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Measurement of Molecular Excitation Spectra
by Laser Raman Effect
ABSTRACT
The phenomenon known as the Raman effect allows us to probe the energy levels intrinsic to a given molecule, giving us knowledge about its rotational and vibrational energies. By illuminating a transparent sample, either liquid, gas, or crystal, with an intense source of light, (preferably monochromatic or at least with sufficiently well- known and distinct spectral lines), inelastic scattering of electromagnetic radiation can be measured perpendicular to the beam line to obtain a spectrum which yields information about the energy levels of the molecule being studied.
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I. INTRODUCTION
In 11, with the foundations of quantum mechanics just being laid, Prof. C. V. Raman began a series of experiments to observe the scattering of light by transparent media. Although such studies were certainly not new as scientists and laymen alike had been studying transparent scattering for centuries (most notable among these researchers were perhaps Sir Isaac Newton and Christiaan Huygens), the depth and breadth of his research led Prof. Raman to observe a very weak secondary radiation scattered from transparent liquids, where the wavelengths were different from those already known. What is perhaps most remarkable about this observation is that it was made with sunlight as the illuminating source.
At a meeting of the South Indian Science Association at Bangalore on March 16, 18, Raman made the first public announcement of the phenomenon, showing his spectrum of carbon tetrachloride [1]. He showed that the frequency shifts, the relative intensities, and the state of polarization, among other features of the new spectral lines were independent of the exciting radiation. Thus, this new scattering method of investigation, which in many ways complemented infrared spectroscopy, revealed an amazingly easy and convenient way of mapping the vibrational and rotational spectra of chemical compounds. In the same year, P. Pringsheim [] labeled this new scattering phenomenon the Raman effect and therefore the spectrum of new lines, the Raman spectrum. A more detailed account of the historical background and subsequent applications of Raman spectroscopy can be found in the text by Anderson [].
In the results to follow, it will be our goal to successfully use the technique of Raman spectroscopy to measure the excitation spectra of several chemicals, most notably carbon tetrachloride CCl4, dichloromethane CHCl, and chloroform CHCl. In this paper we will examine the theory behind the Raman effect, discuss the experimental procedure for measuring spectra of the liquids in question, present our findings and analyses of the respective spectra, and draw the relevant conclusions.
II. THEORY OF THE RAMAN EFFECT
In its simplest description, the Raman effect is the result of a double photon transition involving three energy levels (i.e. stationary states of the time-independent Schrödinger equation). An incident photon from a preferably monochromatic source is absorbed by the material, causing the molecule to transition from its initial state (a) into an excited, intermediate state, often labeled the virtual level. The molecule then transitions into another state (b), emitting a photon. The energy shift of the emitted photon relative to the incident radiation tells us the energy difference between states (a) and (b), as indicated in Fig. 1. The spectral lines corresponding to a loss in energy of the photon are referred to as Stokes lines (as Fig. 1 depicts); those lines corresponding to a gain in energy are referred to as anti-Stokes lines, the terminology being lent from florescence.
In order to identify which vibrational or rotational mode is responsible for producing a given Raman line, it is necessary to consider not only this frequency shift, but also the state of the polarization of the Raman line (which depends upon the symmetry of a particular vibration) and the appearance or absence of the line in infrared absorption spectra. For the materials which we will study in our experiment, these properties are well documented, and we will use them to verify the accuracy and precision of our methods.
As briefly mentioned above, polarization plays a significant role in the Raman effect. Essentially all light scattering is based on the fact that incident radiation of a given frequency 9 induces an oscillating dipole moment in the material in question. Generically, we can say
(1)
where is a second-rank tensor that represents the polarizability of the molecule and is the electric field vector of the incident radiation. If the atoms execute periodic motion, is given by , where is the polarizability in the equilibrium configuration, is the maximum change of polarizability when the atoms vibrate, and 91 is the frequency of the atomic oscillation. This gives us
()
From Eq. () we can quickly see that we would expect the induced dipole moment then to radiate at three different frequencies, first 9, corresponding to the Rayleigh scattering line, and also (9 + 9 1) and (9 - 9 1) corresponding to the Raman anti-Stokes line and Stokes line, respectively. In short, it is the polarizability of the static molecule itself which leads to Rayleigh (elastic) scattering while the changes in polarizability during molecular motions are responsible for Raman (inelastic) scattering. For an example of a typical Raman spectra, illustrating the characteristic frequencies (usually between 100 and 000 cm-1), we refer the reader to a spectra of carbon tetrachloride collected by [4] in Fig. .
