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formatting update, correct references

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Axel Kohlmeyer
2024-01-20 10:53:04 -05:00
parent d6d8a2cd8a
commit 52e76502f4
2 changed files with 54 additions and 53 deletions
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96
doc/src/fix_neb.rst
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@ -109,7 +109,7 @@ Note that in this case the specified *Kspring* is in
force/distance units.
With a value of *ideal*, the spring force is computed as suggested in
ref`(WeinanE) <WeinanE>`
:ref:`(WeinanE) <WeinanE>`
.. math::
@ -120,18 +120,18 @@ and :math:`RD_{ideal}` is the ideal *RD* for which all the images are
equally spaced. I.e. :math:`RD_{ideal} = (i-1) \cdot meanDist` when the
climbing replica is off, where *i* is the replica number). The
*meanDist* is the average distance between replicas. Note that in this
case the specified *Kspring* is in force units. When the climbing replica
is on, :math:`RD_{ideal}` and :math:`meanDist` are calculated separately
each side of the climbing image. Note that the *ideal* form of nudging
can often be more effective at keeping the replicas equally spaced before
climbing, then equally spaced either side of the climbing image whilst
climbing.
case the specified *Kspring* is in force units. When the climbing
replica is on, :math:`RD_{ideal}` and :math:`meanDist` are calculated
separately each side of the climbing image. Note that the *ideal* form
of nudging can often be more effective at keeping the replicas equally
spaced before climbing, then equally spaced either side of the climbing
image whilst climbing.
With a value of *equal* the spring force is computed as for *ideal*
when the climbing replica is off, promoting equidistance. When the climbing
With a value of *equal* the spring force is computed as for *ideal* when
the climbing replica is off, promoting equidistance. When the climbing
replica is on, the spring force is computed to promote equidistant
absolute differences in energy, rather than distance, each side of
the climbing image:
absolute differences in energy, rather than distance, each side of the
climbing image:
.. math::
@ -143,23 +143,22 @@ where *ED* is the cumulative sum of absolute energy differences:
ED = \sum_{i<N} \left|E(R_{i+1}) - E(R_i)\right|,
*meanEdist* is the average absolute energy difference between
replicas up to the climbing image or from the climbing image
to the final image, for images before or after the climbing
image respectively. :math:`ED_{ideal}` is the corresponding
cumulative sum of average absolute energy differences in
each case, in close analogy to *ideal*. This form of nudging
is to aid schemes which integrate forces along, or near to,
NEB pathways such as :doc:`fix_pafi <fix_pafi>`.
*meanEdist* is the average absolute energy difference between replicas
up to the climbing image or from the climbing image to the final image,
for images before or after the climbing image
respectively. :math:`ED_{ideal}` is the corresponding cumulative sum of
average absolute energy differences in each case, in close analogy to
*ideal*. This form of nudging is to aid schemes which integrate forces
along, or near to, NEB pathways such as :doc:`fix_pafi <fix_pafi>`.
----------
The keyword *perp* specifies if and how a perpendicular nudging force
is computed. It adds a spring force perpendicular to the path in
order to prevent the path from becoming too strongly kinked. It can
The keyword *perp* specifies if and how a perpendicular nudging force is
computed. It adds a spring force perpendicular to the path in order to
prevent the path from becoming too strongly kinked. It can
significantly improve the convergence of the NEB calculation when the
resolution is poor. I.e. when few replicas are used; see
:ref:`(Maras) <Maras1>` for details.
resolution is poor. I.e. when few replicas are used; see :ref:`(Maras)
<Maras1>` for details.
The perpendicular spring force is given by
@ -181,10 +180,10 @@ force is added.
By default, no additional forces act on the first and last replicas
during the NEB relaxation, so these replicas simply relax toward their
respective local minima. By using the key word *end*, additional
forces can be applied to the first and/or last replicas, to enable
them to relax toward a MEP while constraining their energy E to the
target energy ETarget.
respective local minima. By using the key word *end*, additional forces
can be applied to the first and/or last replicas, to enable them to
relax toward a MEP while constraining their energy E to the target
energy ETarget.
If :math:`E_{Target} > E`, the interatomic force :math:`F_i` for the
specified replica becomes:
@ -197,33 +196,33 @@ specified replica becomes:
The "spring" constant on the difference in energies is the specified
*Kspring3* value.
