Centrifugal Distortion Corrections Research Articles

Dynamical Tidal Love Numbers of Rapidly Rotating Planets and Stars

Abstract Tidal interactions play an important role in many astrophysical systems, but uncertainties regarding the tides of rapidly rotating, centrifugally distorted stars and gaseous planets remain. We have developed a precise method for computing the dynamical, nondissipative tidal response of rotating planets and stars, based on summation over contributions from normal modes driven by the tidal potential. We calculate the normal modes of isentropic polytropes rotating at up to ≃90% of their critical breakup rotation rates, and tabulate fits to mode frequencies and tidal overlap coefficients that can be used to compute the frequency-dependent, nondissipative tidal response (via potential Love numbers k ℓm ). Although fundamental modes (f-modes) possess dominant tidal overlap coefficients at (nearly) all rotation rates, we find that the strong coupling of retrograde inertial modes (i-modes) to tesseral (ℓ > ∣m∣) components of the tidal potential produces resonances that may be relevant to gas giants like Jupiter and Saturn. The coupling of f-modes in rapid rotators to multiple components of both the driving tidal potential and the induced gravitational field also affect the tesseral response, leading to significant deviations from treatments of rotation that neglect centrifugal distortion and high-order corrections. For very rapid rotation rates (≳70% of breakup), mixing between prograde f-modes and i-modes significantly enhances the sectoral (ℓ = ∣m∣) tidal overlap of the latter. The tidal response of very rapidly rotating, centrifugally distorted planets or stars can also be modified by resonant sectoral f-modes that are secularly unstable via the Chandrasekhar–Friedman–Schutz mechanism.

Structure, Stability, and Spectroscopic Properties of Small Acetonitrile Cation Clusters.

Ionization and fragmentation pathways induced by ionizing agents are key to understanding the formation of complex molecules in astrophysical environments. Acetonitrile (CH3CN), the simplest organic nitrile, is an important molecule present in the interstellar medium. In this work, DFT and MP2 calculations were performed in order to obtain the low energy structures of the most relevant cations formed from electron-stimulated ion desorption of CH3CN ices. Selected reaction pathways and spectroscopic properties were also calculated. Our results indicate that the most stable acetonitrile cation structure is CH2CNH+ and that hydrogenation can occur successively without isomerization steps until its complete saturation. Moreover, the stability of distinct cluster families formed from the interaction of acetonitrile with small fragments, such as CHn+, C2Hn+, and CHnCNH+, is discussed in terms of their respective binding energies. Some of these molecular clusters are stabilized by hydrogen bonds, leading to species whose infrared features are characterized by a strong redshift of the N-H stretching mode. Finally, the rotational spectra of CH3CN and protonated acetonitrile, CH3CNH+, were simulated using distinct computational protocols based on DFT, MP2, and CCSD(T) considering centrifugal distortion, vibrational-rotational coupling, and vibrational anharmonicity corrections. By adopting an empirical scaling procedure for calculating spectroscopic parameters, we were able to estimate the rotational frequencies of CH3CNH+ with an expected average error below 1 MHz for J values up to 10.

Concerning the asymmetric top rotational partition function in astronomical spectroscopy

The partition function plays an important role in determining column densities from emission lines in molecular clouds, since under typical conditions the two are linearly related. Here, we focus on successively applying quantum and centrifugal distortion correction terms to the classical rotational partition function for asymmetric top molecules, in an effort to uncover the relative importance of each term. We do this for example asymmetric top molecules that contain from one to four heavy atoms (water, methanimine, vinyl alcohol, and glycolaldehyde), at temperatures relevant to interstellar molecular clouds. Particular attention is paid to methanimine, for which it was recently attested that the value of the classical partition function significantly differs from the numerically summed (exact) value at several hundred Kelvin [Sharma et al., Astron. Nachrichten. 338, 125 (2017)]. We show that the classical values are in fact within 1% of the exact values from ~50 K to well above 400 K; the addition of three simple correction terms reduces the error to ≲0.001% (down to 10 K).

