Bonded interactions

Harmonic Bonds

A typical bonded interaction is of the form: $$ u(r) = \frac{k}{2}(r-r_0)^2 $$ where \(k\) is the bond strength and \(r_0\) is a reference bond length. There are two helpful limits:

1.) \(k\) large, which approximates a freely jointed chain model with bond length \(r_0\).

2.) a zero-centered \(r_0=0\) model, which is the discrete Gaussian chain model, with average bond length \(b=(3/k)^{1/2}\)

Zero-centered bonds are especially recommended because 1) they are softer and allow for larger coarse grained MD time steps, and 2) the optimization problem for zero-centered bonds is faster, less stiff, and easily allows for co-optimization with other target properties like chain end-to-end distance.

Angular Bonds

While angular bonded potentials can be obtained easily with the coarse-graining procedure, they are expensive to compute in the field theory and are thus usually ignored.