Material properties depend sensitively on the atomic arrangements and atomic bonding, but these are notoriously difficult to measure in nanosized atomic clusters due to the small size of the objects and the challenge of obtaining bulk samples of identical clusters. Here we have combined the recent ability to make gram quantities of identical semiconductor quantum-dot nanoparticles with the ability to measure lattice dynamics on small sample quantities of hydrogenated materials using high energy resolution inelastic x-ray scattering (HERIX), to measure the size-dependence of the phonon density of states (PDOS) in CdSe quantum dots. The fact that we have atomically precise structural models for these nanoparticles allows the calculation of the PDOS using Density Functional Theory (DFT), providing both experimental and theoretical confirmations of the important role that the inertia of the surface capping species plays on determining the lattice dynamics.Colloidal semiconducting nanocrystals, commonly called quantum dot nanoparticles, have been studied exhaustively over the last thirty years due to their unique optoelectronic properties: size-tunable band-gaps, narrow, highly efficient photoluminescence, and long-term stability. For these reasons, they have started appearing in various products on the market ranging from television displays [1,2] to solid-state lightbulbs [3] and biological labels [4,5]. However, despite their commercial success, further development has been hindered by the lack of a detailed understanding of fundamental nanoparticle structure-property relationships, an important example of which is the nature of their lattice dynamics and how it is modified from bulk behavior by nanoparticle size [6]. Although lattice dynamics has a significant effect on the structural, mechanical and electronic properties of materials, it remains poorly understood for small crystallites because current techniques are best suited for bulk single-crystals. In the case of nanoparticles, this requirement is particularly problematic because their structures are often poorly defined, making it challenging even to determine the atomic structure [7], a prerequisite to un-FIG. 1. Structure representation of the cadmium selenide quantum dots in the current study. Their chemical compositions and surface capping ligands are shown.derstanding dynamics and properties.With the development of techniques such as the pair distribution function (PDF) which allows to obtain structure solution from powder x-ray scattering experiments [8], our ability to measure the structure of nanomaterials has improved. Using the PDF methods, we recently reported the first complete structural solution of a set of atomically-precise cadmium selenide quantum dots [9], shown in Fig. 1. Unlike even the most monosdisperse nanoparticle samples which generally possess some degree of heterogeneity in size, shape, and/or composition [10], the class of atomically precise nanoparticles that we prepared have well-defined structures and chemical formulas. We hav...