Spectroscopic cluster size effects

In this paper we examine the spectral moments of the absorption line shapes of aromatic-molecule·(rare gas)_n heteroclusters to provide analytic expressions for the spectral shifts (δν), which are determined by the first moment, and for the homogeneous linewidths (Γ), which are determined by the central second moment (Δ) of the line shape. δν originates from the cumulative contributions of dispersive pair interactions, while Δ and Γ manifest the short-range dynamic nuclear fluctuations. Our analysis elucidates some of the general features of these spectroscopic observables, e.g., their dependence on the cluster structure and their size dependence, as well as some of their specific characteristics, e.g., their temperature dependence. We predict a weak temperature dependence of δν (=a+bT with b≪a/T) and a strong temperature dependence of Δ(∝ T^1/2), which is borne out by molecular dynamics (MD) simulations. We have derived cluster size equations (CSE) relating the spectroscopic observables of the finite cluster with those of the infinite bulk system. The excluded volume corrections for δν(n) ∝ n^-1 and for Δ(n) ∝ n^-3 are different, in accordance with the nonuniversability principle for CSEs. The predictions of the CSEs concur with experimental and MD simulation data for δν(n) and with MD simulation data for Δ(n). Finally, we have addressed dimensionality scaling of spectroscopic cluster properties, applicable for the situation of a common dimensionality (D≠3) for the cluster and for the infinite bulk. This analysis may be useful for the spectroscopic interrogation of doped clusters of low dimensionality, e.g., wire clusters (D=1) and planar clusters (D=2), as well as fractal clusters, e.g., clusters of porous materials.