# Harmonic dihedral angle

Hi Sir,

Shouldn’t the harmonic dihedral potential look something like E=K*(phi_0-phi)^2 ? Why is it a function of cosine of the dihedral angle? I was simulating a system of polymer which has some dihedral angles. I used

dihedral_style harmonic
dihedral_coeff 1 1.0 -1 1

because d=-1 almost replicates a similar behavior as in a quadratic expression (opened upwards). But my system didn’t keep the angle specified and it collapsed. What is the importance of parameter ‘n’?
And also the argument of cosine function is n*phi. Is this ‘phi’ the original dihedral angle (Which I want my system to keep) or the deviation from it?

The utilization of periodic functions for dihedral terms is probably motivated by the

shape of the energy landscape ones obtains from solving the system using ab-initio or even analytical calculations at the quantum level of theory (QM). In the small angle limit the cosine reduces to a quadratic term of the type you mention. Dihedral terms in general are not characterized by high energy barriers and thus under the influence of thermal noise and/or other perturbations such barriers can be actively crossed over leading to conformational changes to be found a many type of systems. There the reason for mapping a wider range of angles in the analytical form to be adopted. As far as I know this is not the case for planar angles which tend to be much more stiff than dihedrals (atoms interact more strongly for variations in the planar angle) and thus only the small limit approximation is typically employed to describe the latter. Someone from the protein/polymer field may have further arguments to add.
Carlos

Hi Sir,

Shouldn't the harmonic dihedral potential look something like
E=K*(phi_0-phi)^2 ? Why is it a function of cosine of the dihedral angle? I

so that you can handle periodicity properly. what you describe is used
for _improper_ dihedrals.

was simulating a system of polymer which has some dihedral angles. I used

dihedral_style harmonic
dihedral_coeff 1 1.0 -1 1

because d=-1 almost replicates a similar behavior as in a quadratic
expression (opened upwards). But my system didn't keep the angle specified
and it collapsed. What is the importance of parameter 'n'?

to have different periodicity and to model complex dihedral
interactions (consider the rotation around the central bond of butane
for example) through superposition of multiple dihedral potentials
with different periodicity.

And also the argument of cosine function is n*phi. Is this 'phi' the
original dihedral angle (Which I want my system to keep) or the deviation
from it?

phi is the actual dihedral angle. if you want to constrain your system
to a specific angle then the harmonic dihedral potential is not the
right choice.

axel.