Rigid molecule approximation

Rotation (Rigid molecule approximation) Linear polyatomic or diatomic molecules... 

ROTATION (Rigid Molecule Approximations) Linear Polyatomic or Diatomic Molecules ... 

The latter systems have only two internal degrees of freedom, however, (in the rigid molecule approximation) and the rare gas dimers have just a single one, of course. Some ab initio studies have been made of molecular Van der Waals (or hydrogen bonded) systems with more internal coordinates but mostly they concern only specific points or one-dimensional cuts (e.g. distance curves for fixed molecular orientations) of the potential (hyper) surface. One exception is the case of the simplest molecular dimer (112)2, which has been studied in detail, both ab and experimentally Another exception form the two Van der Waals molecules, (C2H and ( 2)2, of which the complete potential surfaces have been obtained in our institute via ab initio calculations. The N2—N2 potential, in particular, has been the subject of much previous (s ni-) empirical work . The dimers (N2)2 and (C2HJ2 have been investi-... 

We have studied the potential hypersurfaces for the Van der Waals dimers (Nj) and by varying all the independent internal coordinates (in the rigid molecule approximation, 3 angles for (Nj), 5 angles for (CjH ) and the distance R in both cases). It is of course not possible to present the complete surfaces pictorially we have displayed in figs. 9 and 10 some typical cuts through the surface of (N2)2. 

The external displacements of benzene are much greater in the zeolite than in the crystal, hence the more intense external mode region. We may compare this value with that extracted from diffraction data taken on the same system [19]. The diffraction data were analysed under the constraints of the rigid molecule approximation, the reported anisotropic displacement parameter tensor must, therefore, include both internal and external modes... 

LATTICE DYNAMICS OF HEXAMINE-A RIGID-MOLECULE APPROXIMATION. 

In the rigid molecule approximation it is assumed that the intermolecular potential energy V(i, ( ) depends only on the positions of the centers ofmass r Tirj.-.rN for the N molecules and on their orientations 0) =C0,0)2...0)fj- This implies that the vibrational coordinates of the molecules are dynamically and statistically independent on the center of mass and orientation coordinates, and that the internal rotations are either absent, or independent of the and of coordinates. The molecules are also assumed to be in their ground... 

Conformational Analysis Apart from a few early exceptions [32-34], successful CSP studies have been limited to fairly small, rigid molecules until the past decade. This was partly due to the necessity of making the rigid molecule approximation. This limitation to rigid molecules has restricted the appUcation of CSP methods, particularly in the field of pharmaceutical materials, where typical molecules are becoming larger and more flexible year on year. 

In a rigid molecule approximation (internal rotation and inversion barriers appreciably exceed kT), one may single out contributions from separate degrees of freedom of the translational, rotational, and vibrational motions to the entropy S and the heat capacity, with anharmonicity of vibrations and some other effects neglected ... 

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