Rotational partition functions for linear molecules

Abstract

An accurate closed-form expression for the rotational partition function of linear polyatomic molecules in Il: electronic states is derived, including the effect of nuclear spin (significant at very low temperatures) and of quartic and sextic centrifugal distortion terms (significant at moderate and high temperatures). The proper first-order quantum correction to the classical rigid-rotator partition function is shown to yield Qr -;:;;/3 -I exp(/3 13), where/3=hcB IkTandB is the rotational constant in cm-I ; for /3>0.2 additional power-series terms in/3 are necessary. Comparison between the results ofthis treatment and exact summations are made for HCN and C z H 2 at temperatures from 2 to 5000 K, including separate evaluation of the contributions of nuclear spin and centrifugal distortion.

Line Positions and Absolute Intensities in the Laser Bands of Carbon-12 Oxygen-17 Isotopic Species of Carbon Dioxide

“…Observed and calculated wavenumbers of the laser bands are reported for the 16 (2), which shows the good consistency of our data with those obtained in the different spectral regions of the fundamental bands.…”

“…In the first paper (1), fundamental bands of the x O 13 C 17 O species ( x ϭ 16, 17, or 18) were analyzed. In the second paper (2), accurate sets of molecular constants for the fundamental and first hot bands of the 16 In this paper, line positions and absolute line intensities of the 00011-10001 and 00011-10002 bands of the above species, near 10 and 9 m, respectively, are presented. Note that throughout this article, we will make use of the HITRAN notation for the vibrational levels of carbon dioxide: the 10001 and 10002 notations correspond to the upper and lower interacting levels of the first Fermi dyad, (10 0 0 -0200)I and (1000 -02 0 0)II, respectively.…”

“…The wavenumbers of the laser bands have been very accurately measured for practically all species of CO 2 (3,4) with the noticeable exception of the laser bands of 16 …”

Ammonia monitoring near 15 µm with diode-laser absorption sensors

“…Superimposed on the plot is an estimate for the total partition function at 300, 500, and 1000 K that uses McDowell's detailed rotational partition function sums, but includes contributions from nitrogen spin ͑McDowell's published sums include spin contributions only from the H atoms͒ and the vibrational partition function. 7 The values based on McDowell's calculations agree well with both the classical model and with the polynomial expression by use of Gamache's coefficients. Thus we conclude that Gamache's partition function is more accurate than the data in Hitran96.…”

Absolute Line Intensities in Acetylene: The 1.5-μm Region

“…(18). For 13 C 12 CH 2 , it was calculated to be Q v = 1.15, from the ratio of the total internal partition sum Q, calculated as detailed above, to the rotational partition sum, calculated using the expressions of McDowell (19) and the constants of Ref. (20).…”