Rho Axis Method Research Articles

Westerfit: A new program for spin–torsion–rotation spectra

A new program, westerfit, has been developed to treat Cs molecules with internal rotation and spin angular momentum. It implements a single diagonalization Rho Axis Method approach for the torsion–rotation alongside a complete treatment of nuclear quadrupole interaction and spin–rotation coupling. Unlike other programs designed for internal rotation with spin effects, westerfit includes matrix elements off-diagonal in the rotational angular momentum quantum number, N, rather than the perturbative treatment of the spin–rotation and quadrupole interactions. This full combined approach allows fitting of all symmetrically allowed terms in both the spin–rotation and the quadrupole tensors as well as inclusion of higher order terms coupling the large amplitude motion to the spin angular momentum. The program was benchmarked against other published programs to test molecular cases of torsion–rotation, spin–rotation, and spin–torsion-rotation. All three tests produced a lower RMS. westerfit paves a way forward for complete treatment of spin–torsion–rotation problems regardless of barrier height or quadrupole moment.

Investigation of the rotational spectrum of CH$_3$17OH and its tentative detection toward Sagittarius B2(N)

Methanol is an abundant and widespread molecule in the interstellar medium. The column density of its 18O isotopolog, CH$_3$18OH, is in some star-forming regions so high that the search for CH$_3$17OH is promising. But only very few transition frequencies of CH$_3$17OH with a microwave accuracy have been published prior to our investigation. We want to extend the very limited rotational line list of CH$_3$17OH to be able to search for this isotopolog in the interstellar medium. We recorded the rotational spectrum of CH$_3$17OH between 38 and 1095 GHz employing a methanol sample enriched in 17O to 20<!PCT!>. A torsion-rotation Hamiltonian model based on the rho-axis method was employed to fit the data, as in our previous studies. We searched for rotational transitions of CH$_3$17OH in the imaging spectral line survey ReMoCA obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the high-mass star-forming region Sgr B2(N). The observed spectra were modeled under the assumption of local thermodynamic equilibrium (LTE). The assignments cover $0 J 45$, $K_a 16$, and mainly the $ t = 0$ and 1 torsional states. The Hamiltonian model describes our data well. The model was applied to derive a line list for radio-astronomical observations. We report a tentative detection of CH$_3$17OH along with secure detections of the more abundant isotopologs of methanol toward Sgr B2(N2b). The derived column densities yield isotopic ratios 12C/13C = 25, 16O/18O = 240, and 18O/17O = 3.3, which are consistent with values found earlier for other molecules in Sgr B2. The agreement between the 18O/17O isotopic ratio that we obtained for methanol and the 18O/17O ratios reported in the past for other molecules in Sgr B2(N) strongly supports our tentative interstellar identification of CH$_3$17OH. The accuracy of the derived line list is sufficient for further radio astronomical searches for this methanol isotopolog toward other star-forming regions.

Rotational spectroscopy of CH3OD with a reanalysis of CH3OD toward IRAS 16293–2422

We have started a measurement campaign of numerous methanol isotopologs in low-lying torsional states in order to provide extensive line lists for radio astronomical observations from an adequate spectroscopic model and to investigate how the intricate vibrationtorsion-rotation interactions manifest themselves in the spectra of different isotopic species. After CD3OH and CD3OD, we turn our focus to CH3OD, which is an important species for studying deuteration in prestellar cores and envelopes that enshroud protostars. Notably, deuteration is frequently viewed as a diagnostic tool for star formation. The measurements used in this study were obtained in two spectroscopic laboratories and cover large fractions of the 34 GHz-1.35 THz range. As done in previous studies, we employed a torsion-rotation Hamiltonian model for our analysis that is based on the rho-axis method. The resulting model describes the ground and first excited torsional states of CH3OD well up to quantum numbers J ⩽ 51 and Ka ⩽ 18. We derived a line list for radio astronomical observations from this model that is accurate up to at least 1.35 THz and should be sufficient for all types of radio astronomical searches for this methanol isotopolog in these two lowest torsional states. This line list was applied to a reinvestigation of CH3OD in data from the Protostellar Interferometric Line Survey of IRAS 16293–2422 obtained with the Atacama Large Millimeter/submillimeter Array. The new accurately determined value for the column density of CH3OD implies that the deuteration in methanol differs in its two functional groups by a factor of ~7.5.

