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Documentation update after suggestions of @athomps

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Thomas Swinburne
2023-01-16 14:12:52 +01:00
parent e1a8a70a6c
commit 07da78dfe8
1 changed files with 18 additions and 11 deletions
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doc/src/fix_neb.rst
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@ -120,14 +120,17 @@ 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.
Note that the *ideal* form of nudging can often be more effective at
keeping the replicas equally spaced.
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*
before the climbing stage, then is computed to promote equidistant
spacing in energy rather than distance:
before the climbing stage, then during the climbing stage is modified
to promote equidistant absolute differnces in energy, rather than
distance, each side of the climbing image:
.. math::
@ -137,12 +140,16 @@ where *ED* is the cumulative sum of absolute energy differences:
.. math::
ED = \sum_{i<N} \left|E(R_{i+1}) - E(R_i)\right|, \qquad ED_{ideal} = (N-1) \cdot meanEdist
ED = \sum_{i<N} \left|E(R_{i+1}) - E(R_i)\right|,
and *meanEdist* is the average absolute energy difference between
replicas. This form of nudging is to aid schemes which integrate forces
along NEB pathways such as :doc:`fix_pafi <fix_pafi>`, by providing
optimal quadrature points.
*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, just as for *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>`.
----------