dihedral PCA

[x.tan...@gmail.com]

Dear PLUMED users, 

     

I am using Metadynamics to do simulation. I have found some researches use dihedral PCA. And my system needs to be described by dihedral PCA. 

     

But there is no command to do it in plumed website. Is there some suggestion to do dihedral PCA?

Thanks for your kindly reply.

Xuan

   

    

[Gareth Tribello]

Yes 

You are going to want to compute the sines and cosines of the torsions something like this:

t1: TORSION ATOMS=1,2,3,4 

st1: MATHEVAL ARG=t1 FUNC=sin(x) PERIODIC=NO

ct1: MATHEVAL ARG=t1 FUNC=cos(x) PERIODIC=NO

You thus have a bunch of sine and cosines of the torsions (st1 and ct1 from above) that you can then plug into a 

PCAVARS

action:

https://plumed.github.io/doc-v2.4/user-doc/html/_p_c_a_v_a_r_s.html

This should hopefully get you started.

Gareth

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[xuan tang]

Gareth

  Thanks for your reply. 

  It is very useful.

Xuan

Gareth Tribello <g.tri...@qub.ac.uk> 于2019年1月14日周一 下午5:15写道：

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[Wei-Tse Hsu]

Hi, I have two quick questions about the script that Dr. Tribello posted. 

st1: MATHEVAL ARG=t1 FUNC=sin(x) PERIODIC=NO

ct1: MATHEVAL ARG=t1 FUNC=cos(x) PERIODIC=NO

In the code above, sine and cosine functions are periodic functions, but why it the option "PERIODIC" was specified as "NO".

Was there a specific reason or did I miss something?

The other question is that if the function is "L*sin(x)" instead, where L is another variable (like distance) that also varies in the simulation and we are not sure about its range. 

In this case, how should we set up the periodicity? Can the bounds of the periodicity contain variables?

Thank you so much!

Best,

Wei-Tse

On Tuesday, January 15, 2019 at 7:01:07 PM UTC-7, xuan tang wrote:

Gareth

  Thanks for your reply. 

  It is very useful.

Xuan

Gareth Tribello <g.tr...@qub.ac.uk> 于2019年1月14日周一 下午5:15写道：

Yes 

You are going to want to compute the sines and cosines of the torsions something like this:

t1: TORSION ATOMS=1,2,3,4 

st1: MATHEVAL ARG=t1 FUNC=sin(x) PERIODIC=NO

ct1: MATHEVAL ARG=t1 FUNC=cos(x) PERIODIC=NO

You thus have a bunch of sine and cosines of the torsions (st1 and ct1 from above) that you can then plug into a 

PCAVARS

action:

https://plumed.github.io/doc-v2.4/user-doc/html/_p_c_a_v_a_r_s.html

This should hopefully get you started.

Gareth

On 14 Jan 2019, at 09:06, x.ta...@gmail.com wrote:

Dear PLUMED users, 

     

I am using Metadynamics to do simulation. I have found some researches use dihedral PCA. And my system needs to be described by dihedral PCA. 

     

But there is no command to do it in plumed website. Is there some suggestion to do dihedral PCA?

Thanks for your kindly reply.

Xuan

   

    

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[Gareth Tribello]

Hello

You are correct that sine and cosine are periodic functions.  The objects output by those two actions are scalar quantities, however, and not functions.  The fact that the function being evaluated is periodic is thus irrelevant.

To clarify what I mean by the above statement consider a torsion angle, which is a periodic quantity.  What makes this periodic is the way that we do addition and subtraction.  In particular suppose we do:

\pi/2 + \pi 

we get -\pi/2 and not 3\pi/2 because torsional angles are confined to be in the range from -\pi to pi.  This is what we mean by a periodic scalar.  A periodic scalar is a scalar that does not live on a real axis that stretches from minus infinity up to plus infinity.  Periodic scalars sit on a circular number axis.  As such when we have these types of variables if we keep moving forward we eventually return back to where we started out from.

If you think about the sine and cosine of an angle they do not have this property.  The value of the sine/cosine is constrained to lie between -1 and 1 sure.   There is no sense in which you can immediately go from having sine(x)=-1 to having sine(x)=+1 in other words, we don’t have anything like the following limit that we would have for a torsion angle:

[Wei-Tse Hsu]

Dear Dr. Tribello,

Now I totally understand, thank you for you clear explanation!

Best,

Wei-Tse