Gayberne four parameters (κ, κ', μ, υ)

LAMMPS LAMMPS Beginners
1

i am a student currently researching and studying gayberne and i keep seeing these 4 parameters: (κ, κ’, μ, υ).

κ : “molecular elongation” or “axial ratio”
κ’: “ratio of the potential well depths of the side-by-side and end-to-end configurations” or “well-depth anisotropy parameter”
μ, υ : “influence the attractive forces and hence the phase behavior in a more subtle way”

μ, υ can be set in “pair_style gayberne gamma upsilon mu cutoff”, where mu = 2 and upsilon 1 according to Gay and Berne (J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 ~1981)
κ in this case we can set to 3 by basically letting our ellipsoid shapes be 3, 1, and 1

my question is, how do we set κ’ = 5?
im trying to recreate the parameters i found in a paper where the (κ, κ’, μ, υ) parameters are (3, 5, 1, 2)

if anyone could provide the pair_style gayberne and pair_coeff with complete parameters for ellipsoids of shape 3,1,1 i would greatly appreciate it.

2

You can very easily figure it out yourself by writing down the Gay-Berne equation for a given relative orientation of two ellipsoids – or search the literature for the “12 orthogonal modes of approach”[1].

  1. Disclaimer: this paper of mine contains them! ↩︎

3

Hello

I read the paper of yours, specifically the appendix part wherein gayberne was discussed. am i correct in assuming we cant make κ’ = 5 for uniaxial ellipsoids?

to provide a bit of context, in my work im trying to keep my ellipsoids uniaxial since i am not sure (since i have not read up on it yet) if it is possible to calculate the theoretical diffusion coefficients of biaxial ellipsoids using perrin equations

4

Why not? The convention for ellipsoids is:

Interaction name LAMMPS name
side-by-side \varepsilon_x
width-to-width (or face-to-face) \varepsilon_y
end-to-end \varepsilon_z

The specific ratio suggests that the uniaxial ellipsoid is a prolate, as for \sigma=\ (1,1,3) and \varepsilon=\ (1,1,0.2). For an oblate, it would have been something like \sigma=\ (3,3,1) and \varepsilon=\ (0.2,0.2,1). Of course, you can set the parameters to any value you like, but this would screw up their physical meaning. Please refer to the spheroid wikipidia entry. Also, please search this forum for related discussions on Gay-Berne ellipsoids, which contains useful animations about the physical meaning of the parameters --including \sigma_c.

5

ah i see, you are correct. apologies, i was overthinking it too much. thank you for the help!