Molecular Symmetry and Group Theory |
Consider the effect of the C_{3} operation on the p orbitals of the B atom in BF_{3}.
Although a p_{z} orbital will remain unchanged, the p_{x} and p_{y} orbitals will end up rotated through an angle of 120°. The group character table (point group - D_{3h}) confirms that the p_{x} and p_{y} orbitals are degenerate, but they are neither simply inverted or converted into each other by the C_{3} operation. In this case each orbital contributes cos 120° to the character of the matrix describing the operation.
Use the p_{x}, p_{y} and p_{z} orbitals on the B atom as a basis to determine the characters of the matrices that describe the symmetry operations of BF_{3}.