Raman Spectroscopy
You are already aware that photons interact with molecules to induce transitions between energy states. In the discussion of Raman spectroscopy, we use language from particle theory and we say that a photon is scattered by the molecular system. Most photons are elastically scattered, a process which is called Rayleigh scattering. In Rayleigh scattering, the emitted photon has the same wavelength as the absorbing photon. Raman Spectroscopy is based on the Raman effect, which is the inelastic scattering of photons by molecules. The effect was discovered by the Indian physicist, C. V. Raman in 1928. The Raman effect comprises a very small fraction, about 1 in 107, of the incident photons. In Raman scattering, the energies of the incident and scattered photons are different. A simplified energy diagram that illustrates these concepts is given below.
The energy of the scattered radiation is less than the incident radiation for the Stokes line and the energy of the scattered radiation is more than the incident radiation for the anti-Stokes line. The energy increase or decrease from the excitation is related to the vibrational energy spacing in the ground electronic state of the molecule and therefore the wavenumber of the Stokes and anti-Stokes lines are a direct measure of the vibrational energies of the molecule. A schematic Raman spectrum may appear as:
In the example spectrum, notice that the Stokes and anti-Stokes lines are equally displaced from the Rayleigh line. This occurs because in either case one vibrational quantum of energy is gained or lost. Also, note that the anti-Stokes line is much less intense than the Stokes line. This occurs because only molecules that are vibrationally excited prior to irradiation can give rise to the anti-Stokes line. Hence, in Raman spectroscopy, only the more intense Stokes line is normally measured.
Infrared (IR) and Raman spectroscopy both measure the vibrational energies of molecules but these method rely only different selection rules. Recall that for a vibrational motion to be IR active, the dipole moment of the molecule must change. Therefore, the symmetric stretch in carbon dioxide is not IR active because there is not change in the dipole moment. The asymmetric stretch is IR active due to a change in dipole moment.
For a transition to be Raman active, there must be a change in polarizability of the molecule.
Vibrational motion
(extended) (equilibrium) (compressed)
polarizability
ellipsoid
Notice that the symmetric stretch in carbon dioxide is Raman active because the polarizability of the molecule changes. You can see when you compare the ellipsoid at the equilibrium bond length to the ellipsoid for the extended and compressed symmetric motions. For a vibration to be Raman active, the polarizability of the molecule must change with the vibrational motion. Thus, Raman spectroscopy complements IR spectroscopy.
Experimentally, we only observe the Stokes shift in a Raman spectrum. Recall that the Stokes
lines will be at smaller wavenumbers (or higher wavelengths) than the exciting light. Since the
Raman scattering is not very efficient, we need a high power excitation source such as a laser.
Also, since we are interested in the energy (wavenumber) difference between the excitation and
the Stokes lines, the excitation source should be monochromatic. This is another property of
many laser systems.
Theory
Vibrational spectroscopy of molecules can be relatively complicated. Quantum mechanics requires that only certain well-defined frequencies and atomic displacements are allowed. These are known as the normal modes of vibration of the molecule. A linear molecule with N atoms has 3N - 5 normal modes, and a non-linear molecule has 3N - 6 normal modes of vibration. There are several types of motion that contribute to the normal modes. Some examples are:
Infrared spectroscopy allows one to characterize vibrations in molecules by measuring the
absorption of light of certain energies that correspond to the vibrational excitation of the
molecule from v = 0
v = 1 (or higher) states. As indicated above, not all of the normal modes
of vibration can be excited by infrared radiation. There are selection rules that govern the ability
of a molecule to be detected by infrared spectroscopy.
