The transition dipole moment is the key quentity that determines the intensity of an absorption band in electronic spectroscopy. The square of the transition dipole moment is proportional to the transiton probability and therefore the extinction coefficient for ultraviolet-visible absorption bands. Since the nuclear factor determines the shape (see next section) we will often need to compare the integrated band intensity to quantitative evaluate this contribution. However, qualitatively we can say that the larger the transition dipole moment the large the intensity. The presentation below shows a simple model for the calculation of the transition dipole moment from first principles. The units of the transition dipole moment are Debye, just like the units of teh ground state dipole moment. 1 Debye = 3.33 x 10^-30 Cm (Coulomb-meters). Given thisvery small number you can imagine what scientists like to use a unit like the Debye. To give an example, the ground state dipole moment of H₂O is 1.86 D. In liquid water the polarizability of the molecule combined with the reaction field due to neighboring water molecules amplifies this dipole moment. Liquie water has a dipole moment of ca. 2.3 D. Some charge transfer molecules can have veyr large dipole moments in the ground state (e.g. > 15 Debye). These mlecules tend to be very solvent dependence in their absorption spectrum. Some of then are solvatochromic dyes.

The difference between ground state and 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 electron 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.

The electronic factor determines the intensity of absorption

The important theoretical insight that we gain from the study of the transition dipole moment is that the square of this quantity is proportional to the transition intensity. The transition intensity involves the integrated absorption band since absorption bands have different shapes. In the section on the nuclear factor or Franck-Condon factor we will show how to determine the line shape from the nuclear overlaps. However, here we simply need to understand that the integrated band intensity is proportional to |M₁₂|², where M₁₂ is the transition dipole moment.