A global rho-axis method for fitting asymmetric tops with one methyl internal rotor and two 14N nuclei: Application of BELGI-2N to the microwave spectra of four methylimidazole isomers.

A number of internal rotation codes can deal with the combination of one or two internal rotors with one 14N quadrupole nucleus, but once it comes to two 14N nuclei, no such code is available even for the case of one internal rotor. We present here the extension of our internal rotor program called BELGI-2N using the rho-axis method global approach to deal with compounds containing one methyl rotor and two weakly coupling 14N nuclei. To test our new code, we applied it to the microwave data recorded for N-methylimidazole, 2-methylimidazole, 4-methylimidazole, and 5-methylimidazole using a chirped-pulse Fourier transform microwave spectrometer in the 7.0-18.5GHz frequency range. Compared to the previously published study, BELGI-2N was able to (i) significantly increase the number of assigned and fitted lines, (ii) fit the complete datasets considering both the internal rotation and the 14N nuclear quadrupole coupling effects simultaneously, and (iii) achieve standard deviations within the measurement accuracy for all methylimidazole isomers.

Investigation of the rotational spectrum of CD3OD and an astronomical search toward IRAS 16293-2422

Solar-type prestellar cores and protostars frequently display large amounts of deuterated organic molecules and, in particular, high relative abundances of doubly and triply deuterated isotopologs. Recent findings on CHD2OH and CD3OH toward IRAS 16293–2422 suggest that even fully deuterated methanol, CD3OD, may be detectable as well. However, searches for CD3OD are hampered in particular by the lack of intensity information from a spectroscopic model. The objective of the present investigation is to develop a spectroscopic model of CD3OD in low-lying torsional states that is sufficiently accurate to facilitate searches for this isotopolog in space. We carried out a new measurement campaign for CD3OD involving two spectroscopic laboratories that covers the 34 GHz–1.1 THz range. A torsion-rotation Hamiltonian model based on the rho-axis method was employed for our analysis. Our resulting model describes the ground and first excited torsional states of CD3OD well up to quantum numbers J ⩽ 51 and Ka ⩽ 23. We derived a line list for radio-astronomical observations from this model that is accurate up to at least 1.1 THz and should be sufficient for all types of radio-astronomical searches for this methanol isotopolog. This line list was used to search for CD3OD in data from the Protostellar Interferometric Line Survey of IRAS 16293–2422 obtained with the Atacama Large Millimeter/submillimeter Array. While we found several emission features that can be attributed largely to CD3OD, their number is still not sufficiently high enough to establish a clear detection. Nevertheless, the estimate of 2 × 1015 cm−2 derived for the CD3OD column density may be viewed as an upper limit that can be compared to column densities of CD3OH, CH3OD, and CH3OH. The comparison indicates that the CD3OD column density toward IRAS 16293–2422 is in line with the enhanced D/H ratios observed for multiply deuterated complex organic molecules.

Internal rotation analysis of the microwave and millimeter wave spectra of fluoral (CF3CHO)

The rotational spectrum (4–40 GHz and 50–330 GHz) has been measured and analyzed for trifluoroacetaldehyde, also known as fluoral (CF3CHO), which is one of the degradation products of the fluorinated contaminants emitted into the atmosphere. The complexity of the spectroscopic analysis of this molecule arises from the strong coupling between the internal rotation motion of CF3 group and the overall rotation of the molecule. The value obtained for its coupling constant (ρ = 0.91723481(49)) is comparable to the corresponding value of methanol (CH3OH, ρ = 0.81), which is known for its complex spectrum. A total of 12,322 transitions of the ground, the first and second excited torsional states (ΔE1υt = 62.0183(13)cm−1; ΔE2υt = 120.3315(13)cm−1) with J ≤ 50 were included in the analysis that was performed employing the rho-axis-method (RAM), and the RAM36 code. A fit within experimental error (root mean square deviation equals to 35 kHz) has been achieved for this dataset using 47 parameters of the RAM torsion-rotation Hamiltonian. In the course of the analysis, it became evident that for such high ρ value, as it is determined for fluoral, a larger than usual torsional basis set at the first diagonalization step of the two-step diagonalization procedure is required for achieving a fit within experimental error.

