Potential rigid molecule

Even within the 6-A limit, variations between the predicted atom-atom distribution functions can be quite small. All of the distribution functions predicted by rigid molecule potentials rise from zero more steeply than the experimental curve. There are two reasons for this. First, the rather slow initial increase in the experimental first-neighbor peak is most likely an artifact. Second, the very sharp increase shown by essentially all of the calculated functions is a consequence of the repulsive potential used in these models. This form of repulsion is much too strong, and the softer exponential repulsion gives a slower increase in goo( )-Models that allow for polarization or internal relaxation give a better description of this increase although the value of the maximum is usually overestimated. 

Although translational and rotational contributions to the vibrational density of states can be calculated using rigid molecule potentials, relatively little has been done using such models. Rather, flexible molecule potentials have been used, in which case the band shapes and their frequency ranges can be computed for all three types of vibration. Most calculations to date have used either completely classical studies or introduced quantum effects in an approximate way. We will give an overview of both approaches. 

A small step rotational diffusion model has been used to describe molecular rotations (MR) of rigid molecules in the presence of a potential of mean torque.118 120,151 t0 calculate the orientation correlation functions, the rotational diffusion equation must be solved to give the conditional probability for the molecule in a certain orientation at time t given that it has a different orientation at t = 0, and the equilibrium probability for finding the molecule with a certain orientation. These orientation correlation functions were found as a sum of decaying exponentials.120 In the notation of Tarroni and Zannoni,123 the spectral denisities (m = 0, 1, 2) for a deuteron fixed on a reorienting symmetric top molecule are ... 

Figure 5.7 The role of stress caused by lattice mismatch between SAM and substrate illustrated in (a) and (b) by a cross-section of a SAM (x-z plane), indicated adsorption sides (x-y plane) and the molecule-substrate interaction potential V where the solid circles indicate the energy of an adsorption site for a particular SAM molecule, (a) For rigid molecules, stress is mainly released by defect formation in SAM, which results in a layer of rather low crystallinity and small domains, (b) Molecules...

The Section on Molecular Rotation and Vibration provides an introduction to how vibrational and rotational energy levels and wavefunctions are expressed for diatomic, linear polyatomic, and non-linear polyatomic molecules whose electronic energies are described by a single potential energy surface. Rotations of "rigid" molecules and harmonic vibrations of uncoupled normal modes constitute the starting point of such treatments. 

The empirical potentials can also be used to calculate the frequencies of the surface vibratory modes. Two different methods have been employed (26). In the first case, the molecule-substrate force constants introduced in the model described above are calculated and then used to solve the normal mode problem as before. In the second method, the molecule is treated as a rigid body, since distortions of the molecule induced by adsorption are calculated to be small. The frequencies of the surface vibratory modes are computed from the curvature of the molecule-substrate potential as the rigid molecule is rocked about its two symmetry... 

This illustrates a general principle the optimized structure one obtains is that closest in geometry on the PES to the input structure (Fig. 2.15). To be sure we have found a global minimum we must (except for very simple or very rigid molecules) search a potential energy surface (there are algorithms that will do this and locate the various minima). Of course we may not be interested in the global minimum for example, if we wish to study the cyclic isomer of ozone (Section 2.2) we will use as... 

In many types of observations, for example, in the determination of X-ray structures, the molecule is approximated as a rigid body and is represented by an iconic (static) model. Of course, even supposedly rigid molecules are far from that Their atoms vibrate about time-averaged positions. Nevertheless, the choice of a static model under the rigid-body approximation is reasonable because the corresponding molecule occupies only a single minimum on the potential-energy hypersurface. 

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