Anisotropic long range interactions

Knowing the molecular permanent multipole moments and transition moments (or closure moments derived from sum rules, such as (36)), the computation of the fust and second order interaction energies in the multipole expansion becomes very easy. One just substitutes all these multipole properties into the expressions (16), (20), (21) and (22), together with the algebraic coefficients (24) (tabulated up to terms inclusive in ref. in a somewhat different form ), and one calculates the angular functions (lb) for given orientations of the molecules. 

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Wormer PES, Mulder F, Van der Avoird A (1977) Quantum theoretical calculations of Van der Waals interactions between molecules. Anisotropic long range interactions. Int J Quantum Chem... 

Mulder F, Van Dijk G, Van der Avoird A (1980) Multipole moments, polarizabilities and anisotropic long range interaction coefficient for N2. Mol Phys 39 407 125... 

There are tliree important varieties of long-range forces electrostatic, induction and dispersion. Electrostatic forces are due to classical Coulombic interactions between the static charge distributions of the two molecules. They are strictly pairwise additive, highly anisotropic, and can be either repulsive or attractive. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

This interaction arises from the overlap of the deformation fields around both defects. For weakly anisotropic cubic crystals and isotropic point defects, the long-range (dipole-dipole) contribution obeys equation (3.1.4) with a(, ip) oc [04] (i.e., the cubic harmonic with l = 4). In other words, the elastic interaction is anisotropic. If defects are also anisotropic, which is the case for an H centre (XJ molecule), in alkali halides or crowdions in metals, there is little hope of getting an analytical expression for a [35]. The calculation of U (r) for F, H pairs in a KBr crystal has demonstrated [36] that their attraction energy has a maximum along an (001) axis with (110) orientation of the H centre reaching for 1 nn the value -0.043 eV. However, in other directions their elastic interaction was found to be repulsive. 

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