If a vibration of the atoms of a molecule introduces a corresponding periodic change in its polarizability, the scattered radiation will contain the sum and difference of the incident frequency and the molecular vibration frequency. This is what is known as the vibrational Raman effect. The intensity of any vibrational Raman line is determined by the magnitude of the displacement belonging to the corresponding normal vibration.
Thus, if we are armed with a detection scheme capable of measuring subtle shifts in the frequencies of scattered radiation, as well as a method of measuring the polarization of the scattered radiation (as well as incident), then we will be able to glean some detailed information about the inner structure and allowed vibrational modes of the molecule under study.
III. EXPERIMENTAL PROCEDURE
Generically, any light source can be used to study the Raman effect. Raman himself used sunlight before switching to the more intense mercury arc lamp. For our purpose, we will use an Ar-ion laser, with the obvious benefits of having a narrow band width of the incident spectral line, a well-defined polarization, and distinct and very well-known frequencies. Our setup consists of the Ar-ion laser (with a wavelength of 488nm) and a power output of 100 mW), simple reflecting optics for directing the beam, a sample and sample holder, a condensing lens to focus the scattered light onto the spectrometer (a Spex Industries double monochromator), a photomultiplier tube (PMT) with Peltier cooler, and finally a computer for data analysis. A schematic of this setup can be found in Fig. .
Although the procedure for measuring Raman spectra is fairly straightforward, like any scientific endeavor worth undertaking, extreme care must be taken in order to achieve meaningful results. In accordance with this caveat, the monochromator should be considered the most crucial part of the entire experiment. Internally, it consists of directional optics to reflect and focus incident radiation onto two diffraction gratings in series. A motor drive with an external variable speed control turns the gratings, thereby scanning through different wavelengths which are selected by the gratings and then focused on an exit slit. A PMT is connected to the exit slit of the monochromator, and is in turn connected to a PC for data acquisition.
So, before the experiment can begin in earnest, we must first ensure accurate calibration of the monochromator. To do this we use incident light of known frequencies to match the wavelength-counter reading on the monochromator to specific wavelengths. This can easily be performed with a mercury arc lamp (or any other light source for which a detailed description of emission lines exists). Used in combination with a HeNe laser as a fixed reference point, one can obtain a plot of known wavelength vs. counter reading, whereby the equation of a linear least-squares fit will provide an accurate method of determining the actual wavelength for any measured counter reading.
With calibration complete, the sample (either carbon tetrachloride, chloroform, and dichloromethane) is placed in a cylindrical, transparent container which is wrapped with foil to eliminate further scattering, and then placed in the sample holder in alignment with the incident laser beam. Perpendicular to the incident beam, a condensing lens is used to focus scattered light onto the entrance slit of the monochromator. This scattered light contains a very intense peak corresponding to the Rayleigh scattering, and much fainter spectral lines to either side of the intense peak. The drive on the monochromator can be operated at variable speeds, and quick sweeps are made in order to find the Rayleigh peak. Once this has been accomplished, slow and careful sweeps in only the region of interest are made, with the knowledge that those peaks with lower frequency than the Rayleigh line (Stokes) will have greater intensity than the peaks with higher frequency (anti-Stokes). REFERENCES
[1] C.V. Raman and K.S. Krishnan, Indian J. Phys., , 87, (18).
[] P. Pringsheim, Die Naturwiss, 16, 567, (18).
[] A. Anderson, The Raman Effect, (Marcel Dekker, Inc., New York, 171).
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