be $n_{l-1}$ level-$(l-1)$ moves the result of which is subjected to Boltzmann acceptance using $E_l$. By induction, we see that a level-$l$ move is an $\mathcal E_l$ move, where $$\mathcal E_l(\Gamma) = \sum_{l'=1}^l E_{l'}(\Gamma).$$ It follows that a level-$m$ move is an $\mathcal E_m$ move, i.e., an $E$ move. Typically we sample the zero moves from a Gaussian and we take $n_0 = 1$. Standard Monte Carlo [@metropolis53] is given by $m=1$ and $n_1=1$. Standard MTS [@hetenyi02] is recovered with $m=2$. The early rejection method [@frenkel02 §14.3.2] is recovered with $n_l=1$ (for all $l$). Note that a level-$m$ move entails $\prod_{l'=l}^{m-1} n_{l'}$ level-$l$ moves. At any stage in the recursion, we have the freedom to vary some of the components of $E(\Gamma)$ adiabatically.

In the following sections, we apply these techniques to constrained molecules. In simple cases, we can apply the MTS method semi-analytically to derive a correct constrained move. In more complicated cases, we apply the adiabatic technique to lift and to reapply the constraint.

Stiff molecules
===============

A constrained molecule is a mathematical idealization of a real system in which some degrees of freedom are stiff, i.e., the associated energies are large. Thus we can split the energy 