# Re: Evaluating kinetic energy from a modified DCD file

From: Mert Gür (gurmert_at_gmail.com)
Date: Fri Apr 10 2009 - 12:52:08 CDT

Dear Jeff,
It is true that the modes match the covariance matrix.
But if you perform backtransformation using the eigenvectors you just
generated you will see that the corresponding motion in real space is not
harmonic.
This unharmonic behaviour of course changes to harmonic as you perform
backtransformation using eigenvectores corresponding to faster modes. This
is so since fast modes are harmonic. My problem is the essential subspace
(the unharmonic modes).
So I dont think that I can use the frequencies I obtained to evaluate the
atomic velocites.
I dont understand how I can evaluate the velocities without using the
frequencies.
If I am mistaken at any point please correct me.
I also agree that the verlet scheme is an excellent suggestion. But I am
looking for an easier way to do it.
But if not of course I got to perform one of your suggestion.
Best,
Mert

On Fri, Apr 10, 2009 at 7:36 PM, JT <JTibbitt_at_odu.edu> wrote:

> 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> 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>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 --000e0cd2868007f0ae0467370632--

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