In this paper, we investigate the prediction potential of commonly occurring eigenvalues-based descriptors which are related to chemical matrices corresponding to valency of vertices. The normal boiling point has been chosen to be representative of van-der-Waals and intermolecular type interactions, whereas, the standard enthalpy/heat of formation is selected to represent thermal properties, for our comparative testing. First, we propose a unified computational method to calculate commonly occurring eigenvalues-based valency descriptors. Experimental results show that our proposed method possesses less algorithmic and computational complexities and is more computationally diverse. The proposed method is used to calculate commonly occurring eigenvalues-based descriptors to investigate their correlation ability with the experimental data for the two chosen physicochemical properties. The Randić energy shows the best correlation among all the commonly occurring eigenvalues-based descriptors. Experimental results show some unexpected outcomes as the correlation ability of the well-known adjacency energy and the Laplacian & signless Laplacian Estrada indices is weak. Unlike their reputation among researchers, the harmonic energy and Estrada index outperformed all the well-known eigenvalues-based descriptors. The results warrant further usage of the harmonic energy and Estrada index in the structure-activity and structure-property models. Our study contributes towards putting forward the best spectrum-based topological descriptors while mentioning the ones which do not deserve further attention of researchers. Applications to certain families of titania nanotubes are presented.