The periodic system for free diatomic molecules—III. Theoretical articulation

Periodic trends in constants of triatomic molecules

“…This same downward parabolic trend occurs occasionally throughout the various triatomic spaces considered in this study, and so demonstrates approximate periodic behavior. This approximate behavior serves as a check on our computational and empirical data, and can be observed in all vibrational modes, reminiscent of the parabolic periodic trends demonstrated amongst diatomic species when considering Franck–Condon factor Deslandres tables …”

“…Simple, repetitive behavior is found for many physical constants that characterize small molecules, such as energy of atomization or bond angle, among many others. It is postulated that the chart of the atoms can be manipulated to construct and extend triatomic molecular periodic systems from diatomic and monatomic ones, all of which are found to be visually elegant and which correspond to invariant higher dimensional statistical structures, periodicities, and trends in molecular properties . Of interest in this study are the trends of the three vibrational mode frequencies for any triatomic molecule, along with the bond angles and lengths of these molecules.…”

Patterns of basic knowledge

“…In this scale, entities (atoms) and their properties ( Table 5 ) are relatively well understood and the number of entities in this scale is reasonably stable, albeit still expanding slowly, after a burst of discoveries in the last two centuries ( Scerri, 2019 ; Karol et al., 2016 ). Furthermore, attempts have been made recently to formulate periodic tables for diatomic and triatomic molecules ( Hefferlin and Kuhlman, 1980 ; Hefferlin et al., 1983 ; Kong and Wu, 2012 ) and periodicity in n-atomic molecules has also been contemplated ( Dias, 1984 ; Hefferlin, 2006 ). These works show that at lower molecular weight range, scales can be similarly defined as that for atoms.…”

Kronecker-Product Periodic Systems of Small Gas-Phase Molecules and the Search for Order in Atomic Ensembles of Any Phase

“…But should NO + be placed at CO or at N 2 ? Since the question has nothing to do with dissociation channels, both of these options were rejected and it was assumed that if a molecule having atoms with numbers Z 1 and Z 2 has positive charge q, then its address should be (Z 1 q/2,Z 2 q/2) [16,17].…”

“…If a larger number of molecules are included in Fig. (6) and (7), some beautiful symmetries are seen in the placements of molecular symbols [16,18]. Used by permission from Periodic Systems and their Relation to the Systematic Analysis of Molecular Data, The Edivine Mellen Press, Lewiston, NY, Ref.…”