The heavy atom substitution and semi-experimental equilibrium structures of 2-ethylfuran obtained by microwave spectroscopy

The substitution rs and semi-experimental equilibrium reSE structures of the two conformers of 2-ethylfuran were obtained using a combination of microwave spectroscopy and quantum chemistry. The microwave spectrum was recorded using a molecular jet Fourier-transform spectrometer operating in the frequency range of 2.0 GHz–26.5 GHz. The spectra of all 13C and 18O isotopologues of both conformers could be measured in their natural abundances and the experimental gas-phase heavy atom structures were determined. All spectra were fitted using a semi-rigid rotor model including centrifugal distortion correction. The molecular geometries were compared with those of related molecules within the frame of the current literature. This work indicated that in some cases, the time required for recording survey scans of a Fourier-transform resonator setup can be reduced significantly with supports from adequate quantum chemical methods and spectral analysis skill.

The smell of coffee: the carbon atom microwave structure of coffee furanone validated by quantum chemistry

The rotational spectra of coffee furanone (2-methyltetrahydrofuran-3-one) have been measured in the frequency range from 2.0 to 26.5 GHz using a molecular jet Fourier transform microwave spectrometer. Quantum chemical calculations used for the conformational analysis yielded two stable twist conformers, which were described using the Cremer–Pople notation for five-membered rings. The experimental spectrum of the more stable conformer with the methyl group in equatorial position was assigned and fitted using a rigid rotor model with centrifugal distortion corrections. The spectra of all five 13C-isotopologues could be observed in natural abundance. The carbon atom structure was experimentally deduced using Kraitchman’s equations and compared with the structure calculated by quantum chemistry.

Gas-phase conformations of 2-methyl-1,3-dithiolane investigated by microwave spectroscopy

The conformational analysis of 2-methyl-1,3-dithiolane using quantum chemical calculations at some levels of theory yielded only one stable conformer with envelope geometry. However, other levels of theory indicated two envelope conformers. Analysis of the microwave spectrum recorded using two molecular jet Fourier transform microwave spectrometers covering the frequency range from 2 to 40 GHz confirms that only one conformer exists under jet conditions. The experimental spectrum was reproduced using a rigid-rotor model with centrifugal distortion correction within the measurement accuracy of 1.5 kHz, and molecular parameters were determined with very high accuracy. The gas phase structure of the title molecule is compared with the structures of other related molecules studied under the same experimental conditions.

Characterising molecules for fundamental physics: an accurate spectroscopic model of methyltrioxorhenium derived from new infrared and millimetre-wave measurements.

Precise spectroscopic analysis of polyatomic molecules enables many striking advances in physical chemistry and fundamental physics. We use several new high-resolution spectroscopic devices to improve our understanding of the rotational and rovibrational structure of methyltrioxorhenium (MTO), the achiral parent of a family of large oxorhenium compounds that are ideal candidate species for a planned measurement of parity violation in chiral molecules. Using millimetre-wave and infrared spectroscopy in a pulsed supersonic jet, a cryogenic buffer gas cell, and room temperature absorption cells, we probe the ground state and the Re[double bond, length as m-dash]O antisymmetric and symmetric stretching excited states of both CH3187ReO3 and CH3185ReO3 isotopologues in the gas phase with unprecedented precision. By extending the rotational spectra to the 150-300 GHz range, we characterize the ground state rotational and hyperfine structure up to J = 43 and K = 41, resulting in refinements to the rotational, quartic and hyperfine parameters, and the determination of sextic parameters and a centrifugal distortion correction to the quadrupolar hyperfine constant. We obtain rovibrational data for temperatures between 6 and 300 K in the 970-1015 cm-1 range, at resolutions down to 8 MHz and accuracies of 30 MHz. We use these data to determine more precise excited-state rotational, Coriolis and quartic parameters, as well as the ground-state centrifugal distortion parameter DK of the 187Re isotopologue. We also account for hyperfine structure in the rovibrational transitions and hence determine the upper state rhenium atom quadrupole coupling constant eQq'.

Two Conformers of N,N-Diethylpropionamide As Observed by Microwave Spectroscopy and Quantum Chemistry.

The microwave spectra of two conformers of N,N-diethylpropionamide were recorded using a molecular beam Fourier transform microwave spectrometer operating in the frequency range 2-26.5 GHz. Hyperfine splittings arising from the (14)N quadrupole coupling effect were observed and analyzed. Fits using a rigid rotor model with centrifugal distortion correction and first-order perturbation approach for the quadrupole coupling yielded highly accurate molecular parameters and standard deviations within the measurement accuracy for both conformers. Complementary quantum chemical calculations were carried out for a conformational analysis, theoretical values of the spectroscopic constants, and the (14)N nuclear quadrupole coupling constants.

