APPLICATION OF THE FRANCK-CONDON PRINCIPLE TO THE 2000 {\AA} SYSTEM OF $AMMONIA^{*}$
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Date
1963
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Publisher
Ohio State University
Abstract
“The transition probability of a molecule is proportional to $\infty Re(Q)PS’ v(Q)PS’v(Q)dQ$ $R_{e} (Q)\Psi_{v}’ (Q) \Psi_{v}’’(Q) d Q$ where $R_{e} (Q)$ is the electric dipole moment at point Q. The Franck-Condon principle rests on the assumption that the variation of $R_{e} (Q)$ 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. $NH_{3}$ and $ND_{3}$ are good examples of molecules undergoing large changes in Germany upon transition. The $H-N-H$ or $D-N-D-$ angle changes from $106^{\circ} 47’$ (pyramidal) to $120^{\circ}$ (planar) in going from the ground state to the first excited electronic state. Both $NH_{3}$ and $ND_{3}$ absorption intensities for the $(0000\leftarrow 0\; v_{2}’’\;00)$ transitions where $v_{2}’’ = 0^{+}, 1^{+} , 2^{+}$ 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 $R_{e}(Q)$ it probably Small.”
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$^{*}$Supported by the U. S. Air Force Office of Scientific Research.
Author Institution: Physics Department, Sam Houston State College; Physics Department, A. and M. College of Texas
Author Institution: Physics Department, Sam Houston State College; Physics Department, A. and M. College of Texas