Editing Rotational transition (section)

==== Sigma states ====
Molecular states in which the total orbital momentum of electrons is zero are called [[molecular orbitals|sigma states]]. In sigma states {{math|1=Λ = 0}}. Thus {{math|1=''E''&prime;<sub>s</sub>(''R'') = ''E''<sub>s</sub>(''R'')}}. As nuclear motion for a stable molecule is generally confined to a small interval around {{math|''R''<sub>0</sub>}} where {{math|''R''<sub>0</sub>}} corresponds to internuclear distance for minimum value of potential {{math|''E''<sub>s</sub>(''R''<sub>0</sub>)}}, rotational energies are given by,
<math display="block"> E_r = \frac{\hbar^2}{2\mu {R_0}^2} J(J+1) = \frac{\hbar^2}{2I_0} J(J+1) = BJ(J+1) </math>
with
<math display="block"> J = \Lambda, \Lambda +1, \Lambda+2, \dots </math>
{{math|''I''<sub>0</sub>}} is [[moment of inertia]] of the molecule corresponding to [[mechanical equilibrium|equilibrium]] distance {{math|''R''<sub>0</sub>}} and {{math|''B''}} is called '''rotational constant''' for a given electronic state {{math|Φ<sub>''s''</sub>}}.
Since reduced mass {{math|''μ''}} is much greater than electronic mass, last two terms in the expression of {{math|''E''&prime;<sub>''s''</sub>(''R'')}} are small compared to {{math|''E''<sub>s</sub>}}. Hence even for states other than sigma states, rotational energy is approximately given by above expression.