Knowledge Bank

Using the Wilson FG matrix method and force constants transferred from previous $work1,2$ on $CHCl3$ and $CHBr3$, the three type-A fundamental frequencies of $CHBrCl2$ and $CDBrCl2$ have been calculated. After slight adjustment of one force constant, the agreement between calculated and observed values is within 1 percent. For the calculation of the A' vibrational frequencies, it is necessary to solve a $6\times 6$ secular determinant. The F and G matrices can be written in terms of $3\times 3$ submatrices as $F=(F11F12F12F22)and G=(G11G12G12G22)$ The symmetry coordinates can be constructed in such a way that, upon replacement of the Br atom by Cl in $CHBrCl2,F11,G11$ and $F22,G22$ go over to the corresponding matrices for the $A1$ and E vibrations of $CHCl3$, while $F12$ and $G12$ become zero. Under these conditions, the elements of $F12$ and $G12$ for $CHBrCl2$ are very small compared with those of $F11,F22,G11$, and $G22$. Preliminary calculations, using transferred values of the force constants and assuming $F12=G12=0$, gave values for the frequencies within 3 percent of the observed. Assuming only $F12=0$, nearly the same results were obtained for all but the two lower frequencies. Further calculations are still in progress.