LOCAL_Q3
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.

Calculate the local degree of order around an atoms by taking the average dot product between the q_3 vector on the central atom and the q_3 vector on the atoms in the first coordination sphere.

The Q3 command allows one to calculate one complex vectors for each of the atoms in your system that describe the degree of order in the coordination sphere around a particular atom. The difficulty with these vectors comes when combining the order parameters from all of the individual atoms/molecules so as to get a measure of the global degree of order for the system. The simplest way of doing this - calculating the average Steinhardt parameter - can be problematic. If one is examining nucleation say only the order parameters for those atoms in the nucleus will change significantly when the nucleus forms. The order parameters for the atoms in the surrounding liquid will remain pretty much the same. As such if one models a small nucleus embedded in a very large amount of solution/melt any change in the average order parameter will be negligible. Substantial changes in the value of this average can be observed in simulations of nucleation but only because the number of atoms is relatively small.

When the average Q3 parameter is used to bias the dynamics a problems can occur. These averaged coordinates cannot distinguish between the correct, single-nucleus pathway and a concerted pathway in which all the atoms rearrange themselves into their solid-like configuration simultaneously. This second type of pathway would be impossible in reality because there is a large entropic barrier that prevents concerted processes like this from happening. However, in the finite sized systems that are commonly simulated this barrier is reduced substantially. As a result in simulations where average Steinhardt parameters are biased there are often quite dramatic system size effects

If one wants to simulate nucleation using some form on biased dynamics what is really required is an order parameter that measures:

  • Whether or not the coordination spheres around atoms are ordered
  • Whether or not the atoms that are ordered are clustered together in a crystalline nucleus

LOCAL_AVERAGE and NLINKS are variables that can be combined with the Steinhardt parameters allow to calculate variables that satisfy these requirements. LOCAL_Q3 is another variable that can be used in these sorts of calculations. The LOCAL_Q3 parameter for a particular atom is a number that measures the extent to which the orientation of the atoms in the first coordination sphere of an atom match the orientation of the central atom. It does this by calculating the following quantity for each of the atoms in the system:

\[ s_i = \frac{ \sum_j \sigma( r_{ij} ) \sum_{m=-3}^3 q_{3m}^{*}(i)q_{3m}(j) }{ \sum_j \sigma( r_{ij} ) } \]

where \(q_{3m}(i)\) and \(q_{3m}(j)\) are the 3rd order Steinhardt vectors calculated for atom \(i\) and atom \(j\) respectively and the asterisk denotes complex conjugation. The function \(\sigma( r_{ij} )\) is a switchingfunction that acts on the distance between atoms \(i\) and \(j\). The parameters of this function should be set so that it the function is equal to one when atom \(j\) is in the first coordination sphere of atom \(i\) and is zero otherwise. The sum in the numerator of this expression is the dot product of the Steinhardt parameters for atoms \(i\) and \(j\) and thus measures the degree to which the orientations of these adjacent atoms is correlated.

Examples

The following command calculates the average value of the LOCAL_Q3 parameter for the 64 Lennard Jones atoms in the system under study and prints this quantity to a file called colvar.

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