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use index style variables instead of equal style variable to allow overriding them

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This commit is contained in:
Axel Kohlmeyer
2020-06-16 05:13:16 -04:00
parent 5e238b2cf4
commit ae435536f3
2 changed files with 23 additions and 23 deletions
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38
doc/src/compute_sna_atom.rst
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@ -46,12 +46,12 @@ Syntax
*1* = generate quadratic terms
*chem* values = *nelements* *elementlist*
*nelements* = number of SNAP elements
*elementlist* = *ntypes* integers in range [0, *nelements*)
*elementlist* = *ntypes* integers in range [0, *nelements*)
*bnormflag* value = *0* or *1*
*0* = do not normalize
*1* = normalize bispectrum components
*wselfallflag* value = *0* or *1*
*0* = self-contribution only for element of central atom
*0* = self-contribution only for element of central atom
*1* = self-contribution for all elements
Examples
@ -96,8 +96,8 @@ In this way, all possible neighbor positions are mapped on to a subset
of the 3-sphere. Points south of the latitude :math:`\theta_0` = *rfac0* :math:`\pi`
are excluded.
The natural basis for functions on the 3-sphere is formed by the
representatives of *SU(2)*, the matrices :math:`U^j_{m,m'}(\theta, \phi, \theta_0)`.
The natural basis for functions on the 3-sphere is formed by the
representatives of *SU(2)*, the matrices :math:`U^j_{m,m'}(\theta, \phi, \theta_0)`.
These functions are better known as :math:`D^j_{m,m'}`, the elements of the Wigner
*D*\ -matrices :ref:`(Meremianin <Meremianin2006>`,
:ref:`Varshalovich <Varshalovich1987>`, :ref:`Mason) <Mason2009>`
@ -111,7 +111,7 @@ coefficient as
u^j_{m,m'} = U^j_{m,m'}(0,0,0) + \sum_{r_{ii'} < R_{ii'}}{f_c(r_{ii'}) w_{\mu_{i'}} U^j_{m,m'}(\theta_0,\theta,\phi)}
The :math:`w_{\mu_{i'}}` neighbor weights are dimensionless numbers that depend on
The :math:`w_{\mu_{i'}}` neighbor weights are dimensionless numbers that depend on
:math:`\mu_{i'}`, the SNAP element of atom *i'*, while the central atom is
arbitrarily assigned a unit weight. The function :math:`f_c(r)` ensures that
the contribution of each neighbor atom goes smoothly to zero at
@ -137,7 +137,7 @@ real-valued and invariant under rotation :ref:`(Bartok) <Bartok20101>`.
{j_2} {m_2} {m'_2} \end{array}}
u^{j_1}_{m_1,m'_1} u^{j_2}_{m_2,m'_2}
The constants :math:`H^{jmm'}_{j_1 m_1 m_{1'},j_2 m_ 2m_{2'}}`
The constants :math:`H^{jmm'}_{j_1 m_1 m_{1'},j_2 m_ 2m_{2'}}`
are coupling coefficients,
analogous to Clebsch-Gordan coefficients for rotations on the
2-sphere. These invariants are the components of the bispectrum and
@ -243,14 +243,14 @@ length *ntypes*, with values in the range [0, *nelements* ),
which maps each LAMMPS type to one of the SNAP elements.
Note that multiple LAMMPS types can be mapped to the same element,
and some elements may be mapped by no LAMMPS type. However, in typical
use cases (training SNAP potentials) the mapping from LAMMPS types
to elements is one-to-one.
use cases (training SNAP potentials) the mapping from LAMMPS types
to elements is one-to-one.
The explicit multi-element variant invoked by the *chem* keyword
partitions the density of neighbors into partial densities
for each chemical element. This is described in detail in the
for each chemical element. This is described in detail in the
paper by :ref:`Cusentino et al. <Cusentino2020>`
The bispectrum components are indexed on
The bispectrum components are indexed on
ordered triplets of elements:
.. math::
@ -262,18 +262,18 @@ ordered triplets of elements:
{j_2} {m_2} {m'_2} \end{array}}
u^{\kappa}_{j_1,m_1,m'_1} u^{\lambda}_{j_2,m_2,m'_2}
where :math:`u^{\mu}_{j,m,m'}` is an expansion coefficient for the partial density of neighbors
where :math:`u^{\mu}_{j,m,m'}` is an expansion coefficient for the partial density of neighbors
of element :math:`\mu`
.. math::
u^{\mu}_{j,m,m'} = w^{self}_{\mu_{i}\mu} U^{j,m,m'}(0,0,0) + \sum_{r_{ii'} < R_{ii'}}{\delta_{\mu\mu_{i'}}f_c(r_{ii'}) w_{\mu_{i'}} U^{j,m,m'}(\theta_0,\theta,\phi)}
where :math:`w^{self}_{\mu_{i}\mu}` is the self-contribution, which is either 1 or 0
(see keyword *wselfallflag* below), :math:`\delta_{\mu\mu_{i'}}` indicates
where :math:`w^{self}_{\mu_{i}\mu}` is the self-contribution, which is either 1 or 0
(see keyword *wselfallflag* below), :math:`\delta_{\mu\mu_{i'}}` indicates
that the sum is only over neighbor atoms of element :math:`\mu`,
and all other quantities are the same as those appearing in the
original equation for :math:`u^j_{m,m'}` given above.
and all other quantities are the same as those appearing in the
original equation for :math:`u^j_{m,m'}` given above.
The keyword *wselfallflag* defines the rule used for the self-contribution.
If *wselfallflag* is on, then :math:`w^{self}_{\mu_{i}\mu}` = 1. If it is
@ -289,8 +289,8 @@ following symmetry relation
.. math::
\frac{B_{j_1,j_2,j}}{2j+1} = \frac{B_{j,j_2,j_1}}{2j_1+1} = \frac{B_{j_1,j,j_2}}{2j_2+1}
This option is typically used in conjunction with the *chem* keyword,
This option is typically used in conjunction with the *chem* keyword,
and LAMMPS will generate a warning if both *chem* and *bnormflag*
are not both set or not both unset.
@ -382,7 +382,7 @@ So the nesting order from inside to outside is bispectrum component,
linear then quadratic, vector/tensor component, type.
If the *chem* keyword is used, then the data is arranged into :math:`N_{elem}^3`
sub-blocks, each sub-block corresponding to a particular chemical labeling
sub-blocks, each sub-block corresponding to a particular chemical labeling
:math:`\kappa\lambda\mu` with the last label changing fastest.
Each sub-block contains *K* bispectrum components. For the purposes
of handling contributions to force, virial, and quadratic combinations,
@ -397,7 +397,7 @@ Restrictions
""""""""""""
These computes are part of the SNAP package. They are only enabled if
LAMMPS was built with that package. See the :doc:`Build package <Build_package>`
LAMMPS was built with that package. See the :doc:`Build package <Build_package>`
doc page for more info.
Related commands

8
potentials/InP_JCPA2020.snap
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@ -2,10 +2,10 @@
# Definition of SNAP+ZBL potential.
variable zblcutinner equal 4
variable zblcutouter equal 4.2
variable zblz1 equal 49
variable zblz2 equal 15
variable zblcutinner index 4
variable zblcutouter index 4.2
variable zblz1 index 49
variable zblz2 index 15
# Specify hybrid with SNAP and ZBL