Rotational partition functions for symmetric-top molecules

McDowell, Robin S.

doi:10.1063/1.458865

Cited by 47 publications

(28 citation statements)

References 35 publications

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“…a Nuclear spin degeneracy is considered as 1 (for more details, see Appendix A). b Rotational partition function computed with approximated rotational partition function for slightly asymmetric tops given by McDowell (1990):…”

Section: Discussionmentioning

confidence: 99%

“…In the present paper we address the special case of symmetric (or asymmetric) tops where the degeneracy is state independent, meaning that g (i) ns = g ns . The classical approximation of the rotational partition function (7), based on a rigid rotor model, can also be used for symmetric and slightly asymmetric tops considering the rotational constants defined in the Principal Axis System (McDowell 1990;Herzberg 1991;Mangum & Shirley 2015).…”

Section: Rotational Partition Functionmentioning

confidence: 99%

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Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium

Carvajal

Favre

Kleiner

et al. 2019

A&A

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We emphasize that the completeness of the partition function, that is, the use of a converged partition function at the typical temperature range of the survey, is very important to decrease the uncertainty on this quantity and thus to derive reliable interstellar molecular densities. In that context, we show how the use of different approximations for the rovibrational partition function together with some interpolation and/or extrapolation procedures may affect the estimate of the interstellar molecular column density. For that purpose, we apply the partition function calculations to astronomical observations performed with the IRAM-30m telescope towards the NGC7538-IRS1 source of two N-bearing molecules: isocyanic acid (HNCO, a quasilinear molecule) and methyl cyanide (CH 3 CN, a symmetric top molecule). The case of methyl formate (HCOOCH 3 ), which is an asymmetric top O-bearing molecule containing an internal rotor is also discussed. Our analysis shows that the use of different partition function approximations leads to relative differences in the resulting column densities in the range 9 to 43%. Thus, we expect this work to be relevant for surveys of sources with temperatures higher than 300 K and to observations in the infrared.

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Section: Discussionmentioning

confidence: 99%

Section: Rotational Partition Functionmentioning

confidence: 99%

Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium

Carvajal

Favre

Kleiner

et al. 2019

A&A

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“…Here, Q is the rotational partition function, which for a symmetric‐top molecule belonging to the point group D 3d can be calculated from the expression derived in McDowell . According to our calculation, the partition function, Q , at room temperature for ethane is ~49,123, which is a relatively large value compared to the partition function of linear molecules such as nitrogen, which has a value of ~465 at room temperature.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Rotational CARS thermometry and concentration measurements in ethane‐nitrogen mixtures using Fourier analysis

Hosseinnia

Nordström

Fatehi

et al. 2018

J Raman Spectroscopy

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Rotational coherent anti‐Stokes Raman scattering (CARS) is an established diagnostic technique for thermometry and species concentration measurements of di‐atomics and tri‐atomics in combustion processes; however, studies on hydrocarbon fuel molecules have been scarce. In this work, we have investigated the diagnostic potential for rotational CARS on ethane with emphasis on concentration measurements in mixtures with nitrogen. Rotational CARS spectra have periodic line structures, and because ethane and nitrogen spectra partially overlap, a novel Fourier analysis approach was developed and applied to facilitate evaluation of relative concentrations and temperatures. Instead of the standard procedure of spectral fitting using libraries of theoretically calculated spectra, the fitting was based on an experimental database of temperatures and relative ethane/nitrogen concentrations. The method was successfully demonstrated in an ethane diffusion flame where ethane, initially at room temperature, is heated downstream as well as mixed with increasing amounts of nitrogen. The evaluated temperatures and concentrations are in good agreement with computational fluid dynamic model simulations.

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“…Rotational partition functions were determined using the formulae in (McDowell 1988;McDowell 1990). Vibrational partition functions were calculated using the harmonic oscillator Fig.…”

Section: Laraia Et Al (2011 L2011mentioning

confidence: 99%

Partition functions

Popovas

Jørgensen

2016

A&A

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Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims. We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H 2 . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H 2 are also reported. Conclusions. For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when using polynomial fits to the computed values. Reported internal partition functions and thermodynamic quantities in the present work are shown to be more accurate than previously available data.

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Rotational partition functions for symmetric-top molecules

Cited by 47 publications

References 35 publications

Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium

Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium

Rotational CARS thermometry and concentration measurements in ethane‐nitrogen mixtures using Fourier analysis

Partition functions

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