Slight error in Gay-Berne Potential

[Kischy]

I think there is a slight error in the Gay-Berne Potential calculation in code and documentation:

The term (see http://espressomd.org/html/doc4.1.3/inter_non-bonded.html#gay-berne-interaction)

should really be
.
Note the exponent.

This is accoring to the original equations in "J. G. Gay, B. J. Berne, Modification of the overlap potential to mimic a linear site–site potential, J. Chem. Phys. 1981, 74, 3316."

The equations in the original paper are:

and
.

Am I correct or am I overlooking something?

[jngrad]

I think you're right. However, a quick literature search reveals we are not the only one who dropped the nu exponent on epsilon0:

• Berardi et al. 1993 eqn 4 (doi:10.1039/FT9938904069)
• Rull et al. 2017 eqn 4 (doi:10.1080/00268976.2016.1274437)
• Rull et al. 2017 eqn 4 (doi:10.1021/acs.langmuir.7b02347)
• Hekmatzadeh et al. 2020 eqn 3 (doi:10.1016/j.chemphys.2020.110792, arXiv:2004.05056)
• Berardi et al. 1995 eqn 6 (doi:10.1016/0009-2614(95)00212-M)
• Berardi et al. 1996 eqn 6 (doi:10.1016/S0009-2614(98)01090-2)
• Luckhurst et al. 2006 eqn 4 (doi:10.1080/02678299008047361)
• Bates et al. 1999 eqn A5 (doi:10.1063/1.478563)
• Cleaver et al. 1996 eqn 8 (doi:10.1103/PhysRevE.54.559)
• Miguel et al. 1996 eqn 3a (doi:10.1063/1.472292)

I couldn't find papers citing the Gay et Berne 1981 paper that included the nu exponent. Since epsilon0 is a constant, its nu exponent only rescales the potential and force. I would guess that's the reason why GB papers simply leave the exponent out.

We should add a citation to Gay et Berne 1981 plus a note that we use the convention of epsilon0 without exponent that is prevalent in the GB literature, in both the Sphinx documentation and the C++ source code.

[Kischy]

Ok, sounds good.

[jngrad]

Thanks for pointing out that discrepancy. I'll open a PR.