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Molecules
Molecular Spectra
 Molecular Spectra is observed when the emitting substance
is in the molecular state.
 With high resolving power instrument , the molecular
spectra disclose a three fold structure.
 The three type of bands are:
Electronic, Vibrational, or Rotational spectrum

Erot < Evib < Eelec  hirarchy.
 For a diatomic molecule, the electronic states can be represented
by plots of potential energy as a function of internuclear distance.
 Electronic transitions are vertical or almost vertical
lines on such a plot since the electronic transition
occurs so rapidly that the internuclear distance can't
change much in the process.
 Vibrational transitions occur between different
vibrational levels of the same electronic state.
 Rotational transitions occur mostly between
rotational levels of the same vibrational state,
although there are many examples of combination
vibration-rotation transitions for light molecules.
Rotational Energy Levels
 Incident electromagnetic
waves can excite the
rotational levels of
molecules provided they
have an electric dipole
moment. The
electromagnetic field exerts
a torque on the molecule.
 The spectra for rotational
transitions of molecules is
typically in microwave
region of the
electromagnetic spectrum.
 The rotational energies for
rigid molecules can be
found with the the aid of
the Shrodinger equation.
 For a diatomic molecule the rotational energy is
where J is the rotational angular momentum quantum
number and I is the moment of inertia
 The rotational constant B
enables to calculate the bond length R.
Rotational Transitions
 The allowed transitions for the diatomic molecule are
regularly spaced at interval 2B. The measurement and
identification of one spectral line allows one to calculate
the moment of inertia and then the bond length.
 For a rigid rotor diatomic molecule, the selection rules for
rotational transitions are ΔJ = +/-1
Vibrational Spectra of Diatomic Molecules
 The lowest vibrational
transitions of diatomic
molecules
approximate the
quantum harmonic
oscillator and can be
used to imply the bond
force constants for
small oscillations.
A hamiltonian with a parabolic potential energy is
characteristic to a harmonic oscillator with
1

Ev   v  
2

k
   

1
2
with  = 0, 1, 2,…. Is vibrational quantum number
The selection rules are Δ  = +/-1
Vibration-Rotation Spectra
 Infrared spectroscopy concerns changes of vibrational
and rotational state, without change of electronic state.
Hence, the infrared spectrum is a vibration-rotation
spectrum.
 The selection rules are:
Δn = ± 1
ΔJ = ± 1
 Considering only transitions that involve the ground
vibration state, the energy change is:
Raman Effect
 First postulated by Smekal in 1923
 Dr. Chandrasekhara Venkata Raman
 First observation of Raman Scattering
 Discovered by the Indian scientist Sir C.
V. Raman (1928, together with K. S.
Krishnan).
 Raman won the Nobel Prize in Physics in
1930 for this discovery
Electric dipole moment
 For a single dipole with a distance, d, between charges –
q and +q, the dipole moment is: p = qd
 Heteronuclear diatomics and asymmetric triatomics:
CO, NO, H2O- Have permanent dipole moment:
 Homonuclear diatomics: O2 , N2
No permanent dipole moment
Induced dipole moment
 A dipole moment may be created through:
• electronic excitation
• the polarizability of the molecule in the presence of
an electric field
 Induced dipole moment:
p=αE
α: molecular polarizability
Ε: electric field
(polarization = vector sum of the dipole
moments per unit volume)
Raman spectrum
scattering
 Raman Stokes line –
scattered photon give
up energy
 Raman Anti-stokes line
– scattered photon gain
energy
Light intensity
 Rayleigh line – elastic
Schematic diagram of the process
Schematic diagram of the Raman scattering process
The vertical direction represents energy