[gmx-users] Harmonic dihedral restraints

[Mark Abraham]

Robert Johnson wrote:
> Well, the potential is of the form V=k(x1-x2)^2, but I don't see how
> it's harmonic. What you would want is the x1 and x2 to refer to
> dihedral angles. However, the potential in equation 4.70 has this
> weird phi-phi_0 MOD 2pi term and this delta_phi parameter. It's just
> not obvious to me how equation 4.70 can be expanded or rearranged to
> look like a harmonic potential in the dihedral angles. Am I just not
> seeing something correctly?

A harmonic potential is just one where V is of the form you give above. 
However a dihedral angle (phi) is a circular variable, and so you need 
to take care not to have a huge potential resulting from the difference 
of 2pi+0.01 and zero - hence the "MOD 2pi". Delta-phi allows for your 
potential to be flat-bottomed with variable width; compare with distance 
restraints and Figure 4.13. Try plotting the function for various 
delta-phi to see what I mean (if it's not obvious). phi_0 is the angle 
about which the harmonic potential is applied, in the usual way.

Mark