Rotations in Molecules

FIGURE 14.3 A diatomic (or polyatomic linear) molecule has only two defined rotational motions, which are equivalent to each other. 

The molecule also has angular momentum, which you would expect it to have because it is rotating. The quantum number / is used to define the total angular momentum of the molecule rotating in three dimensions. The total angular momentum of a molecule is given by the same eigenvalue equation from three-dimensional rotational motion  

The square of the total angular momentum is the formally quantized observable. In order to get the magnitude of the angular momentum, you must take the square root of the eigenvalue from equation 14.8. There is also a z component of the total angular momentum for the diatomic molecule, and this z component is also quantized  

Nonlinear molecules that have certain symmetry elements may, however, qualify for simpler treatment (leading, ultimately, to a better understanding of their properties). The key is the value of the moment of inertia of the molecule in the 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

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THE NATURE OF BOND ORBITALS AND THE ORIGIN OF POTENTIAL BARRIERS TO INTERNAL ROTATION IN MOLECULES... 

Although Hq. (152) can in principle be solved by the development of y(x) in a power series, the periodicity of the argument of cosine, namely, 2jc = Na complicates the problem. The most important application of Mathieu s equation to internal rotation in molecules is in the analysis of the microwave spectra of gases and vapors. The needed solutions to equations such as Eq. (152) are usually obtained numerically. 

Swalen, J.D., and C. C. Costain Internal rotation in molecules with two... 

Dreizler, H. Topics in Current Chem. 10, 59 (1968) Orville-Thomas, W.J. Internal Rotation in Molecules. London Wiley 1974. 

In the preface of his book devoted to internal rotation in molecules Orville-Thomas pointed out excellently that In the first half of this century, chemical... 

Orville-Thomas, W. J. Int. rotation in Molecules, John Wiley and sons 1974... 

Problem of Barriers to Internal Rotation in Molecules (Wilson). 2 367... 

Radio waves >1 mm Rotations in molecules, electron spin flips3... 

A. Veillard, in Internal Rotation in Molecules , ed. W. J. Orville-Thomas, Wiley, London, 1974, p. 385. 

Abraham, R.J. Bretschneider, E. Medium Effects on Rotational and Conformational Equilibria, in Internal Rotation in Molecules Orville-Thomas, W.J., Ed. Wi ley-Interscience New York, 1974, pp. 481-584. 

In the present paper, symmetry eigenvectors which factorize the Hamiltonian matrix into boxes are given for the single rotation in phenol (24) for double rotations in benzaldehyde (29), pyrocatechin (34) and acetone (44-46), for double rotation and inversion in non-planar pyrocatechin (40) and pyramidal acetone (49-51). In the same way, symmetry eigenvectors deduced in the local approach are deduced for some of these non-rigid systems (79), (83), and (89). Symmetry eigenvectors for the double internal Czv rotation in molecules with frame of any symmetry are given in reference [36]. 

Orville-Thomas WJ (1974) Internal Rotation in Molecules. Wiley Sons, London... 

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