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
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