RE: Evaluating kinetic energy from a modified DCD file

From: Tibbitt, Jeffrey A. (JTibbitt_at_odu.edu)
Date: Fri Apr 10 2009 - 15:03:24 CDT

Mert,
I may be mistaken about the harmonicity of the quasiharmonic modes. I always thought they still represented harmonic vibrations (quasi in the sense that the potential function does not come from the harmonic approximation to the potential function). Like I said, I'm not an expert on the subject. It helps to keep this discussion going, so that at least I (and possibly others) can learn a little more. But the velocities along each mode must still be given by their frequencies though. Each mode has a frequency. And any subspace of modes would also have its frequency. So wouldn't combining the frequency and the mode vector supply the velocity? What else would the frequency mean except how long it takes to move along the mode?
Jeff

________________________________________
From: owner-namd-l_at_ks.uiuc.edu [owner-namd-l_at_ks.uiuc.edu] On Behalf Of JT [JTibbitt_at_odu.edu]
Sent: Friday, April 10, 2009 12:36 PM
To: Mert Gür
Cc: NAMD list
Subject: Re: namd-l: Evaluating kinetic energy from a modified DCD file

Mert,
I don't think I understand your problem. I thought you are trying to find atomic velocites of atoms along single PCA modes, so that you could calculate the kinetic energy of each mode. The method of PCA incorporates anharmonicity by generating modes that match the covariance matrix supplied from the MD run. But the resultant modes produced are normal harmonic vibrations. And the velocities could be obtained from them. But if you are doing something different, then I Axel already supplied an excellent suggestion. Write out both coordinate and velocity DCD trajectories (each every 100 steps). Then just using the verlet scheme to generate the before and after coordinates.
Good luck.
Jeff

On Apr 10, 2009, at 11:14 AM, Mert Gür wrote:

Dear Jeff,
The link that you posted was quite helpfull. It is explaining the topic very clear. Really thank you for that.

For MD, PCA simplifies to the NMA only in the limit of 0 degree when there is no unharmonicty present. The problem lies at this point if the motion where harmonic of course I would know its Kinetic energy with respect to time. This is so because velocity is defined for NMA as

velocity=w*A*cos(w*t+p)

here w is frewuency and t is time.

The probem is that;
In unharmonic case I wont have this kind of relation. That is why I at least two need subsquent coordinates.
Which brings me unfortunately back to my starting point.

Dear Peter,
As you said since I am doing modal decomposition first and then generate a DCD file for each mode by my own, I wont have the corresponding log file. I have to find somehow the velocities.
Thanks,

Mert

On Thu, Apr 9, 2009 at 6:04 AM, JT <jtibbitt_at_odu.edu<mailto:jtibbitt_at_odu.edu>> wrote:
Mert,
I'm sorry, I was mistaken. The eigenvalue (Lk) of a principal mode is not the same as the frequency (Wk) of the mode. They are related by:

Wk = sqrt [( kB*T) / Lk]

Also, I'm no expert on the subject, but I do understand a little bit. And I'm not sure if the kinetic energy of a single mode derived using Principal Component Analysis makes as much sense as it does in classical Normal Mode Analysis (if it makes any sense in NMA for that matter). It's because in PCA, the harmonic potential describing the system is reconstructed only to satisfy some positional covariance matrix (e.g. one obtained from an MD trajectory). The frequencies thus obtained are much larger than they are in NMA. But surely in certain settings, proper use can be made of the kinetic energies of single PCA modes. And if you are already obtaining the PCA results, you can definitely obtain the kinetic energies of the modes simply with a couple of small calculations.

For more on PCA (Quasiharmonic Analysis) and deriving thermodynamic relations from it, see Appendix C (pp 18-22) of:

http://oolung.chem.ku.edu/~kuczera/Public/web/html/lect/nma/nma.html>.

Jeff

On Apr 8, 2009, at 8:59 PM, JT wrote:

Mert,
Doing modal decomposition gives you both the eigenvalues (frequencies) and their corresponding eigenvectors (modes). Then aren't the individual modal velocities, obtained by just multiplying the two? After all, an eigenvector represents the displacement and the frequency the reciprocal of the time it takes for that displacement to occur.
Jeff

On Apr 8, 2009, at 5:57 PM, Mert Gür wrote:

Thanks Peter for your suggestion but I am doing modal decomposition for the DCD. So if I poceeed as you suggested I have to do also modal decomposition for the velocity DCD file . I dont think that the modes of the velocity file have the same physical meaning as the modes of the DCD file.
That is why I couldnt use it in the first place.
I may be mistaken. Correct me if I am.
Best,
Mert

On Wed, Apr 8, 2009 at 11:15 PM, Peter Freddolino <petefred_at_ks.uiuc.edu<mailto:petefred_at_ks.uiuc.edu>> wrote:
Try writing a velocity DCD
(http://www.ks.uiuc.edu/Research/namd/2.7b1/ug/node13.html#1360)

Peter

Mert Gür wrote:
> I have performed a molecular dynamic simulation in a waterbox. Using the
> dcd file I am doing modal decomposition on the cartesian coordinates .
> By keeping selected modes (for example only the first mode) I go back to
> the cartesian coordinates and generate a new dcd file.
> Using this new DCD file I am trying to evaluate the potential energies
> and the kinetic energies of the selected modes.
> If I am not mistaken , NAMD energy plugin gives me the potential energy
> with respect to this DCD file(atom coordinates).
> But to evaluate the kinetic energy, I was planning to use the
> coordinates of the previous and succesive time frames. Using this frames
> I was going to evaluate the velocity and hence the KE. Unfortunately in
> the light of the answer I received for my previous question I see that
> getting these subsequent time frames is not an easy job.
> This is the point where I am stuck now. Any suggestions about how to
> evaluate the kinetic energy will be appreciated.
> Best,
> Mert

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