Analysis of Raman Contours in Vibration-Rotation Spectra
As is widely known, a Raman band is a gas phase spectrum always exhibits a rotational structure. Even a totally symmetric band of a spherical top, which consists only of a Q-branch, presents a profile which may be calculated in terms of variation of rotational energy, from a lower vibrational state to an upper one.
In most cases, the rotational structure of the Raman bands is not resolved, and one observes contours depending on (i) the various molecular constants entering the expression for the rotational energy, (ii) the temperature, (iii) the type of the rotator and the symmetry of the vibration, and (iv) the polarization of the scattered light (In or I⊥).
Actually, a “band” may be a superposition of a system of bands, associated with several vibrational transitions of slightly different energies, such as a fundamental and the corresponding upper-state transitions (or “hot bands”). In this case, the observed contours depend, in addition to the various aforementioned parameters, on anharmonicity constants, and on the temperature, which is not necessarily the same as above, when the sample is out of thermodynamic equilibrium.
The a priori calculation of an unresolved Raman contour is of interest, as it allows either a measurement of molecular constants or a determination of temperature. In every situation, the possibility of a computer simulation of a Raman band does exist, but, in the simplest cases, approximate analytical expressions can be derived for the “natural” contours (unperturbed by the apparatus function) and also for the convoluted contours. The approximations entering these calculations are allowed when Bhc ≪; kT. The analytical expressions enable one to make an easier analysis of the band contours.
When one is interested in temperature measurement, he may only consider the trace scattering (I‖ — 4/3 I⊥), i.e. the trace contribution to the Q-branch of totally symmetric vibrations. The polarized embranches are generally strong, and the intensity distribution among the individual lines is given by a simple law. Moreover, in a system of bands, the contour of the trace-scattered light is best resolved.
The principles of calculation of the Q-branch profiles will be emphasized for the cases of linear molecules, symmetric tops, and spherical tops, and the case of the asymmetric top will be raised.
KeywordsRaman Band Vibrational State Rotational Energy Polarizability Tensor Linear Molecule
Unable to display preview. Download preview PDF.
- 2.G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic Molecules, 2nd Ed., (D. Van Nostrand Co., Inc., Princeton, 1950).Google Scholar
- 3.G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, (D. Van Nostrand Co., Inc., Princeton, 1945).Google Scholar
- 4.B. P. Stoicheff, in Advances in Spectroscopy, Vol.1, ed. by H. W. Thompson, (Interscience, New York, 1959), p. 91.Google Scholar
- 9.S. Sportouch and R. Gaufrès, J. Chim. Phys. 69, 470 (1972).Google Scholar
- 11.R. Gaufrès and S. Sportouch, Compt. Rend. Acad. Sci. Paris 272, 995 (1972).Google Scholar
- 13.R. Gaufrès and S. Sportouch, in Advances in Raman Spectroscopy, Vol. 1, ed. by J. P. Mathieu, (Heyden and Son, Ltd., London, 1973), Chapt. 62.Google Scholar
- 14.S. Sportouch, Thèse d’Etat Montpellier 1972 (Dissertation).Google Scholar