Search Results (3)

Monodeuterated methane (CH₃D) contributes greatly to absorption in the 1.58 μm methane transparency window. The spectrum is dominated by the 3ν₂ band near 6430 cm⁻¹, which is observed in natural methane and used for a number of planetary applications, such as the determination of the D/H ratio. In this work, we analyze the CH₃D spectrum recorded by high-sensitivity differential absorption spectroscopy in the 6099–6530 cm⁻¹ region, both at room temperature and at 81 K. Following a first contribution to this topic by Lu et al., the room-temperature line list is elaborated (11,189 lines) and combined with the previous 81 K list (8962 lines) in order to derive about 4800 empirical lower-state energy values from the ratio of the line intensities measured at 81 K and 294 K (2T-method). Relying on the position and intensity agreements with the TheoReTS variational line list, about 2890 transitions are rovibrationally assigned to twenty bands, with fifteen of them being newly reported. Variational positions deviate from measurements by up to 2 cm⁻¹, and the band intensities are found to be in good agreement with measurements. All the reported assignments are confirmed by Ground-State Combination Difference (GSCD) relations; i.e., all the upper-state energies (about 1370 in total) have coinciding determinations through several transitions (up to 8). The energy values, determined with a typical uncertainty of 10⁻³ cm⁻¹, are compared to their empirical and variational counterparts. The intensity sum of the transitions assigned between 6190 and 6530 cm⁻¹ represents 76.9 and 90.0% of the total experimental intensities at 294 K and 81 K, respectively. Full article

The effective dipole moment model for molecules of axial C${}_{3v}$ symmetry is derived on the basis of the symmetry properties of a molecule which, on the one hand, is of the same order of efficiency (but much simpler and clearer in applications) as the analogous models derived on the basis of the irreducible tensorial sets theory, and, on the other hand, mathematically more correct in comparison with concepts like the Herman–Walles function used in the models. As an application of the general results obtained, we discuss high-resolution infrared spectra of CH${}_3{}^{35}$Cl, recorded with the Zürich prototype ZP2001 (Bruker IFS125 HR) Fourier transform infrared spectrometer at a resolution of 0.001 cm${}^{-1}$ and analyzed in the region of 880–1190 cm${}^{-1}$ (${\nu }_6$ bending fundamental centered at ${\nu }_0$ = 1018.070790 cm${}^{-1}$). Absolute strengths of more than 2800 transitions (2081 lines) were obtained from the fit of their shapes both with Voigt and Hartmann–Tran profiles, and parameters of the effective dipole moment of the ${\nu }_6$ band were determined by the computer code SYMTOMLIST (SYMmetric TOp Molecules: LIne STrengths), created on the basis of a derived theoretical model. As the first step of the analysis of the experimental data, assignments of the recorded lines were made. A total of 5124 transitions with $J^{\max }$ = 68, $K^{\max }$ = 21 were assigned to the ${\nu }_6$ band. The weighted fit of 2077 upper energy values obtained from the experimentally recorded transitions was made with a Hamiltonian which takes into account different types of ro–vibrational effects in doubly degenerate vibrational states of the $C_{3v}$-symmetric molecule. As the result, a set of 25 fitted parameters was obtained which reproduces the initial 2077 upper “experimental” ro–vibrational energy values with a root mean square deviation $d_{\mathrm{rms}}=4.7\times {10}^{-5}$ cm${}^{-1}$. At the second step of the analysis, the computer code SYMTOMLIST was used for determination of the parameters of the derived effective dipole moment model. Six effective dipole moment parameters were obtained from the weighted fit procedure which reproduces absolute experimental strengths of the 2804 initial experimental transitions with a relative $d_{\mathrm{rms}}=3.4\%$. Full article

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the $3N-6$ approach, of the form $\mid {\nu }_1,{\nu }_2,{\nu }_3^{{\ell }_3};J,k,m⟩$, tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with $k={\ell }_3$, which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C${}_{2\mathrm{v}}$(M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ${\ell }_3=k$ is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D${}_{\infty \mathrm{h}}$(AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D${}_{\infty \mathrm{h}}$(AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications. Full article