From cef4ee7026b4eca15efe8cc97a8e603601060b35 Mon Sep 17 00:00:00 2001
From: Gareth Tribello <gareth.tribello@gmail.com>
Date: Sun, 24 Jul 2016 16:03:45 +0100
Subject: [PATCH] Fixes to manual for FCCUBIC and SIMPLECUBIC
[makedoc]
---
src/crystallization/Fccubic.cpp | 3 ++-
src/crystallization/SimpleCubic.cpp | 16 ++++++++++++++++
2 files changed, 18 insertions(+), 1 deletion(-)
diff --git a/src/crystallization/Fccubic.cpp b/src/crystallization/Fccubic.cpp
index 6ea0ce862..cf27beaf1 100644
--- a/src/crystallization/Fccubic.cpp
+++ b/src/crystallization/Fccubic.cpp
@@ -45,7 +45,8 @@ s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left\{ a\left[ \frac{(x_{ij}y_{ij})^
In this expression \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ are the \f$x\f$, \f$y\f$ and \f$z\f$ components of the vector connecting atom \f$i\f$ to
atom \f$j\f$ and \f$r_{ij}\f$ is the magnitude of this vector. \f$\sigma(r_{ij})\f$ is a \ref switchingfunction that acts on the distance between
-atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression ensures that we are calculating an average
+atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression as well as the fact that we are summing
+over all of the other atoms in the system ensures that we are calculating an average
of the function of \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ for the atoms in the first coordination sphere around atom \f$i\f$. Lastly, \f$\alpha\f$
is a parameter that can be set by the user, which by default is equal to three. The values of \f$a\f$ and \f$b\f$ are calculated from \f$\alpha\f$ using:
diff --git a/src/crystallization/SimpleCubic.cpp b/src/crystallization/SimpleCubic.cpp
index dade67033..1b6787ff9 100644
--- a/src/crystallization/SimpleCubic.cpp
+++ b/src/crystallization/SimpleCubic.cpp
@@ -35,6 +35,22 @@ namespace crystallization{
Calculate whether or not the coordination spheres of atoms are arranged as they would be in a simple
cubic structure.
+We can measure how similar the environment around atom $i$ is to a simple cubic structure is by evaluating
+the following quantity:
+
+\f[
+s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left[ \frac{ x_{ij}^4 + y_{ij}^4 + z_{ij}^4 }{r_{ij}^4} \right] }{ \sum_{i \ne j} \sigma(r_{ij}) }
+\f]
+
+In this expression \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ are the \f$x\f$, \f$y\f$ and \f$z\f$ components of the vector connecting atom \f$i\f$ to
+atom \f$j\f$ and \f$r_{ij}\f$ is the magnitude of this vector. \f$\sigma(r_{ij})\f$ is a \ref switchingfunction that acts on the distance between atom \f$i\f$ and atom \f$j\f$ and its inclusion in the numerator and the denominator of the above expression as well as the fact that we are summing
+over all of the other atoms in the system ensures that we are calculating an average
+of the function of \f$x_{ij}\f$, \f$y_{ij}\f$ and \f$z_{ij}\f$ for the atoms in the first coordination sphere around atom \f$i\f$.
+This quantity is once again a multicolvar so you can compute it for multiple atoms using a single PLUMED action and then compute
+the average value for the atoms in your system, the number of atoms that have an \f$s_i\f$ value that is more that some target and
+so on. Notice also that you can rotate the reference frame if you are using a non-standard unit cell.
+
+
\par Examples
The following input tells plumed to calculate the simple cubic parameter for the atoms 1-100 with themselves.
--
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