Molecules with Internal Rotation

Although it was earlier believed that internal rotation about single bonds is unrestricted, Kemp and Pitzer in 1937 showed that agreement between third law and calculated values of the entropy of ethane required the internal rotation about the C—C bond to be restricted by a potential barrier of about 13 kJ mol. A large number of thermodynamic and spectroscopic studies have established the presence of barriers of this order of magnitude restricting internal rotation about single bonds. In only a very few cases can internal rotation be considered to be unrestricted. 

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Until recently, few attempts have been made to extend the theory of the ammonia inversion to account for the dependence of the inversion splittings on the vibrational and rotational quantum numbers [e.g. )]. These attempts differed not only from the standard approach to the vibration—rotation problem of rigid molecules but also from the approach to the problem of nonrigid molecules with internal rotation [for example )]. 

In the following sections of this paper, we describe a new model Hamiltonian to study the vibration—inversion—rotation energy levels of ammonia. In this model the inversion motion is removed from the vibrational problem and considered with the rotational problem by allowing the molecular reference configuration to be a function of the large amplitude motion coordinate. The resulting Hamiltonian then takes a form which is very close to the standard Hamiltonian used in the study of rigid molecules and allows for a treatment of the inversion motion in a way which is very similar to the formalism developed for the study of molecules with internal rotation [see for example ]. 

This approach has been frequently used in the treatment of molecules with internal rotation. In these molecules, the top and frame parts of the non-rigid reference configuration follow essentially the internal rotation internal rotation is not considered as a vibrational motion but rather as a part of the rotational motion described by a new dynamical variable — the angle of internal rotation. 

MOLECULE WITH INTERNAL ROTATIONAL DEGREES OF FREEDOM 231... 

The rotational spectram of a molecule with internal rotation (torsion) is modified due to torsion-rotation interactioa The interpretation of this modification allows the determination of the internal rotation potential barrier [59Lin, 68Dre, 84Gor]. The molecule is generally taken to be rigid except for internal rotation. However, special methods have been developed to include the interaction with other vibrational degrees of freedom. 

Very recently lijima and Tsuchiya have developed the necessary theory for correcting B to Bz in the case of molecules with internal rotation of one symmetrical group, e.g. molecules containing a single methyl group." The results have been applied to acetaldehyde," acetyl chloride," and acetyl bromide."... 

Let 5 be a molecule with internal rotational degrees of freedom. We assume that the vibrational, electronic, and nuclear partition functions are separable and independent of the configuration of the molecules in the system. We define the pseudochemical potential (PCP) of a molecule with a fixed conformation as the change in the Helmholtz energy for the process of introducing s into the system / (at fixed T, K), in such a way that its center of mass is at a fixed position R. If we release the constraint on the fixed position of the center of mass, we can define the chemical potential of the conformer in the gas and liquid phases as follows ... 

When the internal motion is not well represented as a small-amplitude motion, the analysis becomes more difficult and perturbation treatments are unsatisfactory. Over the last decade, considerable improvements and advances have been made to treat the complicated spectra of certain classes of molecules. These formulations provide more convenient and accurate treatments of large-amplitude motions for (i) molecules with internal rotation, ring puckering, inversion, or umbrella-Uke motions, (ii) quasilinear or quasisymmetric tops, (iii) floppy molecular complexes, and (iv) molecules with two internal rotators. Description of these treatments is beyond the scope of this presentation. For further information the reader is directed to the Bibliography. 

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