When *estyle* is specified as *first*, the force is applied to the
first replica. When *estyle* is specified as *last*, the force is
applied to the last replica. Note that the *end* keyword can be used
twice to add forces to both the first and last replicas.
When *estyle* is specified as *first*, the force is applied to the first
replica. When *estyle* is specified as *last*, the force is applied to
the last replica. Note that the *end* keyword can be used twice to add
forces to both the first and last replicas.
For both these *estyle* settings, the target energy *ETarget* is set
to the initial energy of the replica (at the start of the NEB
calculation).
If the *estyle* is specified as *last/efirst* or *last/efirst/middle*,
force is applied to the last replica, but the target energy *ETarget*
is continuously set to the energy of the first replica, as it evolves
force is applied to the last replica, but the target energy *ETarget* is
continuously set to the energy of the first replica, as it evolves
during the NEB relaxation.
The difference between these two *estyle* options is as follows. When
*estyle* is specified as *last/efirst*, no change is made to the
inter-replica force applied to the intermediate replicas (neither
first or last). If the initial path is too far from the MEP, an
intermediate replica may relax "faster" and reach a lower energy than
the last replica. In this case the intermediate replica will be
relaxing toward its own local minima. This behavior can be prevented
by specifying *estyle* as *last/efirst/middle* which will alter the
inter-replica force applied to intermediate replicas by removing the
contribution of the gradient to the inter-replica force. This will
only be done if a particular intermediate replica has a lower energy
than the first replica. This should effectively prevent the
intermediate replicas from over-relaxing.
inter-replica force applied to the intermediate replicas (neither first
or last). If the initial path is too far from the MEP, an intermediate
replica may relax "faster" and reach a lower energy than the last
replica. In this case the intermediate replica will be relaxing toward
its own local minima. This behavior can be prevented by specifying
*estyle* as *last/efirst/middle* which will alter the inter-replica
force applied to intermediate replicas by removing the contribution of
the gradient to the inter-replica force. This will only be done if a
particular intermediate replica has a lower energy than the first
replica. This should effectively prevent the intermediate replicas from
over-relaxing.
After converging a NEB calculation using an *estyle* of
*last/efirst/middle*, you should check that all intermediate replicas
@ -237,9 +236,10 @@ target energy.
Restart, fix_modify, output, run start/stop, minimize info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
No information about this fix is written to :doc:`binary restart files <restart>`. None of the :doc:`fix_modify <fix_modify>` options
are relevant to this fix. No global or per-atom quantities are stored
by this fix for access by various :doc:`output commands <Howto_output>`.
No information about this fix is written to :doc:`binary restart files
<restart>`. None of the :doc:`fix_modify <fix_modify>` options are
relevant to this fix. No global or per-atom quantities are stored by
this fix for access by various :doc:`output commands <Howto_output>`.
No parameter of this fix can be used with the *start/stop* keywords of
the :doc:`run <run>` command.

11
doc/src/neb.rst
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@ -89,10 +89,11 @@ potentials, and the starting configuration when the neb command is
issued should be the same for every replica.
In a NEB calculation each replica is connected to other replicas by
inter-replica nudging forces. These forces are imposed by the :doc:`fix neb <fix_neb>` command, which must be used in conjunction with the
neb command. The group used to define the fix neb command defines the
NEB atoms which are the only ones that inter-replica springs are
applied to. If the group does not include all atoms, then non-NEB
inter-replica nudging forces. These forces are imposed by the
:doc:`fix neb <fix_neb>` command, which must be used in conjunction
with the neb command. The group used to define the fix neb command
defines the NEB atoms which are the only ones that inter-replica springs
are applied to. If the group does not include all atoms, then non-NEB
atoms have no inter-replica springs and the forces they feel and their
motion is computed in the usual way due only to other atoms within
their replica. Conceptually, the non-NEB atoms provide a background
@ -445,7 +446,7 @@ Related commands
""""""""""""""""
:doc:`prd <prd>`, :doc:`temper <temper>`, :doc:`fix langevin <fix_langevin>`,
:doc:`fix viscous <fix_viscous>`
:doc:`fix viscous <fix_viscous>`, :doc:`fix neb <fix_neb>`
Default
"""""""