Clumped-isotope signatures at equilibrium of CH4, NH3, H2O, H2S and SO2

High precision Δi values at equilibrium determined by theoretical methods are imperatively needed as references for the development of new clumped-isotope thermometers (or tracers). In this study, quantum chemistry methods with corrections beyond the harmonic approximation are used to obtain the clumped-isotope signatures at equilibrium of several gas-phase molecules (i.e., CH4, NH3, H2O, H2S, and SO2). Here, we consider as many corrections to the traditional Bigeleisen–Mayer equation as possible to obtain accurate Δi values at equilibrium and their temperature dependences. The corrections include anharmonic correction for zero-point energy, anharmonic correction for vibrational excited states, vibration–rotation coupling correction for zero-point energy, vibration–rotation coupling correction for vibrational excited states, quantum mechanical correction to rotation, and centrifugal distortion correction, which are important for theoretical understanding of clumped-isotope signals. Specifically, molecular constants are calculated via second-order perturbative analysis at the MP2/aug-cc-pVTZ level. The CCSD/6-311+G(3df,3pd) and CCSD/aug-cc-pVTZ levels are further employed to ensure the precision of harmonic frequencies of methane. For methane, a polynomial fit of ΔCH313D values over the temperature range of from 273.15 to 1000K is obtained: ΔCH313D=0.002551000T4-0.116391000T3+1.013641000T2-0.436271000T Our results are slightly different from previous theoretical calculations, and may serve as new anchors for calibrating experimental observations.

Theoretical and experimental study on line intensities of CO2 and CO transitions near 1.5 μm at high temperatures

Accurate spectroscopic parameters of probed species, especially the line strengths at high temperatures, are important for combustion diagnosis based on tunable diode laser absorption spectroscopy (TDLAS). However, most of the line strengths in databases are measured at normal atmospheric temperature and calculated at high temperatures. For example, the mostly used HITRAN database focuses on atmospheric conditions where the temperature ranging from 200-350 K. The high-temperature parameters in HITRAN database are obtained by calculation and the temperatures are limited to 3000 K. In this paper the line strengths of 30012-00001 transition band of CO2 and 3-0 transition band of CO at normal temperature (300 K) and some high temperatures (400-6000 K) are calculated using our calculated partition function and experimental transition moment squared and Herman-Waills factor coefficients. The total internal partition sums (TIPS) are calculated for CO2 and CO with the product approximation of the vibrational and the rotational partition functions. The vibrational partition function is calculated in harmonic oscillator approximation. For rotational partition sums, the centrifugal distortion corrections are taken into consideration. In order to validate the calculation, a high-temperature measurement system based on TDLAS is developed using a DFB diode laser near 1.573 μm. High-resolution absorption spectra of CO2 and CO can be recorded in a heated cell as a function of temperature and pressure. The 9 lines of CO2 30012-00001 band and 2 lines of CO 3-0 band have been measured by means of direct absorption spectroscopy in the temperature range of 300-800 K. The corresponding line strengths are inferred from the measured direct absorption spectrum. The calculated result and experimental data are compared with the HITRAN values. The calculated and measured data agree well with the existing databases (HITRAN 2012), the discrepancies being less than 3% for most of the probed transitions. All the results confirm the validity of the calculation of total partition function and the line strengths calculated. The variation of the line strength as a function of temperature for a certain transition is also discussed. While the lower state energy determines the equilibrium molecular population in the unabsorbing state as a function of temperature, how the line strength of a particular transition varies with temperature can also be controlled.

Rotational Spectra of Bicyclic Decanes: The Trans Conformation of (−)-Lupinine

The conformational and structural properties of the bicyclic quinolizidine alkaloid (-)-lupinine have been investigated in a supersonic jet expansion using microwave spectroscopy. The rotational spectrum is consistent with a single dominant trans conformation within a double-chair skeleton, which is stabilized by more than 10.4 kJ mol(-1) with respect to other conformations. In the isolated conditions of the jet, the hydroxy methyl side chain of the molecule locks in to form an intramolecular O-H···N hydrogen bond to the electron lone pair at the nitrogen atom. Accurate rotational constants, centrifugal distortion corrections, and (14)N nuclear quadrupole coupling parameters are reported and compared to ab initio (MP2) and DFT (M06-2X) calculations. The stability of lupinine is further compared computationally with epilupinine and decaline in order to gauge the influence of intramolecular hydrogen bonding, absent in these molecules.

