Rotational spectroscopy as a tool to investigate interactions between vibrational polyads in symmetric top molecules: low-lying states $v_8 \le 2$ of methyl cyanide, CH$_3$CN
Spectra of methyl cyanide were recorded to analyze interactions in low-lying vibrational states and to construct line lists for radio astronomical observations as well as for infrared spectroscopic investigations of planetary atmospheres. The rotational spectra cover large portions of the 36$-$1627 GHz region. In the infrared (IR), a spectrum was recorded for this study in the region of 2$ν_8$ around 717 cm$^{-1}$ with assignments covering 684$-$765 cm$^{-1}$. Additional spectra in the $ν_8$ region were used to validate the analysis. The large amount and the high accuracy of the rotational data extend to much higher $J$ and $K$ quantum numbers and allowed us to investigate for the first time in depth local interactions between these states which occur at high $K$ values. In particular, we have detected several interactions between $v_8 = 1$ and 2. Notably, there is a strong $Δv_8 = \pm1$, $ΔK = 0$, $Δl = \pm3$ Fermi resonance between $v_8 = 1^{-1}$ and $v_8 = 2^{+2}$ at $K$ = 14. Pronounced effects in the spectrum are also caused by resonant $Δv_8 = \pm1$, $ΔK = \mp2$, $Δl = \pm1$ interactions between $v_8 = 1$ and 2. An equivalent resonant interaction occurs between $K$ = 14 of the ground vibrational state and $K$ = 12, $l = +1$ of $v_8 = 1$ for which we present the first detailed account. A preliminary account was given in an earlier study on the ground vibrational state. From data pertaining to $v_8 = 2$, we also investigated rotational interactions with $v_4 = 1$ as well as $Δv_8 = \pm1$, $ΔK = 0$, $Δl = \pm3$ Fermi interactions between $v_8 = 2$ and 3. We have derived N$_2$- and self-broadening coefficients for the $ν_8$, 2$ν_8 - ν_8$, and 2$ν_8$ bands from previously determined nu4 values. Subsequently, we determined transition moments and intensities for the three IR bands.