Electromagnatic radiation :- Rotational energy level

 Rotational energy level

Molecular rotations require little energy to excite them. Pure rotation spectra occur in 

the microwave region of the spectrum (~1 - 200 cm-1

). It is important to note that a molecule cannot rotate about some arbitrary axis - the principle of conservation of 

angular momentum dictates that only a few rotations are possible. In general, rotation 

must be about the centre of mass of a molecule, and the axis must allow for 

conservation of angular momentum. In simple cases, this can often be recognised 

intuitively through symmetry - such as with the water molecule.

A pure rotation spectrum can only arise when the molecule possesses a permanent 

electric dipole moment. Like with vibrational spectroscopy, the physical effect that 

couples to photons is a changing dipole moment. Since molecular bond lengths remain 

constant in pure rotation, the magnitude of a molecule's dipole cannot change. 

However, since electric dipole is a vector quantity (it has both size and direction) 

rotation can cause a permanent dipole to change direction, and hence we observe its 

spectra. Since homonuclear molecules such as dinitrogen N2

have no dipole moment 

they have no rotation spectrum. Highly symmetric polyatomic molecules, such as 

carbon dioxide, also have no net dipole moment - the dipoles along the C-O bonds are 

always equal and opposite and cancel each other out. It is important to recognise also 

that if a molecule has a permanent dipole, but this dipole lies along the main rotation 

axis, then the molecule will not have a rotational spectrum - such as for a water 

molecule.

In pure rotational spectroscopy for a simple diatomic molecule, the energy levels - as 

displayed below - are given by EJ = BJ (J+1), where J is the rotational quantum 

number, B is the rotational constant for the particular molecule given by

I

h

B 2

2

8



with the unit of Joules, where I is the moment of inertia, given by I = μr

2

- where r is 

the bond length of this particular diatomic molecule and μ is the reduced mass, given 

by μ = m1m2

/ m1 + m2

.

Most energy level transitions in spectroscopy come withselection rules. These rules 

restrict certain transitions from occuring - though often they can be broken. In pure 

rotational spectroscopy, the selection rule is ΔJ = ±1.

A vibrational spectrum would have the following appearence. Each line corresponds to 

a transition between energy levels, as shown. Notice that there are no lines for, for 

example, J = 0 to J = 2 etc. This is because the pure rotation spectrum obeys the

selection rule ΔJ = ±1. The energy gap between each level increases by 2B as the 

energy levels we consider increase by J = 1. This leads to the line spacing of 2B in the 

spectrum. Each transition has an energy value of 2B more than the previous transition.