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Axel Kohlmeyer
2021-12-06 13:49:13 -05:00
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doc/src/pair_sw.rst
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@ -70,14 +70,14 @@ and K of atom I within a cutoff distance :math:`a `\sigma`.
The *sw/mod* style is designed for simulations of materials when
distinguishing three-body angles are necessary, such as borophene
and transition metal dichalcogenide, which cannot be described
by the original code for the Stillinger-Weber potential.
by the original code for the Stillinger-Weber potential.
For instance, there are several types of angles around each Mo atom in `MoS_2`,
and some unnecessary angle types should be excluded in the three-body interaction.
Such exclusion may be realized by selecting proper angle types directly.
The exclusion of unnecessary angles is achieved here by the cut-off function (`f_C(\delta)`),
which induces only minimum modifications for LAMMPS.
Validation, benchmark tests, and applications of the *sw/mod* style
Validation, benchmark tests, and applications of the *sw/mod* style
can be found in :ref:`(Jiang_1) <Jiang1>` and :ref:`(Jiang_2) <Jiang2>`.
The *sw/mod* style computes the energy E of a system of atoms, whose potential
@ -94,22 +94,22 @@ used in the original energy and force expression is scaled by a switching factor
0 & \vert \delta \rvert > \delta_2
\end{array} \right. \\
This cut-off function decreases smoothly from 1 to 0 over the range :math:[\delta_1, \delta_2].
This smoothly turns off the energy and force contributions for :math:\lvert \delta \rvert > \delta_2.
It is suggested that :math:\delta_1 and :math:\delta_2 to be the value around
:math:0.5 \lvert \cos \theta_1 - \cos \theta_2 \rvert, with
:math:\theta_1 and :math:\theta_2 as the different types of angles around an atom.
This cut-off function decreases smoothly from 1 to 0 over the range :math:[\delta_1, \delta_2].
This smoothly turns off the energy and force contributions for :math:\lvert \delta \rvert > \delta_2.
It is suggested that :math:\delta_1 and :math:\delta_2 to be the value around
:math:0.5 \lvert \cos \theta_1 - \cos \theta_2 \rvert, with
:math:\theta_1 and :math:\theta_2 as the different types of angles around an atom.
For borophene and transition metal dichalcogenide, :math:\delta_1 = 0.25 and :math:\delta_2 = 0.35.
This value enables the cut-off function to exclude unnecessary angles in the three-body SW terms.
.. note::
The cut-off function is just to be used as a technique to exclude some unnecessary angles,
and it has no physical meaning. It should be noted that the force and potential are inconsistent
with each other in the decaying range of the cut-off function, as the angle dependence for the
cut-off function is not implemented in the force (first derivation of potential).
However, the angle variation is much smaller than the given threshhold value for actual simulations,
so the inconsistency between potential and force can be neglected in actual simulations.
The cut-off function is just to be used as a technique to exclude some unnecessary angles,
and it has no physical meaning. It should be noted that the force and potential are inconsistent
with each other in the decaying range of the cut-off function, as the angle dependence for the
cut-off function is not implemented in the force (first derivation of potential).
However, the angle variation is much smaller than the given threshhold value for actual simulations,
so the inconsistency between potential and force can be neglected in actual simulations.
Only a single pair_coeff command is used with the *sw* and *sw/mod* styles
which specifies a Stillinger-Weber potential file with parameters for all