Deriving the isothermal–isobaric ensemble: The requirement of a “shell” molecule and applicability to small systems

The isothermal–isobaric ensemble is derived from the canonical ensemble instead of the customary microcanonical ensemble. By explicitly accounting for interactions between the system and the external bath, an isothermal–isobaric partition function is obtained that is more general than a previous derivation and is better suited to study small systems. The ensemble requires a “wall” or “shell” molecule to identify and count nonredundantly all the volumes and associated configurations of the system, verifying the volume scale obtained by Koper and Reiss J. Phys. Chem. 100, 422 (1996) (under the condition of minimal interaction between the bath and system for which it is valid). In addition, the failure of information theory to arrive at the proper volume scale (or “shell” molecule) for the ensemble (again when interaction between the bath and system is ignored) is demonstrated.