Energetic and thermodynamic size effects in molecular clusters

In this paper we explore the interrelationship between the energetics and the thermodynamic properties of molecular clusters. We advance simple models for the energy spectrum, which are used to derive analytical results for the thermodynamic properties of these clusters. The energy spectrum is characterized by the distribution of the energies of the local minima of the nuclear potential energy hypersurface, i.e., the inherent structures. On each of these energy levels the vibrational density of states of the particular inherent structure is superimposed. The energy spectra were specified in terms of the energy gap, Δ, between the (single) ground state and the excited-state inherent structures, the number, R, of the inherent structures and their energetic spread W. Four classes of energy spectra were considered. (1) A large energy gap with nearly degenerate excited-state manifold, i.e., Δ ≫. (2) A large energy gap with a considerable spread of the excited-state manifold, i.e., Δ ≪ W and W/R ≪ Δ. (3) A gapless spectrum with W/R ≳ Δ. (4) A multiple bunched spectrum with several energy gaps. Explicit analytical relations for the temperature dependence of the internal energy were derived for energy spectra of types (1), (2), and (3) both for the canonical and for the microcanonical ensembles. For energy spectra of types (1) and (2) the caloric curve exhibits a single inflection, which marks the "transition". A unified description of multistate isomerization with large R, which corresponds to rare-gas clusters, and of molecular isomerization with A ≃ I, which prevails for alkali-halide clusters, was provided. For energy spectra of type (3) the transition disappears, while for energy spectra of type (4) hierarchical isomerization is exhibited. Our analytical models have established the ensemble dependence of the transition for types (1) and (2), which is manifested by a considerable broadening of the transition range for the canonical ensemble, reflecting the role of energy fluctuations in the finite system.