In this paper, we investigate the predictive potential of commonly occurring spectrum-based distance descriptors which are based on eigenvalues of distance-related chemical matrices. For our comparative testing, 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. We introduce three new chemical matrices and results show that the spectral descriptors based on these new matrices outperform the existing well-studied spectral descriptors. A computational method is used to calculate commonly occurring spectrum-based distance descriptors to investigate their correlation ability with the experimental data for the two chosen physicochemical properties for lower polycyclic aromatic hydrocarbons. By providing the list of the five best spectrum-based distance descriptors, 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 of our results to certain families of carbon polyhex nanotubes and one-hexagonal nanocones have been presented. The results can potentially be used to determine certain physicochemical of these nanotubes and nanocones theoretically with higher accuracy and negligible error.