FCCUBIC
This is part of the symfunc module
It is only available if you configure PLUMED with ./configure –enable-modules=symfunc . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Measure how similar the environment around atoms is to that found in a FCC structure.

This CV was introduced in this article [4] and again in this article [33] This CV essentially determines whether the environment around any given atom is similar to that found in the FCC structure or not. The function that is used to make this determination is as follows:

\[ s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left\{ a\left[ \frac{(x_{ij}y_{ij})^4 + (x_{ij}z_{ij})^4 + (y_{ij}z_{ij})^4}{r_{ij}^8} - \frac{\alpha (x_{ij}y_{ij}z_{ij})^4}{r_{ij}^{12}} \right] + b \right\} }{ \sum_{i \ne j} \sigma(r_{ij}) } \]

In this expression \(x_{ij}\), \(y_{ij}\) and \(z_{ij}\) are the \(x\), \(y\) and \(z\) components of the vector connecting atom \(i\) to atom \(j\) and \(r_{ij}\) is the magnitude of this vector. \(\sigma(r_{ij})\) is a switchingfunction that acts on the distance between atom \(i\) and atom \(j\) 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 \(x_{ij}\), \(y_{ij}\) and \(z_{ij}\) for the atoms in the first coordination sphere around atom \(i\). Lastly, \(\alpha\) is a parameter that can be set by the user, which by default is equal to three. The values of \(a\) and \(b\) are calculated from \(\alpha\) using:

\[ a = \frac{ 80080}{ 2717 + 16 \alpha} \qquad \textrm{and} \qquad b = \frac{ 16(\alpha - 143) }{2717 + 16\alpha} \]

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 \(s_i\) 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.

Examples

The following input calculates the FCCUBIC parameter for the 64 atoms in the system and then calculates and prints the average value for this quantity.

Click on the labels of the actions for more information on what each action computes
tested on master