FORCE CONSTANTS FOR $CHBrCl_{2}$ AND $CDBrCl_{2}$

Abstract

Using the Wilson FG matrix method and force constants transferred from previous $work^{1,2}$ on $CHCl_{3}$ and $CHBr_{3}$, the three type-A fundamental frequencies of $CHBrCl_{2}$ and $CDBrCl_{2}$ 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 $F = \left(\begin{array}{c|c}F_{11}& F_{12}\\F_{12} & F_{22}\end{array}\right)and\ G = \left(\begin{array}{c|c}G_{11} & G_{12}\\ G_{12} & G_{22}\end{array}\right)$ The symmetry coordinates can be constructed in such a way that, upon replacement of the Br atom by Cl in $CHBrCl_{2}, F_{11}, G_{11}$ and $F_{22}, G_{22}$ go over to the corresponding matrices for the $A_{1}$ and E vibrations of $CHCl_{3}$, while $F_{12}$ and $G_{12}$ become zero. Under these conditions, the elements of $F_{12}$ and $G_{12}$ for $CHBrCl_{2}$ are very small compared with those of $F_{11}, F_{22}, G_{11}$, and $G_{22}$. Preliminary calculations, using transferred values of the force constants and assuming $F_{12} = G_{12} = 0$, gave values for the frequencies within 3 percent of the observed. Assuming only $F_{12} = 0$, nearly the same results were obtained for all but the two lower frequencies. Further calculations are still in progress.

$^{1}$ A. G. Meister, S. E. Rosser, and F. F. Cleveland, J. Chem. Phys. 18, 346 (1950) $^{2}$ J. P. Zietlow, F. F. Cleveland, and A. G. Meister, J. Chem. Phys. 18, 1076 (1950)

Author Institution: Illinois Institute of Technology