Non-spherical molecules

Corner J 1948 The second virial coefficient of a gas of non-spherical molecules Proc. R. Soc. A 192 275... 

Parker G. A., Pack R. T. Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for non-spherical molecules, J. Chem. Phys. 68, 1585-601 (1978). 

Nevertheless, the use of spherical-cavity SCRF models finally led to a dead end, because no meaningful spherical cavities can be defined for non-spherical molecules. Even the attempt to overcome this problem by an extension of the Onsager model to ellipsoidal cavities did not really solve the problem, because this introduces additional fit parameters, while only a small portion of real molecules can still be considered as approximately ellipsoidal. Thus, the need for molecular-shaped SCRF models became more and more obvious. 

As we have seen in connection with the discussion of the data in Table 7, organic systems are even less well-behaved than inorganic ones due to their non-spherical shape. Assumptions of an ad hoc character can, at least for the time being, permit limited application of the spherical model to non-spherical molecules, and non-spherical models show a certain improvement, albeit with loss of computational simplicity. It is therefore hardly surprising that most organic redox systems have been analyzed in terms of log k vs. AG° plots (to evaluate their general appearance, the A value, and slopes in different regions of AG° ). 

The energy parameter e equals the maximum depth of the potential wdl, and ro equals the value of rj where the attractive 6-term and repulsive 12-term are equal. For non-spherical molecules, shape-dependent tmns involving the relative angular orientations of the two molecules are sometimes added to the right side of equation (26). More will be said on this in Section 4. 

Y. T. Wu and J. M. Nitsche, On diffusion limited site specific association processes for spherical and non-spherical molecules, Chem. Eng. Sci., 50 (1995) 1467-1487. 

T. Keyes and B, M. Ladanyi. The role of local fields and interparticle pair correlations in light scattering by dense fluids II. Depolarized spectra for non-spherical molecules. Molec. Phys., 55 1099-1107 (1977). 

The paper presents both calculation results for slit-like and cylinder pores and evaluates these using calculation results from the accepted spherical DFT approach. Beside others the paper points out the consequences of the simplified description through the spherical DFT approach for an inhomogeneous fluid which consists of non-spherical molecules. 

We must however notice that abnormally low values of the entropy of fusion are also encountered with some non-spherical molecules, table 14.7 indicates that some substances classed as associated appear to acquire rotational degrees of freedom before melting. 

Expression (9.58) accounts to some extent for shape selectivity which occurs with non-spherical molecules. 

The conclusion is that for relatively small molecules (H2, CO2, etc.), permeation in microporous (silica) membranes is not limited by surface reactions and direct penetration in the pores is the dominant mechanism in a wide range of temperature and pressure conditions [63]. This conclusion does not hold for large non-spherical molecules. Here sorption is necessary, the sticking coefficient becomes very important and surface reactions probably will limit the permeation as soon as bulk permeation becomes appreciable. To the knowledge of the present author, no investigations of this phenomenon in microporous membranes have yet been reported. 

Guggenheim observed that this principle actually holds very well for many simple fluids, fluids composed of molecules that are roughly spherical. However, in general, this principle does not hold for an arbitrary fluid, in particular, for polar fluids, such as water, and for fluids composed of highly non-spherical molecules, such has 77-hexane. 

Rotational degrees of freedom (e.g., non-spherical molecules in fluids). 

Although the above analysis has been limited to pure liquids containing spherical molecules, the same ideas can be applied to liquids having non-spherical molecules or liquid mixtures. For non-spherical molecules, the radial distribution function depends on the directional angles 0 and from the central molecule as well as on r. However, when we consider non-spherical molecules, not only does the mathematical complexity increase but also much more detailed information on liquid structure and intermolecular forces is required. 

Although in Chapter 5 we mentioned only spherical molecules, it should be obvious that many of the concepts of Chapter 5 apply to the isotropic scattering from non-spherical molecules as well. 

The only justification of Equation 52 which comes to my mind is to develop a perturbation theory for a fluid of non-spherical molecules using a hard-sphere reference fluid. The diameter of the hard spheres could be... 

The earliest molecular dynamics simulations using realistic potentials were of atoms interacting under the Lennard-Jones potential. In such calculations the only forces on the atoms are those due to non-bonded interactions. It is rather more difficult to simulate molecules because the interaction between two non-spherical molecules depends upon their relative orientation as well as the distance between them If the molecules are flexible then there will also be intramolecular interactions, which give rise to changes in conformation. Clearly, the simplest model is to treat the species present as rigid bodies with no intramolecular conformational freedom. In such cases the dynamics of each molecule can often be considered in terms of translations of its centre of mass and rotations about its centre of mass. The force on the molecule equals the vector sum of all the forces acting at the... 

For rigid, non-spherical molecules, the orientations of the molecules must be varied as well as their positions in space. It is usual to translate and rotate one molecule during each Monte Carlo step Translations are usually described in terms of the position of the centre of mass. There are various ways to generate a new orientation of a molecule. The simplest approach is to choose one of the three Cartesian axes x, y or z) and to rotate about the chosen axis by a randomly chosen angle 5a , chosen to lie within the maximum angle variation, [Barker and Watts 1969]. The rotation is achieved by applying routine trigonometric relationships. For example, if the vector (xi,yj,zk) describes the orientation of a molecule then the new vector (x i,y j,z k) that corresponds to rotation by 6w about the X axis is calculated as follows ... 

Here I is a (dimensionless) angular momentum operator. A non-spherical molecule will tumble more rapidly about some directions than about others, causing the diffusion constant Drot to become a tensor ... 

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