TDOS Quantum Mechanical visual analysis for single molecules

We have analyzed with pedagogical purposes the relation of the total densities of states (TDOS/PDOS/OPDOS) and molecular orbital diagrams (MOD) for single and isolated molecules of Water and Nitrogen. We use a calculation level HF/6-311G, spreading the energy eigenvalues around the TDOS spikes and using the Mulliken visual analysis in Multiwfn to showcase our findings. We discuss the possibility to use these electrons orbit population diagrams, in conjunction with the more intuitive MOD diagrams to teach the Quantum Mechanics of simple molecular isolated structures.