Effective Dipole Moment Model for Axially Symmetric C3 v Molecules: Application to the Precise Study of Absolute Line Strengths of the ν6 Fundamental of CH335Cl

Abstract

The effective dipole moment model for molecules of axial C3v 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 CH335Cl, 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 (ν6 bending fundamental centered at ν0 = 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 ν6 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 Jmax = 68, Kmax = 21 were assigned to the ν6 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 C3v-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 drms=4.7×10-5 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 drms=3.4%.

Keywords: C3v-symmetry molecule; CH335Cl; absolute line positions and strengths; effective rotational and effective dipole moment operators.

Figure 1

Upper trace: overview of the experimental spectra I (black) and II (orange) of CH${}_3$Cl in the region of the ${\nu }_6$ band (for the experimental conditions, see Table 1 and Section 2). Lower trace: simulated spectrum I.

Figure 2

Small part of the high-resolution spectrum I in the region of the $Q$—branch of CH${}_3{}^{35}$Cl. The ${}^P{Q}_4\left(J\right)$ transitions are marked by dark circles. Dark triangles denote other transitions (not belonging to the ${}^P{Q}_4\left(J\right)$ set). Unmarked lines belong probably to the CH${}_3{}^{37}$Cl ${\nu }_6$ band transitions.

Figure 3

Part of the high-resolution spectrum I in the region of the $R—$branch of CH${}_3{}^{35}$Cl. Two sets of transitions (${}^R{R}_9\left(J\right)$ marked by dark circles, and ${}^R{R}_8\left(J\right)$ marked by dark triangles) are shown. Some sets of the ${}^R{Q}_K\left(J\right)$ clusters are also seen.

Figure 4

Detail of the infrared spectrum I of the ${\nu }_6$ band of CH${}_3{}^{35}$Cl showing sets of ${}^P{P}_9\left(J\right)$ (dark circles) and ${}^P{P}_6\left(J\right)$ (dark triangles) transitions. Three $Q$-type clusters are also indicated.

Figure 5

Residuals $E_i^{\mathrm{obs}}-E_i^{\mathrm{calc}}$ of effective Hamiltonian fit calculations of the ${\nu }_6\left(E\right)$ band of CH${}_3{}^{35}$Cl dependent on upper state quantum number J.

Figure 6

Some examples of the line shape analysis in the experimental spectrum I (for experimental conditions, see Section 2 and Table 1). The fit of the experimental line shapes was made with the qSDRP profile of individual lines. The bottom part of the figure shows the (exp.–calc.) residuals.

Figure 7

Some examples of the line shape analysis in the experimental spectrum I (for experimental conditions, see Section 2 and Table 1). The fit of the experimental line shapes was made with the qSDRP profile of individual lines. The bottom part of the figure shows the (exp.–calc.) residuals.