Rotational and rovibrational spectroscopy of CD3OH with an account of CD3OH toward IRAS 16293−2422

Solar-type protostars have been shown to harbor highly deuterated complex organics, as evidenced, for instance, by the high relative abundances of doubly and triply deuterated isotopologs. While this degree of deuteration may provide important clues in studying the formation of these species, spectroscopic information on multiply deuterated isotopologs is often insufficient. In particular, searches for triply deuterated methanol, CD3OH, are hampered to a large extent by the lack of intensity information from a spectroscopic model. The aim of the present study is to develop a spectroscopic model of CD3OH in low-lying torsional states that is sufficiently accurate to facilitate further searches for CD3OH in space. We performed a new measurement campaign for CD3OH involving three spectroscopic laboratories that covers the 34 GHz−1.1 THz and the 20−900 cm−1 ranges. The analysis was performed using the torsion-rotation Hamiltonian model based on the rho-axis method. We determined a model that describes the ground and first excited torsional states of CD3OH, up to quantum numbers J ≤ 55 and Ka ≤ 23, and we derived a line list for radio-astronomical observations. The resulting line list is accurate up to at least 1.1 THz and should be sufficient for all types of radio-astronomical searches for this methanol isotopolog. This line list was used to search for CD3OH in data from the Protostellar Interferometric Line Survey of IRAS 16293−2422 using the Atacama Large Millimeter/submillimeter Array. Specifically, CD3OH is securely detected in the data, with a large number of clearly separated and well-reproduced lines. We not only detected lines belonging to the ground torsional state, but also several belonging to the first excited torsional state. The derived column density of CD3OH and abundance relative to the non-deuterated isotopolog confirm the significant enhancement of this multiply deuterated variant. This finding is in line with other observations of multiply deuterated complex organic molecules and may serve as an important constraint on their formation models.

Conversion of ortho and para nuclear spin isomers of methanol studied by internal axis method

Quantum statistics of identical nuclei in molecules gives rise to nuclear spin isomers. Except for methanol (CH3OH) that has internal rotation (i.e., torsion), all the studied molecules so far have overall rotational symmetry. Methanol does not rotate around the overall rotational symmetry axis but the methyl group axis. The identical nuclei in the methyl group produce a specific type of nuclear spin isomers of the ortho-CH3OH and para-CH3OH in methanol. Conversions between these two spin isomers have been observed in the experiment and a theory based on the rho-axis method (RAM) for partially explaining their conversions has been developed by us recently. However, besides RAM the internal axis method (IAM) is a classical method commonly used by many researchers and the coupling of the angular momenta between torsion and overall rotation in methanol can be completely separated from each other in the IAM. In this paper, as a series work we present a general theoretical model about conversion of ortho–para methanol using the IAM based on quantum relaxation theory. The expressions of the ortho–para state-mixing strengths induced by the nuclear spin–spin and nuclear spin–rotation interactions have been analytically deduced and numerically calculated. We found that the ortho–para states-mixings and ortho–para conversion can be induced by all these two intramolecular interactions whereas the nuclear spin–rotation interaction plays a major role. The conversion rate at temperature 300 K and pressure 1 Torr summed over eight ortho–para level pairs with gaps less than 2.7 GHz is calculated to be 1.4 × 10−2 s−1, which is close to the measured value of 2.1 (3) × 10−2 s−1, indicating the quantum relaxation is the leading process in the spin isomers conversions of methanol and suggesting our theory to be valid for other gaseous methanol-like molecules having torsion tunneling of symmetrical group. The most probable gateways in methanol for collision-induced population transfers are found to be levels-pairs in the ground-state A–E species of (υtJ, K, p) = (0, 24, 4, 1)−(0, 25, 2, 1) by nuclear spin–spin coupling, (0, 22, 5, p)−(0, 21, 6, −1) and (3, 34, 1, 0)−(3, 35, 0, 1) by nuclear spin–rotation coupling.

