Isotropic long range interactions second order

2 Isotropic Long Range Interactions (Second Order) 

Note that the mixed-pole terms Ga + U or = = Ig) have disappeared. The are the rotationally averaged 2 -pole oscillator strenghts  

Let us introduce the moments of the oscillator strength distribution These are defmed as  

The simplest (Uns51d) proximation to the summations occurring in the expressions, (31), (33) and (34), is made by assuming that the excitation energies (E — E ) and (E — can be replaced by constant average excitation energies and A . In this manna-, one obtains for the (Unsdld) polarizability (34)  

It is also possible to make ab initio calculations of the A s, however, and at the same time to improve the Uns51d scheme by assuming that the A s are dependent on the indices 1, labelling the multipole operators (2 -poles) associated with the excitations. Such a non-empirical Unsold scheme has been proposed by Mulder et The average excitation energy is defined as the ratio  

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Objects like atoms, molecules, and ensembles of molecules are chiral. Thus, properties connected to the chirality of an object may have very different origins. Therefore, it makes sense to introduce a concept in which four levels of chirality exist. The first level of chirality is the chirality of the atoms [30] caused by weak interaction which is of no interest for the discussion of liquid crystal properties. The second level is the chirality of molecules, while the third level is derived from the ordering of atoms, ions, or molecules in isotropic or anisotropic phases by long-range positional and long-range orientational order. The fourth level of chirality is the form of a macroscopic object which can be, e.g., an enantiomorphic crystalline form (habitus of the crystal). 

Many liquid crystal phase transitions involve broken continuous symmetries in real space and their interactions on a molecular scale are short range [1]. As a result, fluctuations have long been known to be an important feature of liquid crystal phase transitions even weakly first order (discontinuous) ones. Compared to major advances in our understanding of fluctuation controlled second-order (continuous) phase transitions, relatively little is known about fluctuation phenomena (critical phenomena) at first-order phase transitions such as the nematic-isotropic transition. 

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