The Raman effect was originally observed in 1928. It is due to the interaction of the electromagnetic field of the incident radiation, Ei, with a molecule. The electric field may induce an electric dipole in the molecule, given by
p = 
Ei (1)
where
is referred to as the polarizability of the molecule and p is the induced dipole. The
electric field due to the incident radiation is a time-varying quantity of the form
Ei = Eo cos(2
i t) (2)
For a vibrating molecule, the polarizability is also a time-varying term that depends on the
vibrational frequency of the molecule, 
vib
= 
o + 
vib cos(2
vib t) (3)
Multiplication of these two time-varying terms, Ei and 
, gives rise to a cross product term of
the form:
(4)
This cross term in the induced dipole represents light that can be scattered at both higher and
lower energy than the Rayleigh (elastic) scattering of the incident radiation. The incremental
difference from the frequency of the incident radiation, 
i, are by the vibrational frequencies of
the molecule, 
vib. These lines are referred to as the "anti-Stokes" and "Stokes" lines,
respectively. The ratio of the intensity of the Raman anti-Stokes and Stokes lines is predicted to
be
(5)
The Boltzmann exponential factor is the dominant term in equation (5), which makes the anti-Stokes features of the spectra much weaker than the corresponding Stokes lines.
Infrared spectroscopy and Raman spectroscopy are complementary techniques, because the
selection rules are different. For example, homonuclear diatomic molecules do not have an
infrared absorption spectrum, because they have no dipole moment, but do have a Raman
spectrum, because stretching and contraction of the bond changes the interactions between
electrons and nuclei, thereby changing the molecular polarizability. For highly symmetric
polyatomic molecules possessing a center of inversion (such as benzene) it is observed that bands
that are active in the IR spectrum are not active in the Raman spectrum (and vice-versa). In
molecules with little or no symmetry, modes are likely to be active in both infrared and Raman
spectroscopy.
Selection Rules
Point Groups. Molecules can be classified according to symmetry elements or operations that leave at least one common point unchanged. This classification gives rise to the point group representation for the molecule. Very useful information about the point group is contained in character tables. In this experiment we will study three different molecules: CHCl3, CH2Cl2, and CH3Cl. Both CHCl3 and CH3Cl are represented by the C3v point group and CH2Cl2 is represented by the C2v point group. The character tables describing these two point groups are shown below.
This figure is from Cotton, Chemical Applications of Group Theory, 1963.
The upper left corner of the character table identifies the point group. The remainder of the first row of the character table identifies the symmetry operations in the point group. The letters in the left column of the character table represent the symmetry species that label the irreducible representations of the group. The numbers in the table are the characters. To the right of the numbers in the table are a set of six symbols, where x, y, and z are placed in the appropriate row of the table to show how the symmetry operations of the point group affect these axes. The Rx, Ry, and Rz are placed in the appropriate row of the table to show how the symmetry operations of the point group affect rotation about these axes. The far right portion of the character table shows how squares and binary products of coordinates are affected by the symmetry operations of the point group.
Infrared Transitions. For a fundamental transition to occur by absorption of infrared radiation the transition moment integral must be nonzero. The transition moment integrals are of the form:
where 
vo is the wave function for the initial state involved in the transition (the ground state),
and 
vf is the wave function for the final state involved in the transition (the excited state). The
x, y and z involved in the integrals refers to the Cartesian components of the oscillating electric
vector of the radiation. If any of these three integrals is nonzero, then the transition moment
integral is nonzero and the transition is allowed.
We will use symmetry considerations to determine whether the transition moment integral is zero
or nonzero, and hence whether the transitions is allowed or forbidden. The ground state wave
function, 
vo, belongs to the totally symmetric representation of the point group, A1 for the C2v
and C3v point groups shown above. The symmetry representation for the excited state wave
function, 
vf, depends on the symmetry of the normal mode vibration to be excited. If the
product of the three terms in the transition moment integrals above are not the totally symmetric
representation, then the integral will be zero. This leads to a very simple rule for the activity of
fundamentals in infrared absorption:
A fundamental transition will be infrared active (that is, give rise to an absorption band) if the normal mode involved belongs to the same symmetry representation as any one or several of the Cartesian coordinates.
For the C2v point group, this means that if the symmetry representation of the normal mode is A1, B1 or B2, it will be infrared allowed. Only normal modes with the A2 symmetry representation would be infrared forbidden. For the C3v point group, this means that if the symmetry representation of the normal mode is A1 or E, it will be infrared allowed. Only normal modes with the A2 symmetry representation would be infrared forbidden.
