2 Silicon dicarbide molecule

High resolution spectroscopy has shown that Silicon Dicarbide is a three membered ring molecule with equivalent carbon atoms (Michalopoulos et al. 1984). Its linear isomer is less stable than the ring structure (Grev & Schaefer 1984). The bond length of Si-C and C-C are 1.837 Å and 1.268 Å, respectively. The geometry of Silicon Dicarbide molecule is shown in Fig. 1.

  

Figure 1: The geometry of the 28SiC2 molecule

The Silicon Dicarbide molecule is an a-type asymmetric top molecule with dipole moment $\mu$ = 2.393 D (Suenram et al. 1989). SiC₂ has three fundamental vibrational modes at $\nu_1=1742$ cm^-1, $\nu_2= 837$ cm^-1, and $\nu_3 = 177$ cm^-1 (Shepherd & Graham 1985, 1988; Gottlieb et al. 1989). The wavefunction of an asymmetric top molecule can be expressed as linear combination of wave functions for a symmetric top molecule (Chandra & Sahu 1993)

$$\psi_{J \tau M}(\alpha, \beta, \gamma) = \sqrt{\frac{2J+1}{8... ...} \sum_{K=-J}^{J} g_{\tau K}^J D_{MK}^J (\alpha, \beta, \gamma)$$ (1)

where $\alpha$, $\beta$, $\gamma$ are the Eulerian angles specifying the orientation of the molecule, J the rotational quantum number, $g^J_{\tau K}$the expansion coefficient, D^J_{M K} the Wigner D-function.

The rotational transitions are governed by the selection rules

$$\begin{eqnarray} J\!\!:&& \quad \Delta J = 0, \quad \pm 1 \nonumber \\ K_{\rm a... ...ghtarrow {\rm even,\; even} \, {\rm (ortho-transition)}\nonumber \end{eqnarray}$$

$K_{\rm a}$ and $K_{\rm c}$ are sub-quantum numbers and each of them can assume the values ranging from 0 to J. On the basis of the selection rules, the rotational energy levels are grouped into two sets of transitions behaving as if they belong to two independent species. These species are referred to as para- and ortho-species, respectively.

  

Table 1: Molecular constants used in the calculations