Knowledge Bank

“The transition probability of a molecule is proportional to $\infty Re(Q)PS\prime v(Q)PS\prime v(Q)dQ$ $Re(Q)\Psi v\prime (Q)\Psi v″(Q)dQ$ where $Re(Q)$ is the electric dipole moment at point Q. The Franck-Condon principle rests on the assumption that the variation of $Re(Q)$ is negligible with respect to a variation of Q. If a molecule makes a large change in geometry during a transition, the validity of the Franck-Condon principle might be questioned. $NH3$ and $ND3$ are good examples of molecules undergoing large changes in Germany upon transition. The $H-N-H$ or $D-N-D-$ angle changes from $106\circ 47\prime$ (pyramidal) to $120\circ$ (planar) in going from the ground state to the first excited electronic state. Both $NH3$ and $ND3$ absorption intensities for the $(0000\leftarrow 0v2″00)$ transitions where $v2″=0+,1+,2+$ and $3+$, and $3+$ were experimentally measured, and the corresponding relative intensities were calculated using the Franck-Condon principle. The average disagreement is 17%, showing the Franck-Condon principle to be valid for the bands considered. This is reasonable since over 80% of the overlap between ground and excited state vibrational wave functions occurs for an H-N-H or D-N-D angle variation of $120\circ =117\circ$. This indicates that most of the transitions occur when the molecule is nearly planar. Since the transitions occur for such a small range of Q, the corresponding variation of $Re(Q)$ it probably Small.”