Submillimeter wave spectroscopy of propanoic acid (CH3CH2COOH) and its ISM search

Three compounds with a C3H6O2 formula have been detected in the Interstellar Medium (ISM): ethyl formate (CH3CH2OC(O)H), methyl acetate (CH3OC(O)CH3) and very recently hydroxyacetone (CH3C(O)CH2OH). The higher thermodynamic stability of another isomer, the propanoic acid (CH3CH2C(O)OH), clearly suggests that this molecule should be considered as a possible candidate for ISM detection. To provide reliable predictions for astronomical use in the millimeter and submillimeter wave ranges we performed a new study of propanoic acid rotational spectrum up to 545 GHz. The analysis of large amplitude methyl top torsional motion in this molecule was carried out using the rho axis method and the RAM36 program code. More than 3200 lines corresponding to the rotational transitions in the ground and first excited methyl top torsional states were newly assigned and fit within experimental error. This enabled us to produce new predictions which were used to search for propanoic acid in two high-mass star-forming regions: SgrB2 (public IRAM 30 m) and Orion KL (ALMA Science Verification). We report a non-detection of propanoic acid in these clouds and derive upper limits to the column density.

The rotational spectrum of Methylarsine

The rotational spectrum of an organoarsenic compound, methylarsine, CH3AsH2, was studied in the frequency range 10–80 GHz using the Stark-modulated spectrometer in Oslo, and in the frequency range 150–660 GHz using the Lille spectrometer. The experimental work was augmented by high-level ab initio calculations. The analysis of large amplitude torsional motion in CH3AsH2 was performed using the rho axis method and the RAM36 code modified to take into account the nuclear quadrupole hyperfine structure. The final fit used 48 parameters (including 3 parameters of quadrupole coupling) to give an overall unitless root-mean-square deviation of 0.92 for the dataset consisting of 2753, 991, and 414 transitions belonging, respectively, to the ground, first, and second excited torsional states. Compact grouping of rotational transitions due to the small asymmetry (κ=-0.9986), torsional splittings due to internal rotation of the CH3 group, and relatively large hyperfine splittings due to a rather large value of the arsenic nuclear quadrupole moment (χaa=35.4 MHz, χcc=−117.2 MHz, χac=115.7 MHz) represent an interesting case of interplay of different splittings in a molecule with a rather strong coupling between internal and overall rotations (ρ=0.413).

The millimeter-wave spectrum of methyl ketene and the astronomical search for it.

The analysis of isomeric species of a compound observed in the interstellar medium (ISM) is a useful tool to understand the chemistry of complex organic molecules. It could, likewise, assist in the detection of new species. Our goal consists in analyzing one of the two most stable species of the C3H4O family, methyl ketene, whose actual rotational parameters are not precise enough to allow its detection in the ISM. The obtained parameters will be used to search for it in the high-mass star-forming regions Orion KL and Sagittarius B2, as well as in the cold dark clouds TMC-1 in the Taurus Molecular Cloud and Barnard 1 (B1-b). A millimeter-wave room-temperature rotational spectrum of methyl ketene was recorded from 50 to 330 GHz. The internal rotation analysis of its ground state and first torsional excited state was performed with the rho-axis method employing the RAM36 program. More than 3000 transitions of the rotational spectrum of the ground state (Kamax = 18) and first torsional excited state (Kamax = 13) of methyl ketene were fitted using a Hamiltonian that contains 41 parameters with an RMS (root mean square) of 41 kHz. Column density limits were calculated but no lines were detected in the ISM belonging to methyl ketene.

Conformational effect on the almost free internal rotation in 4-hexyn-3-ol studied by microwave spectroscopy and quantum chemistry.

The microwave spectrum of 4-hexyn-3-ol, CH3-C≡C-CH(OH)-CH2CH3, was recorded in the frequency range of 2-26.5 GHz by molecular jet Fourier transform microwave spectroscopy. The conformational analysis based on quantum chemical calculations yielded nine conformers exhibiting C1 symmetry, of which three could be assigned in the experimental spectrum. The propynyl methyl group CH 3 -C≡C- experiences internal rotation with a very low barrier due to the presence of the cylindrically symmetric -C≡C- group serving as a spacer to the rest of the molecule, which is 7.161 012(7) cm-1, 4.236 5(26) cm-1, and 7.901 6(39) cm-1 for the three assigned conformers, respectively. The spectrum was analyzed with the program XIAM using the combined axis method and the program BELGI-C 1 using the rho axis method and a very flexible Hamiltonian which yields fits with root-mean-square deviations within the measurement accuracy.

