Rotational-vibrational spectrum

This Is a readable and fairly comprehensive treatment of rotation-vibration spectra and their Interactions. 

Benedict, W. S., Gailar, N. Plyler, E. K. (1956). Rotation-vibration spectra of deuterated water vapour. Journal of Chemical Physics, 24, 1139-65. 

Values for the partial charges of atoms can be derived from quantum mechanical calculations, from the molecular dipole moments and from rotation-vibration spectra. However, often they are not well known. If the contribution of the Coulomb energy cannot be calculated precisely, no reliable lattice energy calculations are possible. 

Quite often, rotational-vibrational spectra of molecules are analyzed by means of empirical formulas. A convenient formula for diatomic molecules is the Dunham expansion (Dunham, 1932 Ogilvie and Tipping, 1983)... 

The Hamiltonian operator for molecular rotational-vibrational spectra, which in the uncoupled form is written as in Eq. (2.17), can now be written in the coupled form as... 

Iachello, F. (1981), Algebraic Methods for Molecular Rotation-Vibration Spectra, Chem. Phys. Lett. 78, 581. 

Leviatan, A. (1992), Algebraic Approach to Molecular-Rotation-Vibration Spectra. IV. Raman Intensities (to be published). 

Leviatan, A., and Kirson, M. W. (1988), Intrinsic and Collective Structure of an Algebraic Model of Molecular Rotation-Vibration Spectra, Ann. Phys. 188,142. 

McCoy, A. B., and Sibert HI, E. L. (1992a), An Algebraic Approach to Calculating Rotation-Vibration Spectra of Polyatomic Molecules, Mol. Phys. 77,697. 

The present volume deals exclusively with rotation-vibrational spectra. Electronic excitations can also be described algebraically, but this description is still at too preliminary a stage for inclusion in a book format. 

All together one would obtain an effeetive moment of inertia tensor which includes the rotational g tensor again. This correction is normally ignored for polyatomic molecules, but allows to estimate the rotational g factor of diatomic molecules from field-free rotation-vibration spectra [5,10,11]. 

Stecher, T. P. 1969 Interstellar extinction in the ultraviolet. Astrophys. J. 157, L125-L126. Weeks, D. E. Harter, W. G. 1989 Rotation-vibration spectra of icosahedral molecules. Icosahedral symmetry, vibrational eigenfrequencies, and normal modes of buckminsterfullerene. J. chem. Phys. 90, 4744. 

It is more difficult to obtain rotational and rotation-vibration spectra with high resolution in Raman than in IR spectroscopy. This is because Raman spectra are observed in the UV-visible region where high resolving power is difficult to obtain. 

Although the interpretation of rotational spectra of diatomic molecules is relatively simple, such spectra lie in the far infrared, a region that at present is not as easily accessible to study as are the near infrared, visible, cr ultraviolet. Consequently, most information about rotational energy levels has actually been obtained, not from pure rotation spectra, but from rotation-vibration spectra. Molecules without dipole moments have no rotation spectra, and nonpolar diatomic molecules lack rotation-vibration spectra as well, Thus, II2, N2, 02, and the molecular halogens have no characteristic infrared spectra. Information about the vibrational and rotational energy levels of these molecules must be obtained from the fine structure of their electronic spectra or from Raman spectra. 

This expression is roughly consistent with the band structure of rotation-vibration spectra. Since the rotational quantum number J assumes integral values, the lines comprising a rotation-vibration band of a rigid rotator are equally spaced. The separation of such lines allows calculation of the moment of inertia of the molecule without the necessity for exploring the far infrared. 

Detailed analyses of the rotation-vibration spectra of molecules having four or more atoms are generally quite difficult, even if the vibrations are... 

Show how in equation (10) the expression for an energy change leading to a line in the rotation-vibration spectra is derived. Show that this expression predicts only one set of lines, equally spaced, with frequencies independent of the vibrational quantum numbers in initial and final states. 

In many cases, the infrared and Raman rotation-vibration spectra contribute complementary structure data, particularly for highly symmetric molecules. Due to the significantly different selection rules a greater line density is observed for Raman due to a larger selection of allowed changes in the rotational energy compared to infrared gas spectra. Raman spectroscopy is, on these grounds, also a valuable supplement to infrared studies. 

The study of the rotation-vibration spectra of polyatomic molecules in the gas phase can provide extensive information about the molecular structure, the force field and vibration-rotation interaction parameters. Such IR-spectra are sources of rotational information, in particular for molecules with no permanent dipole moment, since for these cases a pure rotational spectrum does not exist. Vibrational frequencies from gas phase spectra are desirable, because the molecular force field is not affected by intermolecular interactions. Besides, valuable support for the assignment of vibrational transitions can be obtained from the rotational fine structure of the vibrational bands. Even spectra recorded with medium resolution can contain a wealth of information hot bands , for instance, provide insight into the anharmonicity of vibrational potentials. Spectral contributions of isotopic molecules, certainly dependent on their abundance, may also be resolved. 

Principal axes can easily be identified in a molecule which possesses symmetry elements e.g., symmetry axes that coincide with principal ones, and a symmetry plane that is oriented perpendicularly to one of the principal axes. The simplest models discussed here are rigid rotor - harmonic oscillator models, which can be extended on demand to better fit the spectral data. For a more complete coverage, the reader is referred to other text books. As a first introduction to infrared rotation-vibration spectra the author prefers Barrow (1962). The topic is discussed in greater details by publications such as by Allen and Cross (1963), Herzberg (1945, 1950), and Hollas (1982). 

Rotation-vibration spectra of gases (H.M. Heise and H.W. Schrotter) 253... 

---