The Debye temperature and the total mean square relative atomic displacement (MSRD) of nanosolids are investigated using an atomistic model from the perspective of size dependent cohesive energy correlation. A shell−core configuration of nanosolids and the coupling contributions of energy gain caused by coordination reduction, pressure, and temperature have been taken into account. This atomistic model allows us to identify details of Debye temperature and total MSRD of metallic nanosolids as a function of solid size, pressure, and temperature. The theoretical predictions are consistent with experimental measurements and computational results.