[lammps-users] Inquiry about the Lennard Jones 9-6 equation used in LAMMPS

shahin_mohamadnejad1 · December 8, 2020, 7:41am

Dear Lammps Users,

I have a question regarding the correct form of the Lennard Jones 9-6 (LJ 9-6) equation. The thing is in the LAMMPS documentation, the following equation in terms of Sigma is written for LJ 9-6:

but by going through the reference article mentioned in the lammps documentation for compass force field I noticed that the used equation for LJ (9-6) potential in terms of r_m is :

Besides that, in this wikipage (http://www.sklogwiki.org/SklogWiki/index.php/9-6_Lennard-Jones_potential) I found another equation for LJ (9-6) potential in terms of sigma, which is:

I highly appreciate it if someone could tell me why the equation employed in LAMMPS is different from the other sources.
Thank you in advance for your time. I look forward to your answers.

Best regards,

Shahin Mohammad Nejad

akohlmey · December 8, 2020, 10:06am

there are no pictures included and it is thus not possible to see what you are comparing.
most likely there are differences in the definition of whether sigma constitutes the point where the LJ potential is zero or whether it represents the minimum of the potential.
the wikipedia article shows both variants. similarly epsilon may be given with a different prefactor.

axel

evoyiatzis · December 8, 2020, 10:27am

Hi Shahin

If you want to use COMPASS or PCFF with LAMMPS then it is better to use the lj/class2 pair_style (see https://lammps.sandia.gov/doc/pair_class2.html). Have a look also at https://lammps.sandia.gov/doc/Howto_bioFF.html

Cheers
Evangelos

Στις Τρί, 8 Δεκ 2020 στις 10:44 π.μ., ο/η shahin mohamadnejad <[email protected]> έγραψε:

shahin_mohamadnejad1 · December 8, 2020, 1:17pm

Dear Axel and Evangelos,

Thank you for your replies. First of all, I rewrite the equations missed in my previous email. The equation for Lj 9-6 from LAMMPS documentation is :

$\displaystyle E=\epsilon [2(\frac{\sigma}{r})^9-3(\frac{\sigma}{r})^6]$

In the LAMMPS documentation page for Lj 9-6 potential there is no definition for Sigma, but in the page for Lj 12-6, it is mentioned that Sigma is the distance in which the potential is zero and NOT as the energy minimum at r_m=2^(1/6)Sigma.

In the following Wiki page (http://www.sklogwiki.org/SklogWiki/index.php/9-6_Lennard-Jones_potential) the equation for Lj 9-6 in term of Sigma is:

$\displaystyle E=6.75 \epsilon [(\frac{\sigma}{r})^9-(\frac{\sigma}{r})^6]$

which as you may notice it is different from the equation used in LAMMPS. Besides, at r_m=1.5^(1/3)Sigma the equation is :

$\displaystyle E=\epsilon [2(\frac{r_m}{r})^9-3(\frac{r_m}{r})^6]$

I was wondering if in the equation used in LAMMPS for LJ 9-6, the Sigma has the same meaning as the one for LJ 12-6, then why the equation used by LAMMPS is different from the aforementioned wikipage and also the reference article for COMPASS force field (Sun, J Phys Chem B 102, 7338-7364 (1998)).
The thing is I have some compass pair potential parameters (r_m,epsilon), I want to know if I have to compute the Sigma beforehand and use those Sigma values in LAMMPS, or I can directly provide r_m values into the LAMMPS.

Best regards,

Shahin Mohammad Nejad