The effect of internal rotation in p-methyl anisole studied by microwave spectroscopy

The Fourier transform microwave spectrum of p-methyl anisole, CH3C6H4OCH3, was measured in the frequency range from 2 to 26.5GHz under molecular jet conditions. The conformational analysis yielded only one stable conformer, in which all heavy atoms are co-planar, and which was identified after analyzing the spectrum by comparison with the results from quantum chemical calculations. The barrier of the V3 potential of the ring methyl rotor was found to be 49.6370(1) cm−1, and was compared with that found in other para-substituted toluenes as well as in o-methyl anisole. A comparison between two theoretical approaches treating internal rotations, the rho axis method (program BELGI-Cs) and combined axis method (program XIAM), was also performed.

Rotational spectroscopy, tentative interstellar detection, and chemical modeling of N-methylformamide

N-methylformamide, CH3NHCHO, may be an important molecule for interstellar pre-biotic chemistry because it contains a peptide bond. The rotational spectrum of the most stable trans conformer of CH3NHCHO is complicated by strong torsion-rotation interaction due to the low barrier of the methyl torsion. We use two absorption spectrometers in Kharkiv and Lille to measure the rotational spectra over 45--630 GHz. The analysis is carried out using the Rho-axis method and the RAM36 code. We search for N-methylformamide toward the hot molecular core Sgr B2(N2) using a spectral line survey carried out with ALMA. The astronomical results are put into a broader astrochemical context with the help of a gas-grain chemical kinetics model. The laboratory data set for the trans conformer of CH3NHCHO consists of 9469 line frequencies with J <= 62, including the first assignment of the rotational spectra of the first and second excited torsional states. All these lines are fitted within experimental accuracy. We report the tentative detection of CH3NHCHO towards Sgr B2(N2). We find CH3NHCHO to be more than one order of magnitude less abundant than NH2CHO, a factor of two less abundant than CH3NCO, but only slightly less abundant than CH3CONH2. The chemical models indicate that the efficient formation of HNCO via NH + CO on grains is a necessary step in the achievement of the observed gas-phase abundance of CH3NCO. Production of CH3NHCHO may plausibly occur on grains either through the direct addition of functional-group radicals or through the hydrogenation of CH3NCO. Provided the detection of CH3NHCHO is confirmed, the only slight underabundance of this molecule compared to its more stable structural isomer acetamide and the sensitivity of the model abundances to the chemical kinetics parameters suggest that the formation of these two molecules is controlled by kinetics rather than thermal equilibrium.

Probing the Methyl Torsional Barriers of the E and Z Isomers of Butadienyl Acetate by Microwave Spectroscopy.

The Fourier transform microwave spectra of the E and Z isomers of butadienyl acetate were measured in the frequency range from 2 to 26.5 GHz under molecular-jet conditions. The most stable conformer of each isomer, in which all heavy atoms are located in a symmetry plane, was identified after analyzing the spectrum by comparison with the results from quantum-chemical calculations. The barriers to internal rotation of the acetyl methyl group were found to be 149.1822(20) and 150.2128(48) cm(-1) for the E and Z isomers, respectively, which are similar to that of vinyl acetate. A comparison between two theoretical approaches treating internal rotation, the rho axis method and combined axis method, was also performed. The influence of the alkyl R chain on the methyl torsional barriers in CH3 -COOR acetates was explored.

THz extended spectrum of the monodeuterated methyl formate (DCOOCH3)

Context. Laboratory spectral recordings and an accurate molecular spectral analysis of any potential interstellar molecule are essential for generating a complete spectroscopic line list. This permits predicting the frequencies and intensities of any transition so that subsequently, it can be identified in the interstellar medium. Aims. Our analysis of DCOOCH3 aims to provide a comprehensive spectral catalog that encompasses as much as possible the frequency coverage of the new-generation far-IR and submillimeter wave observation facilities. Methods. We newly measured the rotational spectrum of DCOOCH3 in the laboratory of the Jet Propulsion Laboratory in the frequency range of 0.85 to 1.5 THz. We jointly analyzed the new data with literature data using the rho axis method, which is a tool developed for the spectral analysis of molecules with large-amplitude internal CH3 rotors. Results. We fit 27 spectroscopic constants of DCOOCH3 to 3763 transitions with highest values of J = 69 and Ka = 36 of the ground torsional state with a standard (unitless) deviation of 0.97. With respect to previous work, this is a significantly better result that was obtained with 2060 more transitions, and we also achieved a better accuracy for the new parameter values.