Theoretical studies of partition functions of flue gas SO <sub><em>2</em></sub> isotope

The geometrical structure of flue gas 32 S 16 O2 and 34 S 16 O2 molecule have been optimized at B3P86/cc-PV5Z level using Gaussian03 program, we gain theirs equilibrium geometry, resonance frequency and rotational constants et al.. The total internal partition functions are calculated at the temperatures from 70 K to 6000 K for 32 S 16 O2 and 34 S 16 O2 with the product approximation. Thereinto, the rotational partition sums Qrot adopt the WATSON rigid rotator model, which take into account centrifugal distortion corrections. The vibrational partition sums Qvib use the harmonic oscillator approximation model. It is found that the calculated total internal partition functions are consistent with those of- fered by HITRAN database from 70 K to 3000 K, and the errors shows linear correlation approximately. By fitting the errors, the total internal partition functions values at high temperature range of 3000 K to 6000 K were corrected. The corrected total internal par- tition functions are fitted to a four-order polynomial expression in T, and the coefficients are gained at high temperature. This allows a rapid and accurate calculation of the total internal partition functions at the temperature from 3000 K to 6000 K.

Study of the partition functions of SiO2 molecules

The total internal partition functions are calculated for 16O28Si16O at temperatures from 20—6000 K. In deducing the rotational partition sums Qrot, the centrifugal distortion corrections are taken into account. The method used for calculating the vibrational partition sums Qvib is the harmonic oscillator approximation. The temperature range is divided into five regions and the calculated total internal partition functions are fitted to a fourth-order polynomial in T, and the coefficients are evaluated in the five temperature regions. This permits rapid and accurate calculation of the total internal partition functions in the temperature range from 20—6000 K.

Line intensities of 3000—0200 and 1001—0110 transition bands of 14N216O at high temperature

The total internal partition sums (TIPS) were calculated for nitrous oxide with the product approximation. For rotational partition sums Qrot, the centrifugal distortion corrections are under consideration. The calculation method for the vibrational partition sums Qvib used is the harmonic oscillator approximation. Using experimental transition moment squared and Herman-Waills factor coefficients and the calculated partition functions, we computed the line intensities of 3000—0200 and 1001—0110 transitions of nitrous oxide at several temperatures. The agreement between the calculated line intensities and experimental results and those extrapolated from HITRAN database is fairly good at temperatures up to 3000 K, which shows that the calculation of partition function and line intensity at high temperature is reliable. Furthermore, the line intensities and spectral simulations at the higher temperatures of 4000 and 5000 K are also presented.

Determination of the spin–spin centrifugal distortion parameters for deuterated selenoformaldehyde in its first excited triplet state

Recently-formulated centrifugal distortion corrections to the spin–spin Hamiltonian have been used to analyse the first excited triplet state ( ã 3 A 2) of deuterated selenoformaldehyde. By including six spin–spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required.

Analysis of the rotational spectrum of methylene (CH2) in its vibronic ground state with an Euler expansion of the Hamiltonian

We present an analysis of a global, field-free data set of the methylene radical CH2 in its X 3B1 vibronic ground state by means of a novel Euler expansion of the Hamiltonian. The data set comprises pure rotational transitions up to 2 THz obtained with microwave accuracies of 30-500 kHz as well as nu2 ground-state combination differences and pure rotational data obtained with infrared accuracies of 0.001-0.010 cm(-1). Highly accurate spectroscopic parameters have been determined. These include rotational, spin-spin, spin-rotation, and electron-spin-nuclear-spin coupling terms along with several centrifugal distortion corrections. The spectroscopic model has been tested and improved by recording newly three weak DeltaN not equalDeltaJ fine-structure components of the N(KaKc)=2(12)-3(03) and 5(05)-4(14) transitions near 434, 454, and 581 GHz. These lines were rather close to the predictions. Overall weighted root mean squares of 1.28 and 0.83 were achieved for fits in which the Euler expansion was used only for the rotational part of the Hamiltonian or for the rotational and spin-spin terms of the Hamiltonian, respectively. The resulting spectroscopic parameters allow for precise frequency predictions of astrophysically important rotational transitions of methylene.

