Osmotic framework adsorbed solution theory is a useful molecular simulation method to predict the evolution of structural transitions upon adsorption of guest molecules in flexible nanoporous solids. One challenge with previous uses of this approach has been the estimation of free energy differences between the solid phases of interest in the absence of adsorbed molecules. Here we demonstrate that these free energy differences can be calculated without reference to experimental data via the vibrational density of states of each phase, a quantity that can be obtained from molecular dynamics simulations. We show the applicability of this method through case studies of the swelling behaviors of two representative systems in which swelling upon adsorption of water is of importance: single-walled aluminosilicate nanotube bundles and cesium montmorillonite. The resulting predictions show that the aluminosilicate nanotube bundles swell significantly with increasing interstitial adsorption and that the layer spacing of cesium montmorillonite expands up to about 12.5 Å, giving good agreement with experiments. The method is applicable to a wide range of flexible nanoporous materials, such as zeolites, metal-organic frameworks, and layered oxide materials, when candidate structures can be defined and a force field to describe the material is available.