[gmx-users] hessian_matrix_from_ordered_trajectory

[H.J.Risselada]

On Thu, 5 Apr 2007 18:53:58 +0200
  Sang-Min Park <sanni at theochem.uni-frankfurt.de> wrote:
> Dear all,
> 
> I calculated the eigenvalues and eigenvectors from a 
>small peptide with a 
> closest water neighboorhood watersurrounding. 
> 
> To do this I generated a new trajectory with the command 
>"trjorder" to order 
> the watermolecules in a way so that they are close to 
>the center of mass of 
> the peptide. 
> 
>From this new trajectory I took only the subsystem 
>"Peptide+ the first 20 
> closest water" and generated the Hessian. 
> 
> When I look at the input-files,needed to generate the 
>matrix I see that one 
> need only the configuration, a top file and a mdp file. 
>(for grompp). So this 
> would mean, that gromacs would calculate the Potential 
>(the second derivate 
> of the potential) from this configuration and then 
>calculate the hessian 
> matrix. Furthermore I calculated the Hessian at every 
>snapshot of the 
> trajectory.
> 
> I tested if its work right and calculated the hessian 
>matrix from the same 
> configuration, but only changed 2 watermolecules in 
>their index i. (see the 
> tables below)
> for example: 
>             
> old configuation 
>                                           new 
>configuration
> 
> i     coordinates 
>                                             i     coord. 
>    
> ....				                                     ....
> 12   O xO1   yO1  zO1 
>                                  12   O  xO2   yO2  zO2 
>                     
> 12   H  xH11 yH11 zH11        (change index)    12   H 
> xH21  yH21 zH21 
>                                            
> 12   H  xH12 yH12 zH12                -->             12 
>  H  xH22  y22   zH22                
> ... 
>                                                           
>       ... 
>                                                           
>       
> ... 
>                                                           
>       ... 
>                                                           
>       
> 22   O  xO2   yO2  zO2 
>                                 22   O xO1   yO1  zO1 
>                 
> 22   H  xH21  yH21 zH21 
>                                22   H  xH11 yH11 zH11 
>                                
> 22   H  xH22  yH22 zH22 
>                                22   H  xH12 yH12 zH12 
>                                
> ... 
>                                                           
>       ...
> ...		 
>                                                    ...
>   
> In most cases I got the same eigenvalues and 
>eigenvectors but in some cases 
> the results were very different. 
> 
> What could be the reason? 
> 
> Thank you in advance
> Sang Min  
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I'm not sure if I understand you correctly :

You generated a configuration file of the 20 nearest water 
molecules. That means that the index and identity of the 
20 waters can differ in each snapshot, however in the top 
file 20 is 20 and names neither numbers don't matter. So 
the actual identity should not play a role in for the 
production of tpr. No you switch the order of lets say: 
water molecule 19 with 20.
When you do this you find different eigenvalues of the 
hessian in some cases....correct ?

The dimension of the hessian is Nx3,Nx3, in which you have 
i=1,2....Nx3 rows and collums. Each element i has the same 
order as in the gro file (1,2....N).
So if you switch a line in the gro the hessian is 
different too. Although the hessian will allways be build 
up from the same set of numbers...it will simply not be 
the same matrix (permutations).

So actually I don't really think this way is a good way to 
study the time evolution of the hessian.
Better just take the protein, peptide or wathever without 
the water.

Did you check if the trace of the hessian (sum of all 
eigen values) is more close to constant ?

Anyway,

Good luck.....

greetings

Jelger