Abstract
The present work illustrates a predictive method, based on graph theory, for different types of energy of subatomic particles, atoms and molecules, to be specific, the mass defect of the first thirteen elements of the periodic table, the rotational and vibrational energies of simple molecules (such as , H2, FH and CO) as well as the electronic energy of both atoms and molecules (conjugated alkenes). It is shown that such a diverse group of energies can be expressed as a function of few simple graph-theoretical descriptors, resulting from assigning graphs to every wave function. Since these descriptors are closely related to the topology of the graph, it makes sense to wonder about the meaning of such relation between energy and topology and suggests points of view helping to formulate novel hypotheses about this relation.
Highlights
In an article published by the author a few years ago [1], it was proved that the masses of the 12 elementary particles of the standard model and the vibrational energies of the hydrogen molecule can be accurately predicted using the same approach
Mass defect is defined as the mass loss produced when nuclei are formed from their constitutive particles [8]
The wave functions associated with quantum-mechanical models, like particle in a box, rigid rotor or harmonic oscillator, are assimilated to simple graphs whose topology coincides with that of the standing waves, as for instance those that appear on the strings of musical instruments
Summary
In an article published by the author a few years ago [1], it was proved that the masses of the 12 elementary particles of the standard model (fermions) and the vibrational energies of the hydrogen molecule can be accurately predicted using the same approach. The same model, namely the classical model of the stationary waves, can be used to predict very different types of energies (rotational, vibrational and electronic) at different levels (subatomic particles, atoms and molecules). J. Galvez (from the particle in a box to the harmonic oscillator), the topology of the wave functions, and of the graphs associated, remains unaltered. Galvez (from the particle in a box to the harmonic oscillator), the topology of the wave functions, and of the graphs associated, remains unaltered This is the key basis for this work because one unique type of graphs accounts for any of the wave functions associated to every of the physical models mentioned above. 13 elements of the periodic table (from hydrogen to aluminium) It will be predicted the HOMO-LUMO gap of conjugated alkenes.
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