Discussion of a Wiener-Hopf type integro-differential equation

Summary An integro-differential equation is considered, which can be solved by the Wiener-Hopf technique. The quotient of the solution and its first derivative, for the value zero of the independent variable, is expanded in terms of a small parameter.     

The millimeter-wave spectrum of 2-cyanoethanol

In order to better characterize the chemistry involving CN groups in regions of star-formation, we have recorded the millimeter-wave rotational spectrum of 2-cyanoethanol. Almost 6000 new transitions were assigned to two separate conformers and three torsionally excited states. The lowest energy conformer, gauche-2-cyanoethanol, its 1st excited torsion, and the ground state for the anti-I-conformer are best characterized with basic asymmetric rigid-rotor Hamiltonians including distortion. All fit close to experimental uncertainty. Fits for the 2nd and 3rd excited torsional states for the gauche-conformer are of somewhat lower quality, which might be explained by a potential interaction between these states. The results of the various fits are discussed in this paper. In all, the present characterization of the spectrum and extensions through prediction should be more than sufficient to guide future millimeter-wave observational studies of this species in the interstellar medium.     

Extended analysis of hydroxyacetone in the torsional ground state

The torsion-rotation spectrum of hydroxyacetone presents a highly challenging analysis problem in molecular physics. Continuing analyses of this species are compelling due to a nascent interest from astronomers, who believe hydroxyacetone may link a variety of organic chemical families observed in the interstellar medium (ISM). Recent work has demonstrated the difficulties in analysis of the millimeter spectrum, and the modestly weaker spectrum in this region has not afforded an ISM detection. We present an extension of the laboratory measurements and analysis up to the room temperature Boltzmann peak near 300 GHz, thus providing sufficient coverage to examine the ISM for the strongest features expected in star-forming hot cores. Even without subsequent detection, searches for the stronger features will produce the lowest possible upper limits of this elusive species.     

The millimeter and submillimeter rotational spectrum of 1,3-dihydroxyacetone

Recent detection of the 2C sugar glycolaldehyde in the Sgr B2(N-LMH) hot core source as well as the presence of several sugars and other polyhydroxylated species in the Murchison meteorite have led to interest in observational searches for higher order sugars in the interstellar medium. 1,3-Dihydroxyacetone, the simplest 3C sugar, is one of the species detected in Murchison and is of considerable importance for observational searches as the next step in complexity for interstellar sugars. However, little spectroscopic information is available for this molecule. We present here the Doppler-limited rotational spectrum of 1,3-dihyroxyacetone to 450 GHz. Assignments include the ground state up to J=104 and four additional vibrational states. Standard rotational and quartic centrifugal distortion constants have been determined for each of these states.     

The millimeter-wave spectrum of methoxyacetonitrile

This paper is the second as part of a study to elucidate cyano group chemistry in the interstellar medium, wherein we present a characterization of the millimeter-wave spectrum of methoxyacetonitrile. Its structural isomer, 2-cyanoethanol was described in paper Braakman and Blake (submitted for publication) [1]. The rotational spectrum of methoxyacetonitrile shows the characteristics of a well-behaved asymmetric rigid-rotor. We assigned nearly 7400 transitions to 2 conformers and 2 excited states. All were fit to Watson A-reduced Hamiltonians, including only the effects of centrifugal distortion. The lowest energy states are fit close to experimental accuracy, with a gradual decrease in quality for higher energy states. No repulsive interactions are apparent. The measurements and predictions from the fits reported here are being used as a basis for observational studies of this species.