add Exercise 2

user-doc/tutorials/a-trieste-4.txt

@@ -27,6 +27,8 @@ The \tarball{trieste-4} for this project contains the following files:
 This tutorial has been tested on a pre-release version of version 2.4. However, it should not take advantage
 of 2.4-only features, thus should also work with version 2.3.
 
+\note We suggest to run the three exercizes in separate directories
+ 
 \section trieste-4-intro Introduction
 
 We have seen that PLUMED can be used to compute collective variables. However, PLUMED
@@ -128,7 +130,7 @@ phi: TORSION ATOMS=__FILL__
 psi: TORSION ATOMS=__FILL__
 
 # Activate well-tempered metadynamics in phi
-metad: __FILL__ ARG=phi ...
+metad: __FILL__ ARG=__FILL__ ...
 # Deposit a Gaussian every 500 time steps, with initial height equal
 # to 1.2 kJoule/mol, biasfactor equal to 10.0
 PACE=500 HEIGHT=1.2 BIASFACTOR=10.0
@@ -139,7 +141,7 @@ FILE=HILLS GRID_MIN=-pi GRID_MAX=pi
 ...
 
 # Print the collective variables and the value of the bias potential on COLVAR file
-PRINT ARG=phi,psi,__FILL__ FILE=COLVAR STRIDE=10
+PRINT ARG=__FILL__ FILE=COLVAR STRIDE=10
 \endplumedfile
 
 The syntax for the command \ref METAD is simple.
@@ -256,11 +258,40 @@ suggest that the simulation is converged.
 of your metadynamics simulation!
 
 \note The two observations above are necessary, but qualitative conditions for convergence.
-A quantitative analysis of convergence can be obtained by proper error analysis of the
-recontructed free energy, as explained in the last exercize
+A quantitative assessment of convergence can be obtained by performing an error analysis of the
+reconstructed free-energy profile, as explained in the last exercize
 
 \section trieste-4-ex-2 Exercize 2: playing with collective variables
 
+In this exercise, we will run a well-tempered metadynamics simulation on alanine dipeptide in vacuum, this time
+using as CV the backbone dihedral \f$ \psi \f$. 
+Please complete the template `plumed.dat` file used in the previous exercise to run this calculation.
+
+Once your `plumed.dat` file is complete, you can run a XX-ns long metadynamics simulations with the following command
+\verbatim
+> gmx mdrun -s topol.tpr -plumed plumed.dat
+\endverbatim
+
+As we did in the previous exercise, we can use COLVAR to visualize the behavior of the CV during the simulation.
+Here we will plot at the same time the evolution of the metadynamics CV \f$ \psi \f$ and of the other dihedral \f$ \phi \f$.
+
+\verbatim
+gnuplot> p "COLVAR" u 1:2, "" u 1:3
+\endverbatim
+
+\anchor trieste-4-metad-psi-phi-fig
+\image html munster-metad-psi-phi.png "Time evolution of the dihedrals phi and psi during a 10-ns long metadynamics simulation using psi as CV."
+
+By inspecting Figure \ref trieste-4-metad-psi-phi-fig, we notice that something different happened compared to the previous exercise.
+At first the behavior of \f$ \psi \f$ looks diffusive in the entire CV space. However, around t=1 ns, \f$ \psi \f$ 
+seems trapped in a region of the CV space in which it was previously diffusing without problems. 
+The reason is that the non-biased CV \f$ \phi \f$ after a while has jumped into a different local minima.
+Since \f$ \phi \f$ is not directly biased, one has to wait for this (slow) degree of freedom to 
+equilibrate before the free energy along \f$ \psi \f$ can converge.
+
+Try to repeat the analysis done in the previous exercise, i.e.  calculate the estimate of the free energy as a function of time,
+first step to assess the convergence of this metadynamics simulation.
+
 \section trieste-4-ex-3 Exercize 3: quantifying the error in free-energy reconstructions