region 8–37 GHz. Both a- and b-type transitions were observed. These measurements have been combined with those made in other frequency regions to calculate refined rotational constants and to obtain all quartic and some sextic centrifugal distortion constants. A comparison is made between the quartic centrifugal distortion constants measured here and those calculated from vibrational data.     

The microwave spectrum and centrifugal distortion constants of difluoroborane,HBF2

The microwave spectra of two isotopic species of the unstable molecule difluoroborane have been measured between 8 and 36 GHz. Transitions have been measured up to J = 56 and K_a = 9 for H¹⁰BF₂, and up to J = 66 and K_a = 11 for H¹¹BF₂. Improved values for the rotational constants, boron nuclear quadrupole coupling constants, and quartic and sextic centrifugal distortion constants have been evaluated for both species.     

Origin bands of electronically forbidden spectra made allowed by centrifugal distortion

Watson’s theory of pure rotational spectra in nonpolar molecules is adapted to show that, if appropriate symmetry conditions are met, centrifugal distortion can lead to the appearance of the forbidden 0-0 origin band in an electronically forbidden spectrum. The intensity of such bands will be low; in the case of the benzene ùB_2u-¹A_1g system the maximum intensity of the forbidden origin is estimated to be about 10⁻⁷ of that of the 6¹₀ band in the main vibronic spectrum. The prospects for the experimental detection of such weak bands are discussed.     

Centrifugal distortion effects in the microwave spectra of 1,3-dioxane, tetrahydropyran and piperidine

Applying a bootstrap approach to transition assignment, a first-order centrifugal distortion analysis has been performed on 1,3-dioxane, tetrahydropyran, and piperidine (axial NH conformer). Q-branch transition frequencies for J up to 32 have been combined with previously published or remeasured frequencies for low J, R-, and Q-branch transitions to yield values for the quartic centrifugal distortion parameters. Comparison is made between the results obtained using two forms of the quartic Hamiltonian.     

On the Doppler distortion of the sea-wave spectra

Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum have continued for the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation [O.M. Phillips, J. Fluid Mech. 4 (1958) 426]. That leads to the spectrum decay ∼ω⁻⁵, where ω is the frequency of waves. There is a contradiction between the numerous experimental data and this spectrum. Experiments frequently show decay ∼ω⁻⁴ [Y. Toba, J. Oceanogr. Soc. Japan 29 (1973) 209; M.A. Donelan, J. Hamilton, W.H. Hui, Phil. Trans. R. Soc. London A315 (1985) 509; P.A. Hwang, et al., J. Phys. Oceanogr. 30 (1999) 2753]. There are several ways of the explanation of this phenomenon. One of them (proposed by Banner [M.L. Banner, J. Phys. Oceanogr. 20 (1990) 966]) takes into account the Doppler effect due to surface circular currents generated by underlying waves in the Phillips model.In this article the influence of the Doppler effect on an arbitrary averaged spectrum is considered using both analytic and numerical approaches. Although we mostly concentrated on the very important case of Phillips model, the developed technique and general formula can be used for the analysis of other spectra.For the particular case of Phillips spectra we got analytic asymptotics in the vicinity of spectral maximum and for high frequencies. Results were obtained for two most important angular dependences of the spectra: isotropic and strongly anisotropic. Together with the analytic investigation we performed numerical calculations in a wide range of frequencies. Both high and low frequency asymptotics are in very good agreement with the numerical results.It was shown that at least at low frequencies, the correction to the spectrum due to the Doppler shift is negligible. At high frequencies there is an asymptotic with tail ∼ω⁻³.     

Quadrupole coupling constants and centrifugal distortion constants of 3-bromopyridine from its microwave spectrum

The microwave spectrum of 3-bromopyridine has been investigated in the frequency range of 12–18 GHz and 30–40 GHz at dry ice temperature. The rotational, centrifugal distortion and quadrupole coupling constants of the two isotopic species ⁷⁹Br and ⁸¹Br have been evaluated. From the quadrupole coupling constants, double bond character in the CBr bond has been found to be 2.2% and the group electronegativity of the pyridyl radical to be 2.34.     

