Large-amplitude motions internal rotations

Internal coordinates in the large-amplitude-motion (LAM) rotation model... 

In order to understand the large amplitude motion, the allowed conformations brought about the multiple internal rotations were calculated for a single... 

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 ]. 

We shall divide these molecules into two categories (i) molecules with one large amplitude motion (inversion) which will be dealt with in Section 6.1 (ii) molecules with inversion and internal rotation (Section 6.2). Only such molecules will be considered, where the inversion barrier is low enough that inversion splittings can be resolved by microwave or infrared spectroscopy. As for the pyramidal inversion with higher barriers, description of the methods for determination of the barrier heights and the chemical consequences of the existence of the so-called invertomers, the reader is referred to review papers ... 

Another interesting example of a molecule with amino inversion and internal rotation is hydrazine, H2N NH2 (Fig. 20). In hydrazine, there are three large amplitude motions (i) two wagging vibrations of the NH2 groups which may be... 

The description of the forces between these atoms (bond-stretching and bending-force constants, barriers to internal rotation, and other large amplitude motions) and... 

The origin of the heat capacity is the vibrational energy, and effects connected with large-amplitude motion, such as translation, rotation and internal rotation. The internal rotation is also called conformational motion since the rotation about C-bonds leads to distinctly different isomeric structures. Figure 4.1 shows the fully analysed heat capacity of polyethylene [11]. 

Undoubtedly, the skeletal vibrations must control to a considerable extent the probability of relaxation transitions originating from a large-amplitude motion in a backbone chain, and requiring surmounting of the barriers to internal rotation. 

D. G. Lister, J. N. MacDonald, and N. L. Owen, Internal Rotation and Inversion An Introduction To Large Amplitude Motions In Molecules , Academic Press, New York, 1978, pp. 66-77. 

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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