A comparison of different approaches to the calculation of franck-condon factors for polyatomic molecules

Abstract

In the customary calculation of vibrational intensity distribution in electronic spectra of polyatomic molecules, the Franck-Condon factors are expressed in terms of the difference of the equilibrium geometries of the initial and the final state. It is pointed out that it is more advantageous to express the Franck-Condon factors in terms of the gradient of the final state potential energy surface at the equilibrium geometry of the initial electronic state. The ionization and excitation of the NH₃ molecule are considered to illustrate this fact. Although the change in geometry is known accurately in this case, rather poor Franck-Condon factors are obtained with the customary harmonic method. Remarkably enough, even the use of anharmonic potential energy functions, though rather laborious, does not improve the situation. The reason for this failure is discussed. Expanding, on the other hand, the final state potential energy around the initial state equilibrium geometry, we obtain satisfactory Franck-Condon factors already in the lowest order of the expansion.