There are two kinds of emission, stimulated and spontaneous. Stimulated emission was shown by Einstein to have a probability equal to absorption. However, spontaneous emission is also oberved. In a molecule spontaneous emission occurs from a nuclear geometry that is shifted because of the change in the charge distribution of the excited state. Absorption of radiation by a Franck-Condon mechanism involves a vertical transition to a region of the excited state potential surface with a slope. The slope of the potential surface is synonymous with a force that pushes the nuclei and causes them to oscillate in the excited state. The nuclei can then relax to a new equilibrium geometry by vibrational relaxation.
The difference between ground state snd transition dipole moments
A ground state dipole moment represents a charge displaced through a distance. In quantum mechanics, we can calculate that using the gorund state wave function. Using Braket notation that is mu = e where e is the charge on an fluorescencetron and psi_g is the ground state wave function. We are assuming a calculation along the x direction. The transition sipole moment has the form mu = e. The subscript e represents the excited state. A transition dipole moment connects two states. For example, hydrogen atom has no ground dipole moment (obviously). However, even hydrogen has a transition dipole moment that gives rise to the transition from 1s -> 2p. Is has the appearance mu = e<2p_x|x|1s>. Note that if we are assuming a calculation along the x axis then we must use the 2p-_x orbital and not one of the other 2p orbitals.
