From all-atom to rigid monomer treatment of molecular clusters

Given a system of M molecular monomers, represented with a presumably accurate all-atom potential energy surface (PES), V(r), we partition the configuration space by setting a one-to-one correspondence r ↔ (R, q), where R describes the centers and orientations of all the M monomers and q describes all the vibrational intra-molecular degrees of freedom. We then define a temperature-dependent free-energy surface of the corresponding rigid monomer system, F(R;T), by averaging over the intra-molecular degrees of freedom. F(R;T) is here estimated directly using the local harmonic approximation. While conceptually simple and numerically inexpensive, the coarse-grained PES defined in this manner turns out to be surprisingly accurate for the model systems considered, namely water and ammonia clusters. The proposed framework can be used in a more general context for local rigidification of other molecular systems in non-uniform environments.