Vibrational spectra, of polyatomic molecules

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

Stepanov, B. A theory of vibrational spectra of polyatomic molecules. V. Calculation and interpretation of spectra of normal hydrocarbons. Acta physicochim. USSR 22, 238—262 (1947). 

L. A. Gribov, Introduction to the Theory and Computation of Vibration Spectra of Polyatomic Molecules, Leningradsk. Gos. Univ., Leningrad, 1965. 

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. 

L. M. Sverdlov, M. A. Kovner, E. P. Krainov, Vibrational Spectra of Polyatomic Molecules, Nauka, Moscow, 1970. 

This type of treatment has been very useful as a basis for the interpretation of the vibrational spectra of polyatomic molecules. Symmetry considerations have been widely employed to simplify the solution of the secular equation and in that connection the branch of mathematics known as group theory has been very helpful.1... 

D. M. Dennison Rev. Mod. Phys. 3, 280 (1931). A discussion of the methods of treating the rotational and vibrational spectra of polyatomic molecules. 

This review describes methods for computing directly the anharmonic vibrational spectra of polyatomic molecules from potential surface points obtained from electronic structure theory. The focus is on the state of the art of the methodology, on the approximations and the algorithms involved and their limitations, and on the scaling of the computational effort with the number of vibrational modes. The performance of dilferent electronic structure methods in obtaining accurate vibrational spectra is assessed by comparing the theoretical predictions with experiment for various test cases. Finally, some of the many open problems and challenges in this field are discussed. 

More examples of similar series in diatomic molecules are found in Sec. 2.1. These simple rules, obtained for a diatomic molecule, are helpful in understanding the vibrational spectra of polyatomic molecules. 

According to Eq. 2.6, the frequency of the vibration in a diatomic molecule is proportional to the square root of K/. If K is approximately the same for a series of diatomic molecules, the frequency is inversely proportional to the square root of fi. This point is illustrated by the series H2, HD, and D2 shown in Table 11-1 o. If is approximately the same for a series of diatomic molecules, the frequency is proportional to the square root of K. This point is illustrated by the series HF, HCl, HBr, and HI. These simple rules, obtained for a diatomic molecule, are helpful in understanding the vibrational spectra of polyatomic molecules. 

Diatomic Molecules (Spin Neglected), 258. Symmetry Properties of the Wave Functions, 261. Selection Rules for Optical Transitions in Diatomic Molecules, 262. The Influence of Nuclear Spin, 265. The Vibrational and Rotational Energy Levels of Diatomic Molecules, 268. The Vibrational Spectra of Polyatomic Molecules, 273. 

L.M. Sverdlov, M.A. Kovner and E.P. Krainov, "Vibrational Spectra of Polyatomic Molecules", John Wiley, New York (1974). 

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