Model dumbbell rotator

At low energies, the rotational and vibrational motions of molecules can be considered separately. The simplest model for rotational energy levels is the rigid dumbbell with quantized angular momentum. It has a series of rotational levels having energy... 

It is instructive to start with the simplest possible model of a rotating diatomic molecule, the so-called dumbbell model, as illustrated in figure 6.19. The two atoms, of masses ni and m2, are regarded as point-like, and are fastened a distance R apart... 

The simplest model of a rotating diatomic molecule is a rigid rotor or dumbbell model in which the two atoms of mass and m2 are considered to be joined by a rigid, weightless rod. The allowed energy levels for a rigid rotor may be shown by quantum mechanics to be... 

In the chain-of-rotators (COR) equation proposed by Chien, Greenkom, and Chao [17], a chain molecule is modeled as joined spheres in which adjacent covalent bonds can rotate. Rotation takes place because the chain is not straight any two adjacent bonds are joined at an angle like the radials from the center of a pyramid to the four comers. Chien et al. found the pressure of rotation by comparing the pressure of Boublik and Nezbeda s hard dumbbell fluid [18] with the pressure of Carnahan and Starling s hard spheres. The rotational pressure found is... 

This section describes how information on M-H2 binding can be extracted from series of measurements of the barrier to H2 rotation. Background is given in Section 62.1 on the model for hindered rotation of a dumbbell molecule and the measurement of transitions of this hindered rotator by INS. Section 62.3 discusses the relationship of the rotational barrier to the various factors that give rise to it and the conclusions that can be drawn concerning M-H2 binding. 

The geometry and height of the barrier can be derived by fitting the observed rotational transitions to a model for the barrier. The simplest possible model for the rotations of a dumbbell molecule is one of planar reorientation about an axis perpendicular to the midpoint of the H-H bond in a potential of twofold symmetry (Figure 6.1). More generally, terms with higher symmetry than twofold may be included in the Fourier expansion13 of the rotational potential ... 

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