 QM systems have a discrete energy spectrum • hn = DE • an absorption/emission spectrum consists of individual peaks, each of which is associated with a transitions between two allowed energy levels of the system  Rotational energy levels more closely spaced than vibrational energy levels (Microwave region)  Stimulated absorption

 Spontaneous emission

 Stimulated emission  Strategy: • Find expression for the energy levels of molecules and then calculate the transition frequency by applying selection rules

 Information obtained from rotational Spectroscopy • Bond length • Moment of Inertia • Angles (Polyatomic molecules)  Assume the molecule is a rigid rotor • i.e. does not distort under stress of rotation

 Assume potential energy is = 0 • Since the bond length is not changing

 The energy levels we get for rigid rotors by solving the Schrodinger equation  B = rotational constant (units in cm-1)

 Energy levels  Gross selection rule • Molecule must have a permanent dipole moment to absorb energy in the microwave frequency range in which rotational transitions occur  Intensity of the lines is proportional to the square of the permanent electric dipole moment, so strongly polar molecules give rise to much more intense rotational lines than less polar molecules  Homonuclear diatoms don’t undergo transitions described here. (Raman spectroscopy used for such molecules)

 Specific selection rule

 Origin of selection rules  Difference between successive transitions is 2B  Measurement between line spacing gives B  From which moment of inertia can be found  Since we know the mass of the atoms we can get bond distances

 The appearance of the spectrum / or the intensity of the lines depends on the boltzman population density and degeneracy

 To get the line with the maximum intensity  Since, in reality the chemical bonds are not rigid rotors and are in fact distorted due to rotation an empirical term is included

 As a consequence the energy levels are slightly closer as compared to the rigid rotor  Spherical

 Symmetric

 Linear (diatomics)

 Asymmetric  Have equal I about all the three principal axes • Eg. CH4, SiH4, SF6

• No permanent dipole moment, therefore no pure rotational transition  However, is sufficient distortion occurs, rotational transition can occur  Like Diatomics  Has one I = 0  Has I equal about two principal axes • The unique axis is called the figure axis • Eg. NH3, CH3Cl

Prolate (like a cigar) e.g. CH3Cl

 Selection rule Oblate (like a pancake) e.g. C6H6  Has no equal I about any of the three principal axes • Eg. H2O, CH3OH