text: The vibronic spectra of diatomic molecules in the gas phase also show rotational fine structure. Each line in a vibrational progression will show P- and R-branches. For some electronic transitions there will also be a Q-branch. The transition energies, expressed in wavenumbers, of the lines for a particular vibronic transition are given, in the rigid rotor approximation, that is, ignoring centrifugal distortion, by
  Here  are rotational constants and  are rotational quantum numbers. (For B also, a double prime indicates the ground state and a single prime an electronically excited state.) The values of the rotational constants may differ appreciably because the bond length in the electronic excited state may be quite different from the bond length in the ground state, because of the operation of the Franck-Condon principle. The rotational constant is inversely proportional to the square of the bond length. Usually  as is true when an electron is promoted from a bonding orbital to an antibonding orbital, causing bond lengthening. But this is not always the case; if an electron is promoted from a non-bonding or antibonding orbital to a bonding orbital, there will be bond-shortening and .
  The treatment of rotational fine structure of vibronic transitions is similar to the treatment of rotation-vibration transitions and differs principally in the fact that the ground and excited states correspond to two different electronic states as well as to two different vibrational levels. For the P-branch , so that
  Similarly for the R-branch , and
  Thus, the wavenumbers of transitions in both P- and R-branches are given, to a first approximation, by the single formula
  Here positive  values refer to the R-branch (with ) and negative values refer to the P-branch (with ). The wavenumbers of the lines in the P-branch, on the low wavenumber side of the band origin at  increase with . In the R-branch, for the usual case that , as  increases the wavenumbers at first lie increasingly on the high wavenumber side of the band origin but then start to decrease, eventually lying on the low wavenumber side. The Fortrat diagram illustrates this effect. In the rigid rotor approximation the line wavenumbers lie on a parabola which has a maximum at
  The line of highest wavenumber in the R-branch is known as the band head. It occurs at the value of  which is equal to the integer part of , or of .
  When a Q-branch is allowed for a particular electronic transition, the lines of the Q-branch correspond to the case ,  and wavenumbers are given by
  The Q-branch then consists of a series of lines with increasing separation between adjacent lines as  increases. When  the Q-branch lies to lower wavenumbers relative to the vibrational line.