Free-rotor expression

Fig. 6. Free energy (at zero pressure) for a-nitrogen and /3-nitrogen, in different mean field models (closed lines). The dashed free rotor curve has been calculated from the isotropic (/, 12, ly) - (0,0, 0) term of the ab initio potential by adding the free rotor expression for the free energy. The dashed jump model curve has been obtained from the localized mean field solution (with the full anisotropic potential) by adding an entropy term -kBT In 6 (see the text).

The eigenvalue problem for the simple cos y potential of Eq. (4) can be solved easily by matrix diagonalization using a basis of free-rotor wave functions. For practical purposes, however, it is also useful to have approximate analytical expressions for the channel potentials V,(r). The latter can be constructed by suitable interpolation between perturbed free-rotor and perturbed harmonic oscillator eigenvalues in the anisotropic potential for large and small distances r, respectively. Analogous to the weak-field limit of the Stark effect, for linear closed-shell dipoles at large r, one has [7]... 

We have obtained the expression given in GT, p. 225 for the spectral function of free rotors moving in a homogeneous potential in the interval between strong collisions see also VIG, Eqs. (7.12) and (7.13). So, the subscript F means free. The subscript R in Eq. (74c) is used as an initial letter of restriction. Indeed, as it follows from the comparison of Eq. (77) with Eq. (74a), the second term of the last equation expresses the steric-restriction effect arising for free rotation due to a potential wall. If we set, for example, p = 7t, what corresponds to a complete rotation (without restriction) of a dipole-moment vector p, then we find from Eqs. (74a)-(74c) that LR z) = 0 and L(z) = Lj,(z). This result confirms our statement about restriction. ... 

A classical resonance-absorption theory [66, 67] was aimed to obtain the formulas applicable for calculation of the complex permittivity and absorption recorded in polar gases. In the latter theory a spurious similarity is used between, (i) an almost harmonic perturbed law of motion of a charge affected by a parabolic potential (ii) and the law of motion of a free rotor, this law being expressed in terms of the projection of a dipole moment onto the direction of an a.c. electric field. 

In this expansion the orientational dependence (anisotropy) of the intermolecular potential between two molecules A and B is explicitly expressed in a (complete) basis of symmetry-adapted free-rotor functions, defined as ... 

The free rotor model is not adequate for most molecules as there is in general some potential barrier to internal rotation. As an example, consider ethyl fluoride. Ethyl fluoride, just like ethane, has a predominately threefold potential barrier as shown in Figure 7-3. The potential barrier can be expressed as the following function. 

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