It is a very convenient approximation to treat the total energy of a molecule as a sum of electronic, vibrational, rotational, nuclear spin, electron spin and other energy levels.

E _total = E _electronic + E _Vibrational + E _rotational + ……                (12.1)

The above equation follows from the following approximation

H _total = H _electronic + H _vibrational + H _rotational +……                  (12.2)

On solving the equation (12.2), the following solutions emerge

H _{total total} = E _{total total}                                                  (12.3a)

H _{electronic electronic} = E_{electronic electronic}                       (12.3b)

H _{vibrational vibrational} = E _{vibrational vibrational}                       (12.3c)

H _{rotational rotational} = E _{rotational rotational}                            (12.3d)

For simplicity we will denote rotational vibrational and electronic by subscripts ‘r', ‘v' and ‘e' respectively. The nature of E_e and _e has already been discussed in the first few lectures by using atomic and molecular orbitals. In the present lecture, we are considering transitions between electronic energy levels. The energy levels have to be calculated by solving the approximate Schrodinger equation (12.3b).