Oblate molecules

It is noticeable that the monosaccharides, which are oblate molecules able to pack efficiently, form significantly less hydrates than do the disaccharides or nucleosides, which are more awkward-shaped molecules from the packing point of view. 

For oblate molecules the dichroism is further influenced by the transverse-axis order parameter D. Its influence is the larger the more the orientation of the transition moment differs from the preferred molecular axis. Largest contributions should be found for perpendicular bands (a = 90°), in any case the sign of the contribution depends on whether the transition moment projects primarily on the shortest or the intermediate molecular axis. For a transition moment under the magic angle the dichroism is governed by D alone due to the vanishing contribution from S. 

Two different classes of distortion may be recognized, namely oblate and prolate. A prolate molecule, like CH3F, has two equal principal moments of inertia, which are greater than the third, while an oblate molecule, like NH3, has two equal moments of inertia, which are less than the third. In each case, the unique axis corresponds to a rotational axis of order 3 or more. The classification may be loosely extended to less symmetrical species, where two of the principal moments of inertia are similar and different from the third. 

The entropy production is consequently dependent on the orientation of the director. In a nematic liquid crystal consisting of prolate molecules A II >Aj l. The entropy production is consequently minimal in the perpendicular orientation. In a system consisting of oblate molecules the reverse is true, Ajj > A. Thus the entropy production is minimal in the parallel orientation. 

The enfries af fhe leff and right ends correspond to the symmetric prolate and oblate molecules with analytical expressions for fheir energies... 

The relations between the different sets of parameters are given in [77Wat, 84Gor]. The notation of the centrifugal distortion constants permits to know which reduction is used, and therefore the rotational constants are simply called A, B, C (without the superscript A or S). There are six different ways (representations) to identify the (x, y, z) reference system with the (a, b, c) principal axis system. In practice two different representations are used F where x=b, y=c, z=a and which is best for prolate molecules (Ray s asymmetiy parameter k = 1B-A-C)I A-C) <0), and IIF where x=a, y=b, z=c which is thought to be better for oblate molecules (k > 0). Representation IlF is also used where x = a, y = c, z = b ) xXiX is equivalent to representation mf Maity authors use codes written in F representation for oblate molecules, in particular for the analysis of inCnared spectra. 

This potential has been studied in connection with two prolate molecules, CO2 and N2, and one oblate molecule, benzene. The potential parameters were chosen to optimize agreement with the temperature dependence of measured second virial coefficients. These potentials were then used to compute the cohesive energy of the respective solids with some success. " ... 

In this case, because C is always less than B, the second term in equation 14.17 will always be negative, so the second term contributes to an overall decrease in the rotational energy of the oblate molecule relative to a diatomic or spherical top molecule. 

For prolate (7c = 7b > la) and oblate (7a = 7 >7c) molecules, two of the moments of inertia are the same canceling one term from the Hamiltonian in Equation 7-17. This results in two different Hamiltonians, one for prolate molecules and the other for oblate molecules. 

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