E_\mathrm s$.

Let us apply this method to a system of “rigid” molecules, e.g., water molecules, taking $E_\mathrm h$ to include the intra-molecular energies (responsible for maintaining the rigidity) and $E_\mathrm s$ to include the inter-molecular energies. Suppose the level-$0$ moves consist of symmetrically displacing the atoms in each molecule. The result of the $n_1$ level-1 Monte Carlo steps will clearly be a symmetric, independent, and nearly rigid displacement (translation and orientation) of each molecule. This configuration is then subjected to Boltzmann acceptance with the inter-molecular energies. In this case, we can easily pass to the constrained limit (with exact rigidity), merely by ensuring that the trial (level-1) moves of the molecules are rigid. In this case, we have just rederived the “standard” move for a system of rigid molecules.

In order to illustrate the application to flexible molecules, we shall treat the molecules as being made up of several rigid subunits or “fragments” connected by flexible bonds. However we are interested in the limit where the inter-fragment bonds constrain the relative motions of fragments in certain ways, either by fixing the bond lengths (allowing the bond angles and bond dihedrals to vary) or by fixing the bond lengths and 