From 2e8b95f0c164b799874fff61fa98a5ff97e4be5c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Mateo=20Rodr=C3=ADguez?= Date: Wed, 23 Apr 2025 19:34:06 +0200 Subject: [PATCH] Update pair_lj_pirani.rst Documentation update --- doc/src/pair_lj_pirani.rst | 50 ++++++++++++++++++++++---------------- 1 file changed, 29 insertions(+), 21 deletions(-) diff --git a/doc/src/pair_lj_pirani.rst b/doc/src/pair_lj_pirani.rst index 3c3d7b10d8..abeae12ecf 100644 --- a/doc/src/pair_lj_pirani.rst +++ b/doc/src/pair_lj_pirani.rst @@ -30,7 +30,12 @@ Description .. versionadded:: TBD Pair style *lj/pirani* computes pairwise interactions from an Improved -Lennard-Jones (ILJ) potential according to :ref:`(Pirani) `: +Lennard-Jones (ILJ) potential according to :ref:`(Pirani) `. +The ILJ force field is adequate to model both equilibrium and +non-equilibrium properties of matter, in gaseous and condensed phases, +and at gas-surface interfaces. In particular, its use improves the +description of elementary process dynamics where the traditional +Lennard-Jones (LJ) formulation is usually applied. .. math:: @@ -46,37 +51,40 @@ Lennard-Jones (ILJ) potential according to :ref:`(Pirani) `: An additional parameter, :math:`\alpha`, has been introduced in order -to be able to recover the traditional Lennard-Jones (LJ) 12-6 with a specific +to be able to recover the traditional Lennard-Jones 12-6 with a specific choice of parameters. With :math:`R_m \equiv r_0 = \sigma \cdot 2^{1 / 6}`, :math:`\alpha = 0`, :math:`\beta = 12` and :math:`\gamma = 6` -it is straightforward to prove that LJ 12-6 is obtained. +it is straightforward to prove that LJ 12-6 is obtained. Also, it can be +verified that using :math:`\alpha= 4`, :math:`\beta= 8` and +:math:`\gamma = 6`, at the equilibrium distance, the first and second +derivatives of ILJ match those of LJ 12-6. The parameter :math:`R_m` +corresponds to the equilibrium distance and :math:`\epsilon` to the +well depth. This potential provides some advantages with respect to the standard LJ -potential, as explained in :ref:`(Pirani) `. -It can be used for neutral-neutral (:math:`\gamma = 6`), +potential, as explained in :ref:`(Pirani) `: it provides a more +realistic description of the long range behaviour and an attenuation of +the hardness of the repulsive wall. + + +This force field can be used for neutral-neutral (:math:`\gamma = 6`), ion-neutral (:math:`\gamma = 4`) or ion-ion systems (:math:`\gamma = 1`). -These settings remove issues at short- and long-range for these systems when -a standard LJ model is used. - - -It is possible to verify that using :math:`\alpha= 4`, :math:`\beta= 6` -and :math:`\gamma = 6`, at the equilibrium distance, the first and second -derivatives of ILJ match those of LJ 12-6. In this case, the standard LJ -energy is two times stronger than ILJ at long distances. Also, strength -of the short-range interaction is overestimated by LJ. -The ILJ potential solves both problems. +Notice that this implementation does not include possible electrostatic +interactions which should be eventually added by means of a hybrid style +(e.g. :doc:`pair_style hybrid/overlay ` or variants). As discussed in :ref:`(Pirani) `, analyses of a variety of systems showed that :math:`\alpha= 4` generally works very well. In some special cases (e.g. those involving very small multiple charged ions) -this factor may take a slightly different value. The parameter :math:`\beta` -codifies the hardness (polarizability) of the interacting partners, and for -neutral-neutral systems it ranges from 6 to 11. Moreover, the modulation of -:math:`\beta` can model additional interaction effects, such as charge -transfer in the perturbative limit, and can mitigate the effect of some -uncertainty in the data used to build up the potential function. +this factor may take a slightly different value. The parameter +:math:`\beta` codifies the hardness (polarizability) of the interacting +partners, and for neutral-neutral systems it usually ranges from 6 to 11. +Moreover, the modulation of :math:`\beta` can model additional interaction +effects, such as charge transfer in the perturbative limit, and can +mitigate the effect of some uncertainty in the data used to build up +the potential function. The following coefficients must be defined for each pair of atoms