Extension of the measurement, assignment, and fit of the rotational spectrum of the two-top molecule methyl acetate

New and previous spectroscopic data were recorded for the two-top molecule methyl acetate using five spectrometers in four different labs: a room temperature chirped-pulse Fourier transform microwave (FTMW) spectrometer in the frequency range from 8.7 to 26.5GHz, two molecular beam FTMW spectrometers (2–40GHz), a free jet absorption Stark-modulated spectrometer (60–78GHz), and a room temperature millimeter-wave spectrometer (44–68GHz). Approximately 800 new lines with J up to 40 and K up to 16 were assigned. In total, 1603 lines were fitted with 34 parameters using an internal rotation Hamiltonian in the Rho Axis Method (RAM) and the program BELGI-Cs-2tops to standard deviations close to the experimental uncertainties. More precise determinations of the top–top interaction and the J, K dependent parameters were carried out.

Structure and rotational dynamics of methyl propionate studied by microwave spectroscopy

We report on the rotational spectra of the most abundant conformer of methyl propionate, CH3CH2COOCH3, recorded with a Fourier transform microwave spectrometer under molecular beam conditions. We present accurate rotational constants and centrifugal distortion constants. For the propionyl CH3 CH2CO– methyl group and the methoxy –OCH3 methyl group, barriers of 820.46(99) cm−1 and 429.324(23) cm−1, respectively, were found. For spectral analysis, two different computer programs were used, the code BELGI-Cs-2tops based on the rho axis method (RAM) and the code XIAM based on the combined axis method (CAM). The results are compared. The experimental work was supplemented by quantum chemical calculations. Potential energy functions for the rotation of the terminal methyl groups and also of the entire ethyl group were parametrized.

Synchrotron FTIR spectroscopy of weak torsional bands: A case study of cis-methyl formate

The far infrared spectrum of cis-methyl formate has been recorded on the AILES beamline of the synchrotron SOLEIL using a Fourier transform infrared spectrometer coupled to a long path cell. The very weak fundamental band associated with the methyl-top torsion mode (ν(18)) was observed. The frequency analysis was performed using the "rho axis method", and the microwave and millimeter-wave data from the literature. A precise determination of the band origins (ν(18)(A) = 132.4303 cm(-1) and ν(18)(E) = 131.8445 cm(-1)) and of the barrier height [V(3) = 370.7398 (58) cm(-1)] have been obtained. The intensity of the ν(18) fundamental band was determined to be 3.4 × 10(-21) cm(-1)∕(molecule cm(-2)) at 297 K, equally shared among A-A and E-E transitions, thus leading to a dipole moment component μ(c)(3) equal to 0.0483 D. The results were compared with the ab initio calcula-tions of Senent et al. [Astrophys. J. 627, 567 (2005)].

Microwave and submillimeter spectroscopy and first ISM detection of18O-methyl formate

Context. Astronomical survey of interstellar molecular clouds needs a previous analysis of the spectra in the microwave and sub-mm energy range to be able to identify them. We obtained very accurate spectroscopic constants in a comprehensive laboratory analysis of rotational spectra. These constants can be used to predict transition frequencies that were not measured in the laboratory very precisely. Aims: We present an experimental study and a theoretical analysis of two 18O-methyl formate isotopologues, which were subsequently detected for the first time in Orion KL. Methods: The experimental spectra of both methyl formate isotopologues recorded in the microwave and sub-mm range from 1 to 660 GHz. Both spectra were analysed by using the rho-axis method (RAM) which takes into account the CH3 internal rotation. Results: We obtained spectroscopic constants of both 18O- methyl formate with high accuracy. Thousands of transitions were assigned and others predicted, which allowed us to detect both species in the IRAM 30 m line survey of Orion KL. Full Tables A.1 et A.2 are available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/538/A119