The scale parameter σ now is determined as the contact parameter between the pair of molecules, and is different for each pair:
^{0}The shape anisotropy parameter χ is now defined by: And we can see that for identical particles this definition degenerates to the familiar definition of χ in the classical Gay-Berne model (where all particles are identical). Since σ, _{ee} = 2lσ, _{ss = 2d} κ = l/d.
Hence, also the definition of σ(u converges to the original definition (recalling that in this case =1) in the classical GB model.
_{i},u_{j},r_{ij})Another special case is when one molecule of the pair is spherical, i.e d = l, so that χ=0 and = 0 or infinity.
In this case the separation σ depends only on the angle between the nonspheric molecule and the vector beween the molecules (and as expected - the energy doesn't depend on the orientation of the spherical molecule).
In this limit σ approaches:
The well depth of the interaction potential is defined: and with and , where ε is now different for each molecule.
For identical particles, again, we can see that the definition degenerates to the familiar definion of_{0 } ε(u in the classical Gay Berne model.
_{i},u_{j},r_{ij})In the most degenerate case when the particles are spherical and identical it can be seen that the equations reduce back to the Lennard Jones potential. |