Raman Transitions. For a fundamental transition to occur by Raman scattering of radiation the transition moment integral must be nonzero. The transition moment integrals are of the form:
where 
represents the polarizability of the molecule. The symmetry representations for the
polarizability is the same as that of quadratic terms involving the Cartesian coordinates, x2, y2, z2,
xy, yz, and xz. The symmetry representations of these terms are presented in the character table.
These 
's are components of the polarizability tensor and the requirement that the above
integrals be nonzero means that there must be a change in polarizability of the molecule when the
transition occurs. This leads to a very simple rule for the Raman activity of fundamentals:
A fundamental transition will be Raman active (that is, give rise to a Raman shift) if the normal mode involved belongs to the same symmetry representation as any one or more of the Cartesian components of the polarizability tensor of the molecule.
For the C2v point group, this means that all of the symmetry representations of the normal mode: A1, A2, B1 and B2, will be Raman allowed. No normal modes for molecules in the C2v point group will be Raman forbidden. For the C3v point group, this means that if the symmetry representation of the normal mode is A1 or E, it will be Raman allowed. Only normal modes with the A2 symmetry representation would be Raman forbidden.
Normal Modes of Vibration. The normal modes of vibration for CH3Cl and CHCl3 (both molecules have the same symmetry) are shown in the figure below.
This figure is from Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, 1945.
This shows that the first three vibrations for these C3v molecules are of A1 symmetry, and that the other three are doubly degenerate E symmetry vibrations.
The normal modes for CH2Cl2 are shown in the figure below.
This figure is from Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, 1945.
This shows that the first four vibrations for this C2v molecule are of A1 symmetry, vibration five
is of A2 symmetry, vibrations six and seven are of B1 symmetry and vibrations eight and nine are
of B2 symmetry.
Experimental
In this experiment you will collect infrared and Raman spectra of liquid samples of the three
chloromethanes: methyl chloride, methylene chloride and chloroform. The infrared spectra will
be collected using a liquid cell and the FTIR spectrometer. Raman spectra will be collected using
the argon ion laser - PTI spectrometer system show in the photograph. Liquid samples are placed
in a fluorescence cell and in the sample compartment for the Raman experiments. The excitation
of the Raman spectra uses the 488 nm line from the argon ion laser. A computerized
spectrometer control and data acquisition is used for this experiment. A photograph is shown of
the computerized spectrometer control and data acquisition program. Data can be saved to a data
file that can be easily imported into a spreadsheet program for further analysis. The data file
consists of a column of wavelengths and a column of signal intensities. These signal intensities
are an average of 100 reading of the photomultiplier (PMT) signal. Be sure to record the
photomultiplier voltage, and the amplifier and time constant settings (built into the PMT
housing).
Results
You will need to analyze the Raman data to construct a Raman spectra for the Stokes portion of
the spectra. Determine the locations of the fundamental vibrations observed in the Raman
spectra. Determine the locations of the fundamental vibrations observed in the infrared spectra. It
will be necessary for you to use the literature to help assign the peaks to the particular vibrations
in the molecule. Compare the infrared, Raman and literature values of the fundamental
frequencies for the transitions for each of the molecules. Are any of the transitions that are
infrared or Raman forbidden observed? Discuss the similarities and differences in the data
obtained in the infrared and Raman spectra.
References
1. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold, New York, NY, 1945.
2. J. C. de Paula, http://www.haverford.edu/chem/302/Raman.pdf.
3. G. Shalhoub, Raman Spectroscopy, La Salle Univ.
4. D. P. Shoemaker, C. W. Garland and J. W. Nibler, Experiments in Physical Chemistry, 6th ed., McGraw-Hill, New York, NY, pp. 389 - 397.
5. F. A. Cotton, Chemical Applications of Group Theory, Wiley Interscience, New York, NY,
1963.
© 2000 Larry G. Anderson