The Chiral Molecule CHClFI: First Determination of Its Molecular Parameters by Fourier Transform Microwave and Millimeter-Wave Spectroscopies Supplemented by ab Initio Calculations

The rotational spectrum of chlorofluoroiodomethane (CHClFI) has been investigated. Because its rotational spectrum is extremely crowded, extensive ab initio calculations were first performed in order to predict the molecular parameters. The low J transitions were measured using a pulsed-molecular-beam Fourier transform spectrometer, and the millimeter-wave spectrum was measured to determine accurate centrifugal distortion constants. Because of the high resolution of the experimental techniques, the analysis yielded accurate rotational constants, centrifugal distortion corrections, and the complete quadrupole coupling tensors for the iodine and chlorine nuclei, as well as the contribution of iodine to the spin-rotation interaction. These molecular parameters were determined for the two isotopologs CH35ClFI and CH37ClFI. They reproduce the observed transitions within the experimental accuracy. Moreover, the ab initio calculations have provided a precise equilibrium molecular structure. Furthermore, the ab initio molecular parameters are found in good agreement with the corresponding experimental values.

Perturbations in the pure rotational spectrum of CoCl (X 3Φi): A submillimeter study

The millimeter/submillimeter-wave spectrum of the CoCl radical (X (3)Phi(i)) has been recorded using direct absorption techniques in the frequency range 340-510 GHz. This work is the first pure rotational study of this molecule. The radical was created by the reaction of Cl(2) with cobalt vapor. Rotational transitions arising from the Omega=4, 3, and 2 spin-orbit components of Co(35)Cl have been measured, all of which exhibit hyperfine splittings due to the (59)Co nucleus (I=7/2). Transitions arising from the Co(37)Cl species were also recorded, as well as those originating in the v=1, 2, 3, and 4 vibrational states of both isotopomers. The spin-orbit pattern exhibited by the molecule is unusual, with the Omega=3 component significantly shifted relative to the other spin components. In addition, the regular octet hyperfine splittings become distorted above a certain J value for the Omega=3 transitions only. These effects suggest that the molecule is highly perturbed in its ground state, most likely a result of second-order spin-orbit mixing with a nearby isoconfigurational (1)Phi(3) state. The complete data set for Co(35)Cl and Co(37)Cl were fit successfully with a case (a) Hamiltonian but required a large negative spin-spin constant of lambda=-7196 GHz and higher order centrifugal distortion corrections to the rotational, spin-orbit, spin-spin, and hyperfine terms. The value of the spin-spin constant suggests that the Omega=3 component is shifted to higher energy and lies near the Omega=2 sublevel. The hyperfine parameters are consistent with a delta(3)pi(3) electron configuration and indicate that CoCl is more covalent than CoF.

The microwave spectrum of cobalt monoxide: Hyperfine interactions in the X 4Δ state

The rotational spectrum of CoO in the Δ4 ground state was observed using a source-modulated submillimeter-wave spectrometer. A direct current sputtering method using cobalt powder placed in the hollow cathode electrode was used to generate the CoO radical in an atmosphere of oxygen and helium. In total 84 spectral lines were precisely measured in the frequency region of 255–465 GHz for eight rotational transitions of the two lowest spin substates. Each rotational transition consists of eight components due to the Co59 (I=7/2) hyperfine interaction. A least squares analysis of the measured frequencies gave a new set of molecular parameters: rotational constant, hyperfine coupling constants, a, bF, c, and eQq, centrifugal distortion corrections to rotation and spin–orbit interaction, and the less well known higher-order spin–orbit distortion term to the Fermi contact interaction, bS. A comparison of the determined molecular hyperfine coupling constants was made with those of atomic/ionic Co in order to assess the inherent characteristics of the molecular orbitals around the Co nucleus.

Equilibrium conformation of dimethylaminodichlorophosphine molecule: the use of the results of quantum-chemical calculations and spectroscopic measurements in the analysis of gas-phase electron diffraction data

Geometric parameters and force fields of two stable isomers of dimethylaminodichlorophosphine molecule, a gauche-conformer with C1 symmetry (A) and anti-conformer with C s symmetry (D), resulting from internal rotation about the P—N bond, were calculated in the RHF/6-31G* approximation. Using the scaled quantum-chemical force field for the most stable conformer A, the first reliable interpretation of the vibrational spectra of the light and perdeuterated isotopomers of dimethylaminodichlorophosphine was obtained. The root-mean-square vibrational amplitudes, harmonic and anharmonic vibrational corrections, and centrifugal distortion corrections were also calculated. Structural analysis of electron diffraction data was performed with consideration of nonlinear kinematic effects at the first-order level of perturbation theory. The experimental values of the equilibrium geometric parameters were estimated. The results obtained suggest a nonplanar equilibrium configuration of the amino group in the dimethylaminodichlorophosphine molecule.