Conventional metadynamics
=========================

The metadynamics method is implemented according to the original paper by Laio and Parrinello
(A. Laio, M. Parrinello, Proc. Nat. Acad. Sci. USA **99** (20), *12562* (2002)).
In this method, one or multiple collective variables (CVs) :math:`s(t)` are used to add Gaussians
of fixed height :math:`w` and width :math:`\delta s` every :math:`\tau_G` steps to a
history-dependent bias potential of the form

.. math::
    V_{G}(t)= &\sum_{t'=\tau_{G},2\tau_{G},\ldots}^{t}w\exp\left(-\frac{\left(s(t)-s(t')\right)^{2}}{2\delta s^{2}}\right).

Input preparation
-----------------

As a preparation, open the GUI application and fill out the forms in the `Molecular Dynamics`
tab to perform a MD simulation of 1,3-butadiene at constant temperature of 300 K for several ps of
equilibration (:download:`butadiene.xyz`). Then run the simulation and create a new folder for the
metadynamics run.
When you start the GUI application in the new folder, choose `Import` from the
`File` menu to import the configuration of the equilibration. You want to use the coordinates and
velocities from the last step of the equilibration, so take the bottom option for the generation of
initial conditions and specify the path to the previous results. The last step of the dynamics is
taken, if no other value is given in the `step` form. Finally, switch to the `Metadynamics` tab and
check the `Do metadynamics` box.

.. figure:: gui_meta.png

Enter the Gaussian height and the number of time steps :math:`\tau_{G}` that should pass between
the addition of two Gaussians. The definition of collective variables (CV) is done in the third tab.

.. figure:: gui_cvs.png

Click `Add` to create a new CV.

.. figure:: gui_cvs_add.png

Choose a name and a type for the CV, in our case we want to describe
the transition between the cis- and trans-forms of butadiene, so choose `torsion` from the drop-down
menu. The atom indices that define the torsion angles are provided as a python list in the
`Configure...` dialog.

.. figure:: gui_cvs_conf.png

The last thing to be entered is the Gaussian width. We can choose a value of 10 degrees as a
starting point. After saving the CV, you can edit and delete it again or add another one. You can
download the complete :download:`meta-config.json` file, if you have any problems.

.. seealso::
    For a detailed description of all available collective variables see the :doc:`../cvs/cvs`.
.. seealso::
    For the application of user-defined collective variables, see :doc:`customcvs`.

Run metadynamics
----------------

Start the metadynamics run just as a normal MD run::

    metaFALCON run

Analyze results
---------------

A plot of the current metadynamics potential is obtained during or after the dynamics run with the 
`reconstruct` command line tool. In this program, the potential is reconstructed by summation of
all Gaussians on a grid of CV values. The grid is most easily adjusted in the `plot` tab of the CV
editing function of the GUI application.

.. figure:: gui_plot.png

Use

::

    metaFALCON reconstruct --help

for an overview of all options of the reconstruction utility. For example, if you want to animate
the potential evolution along the addition of Gaussians instead of the last frame only, the 
`animate` option is helpful::

    metaFALCON reconstruct --animate

Reconstruction works well for metadynamics with one or two collective variables. For higher
dimensions, the grid and :math:`V_G` values are also saved as binary numpy array files, but it is
not possible to obtain a potential plot without further processing.