Molecular potential spatial symmetry

Our discussion of spatial inversion symmetry concludes our project of demonstrating the symmetry properties of the Dirac equation under transformations of spin and spatial coordinates. With a spherical potential, the symmetry group is SU(2) 0 0(3). For potentials of lower (e.g., molecular) symmetries the appropriate group is SU (2)0G, where G is the nonrelativistic (spatial) point group of the potential—that is, the... 

Whichever kind of interaction prevails, the molecular or ionic units must tend to set themselves into arrays which possess a minimum of potential energy. Hence the existence of the crystaUine state and its characteristics of symmetry. Symmetrical orderings naturally allow potential energies lower than the unsymmetrical arrangements which would result from their distortion. To represent a possible spatial configuration of ions or molecules the system need not possess a potential energy which is an absolute minimum. Several relative minima may be separated from one another and from the absolute minimum by intervening maxima. 

Finally, it should be noted that surface effects on nematic elasticity do not amount only to the appearance of the and K24. elastic terms. Changes in the order parameter in a surface layer (see Barbero and Durand [239]) and references 1-6 therein), as well as unbalanced molecular interaction forces due to the broken symmetry of the nematic interaction potential at the surface [240], may lead to a spatial variation in the bulk elastic constants and the emergence of new elastic terms near the surface. 

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