**From:** Mortimer Hemmit (*mortimer.hemmit_at_gmail.com*)

**Date:** Wed Sep 02 2020 - 20:02:03 CDT

**Next message:**Alex Balaeff: "Re: Re:Re: Wrong number of basis-sets stored!"**Previous message:**辛志宏: "Re:Re: Wrong number of basis-sets stored!"**In reply to:**Jérôme Hénin: "Re: Colvars Harmonic Bias Force Direction"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi Jerome,

Thank you very much, it makes a lot more sense now. The visualization

with the dashboard was very helpful.

Mortimer

On Wed, Sep 2, 2020 at 9:03 AM Jérôme Hénin <jerome.henin_at_ibpc.fr> wrote:

*>
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*> Hi Mortimer,
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*>
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*> If x are the Cartesian coordinates of atoms, let's define a collective variable f(x).
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*> A harmonic potential on the colvar, centered on f0 and with force constant k will be:
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*> V(x) = 1/2*k*(f(x)-f0)^2
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*>
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*> This is a function of x indirectly, through the function f(x). The corresponding force on atoms is the negative gradient of the potential with respect to atomic positions x:
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*> F(x) = - dV(x) / dx = - k * (f(x)-f0) * df(x)/dx
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*>
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*> Here df(x)/dx means the gradient of the colvar with respect to Cartesian coordinates x. That's a vector pointing in the direction in Cartesian coordinates along which f(x) increases the fastest.
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*> The magnitude and direction of the force also depend on the magnitude and sign of (f(x)-f0), that is where the colvar is with respect to the set restraint center.
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*>
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*> So to summarize, the biasing force will be applied in the direction that causes the maximum change in the value of the colvar.
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*>
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*> If you use the latest VMD under Linux, you can easily visualize the gradients of any scalar colvar using the Colvars Dashboard plugin.
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*>
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*> Best,
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*> Jerome
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*>
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*>
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*> ----- On 2 Sep 20, at 14:28, Mortimer Hemmit mortimer.hemmit_at_gmail.com wrote:
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*>
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*> > Hello,
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*> >
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*> > I am performing some steered molecular dynamics simulations. I was
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*> > wondering how the harmonic biases worked.
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*> >
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*> > I understand how a simple colvar with a harmonic bias on the distance
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*> > between atoms could work. I can picture it as a spring attached
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*> > between the atoms which exerts a force that pulls each atom towards
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*> > the other.
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*> >
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*> > However, for more complicated colvars such as radius of gyration,
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*> > coordination number, dihedral angle, RMSD, to name a few, how exactly
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*> > does the added potential manifest itself to restrain these quantities
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*> > to their desired values? In which direction do the forces/springs
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*> > point (or are there even forces at all) if I put a harmonic bias on
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*> > these colvars?
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*> >
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*> > I have looked at the user guide and the Colvars paper, but I am still
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*> > confused about the forces.
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*> >
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*> > If anyone could help me clear this up or point me in the right
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*> > direction with some references, that would be greatly appreciated.
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*> >
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*> > Thank you very much,
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*> > Mortimer
*

**Next message:**Alex Balaeff: "Re: Re:Re: Wrong number of basis-sets stored!"**Previous message:**辛志宏: "Re:Re: Wrong number of basis-sets stored!"**In reply to:**Jérôme Hénin: "Re: Colvars Harmonic Bias Force Direction"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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