Theoretical analysis of the centrifugal distortion contributions to the rotational spectra of 2Π diatomics

The centrifugal distortion contributions to the rotational energies of diatomic molecules are derived from the resolution of the vibration-rotation wave equation. The unknown radial dependence of the fine structure constants is taken into account by means of a Taylor expansion around the equilibrium distance. Hence, one obtains the expressions of the centrifugal corrections associated with each fine structure constant in terms of the equilibrium values of its radial derivatives. The case of ²Π states is examined in detail. The dependence of the centrifugal distortion effects upon the choice of the coupling scheme representation is exhibited and a ²Π energy matrix containing the centrifugal constants of any order is proposed. Such a matrix is appropriate to fit the data for any value of the rotational quantum number. The theoretical expressions of the energy levels are related to the experimental data and the correlations between the spin-orbit centrifugal and spin-rotation contributions are put in evidence. It is shown that very compact formulas can be derived allowing a straightforward evaluation of the successive radial derivatives of the spin-orbit function in terms of the spectroscopic data $\text{A}{}^{\mathrm{(1)}}\text{? ?α}{}_{\mathrm{A}}\text{(}\text{w}{}_{\mathrm{e}}\text{B}{}_{\mathrm{e}}\text{)}$; $\text{A}{}^{\mathrm{(2)}}\text{? ?(1 +}\text{α}{}_{\mathrm{B}}\text{w}{}_{\mathrm{e}}\text{2B}{}_{\mathrm{e}}{}^2\text{)A}{}^{\mathrm{(1)}}$; …. Application of these results to the case of several molecules is considered and discussed.     

Microwave spectra and centrifugal distortion constants of formic acid containing 13C and 18O: Refinement of the harmonic force field and the molecular structure

Pure rotational spectra of H¹³COOH, HC¹⁸OOH, and HCO¹⁸OH have been measured in the frequency region 8–185 GHz. Analysis of the spectra has given improved rotational constants and quartic and sextic centrifugal distortion constants. The quartic distortion constants have been combined with previously published distortion constants of four other isotopic species, and with the vibrational wavenumbers of seven isotopic species, to produce a refined harmonic force field. An improved substitution structure and the ground state average structure have been obtained. Some unmeasured transition frequencies which may be of importance in radioastronomy are also presented.     

Raman spectra of mirabilite,Na2SO4·10H2O and the rediscovered metastable heptahydrate,Na2SO4·7H2O

Salt crystallisation in pores is known to cause serious damage to masonry. Sodium sulphate, often regarded as one of the most damaging salts, has a rich hydrate chemistry including one rediscovered metastable hydrate and a new high pressure octahydrate plus five known polymorphs of the anhydrous phase. The difficulty in working with these hydrates lies in their strong tendency to dehydrate or to convert to the stable phase, in the case of the heptahydrate. We present Raman spectra and a table of peak wavenumbers for randomly oriented crystals of mirabilite and the metastable heptahydrate, sufficient to distinguish between these phases that have SO₄ν₁ values of 989.3 and 987.6 cm⁻¹, respectively. Mirabilite has a Raman spectrum very similar to the free sulphate anion in solution, which is probably due to the mobility of oxygen atoms within the sulphate tetrahedron. The oxygen atoms in the heptahydrate sulphate groups have no partial occupancy, and predicted peak splitting is observed in the region 400–1200 cm⁻¹. Copyright © 2010 John Wiley & Sons, Ltd.     

Sextic centrifugal distortion constants of ozone

Theoretical expressions for the sextic centrifugal distortion constants of triangular triatomic molecules, as given by Sumberg and Parker, have been evaluated for the ozone molecule. For this calculation, the harmonic frequencies and cubic anharmonic potential constants determined by Barbe, Secroun, and Jouve were used. The calculated distortion constants were compared to complete sets of measured distortion constants recently determined by Maki, and by Barbe et al. Even though the measured constants range over more than four orders of magnitude, we find that the theory reproduces the relative magnitudes and the algebraic signs of the constants quite well. Absolute quantitative agreement is considerably better than order-of-magnitude.