[CP2K-user] [CP2K:17743] (HNO3 + graphene) Metadynamics tutorial

[Oliver]

Hi cp2k users,
I read carefully the (HNO3+graphene) tutorial related to Metadynamics and 
came through several questions:

1. the CVs are based on the definition (1/N0) Sum_i Sum_j 
(1-Rij/R0)^n/(1-Rij/R0)^m which represents a coodination number. N0 is not 
clearly defined in the text: is it a normalisation factor and if yes how is 
it defined, or is it the total number of atoms which could be involved in 
the CV definition? 

Moreover, this CV definition is not quite the same as the one reported in 
litterature where there is no N0 at all. This point needs clarification in 
relation with cp2k usage and  its reference manual. 

2. from the files included in ../gr_2Hno3/dftb_mtd_3cv/; i tried to apply 
the graph.popt tool to calculate the curves FES=f(CVs). The abscissa ranges 
calculated for the three possible FES  are: [-0.596: 1.532], [1.247: 4.315] 
and  [-0.599: 3.975], but the CVs in the COLVAR file give something very 
different: [~0.04: ~0.98], [~2.18: ~3.45] and [~0.005 : ~3.52]. I can't 
understand why the ranges are not the same in both calculations. Moreover, 
all the CVs should be always positive. Therefore, how the FES abscissa are 
calculated in graph.popt tool?

3. In the FORCE_EVAL module appears three &EXTERNAL_POTENTIAL submodules 
with different definitions (one related to x coordinate, one for y 
coordinate and one for z coordinate). But in the user's manual it is 
written that the function definition cannot be repeated. Therefore, what is 
calculated exactly and isn't there a bug somewhere?

Moreover, if i well understand, the external potential is added to the 
hamiltonian in the form:  Sum_i p_i^2/2m_i+U+V_ext. Therefore, the field 
potential is modified and so the CVs. The barrier height which appears in 
the FES of the order of -0.35 Ha is unfortunately biased and cannot be 
corrected. Am i right? 
Finally, All the FES curves have a U shape with several inflection points 
(in particular FES=f(CV1) and FES=f(CV3)). Do these special points have a 
particular meaning from the structural point of view?

I'm looking forward to reading your comments.
Thank you very much for your help.
Best regards
Oliver

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