Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero‐point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2.In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure on...

A new criterion for the determination of molecular structures from ground state rotational constants

This article describes the parameterization and performance of MMFF94 for molecular geometries and deformations. It defines the form used for the valence-coordinate terms that represent variations in bond lengths and angles, and it describes the derivation of quadratic force constants from HF/6-31G* data and the derivation of reference bond lengths and angles from fits to MP2/6-31G*-optimized geometries. Comparisons offered show that MMFF94 accurately reproduces the computational data used in its parameterization and demonstrate that its derivation from such data simultaneously confers the ability to reproduce experiment. In particular, MMFF94 reproduces experimentally determined bond lengths and angles for 30 organic molecules with root mean square (rms) deviations of 0.014 A and 1.2°, respectively. MM3 reproduces bond angles to the same accuracy, but reproduces experimental bond lengths more accurately, in part because it was fit directly to thermally averaged experimental bond lengths; MMFF94, in contrast, was fit to (usually shorter) energy-minimum values, as is proper for an anharmonic force field intended for use in molecular-dynamics simulations. The comparisons also show that UFF and a recent version of CHARMm (QUANTA 3.3 parameterization) are less accurate for molecular geometries than either MMFF94 or MM3. For vibrational frequencies, MMFF94 and MM3 give comparable overall rms deviations versus experiment of 61 cm−1 and 57 cm−1, respectively, for 15 small, mostly organic molecules. In a number of instances, MM3's derivation employed observed frequencies that differ substantially—by nearly 400 cm−1 in one case—from other published frequencies which had themselves been confirmed theoretically by good-quality ab initio calculations. Overall, the comparisons to experimental geometries and vibrational frequencies demonstrate that MMFF94 achieves MM3-like accuracy for organic systems for which MM3 has been parameterized. Because MMFF94 is derived mainly from computational data, however, it has been possible to parameterize MMFF94 with equal rigor for a wide variety of additional systems for which little or no useful experimental data exist. Equally good performance can be expected for such systems. © John Wiley & Sons, Inc.

Merck Molecular Force Field. III. Molecular Geometries and Vibrational Frequencies for MMFF94

Context. The discovery of amino acids in meteorites fallen to Earth and the detection of glycine, the simplest of them, in samples returned from a comet to Earth strongly suggest that the chemistry of the interstellar medium is capable of producing such complex organic molecules and that they may be widespread in our Galaxy. Aims. Our goal is to investigate the degree of chemical complexity that can be reached in the interstellar medium, in particular in dense star-forming regions. Methods. We performed an unbiased, spectral line survey toward Sgr B2(N) and (M), two regions where high-mass stars are formed, with the IRAM 30 m telescope in the 3 mm atmospheric transmission window. Partial surveys at 2 and 1.3 mm were performed in parallel. The spectra were analyzed with a simple radiative transfer model that assumes local thermodynamic equilibrium but takes optical depth effects into account. Results. About 3675 and 945 spectral lines with a peak signal-to-noise ratio higher than 4 are detected at 3 mm toward Sgr B2(N) and (M), i.e. about 102 and 26 lines per GHz, respectively. This represents an increase by about a factor of two over previous surveys of Sgr B2. About 70% and 47% of the lines detected toward Sgr B2(N) and (M) are identified and assigned to 56 and 46 distinct molecules as well as to 66 and 54 less abundant isotopologues of these molecules, respectively. In addition, we report the detection of transitions from 59 and 24 catalog entries corresponding to vibrationally or torsionally excited states of some of these molecules, respectively, up to a vibration energy of 1400 cm-1 (2000 K). Excitation temperatures and column densities were derived for each species but should be used with caution. The rotation temperatures of the detected complex molecules typically range from ~50 to 200 K. Among the detected molecules, aminoacetonitrile, n- propyl cyanide, and ethyl formate were reported for the first time in space based on this survey, as were five rare isotopologues of vinyl cyanide, cyanoacetylene, and hydrogen cyanide. We also report the detection of transitions from within twelve new vibrationally or torsionally excited states of known molecules. Absorption features produced by diffuse clouds along the line of sight are detected in transitions with low rotation quantum numbers of many simple molecules and are modeled with ~30–40 velocity components with typical linewidths of ~3–5 km s-1 . Conclusions. Although the large number of unidentified lines may still allow future identification of new molecules, we expect most of these lines to belong to vibrationally or torsionally excited states or to rare isotopologues of known molecules for which spectroscopic predictions are currently missing. Significant progress in extending the inventory of complex organic molecules in Sgr B2(N) and deriving tighter constraints on their location, origin, and abundance is expected in the near future thanks to an ongoing spectral line survey at 3 mm with ALMA in its cycles 0 and 1. The present single-dish survey will serve as a solid basis for the line identification and analysis of such an interferometric survey.

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Complex organic molecules in the interstellar medium: IRAM 30 m line survey of Sagittarius B2(N) and (M)

Methanol and deuterated species: Infrared data, valence force field, rotamers, and conformation

The class II masers of methanol are associated with the early stages of formation of high-mass stars. Modelling of these dense, dusty environments has demonstrated that pumping by infrared radiation can account for the observed masers. Collisions with other molecules in the ambient gas also play a significant role, but have not been well modelled in the past. Here we examine the effects on the maser models of newly available collision rate coefficients for methanol. The new collision data do not alter which transitions become masers in the models, but do influence their brightness and the conditions under which they switch on and off. At gas temperatures above 100 K the effects are broadly consistent with a reduction in the overall collision cross-section. This means, for example, that a slightly higher gas density than identified previously can account for most of the observed masers in W3(OH). We have also examined the effects of including more excited-state energy levels in the models, and find that these play a significant role only at dust temperatures above 300 K. An updated list of class II methanol maser candidates is presented.

/pdf/models-of-class-ii-methanol-masers-based-on-improved-2c394cgfic.pdf

Models of class II methanol masers based on improved molecular data

In a study of internal rotation in methanol, the millimeter wave spectra of CH3OH, CD3OH, and CH3OD have been investigated between 90 and 200 Gc/sec. In the analysis of the spectra, torsion–vibration–rotation interactions were treated as adjustable parameters in semiempirical formulas. Kivelson's formula for a‐type ΔK = 0 transitions was tested over a wide range of quantum numbers. It reproduced the CH3OH and CD3OH spectra quite well, but the approximations used in the calculations appear to start breaking down for the larger asymmetry of CH3OD. For assignment of b‐type ΔK = ± 1 transitions, a method was developed based on the wide spectral range of the millimeter wave spectrometer. Sufficient b‐type data were obtained for CH3OH to permit a test of Kirtman's formula for origins of Q branches. Convergence difficulties in the Q‐branch least‐squares fit prompted a re‐examination of the theory, which revealed an interesting linear relation coupling six of the parameters. This relation shows that for any molec...

R. M. Lees

Papers

Torsion–Vibration–Rotation Interactions in Methanol. I. Millimeter Wave Spectrum