the fragment by $\abs{\v
s}$ about an axis $\hat{\v s}$ where $\v s$ is a “rotation vector” also sampled from an isotropic 3-dimensional Gaussian. The variances for the two Gaussians should be adjusted so that the translational and rotational components result in comparable displacements of the atoms of the fragment.

Provided that the inter-fragment constraint terms $E_\mathrm h$ are sufficiently stiff, it is not important to include a detailed model of these terms; because the motion will take place near the bottom of the constraint potential well, a harmonic (i.e., quadratic) approximation to the constraint potential will suffice. On the other hand, if the stiffness of the constraint energy depends on any of the soft degrees of freedom, it is important that this effect be included.

It is frequently the case that $E_\mathrm h$ may be computed much more rapidly than $E_\mathrm s$. For example, when imposing bond constraints on a molecule, $E_\mathrm h$ requires $O(N)$ computations, where $N$ is the number of atoms, while $E_\mathrm s$ requires $O(N^2)$ computations for the electrostatic and implicit solvation energies. Thus we might be able to take $n$ reasonably large and still have the computational cost dominated by the evaluation of $E_\mathrm s(\Gamma)$.

